-С

TEST 2006: Vanant
101
Matematika
1
Matemat-ika
1.	17 • 11 — 14  11 + 27  23 — 24 • 23 + 21 • 19 — 18 • 19
ш hisobtaug.
A) 159 B) 165 C) 203 D) 143
2.	3.3: x va —2,1 sonlarining o’rta arifmetigi 0,6 ga
teng. r ni toping.
A) -0,6 B) 0,6 C) *2 D) 0s8
3.	a(b — c) — b[c — я) — c(b — o) ni soddalashtiring.
A) "lab
В) -2ac C) 2a6-2k D) 0
4.	2x(x — 1) — (2z 4- l)(x — 2) ko'phadni standart
shaklga keltiriug.
A) 2x3-3z В) 4P-1 C) -z + 1
D) x + 2
5.	a ning qanday qiymatlarida ax = 3rd- 1
tenglarna yechirnga ega bo’huaydi?
A) a -2 B)e#l 0/7=3 D)
6.	Ti va x2 x~ — 17т 4- 6 = 0 tenglamaning ildizlari
bodsa. -ri-r? + TjT’j ning qiyrnatini toping.
A) -102 B) -32 C) 10’2 D) 77
7.	(x — l)(z + 2) < 0 tengsizlikni yecbing.
A) (1:2) В) (-ос;Пи(2;ос) C) (-2; 1)
D) (—эс; —2)U(l;cc)
8.
Geomefrik progressiva uchun quyidagi
formulalardan qaysilari notcrgYi?
1)6п=&1?«-г.2)^=^.г
3) on —
Mi-V)
I - Ц
r*+21
 b
A) 1 B) }; 3 C) 3 D) 2
9.	у = 5T — 5 funksiyaning grafigi koordinata
tekisiigming qaysi choraklarida yotadi?
A) !. III. IV В) I, IV C) 111. IV D) I, 11
10.	Qo’shni burchaklardan biri ikkinchisidan
14е katta. Shu qo'shni burchaklarni toping.
A) 83°:97° B) 16°; 164° C) 82°;98°
D) 93° :87й
11,	Quyidagi tasdiqlarning qaysilari noto‘g:ri?
1)	tomordari c, b va c bollgan"ucbbnrchakka ichki
chizilgan aylananing radiusi r = c'+TTc formula
bila.it liisoblanadi;
2)	tornoulari a va b ga, uiar orasidagi
burchaklaridan biri a ga teng bcrlgan
parallelogrammning yuzi S’ — absina formula
bi lan h isobl an ad i;	<
3)	o'xshash figuralar yuzlarining nisbati «laming
mos chiziqli odchovlarining nisbatiga teng.
A) 2;3 B) 1:2 C) 1;2;3 D) 1:3
Tekislikka og'/na va perpendicular tnshirilgan.
Og’ma va tekislik orasidagi burchak arccos-L. g-,,
1	25
og'waning tekislikdagi proyeksiyasi 14 ga teng.
Perpendikularning uzunltgini toping.
A) 14 B) 48 C) 28 D) 36 .
13.	——————ni soddalashtirinr.
tg2a-ctg2n	*
A) ™2tg4a B) cos4a1 C) — tg 4a
D) tg4a
14.	Agar a € bo'lsa, quyidagi ifodalardan qaysi
biiiiiing qiymat-i bar doitn bntun son bo:ladi?
n\ iq3 + aHg +
}	6
38	47	3	4
15.	Agar — + — = в bo'lsa. Jr 4-
41	ol	41	al
qnyidagilardan qaysi biriga teng?
A) 4-u B) 3-a C) 3-^ D] 2-a
16.
funksiyaning eng kichik qiymatini toping.
A) 5 B) 6 C) 10 D) 4
{ 3z + 1 < 2зМ-11	sistemasining
butam yechiralan yig'indisini toping.
A) 5 B) 30 C) 21 D) 20
18. f(x) 3x2 - 2 funksiya boshlang‘ich
funksiyalaridan qaysi binning grafigi Af(2; 10)
nuqtadan o:t adi?
A) F(x) = x3 - -2т -4- 6 B) F(x) = z3 - 2z
C) F(z) = r3-2z + 8
U) F(z) = x3-2Jf+5
19 n — /0^0,28. b = fo^<2, e= Mgn.&0.6,
d ~ va I — Ingo.g2 sonlardan qaysilari
innsbat?
A) «r d va ( В) Ь va с C) a,c va d
D) c v'a d
20 Teng yonli nchburchakning uchldagi burchagi 70°
ga teng. Yon tomonga o‘tkazilgan balandlik va
asosi orasidagt burchakni toping.
A) 45° R) 35° C) 40° D) 30°
21. Tocnonlari 4 va 8 rn bo'lgan parallelogrammning
yuzi 16>/3 rrf2. Parallelogranimning oTmas
burchagini toping.
A) 150° B) 120° C) 105° D) 135е
1
I
I IS I 2(HM> Xnriant
101
Matenmtika
, Io f' и buiilinkb p.*»iлИсЬ-piped asosining
toi.K.iilnn i> ;л H р,л h*ng lining diagonal asos
trkг Им/',1 30" h burchak ost-ida og’ishgan.
I’mallrkpiprdmng hajmini toping.
Л) НОЛ В) 20/3 C) 240 D) 160/3
33.
3
a) £ + 2<ri-.t-ez B) ±^ + ~-.kez
3	6	2
C) ±J + ri-:t€Z D) (-l)nj + 2%nz-ez
} 1 Копил xasovthisi 4 ga teug va и asos tekisligi
lnbn fio° |i bnnhak fashkd etadi. Konusning
lm|iinni toping.
w5,	!£, с, Ь „ •&
*’4 m con6'»°, n =: ««45°, q = sm50* va
ji rosH0° sonlarni o’sish tartibida yozing.
A)
C)
rn < n < p < q
p < ТП < q < n
B) p< m < n < q
D) q < n < p < m
2 > hjx 4- — = 2 tenglama [~3tr; Зтг] kesniada
tgr
nrchta ildizga ega?
A) 5 B) 3 C) 6 D) 7
25. Vlaosh ikki rnarta ketma^ket bit xil foizga
oshirilgach, inaoshning 625 so‘ini 900 seringa
aylandi. Maosh bar safar necha foizdan
oshirilgan?
A) 12 B) 10 C) 14 D) 20
34.	(x - 2)lO€1/i(‘r‘,“5T+5) < (x - 2)lo^/A*-3)
tengsizHk x ning qanday qiyrnatlarida o'rinli?
A) (2; 4) B) (~oc:2)U(4:oc) C) (4:oq)
D) (ЦгМ
35.	Radiusi 5 ga t-eng bo’lgan doiraga to‘g‘ri
burchakli uchhurchak ichki chizilgan. Shu
uchburcbakka, ichki chizilgan doiraning radiusi 1
ga Ung. Uchburchakning yuzini taping.
A) 8x/2 B) 12 C) 22 D) 11
36.	Konusning o'q kesimi teng totnonb
uchburchakdan. silindnriki esa kvadratdan
iborat. Agar ularning tovla sirtlari Ungdosh
boisa. hajndarining nisbatini toping.
A) 1:3 B) 2:3 С) >/2 : >/3 D) 1 : ^2
27. у = -x2 -p 6x — 10 funksiyaning eng katta
qiyinatmi toping.
A) I B) -1 C) 2 0) 0
j z — 3y — 5 , ..	...
Agar 4 + 2^| _ rj boisa, x - 2jf Ding qiymatmi
toping.
A) 2 В) 3 C) -1 D) 1
29.	x1 4- px 4- q ss 0 tenglamaning ildizlari
x2 — 3x — 10 t= 0 tengiarnanihg ildiziaridan ikki
marta katta р-4-fl ning qjyinatini toping.
A) 2 В) ~7 C) -14 D) -46
30.
Tomonlari 13; 14 va 15 sdj bo lgan
uchburchakning eng katta balandligi necha srn?
84
13
D) 13
31.	Rornbning kkhik diagonal! Уз ga, yuzi 1.5 ga
(eng. lining о tkir burchagiiii toping.
A) 60° B) 30° C) 70° D) 45°
32.	b vektor а (2; 4: 4) vektorga kollinear hainda bu
vektorlarniug skalyar ko paytnuxsi 144 gA teng. b
vektorning uzunligiui toping.
A) 16 B) 24 C) 18 D) 12
TEST 2006: Variant
102
Matematika
1
Matematika
1. Natural sonni 18ga bo:]ganda; boiinnia 19 ga.
qoldiq 8 ga teng bo’Idi. Bo'litmvrhini toping.
A) 243 B) 263 C) 273 D) 350
2. 1,25 songa teskari sonni toping.
A) 8 B} -0,8 C) 0.8 D) -7
4
ni qisqart-iring.
11.	Quyidagi lasdiqlarning qaysilari noto'g'ri?
1)	uchburchakka tashqi chizilgan aylan&uing
radiusi /?. — ^y(a, b, c— uchburchakning
tomoulari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi Я ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S — formula bilan
hisoblanadi:
3)	diagonallari dy va d2 ga. ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
tosrtburchakning yuzi S = l;did^ina formula
bilan hisoblanadi.
A) 1:3 B) 1:2 C) 1;2;3 O) 2:3
А) -г' + у1 B) гЧ/
D) z-y
4.
— x“2 ni soddalashtirmg.
C) z’-y*
12.	Tekislikka og'ma va perpendikular tushinlgan.
40
Og'ma va tekislik orasidagi burchak arccos — ga.
41
og;maning tekishkdagi proyeksiyasi 80 ga teng.
Perpendikularning uzunligini toping.
A) 36 B) 40 C) 30 D) 18
A) x- В) 0 C) 1-1 D)
X	I*
5.
19	1
(2— 4- x) : 4 — =5 tenglamani yeching.
ZZ	O
*	IQ	7
A) .18— B) 17- C) 21 D) 17±
6. zi va x2 z2 — llr -F 12 = 0 tenglamaning
ildizlari bo‘lsa} xjx| -F r|x2 ning qiymatini
toping.
A) 132 B) -78 С/ -132 D) -168
, _ 1 — cos4a + s?n’2o .	,, , ...
13.		-------------- ш soddalashtinng.
3cos22o
A) 3fp22o B) 3dff22a C) tg22a
D) 1.5c/^2a
14.	41 17- 28 - 35 — 24 • 12 • 87 ayirma qanday raqam
bi lan tugaydi?
A) 2 В) 0 C) 6 D) 4
15.	Agar x < z < у bo‘Isa, |z - jr| — - j/| - - x|
ni so ddalashtiri ng.
A) 2y-2x В) 0 C) 2y-2c D) 2з - Чу
x~ — 4x -F 5
r — 3
> 0 tengsizlikni yeching.
A) (—co: 3) B) [3; oc) C) (3; oc)
D)’ (-oc; 3]
x 4- 1
2 — 3r
funksiyaga teskari funks’iyani toping.
8.	0,6(3) ni oddiy kasrga aylantiring.
a>A C)l D)S
9.	logzine^3 ni hisoblang.
A) 4ye B) 5 C) 3 D) 4
10.	Ikkita to'gVi chiziqning kesisbishidan hosil
bo'lgan qo’shni burchaklarning gradus o’lovlari
5 : 7 nisbatda bo'lsa, shu burchaklarni toping.
А) 30е; 150’ В) 75°, 105° С) 62е; 118°
Ь) 54е; 126°
(x - 4)(x + 2)	, ... .
17. ———~j2" • < 0 tengsizhkniug eng katta va
eng kichik butun yechimlari ayinnasini toping.
A) 4 В) 3 C) 2 D) 5
18. I (1 + cty2x)dr nt hisoblang.
A) 1 В) C) -1 D) Л - 1
19.
а = Iog9S 112 bo fsa, logT 2 ni a orqali ifodaiang.
*' fcr « Й- c> S
3
I Г5 Г МОв ’ Variant
102
Maternatika
Д) ЛЛВ(’ <!» /ВАС'- 15’, ZACH =30° vaBC=16\/2
f., ДВ toinonning uzouligini loping.
A) in B) 12 C) 12/2 D) 14
21 lUntibning, tomoni 6 ga. yuzi 18л/*3 ga teng.
Ihnnbning a lmas burchagini toping.
A) 120’ B) 135° C) 140° D) 150°
30. Katetlarining nisbati 3:2 kabi bo'igan t-o g ri
burchakli ucbburchakning balancBigi
gipotenuzasini uzunliklaridan biri
ikkindiishukidan 3 ga ko p bo’lgan ikki qisrriga
ajratadi. Beriigan uchburchakning gipotenuzasini
toping.
A) 7.8 B) 5,2 CJ8 D) 6
22 Agar kiibning bar bir qirrasini 2 sni ga
uzaylirsak, uning hajnri 15*2 sm3 gaortadi.
Ut jilgan kitbning qirrasini toping.
A) 3 B) 2
C) 4
31.	Teng yonli trapetsiyaning diagonal! 16\/3 ga teng
va и nsosi bilan 30е li bnrchak tashkil etadi.
Trapetsiyaning o:rta chizigJi nechaga teng?
A) 12 B) 16 C) 20 D) 24
23.	Копия asosining radiusi 2\/3 ga. yasovchisi va
asm tekisligi orasidagi burcbak 60° ga teng.
Konusning hajmini toping.
A) L2 В) 16r C) 8x^3 D) 21»
cos\2a - cos8o .. „	.	. ...
24 ------—---------qtiyiaagilardan qaysi binga
sm 10a
tcng?
A) 2cos'2(i B) ~2sin'2<x C) —sin2a
D) -2cos2a
32.	m mhg qanday qiymatlarida a(?n— 1: m — 2:2)
vektorning uzunligi 3 dan kichik boiadi?
A) —2 < 7П < 1	B) 0 < tn < 3
C) —1 < 77i < 2	D) —1 < m < 3
33.	- 3co.t2r 4 t-englamani yeching.
A) ~ + m, n G Z B) - ~ •+ 2trn. n G Z
<	2
С) + '2тп,n € Z D) ir4~^n,n^Z
25.
cos 2x sin 3x + sin 2je cos 3± =
yeching.
tenglamani
A)	(_lr.’+2„,n6z
B)	(-ly-^ + in. nez C)^n, nez
2 (J о	oU
О) (-’Г • £ + ?n- " e 2
15	5
26.	520 soni shunday ikki boiakka bo4inganki,
ulardan birining 80% i ikkin ch isining 24% ini
tashkil qiladi. Bo'laklarni kichigini toping.
Л) 120 B) 400 C) 460 D) 420
27.	Agar .4(1;—3) nuqta у — т2 -f- рт 4- q
parabolaning uchi bo'ka, p va q ning qiymatini
toping.
A) p = 4 q-2 H) p-. 2,g^-l
C) P - 1, Q - -2 D) p - q - -2
28.	Ikki sonning ayirrnasi 27 gn, U ng. Agar hirinchi
sonni ikkinchisiga bo’Lsak, bo'linrna 4 ga va
qoldiq 3 ga leng chitpuli Beiilgan sonlarning
yig’indisini toping.
A) 38 B) 31 C) 43 D) 20
34.
/09$ /о$б(\/2+ 1)
ni soddalashtiring.
А)	B) Zoffs(72+1)
C) >/2-1-1 D) -yJ—
35.	R asm da AE = 3 * EB. AF ~ FC. S^abc 120.
BE FC Wrtburchakning yuzini toping.
A) 75 B) 80 C) 40 D) 60
36.	Konusning o‘q kesimi muntazam uchburchakdan,
silindrniki esa kyadratdan iborat- Agar konus
hajmining silindr hajmiga nisbati /З : 2 kabi
bo'ha. to‘la sirt-larining nisbat-ini toping.
A) ^3 : y/2 B) /3 : /2 C) ^9 : 2
D) 3:2
D} 1
20.
(2|z| — 3)~ = |x[ tenglamaning l>auha ildizlari
ko'paytmasini toping.
A) ~ В) ± C) D) ~
TEST 2006: Varhuit
103
Matematibi
1
Matematika
L 18-13-15-13+ 21 -17-18-17+17-15- 15-14
ni hisoblang.
A) 135 B) 125 C) 180 D) 205
2. 8 soniga teskari sonni toping.
A) 0,125 B) -0,8 C) 1,25 D)
3.
ni qisqartiring.
A) r^ + j/V* B)
- У
4. (it - l)2 ~(1T ~ 1)(И + / + 1) + У ni
soddalashtirgandan keyin nechta haddan iborat
boiadi?
11.	Quyidagi tasdiqlarnmg qaysilari notolgsri?
1)	tonioui a ga. burchaklaridan bid ex ga teng
rorribning ynzi S ^~a2^incr formula biJan
hisoblanadi:
2)	diagonallarLdj va d2 ga5 ular orasidagi
burchagi f9 ga teng ixtiyoriy qavariq
to’rtbwrchakning yuzi 5 d^doainot formula
bi lari hisoblanadb
3)	o;xshash ftguralar yuzlarining nisbati darning
»nos chiziqli crkhovlari kvadratlanning nisbatiga
teng.
A) 2:3 B) 1;2 C) 1;2;3 D) 1:3
12.	Tekislikka ogsnia va perpendikular t-ushirilgan.
(^mailing t-ekislikdagi proyeksiyasi 11 ga,
perpendikulamiiig uzunligi 60 ga teng- Og’ma va
perpendikular orasidagi burchakni toping.
22	11	11
А)	агссоз^-	B)	arcain-^	C)	arcrt£f—
Ы	Ы	QU
60
D) ar&nn-~-
A) 5 B) 4 C) 3 D) 6
5.	(8* + 1) • (x — -) = 0 bo'lsa. 8r +1 qanday
4
qiymatlar qabul qilishi inuinkin?
A) faqatj B) faq&t C) 0 yoki3
D) faqat 0
6.	3 — x = — tenglamaning nechta haqiqiy ildizi
at
bor?
A) 2 B) 1 C) ildiziyo'q D) 3
7.	16x2 — 8x + 3 > 0 tengsizlikni yeching.
A) [0;oo) B) 0 C) (—oo;0)
D) (—oo;oc)
8.	Quyidagi ketma-ketliklardan qaysilan geometrik
progressiyani tashki! etmaydi?
1)	o„ = 2rn, (x /0);
2)	cn - ахп. (az 0);
3)	bn =. (I)" • «пбО» + I.
A) 3 B) 1:3 C) 2 D) 1
, cos do sin За .	.
13		- + —r—- ni soddalashtinng.
cos a sm er
A) 4 cos 2а В) 4 cos а С) —2
D) 2 cos 2а
14.	22-43'98 + 16-27 - 38 - 19 yig'indining oxirgi
raqamini toping.
A) 6 B) 8 C) 2 D) 4
15.	Agar 0 < q < p < fe boisa.
|p + ^| + |k —	— p| ni soddalashtiring.
A) 2p+29-2k В) 2p C) 2p+2fc
D) 2?
,.	/(z — 2)(4 - r) ...	.	. . . ,
16.	у —	—-——гт— funksiyanmg amqlanish
у ar(T + d)
sohasini toping,
A) (—3:0) U [2:4] B) (-3:0]U(2;4)
C) (-oc;-3)U(0:2)U(4:oc)
D) (-3;0]U[2:4)
(t-7)(z + 3) a .	.
11	---- < q tengsizlikmng eng katt-a va
2x’ — z + 4
eng kichik butun yechimlari ayirmasini toping.
A) 9 B) 10 C) 7 D) 8
9.	< 4 tengsiztikning eng kaUa but-un
yeehimini toping.
A) 10 B) 6 C) 9 D> 11
10.	Ikkita t-o'*g*ri chiziqning kesishidan hosil bo’lgan
qo^sbni burchaklaming ayirinasi 50° ga teng. Shu
burchaklardan kichigini toping.
A) 65* В) 60е C) 70’ D) 50°
18.-------	ning boshlang;ich funksiyasini
COo'2(~ + ])
toping.
A) 4f<^ + l)+C B) lti,(i + l)+C
Tt	т Ж
C)	-4!5(j + D + C D) -lts(^ + l) + C
4	4	4
5
VUST20V6: Vari/ud
103
Matematika
1') Лцпг b )’rA Ы =z 3 va logb 243 =• 5 bolsa. ob Ding
rpviu ttmi toping
A) .’> B) 12 C) 8 D) 6
/о Brninrtn 28 bo'tgan uchburchakning
l»i-u.rkt nsasi uni perimetrlari 16 va *24 bo’lgan
u< hbtirchaklarga ajratadi. Berilgan
u< hbmchakning bissektrisasini toping.
A) 8 B) 5 C) 7 D) 6
21 к Atctlarining nisbati 2:3 kabi bo'lgan t-o'g'n
bun hakli uchburchakning gipotenuzasi >/182 ga
teng. Uchburchakning yuzini toping.
Л) 24 B) 42 C) 36 D) 39
22 Muntazam pirarnidaning yon sirti to*la sirtining
60% ini tashkil etadi. Pirarnidaning yon yoqlari
va asos tekisligi orasidagi burchakni toping.
A) arccos-i B) 60° C) arccos
4	3
r>. 1
D)	arccos -
о
23.	Yasovchisi 26 ga va balandligi 10 teng bo lgan
konus asosining yuzini toping.
А) 144т2 В) 144т С) 576т D) 288т

24.	р — со$88°. q = со$42° va г ж sfn222° sonlarni
kamayish tartibida yozing.
A) p>q>r B) q>p>r C) q>r>p
D) p > r > q
28. Qisqannaydjgan oddiy kasrning maxraji
suratidau 6 birlikka katta. Agar kasrning surat
va rnaxrajiga 5 ni qo shsak, hosil bo!lgan
4
kasrning qjymati - ga teng bo‘Iadi. Berilgan
о
kasrning suratini toping.
29.
Agar z- — x + q = 0 tenglamaning rj va хз
ildizlari x^ +	= shartni qancatlantirsa. q
ning qiymatini toping.
A) -11 B) -5 C) -19 D) -12
30.
A) 7.5 B) 9 C) 7,2 D) 6
AB=18 sm, DB=xlO,8 sm.
ABC uchburchakka
ichki chizilgan ayla-
naning radiusi
necha sm?
31.
Koordinatalar boshidan 7x 4- 24y = 168 to‘g’ri
chiziqqacha bo'lgan masofani aniqlang.
.. _	-18 л 24	.	9
A) 5 В) 6—	C) 6rr	D) 5rr
25	25	25
32.
25.	cosf>x 4- cos4x = 0 tenglarnani yeching,
А)	(~П‘•£> + {*; v + 2ri, kez
10	5	2
B)	— +	kez
x_.	7t	T	"К ч i >	—
Q	^Tn4"^	~ +	k€Z
10	3	2
0) ^ + ~k: £ + 2ii, kez
10	5	2
26.	Yig’indisi 38 va 62 sonlarining o’rta arifmet-igiga
teng bo4ishi uchun 62 ning 60%i olinsa. 38 ning
necha foizini olish kerak?
7	13	12
A) 17Tq B) 33To О 33w D) 32
4 У	J. У	j /
27.	у — ax3 -f- b kubik parabolamng grafigi
A(l; —52) va B(—1; —56) nuqtalardan o'tadi.
Qaysi nuqtada bu funksiyaning grafigi Ox o’qini
kesib o4adi?
A) (-3: 0) B) (2; 0) C) (-2: 0)
D) (3; 0)
berilgan bo:Isa, 2a va - vektorlar orasidagi
burchakni toping.
5
A) -T B) arccosj C) — D) arccosg
33.	у =. y/l - logj/2 cosx funksiya x (x G {0:2т])
ning qanday qiymatlarida arriqlangan?
. . / 3т 5t.	. T T ,	г5*Т ~	- 7Г.
A) (V’ V} B) C) hr:2T)UI0:V
-v	<?	v	U
г"’1’ ./Зтг 5т.
О) [-г! т) U(--: —“1
34.	((0I25)l°S1^’+’ + ^+-' >) ni hisoblang.
Q	О	9	1
ЛМ в> 7 СЧ D’ й
35.	ABC uchburchakning yuzi 12 ga teng. Uning В
uchidan BD = 3 mediana tushirilgan. Agar
idBD = 90° bo‘lsa, AC tomonning uzunligini
toping.
А) У73 В) 2>/73 C) 10 D) 8
6
TEST 2006: Variant
103
Malcrnatika
3
36.	Asosi a ga, asosidagi burchagi a ga teng boMgan
tengyonli uchburchakni yon tornom atrofida
aylantirishdan hosil bo^g&n jismning hajiriini
toping.
*<?sin2a % Carina xa3cosa
A)	~6^~	B) —3— c) 6^V
D)
7
TEST 2006 : Variant
104
Matematika
1
Matematika
1 Quyidagi inulohazalarning qaysi biri natural
sonlarga nisbatan noto*g‘ri?
A) 3 hamda 4 ga bo'lingan son 12 ga ham
boiinadi.
B)	Berilgan sonlarga bo'linadigan sonlarning eng
kicbigi bu sonlarning eng kichik karralisi
bo'Jadi.
C)	Oxirgi raqami 0 yoki 5 bo'lgan son 5 ga
bo‘tinadi.
D)	Oxirgi raqami 6 yoki 9 bo(lgan son 3 ga
bo'linadi.
2. —I tcskari sonni toping.
A) -0,75 B) 1,5 C) | D)
10.	Ikki to4g’ri chiziqning kesishishidan hosil bo'lgan
burchaklarning kat talik lari nisbati 7:5 ga teng.
Shu burchaklardan kichigini toping.
A) 49° B) 63° C) 75° D) 54°
11.	Quyidagi tasdiqlarning qaysilari to‘g‘ri?
1)	uchburchakka tashqi cbizilgan aylananing
radiusi R=s ^~-[a.b}c— uchburchakning
tomonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi:
2)	tomonlari a.b va c boigan uchburchakka ichki
cbizilgan aylananing radiusi r — formula
bitan hisoblanadi;
3)	diagonallari dj va d2 ga> ular orasidagi
burchagi n ga teng ixtiyoriy qavariq
to’rtburcbakning yuzi S = -did^sina formula
bilan hisoblanadi.
A) 2;3 B) 1;3 C) 1;2;3 D) 1;2
3. Uchburchakning birinchi tomoni x(x > 13) sm,
ikkinc.hi totnoni undan 8 sin qisqa. uchinchi
tomoni esa birinchisidan 5 sm uzun. Shu
uchburchakning perimetrini (sm) toping.
А) 3x4-2 В) Зх-З С) 3x4-3
D) Зх-2
4. (4х — З)2 - x(“4z 4- 5) ko:phadni standart
shakliga keltiring.
A) 12x3 —25x4-9 B) 20x2 — 29x4-9
C) 8x2-z4-7 D) 20z2 —25x4-9
- tcnglamani yeching.
•i	1	13	2
А) -т. B) -1 C) -- 0) -
<J	О	Ju i	IJ
12.	Tekislikka og ina va perpendikular tushirilgan.
Og rnaning tekislikdagi proyeksiyasi 12 ga.
perpendikulanring uzunligi 35 ga teng. Og'nia va
perpendikular orasidagi burchakni toping.
A)
D)
. 12
(jrcstn-
. 35
arcszn—
37
B)
24
arccos—
3i
лх л 35
C) nrcrp-y
13.	tg( 7 4- a) = x b6‘lsa, ctg <x ning qiymatini
4	3
toping.
A) 4 B) |	C) |	D) |
Z	Э	•
6. Z[ va x2 z2 — 13.x 4-12 — 0 tenglamaning
ildizlari bcrlsa. XjZj 4- x3x2 ning qiymatini
toping.
A) 156 B) 94 C) -156 D) -152
14.	O‘lchainlari 22m x 15m bo:lgan zalni tomoni 20
sm bo'lgan kvadrat- shaklidagi plitkalardan
necht asi bilan qoplash mumkin?
A) 18000 B) 1650 C) 8250 D) 9000
7. (x 4- 3)(i - 2) < 0 tengsizlikni yeching.
A) (—oc,-3) U (2: do) B) (—oq;2)U (3; oc)
C) (-3:2) D) ( -oc; —2) U (3; oq)
15.	Agar 0 < k < m < n bo'lsa,
\	— m) — ‘pi 4*	so&Aa'ias'n'riring.
A) 2k — 2n В) —2n C) 2m—2k
D) -2m
8. Arifrnetik progressiya uchuu quyidagi
formulalardan qaysilari to'g’ri?
1) Ci — 2a2 4- аз — 0;
2j U) — G3 —
... «n - ni 4- d
t) —------------------
A) 1 В) 2;3 C) 1;2 D) 2
16.
у------ 2z — 3
у " У16 — x- 4- —~т“
x 4-1
sohasini toping.
A) (-1; 4]
C) [—4: 4]
funkaiyaning arnqlanish
B) [-4: —1)U(—1; 4]
D) [-4: -1)
9. r ning qanday qiymaUarida n — 3 — Igx funksiya
nomusbat qiyrnatlar qabul qiladi?
A) x > 1000 B) x > 100 C) x < 1000
D) x < 100
Г "2т -4- 1 5т 2
П- С п ; о tengsizliklar sisternasi butun
I 2x -f- 3 < 18 — 3x
yechimlanning crrta ariftnetigini toping.
A) 2.5 В) 3 C) 1.5 D) 2
8
2
TEST 2006: Variant
104
Matematika
18.	I ---ni hisoblang.
2am2 -
A) 3-/5 B)	C) з/5-з
“>M
19.	2/о^тЗ -- Z05F3—- ni hisoblang.
243
A) -9 B) -10 C) -S D) -4
20.	A(—6:1) aylanadagi nuqta. C’(6; 10) nuqta
aylananing markazi boisa, aylaning radiusini
toping.
A) 13 B) 14 C) 15 D) 16
21-	Rombning balandligi 5 ga, diagonallarining
ktrpaytrnasi 90 ga teng. Uning perimetrini
toping.
A) 16 B) 32 C) 28 D) 36
22.	Muntazam to:rtburchakli pirarnida asosin'mg
tomoni 6\/3 ga va apofemasi 6 ga teng. Piramida
bajmini toping.
A) 54 B) 108 C) 162 D) 324
23.	Radiusi 17 sm bo igan shar markazidan 8 sm
masofada tekisbk bilan kesilgan. Kesimning
yuzini (sm2) toping.
A) 225r В) 64т C) 64 D) 514*
5	б73 — 5
24.	Agar igor +tgp = — va igotgp = -----— bo'lsa,
6	673
cr 4- p nimaga teng bo'ladi?
A) £ + irt, kzz B) £ + rit, i-ez
0	6
C) ~ + Tfc, keZ D) + k€Z
4	6
3*
25.	sin2x 4- cos(™ 4 6x) ~ stn4z tenglamani
yeching.
,. , t rn _ rn „
A) ±- + *n:	n £ Z B) -7-, n eZ
6	4	4
C) xn, n E Z D) — ~ + *n, n € Z
xj
26.	Mahsulotning narxi birinchi marta 20% ga.
ikkinchi marta yangi bahosi yana 10% ga
oshinidi. Mahsulotning oxirgi bahosi necha
foizga kamaytirilsa, uning narxi dastlabki narxiga
teng bo'ladi?
8	1
A) 24— B) 25 С) 33- D) 30
oo	♦>
28.	(k — 5)-(/ =	— 36 tenglarnaning ildizlari manfiy
boladigan k ning bare ha butun musbat
qiymatlari yjg'indisini toping.
A) 13 B) 10 C) 8 D) 11
29.	Agar z~ 4- x — 4 = 0 tenglarnaning ildizlari va
x2 bo1 Isa, rf -4 ning qiymati qanrhaga teng
bo’ladi?
A) 3 B) 1 C) -13 D) 2
30.	To'g^i burchakli uchburchakka ichki va tashqi
cbizilgan aylanajar radiuslanning nisbati 4:13
kabi. Kichik katet uzunligining katta katet
uzunligiga nisbatini aniqlang
A) 5:12 B) 3:4 C) 4 : U D) 5:13
3L Rombning tomoni 6 ga, o'tkir burchagining
2
smusi - ga teng. Uning diagonallari
ko'paytmasini toping.
A) 18 B) 27 C) 48 D) 42
32.	Agar n(—6;3:3) va Г(3; —3:0) bcrlsa. 2a va ~rb
2
vektorlar orasidagi burchakni (oping.
А) 60й В) 150® С) 135® D) 120®
33.	Agar < 1,	< 1 bo’lsa, arccvsa — 4arcsinb
ifodaning eng katta qiymati qanchaga teng
bo4adi?
A) 1 В) 2т C) 5x D) 3r
34.	у = log2 logt^2 ""	~ 2 funksiyaning
amqlanish sohasini toping.
А) (2-л/5;2 + Л)
В) (2-,/2:1) LI (3:2+72)
C) (—oo;l)U(3;oc)	D) (1;3)
35.	Muntazam uchburchakning yuzi 9/5 ga teng.
Shu uchburchakdan eng katta yuzaga ega bo‘lgan
kvadrat qirqtb olingan. Shu kvadratning
perimetrini toping.
A) 48/3- 72 B) 18/3-12
C) 54-16/3 D) 64/3-96
36.	Konusning o*q kesimi muntazam uchburchakdan,
silindrniki esa kvadratdan iborat. Agar kouus
to la sirt-ining silindr to‘la sirtiga nisbati 1:3 kabi
bo‘lsa, hajmlarining nisbatini toping.
A) 2:9 B) 1 : 9 C) 4 : 9 D) 72 : 9
27. A(l; 9} nuqta у = — x2 4* ax 4-2 parabolaga
tegishli. Parabola uchining ordinatasini toping.
A) 18 B) 13 C) 2 D) 4
9
1'ICS r 2006 : Variant	105
Matem&tika
Matcmatika
I, 392 ni qanday songa boiganda bo‘iinma 17 va
qoldiq 1 boMadi?
A) 21	8) 19 C) 23 D) 22
2 3; y; 2,1 va 2.1 sonlarining o'rta arifmetigi 2,3 ga
teng </ ni toping.
A) 2,6 B) 2,1 C) 3,4 D) 2
3. Uchburchakning birinchi tomoni x {x > 12) sm,
ikkinchi tomoni nndan 7 sm qisqa. uchinchi
tomoni esa birinchisidan 5 sm uzun. Shu
uchburchakning perinietrini (sm) toping.
A) 3z - 1 В) 3г + 2 С) 3г + 1
D) 3r - 2
4. (z — 1)(2 - x) 4- (r — 3)2 ko’phadni standart
shaklga keitinng.
A) 3r2 + 15г 4 7 B) —3z 4- 7
С) ГЗх-М-х2 D) 9г+ 7
11.	Quyidagi tasdiqlarning qaysilari noto:glri?
1)	tomonlari a,b va c bo‘lgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
2)	diagonallari di va rfs g3- ular orasidagi
burchagi tr ga teng bctiyoriy qavariq
to'rtburthakning yuzi S’ = ^did^sincx formula
bilan hisoblanadi:
3)	o'xshash Hguralar yuzlarining nisbati ularning
tnos chiziqli o‘khovlarinmg nisbatiga teng.
A) 2:3 B) 1:2 C) 1;2:3 D) 1:3
12.	Tekislikka tushirilgan og'maning uzunligi 75 ga,
uning tekislikdagi proyeksiyasi esa 60 ga teng.
Ogcma va tekislik orasidagi burchakni toping.
3	3	3
arcsin- B) arccos— C) arcsin-
D) arcstn-
5
13.	------------zr~ ni soddaiashtiring.
ctg 2rr ~ tg 2or
A) sin4o B) 2tg4o C) cos 4a D) tg4o
i25:2I=i4
tenglamani yeching.
У
2
А) б| В) Gj С) б| D)
6. zi va Z'j — cur + 20 = 0 tenglamaning ildizlari
1	19
bo*lib, — 4- — = —- tenglikni qanoat-lantirsa, a
jt } x	4» 0
ning qiyraatini toping.
A) 9 B) -1 C) 3 D) -3
7. Agar a > b va ab / 0 bo'lsa, quyidagi
tengsizliklardan qaysi bin bar doim o'rinli?
A) a2 > b2 B) 1>1 C) 2a > 3л -b
a b
D) 3a < 4a — b
14.	264 va 840 ning uniumiy boMuvchilari nechta?
A) 4 B) 9 C) 8 D) 6
15.	9; 10; 15 va 27 sou lari dan nechta o'zaro tub
sonlar jufti hosil qilish mumkin?
A) 3 B) 4 C) 6 D) 2
16.	у — у -—;---------- funksivaning aniqlanish
у (г + 1)т
sohasini toping.
A) [-l;0]U(2;4) B) {-l:0)U[2;4]
C) (—oc:—1) U (0:2] U [4; oc)
D) (~l;0]U[2;4)
17.	Agar a < -1 bo'isa, quyida keltirilgan
ifodalardan qaysi birining qiymati eng katta
boiadi?
Л) я"3 B) a"9 C) a7 D) a’5
8. Quyidagi sonlaidan qaysi biri 0.3(6) ga teng?
4 U 9	4
A) 18 B) 30 C> 27 D> П
9. у = 5r — 1 funksiyaning grafigi koordinatalar
tekisligining qaysi choraklarida yotadi?
A) J, II B) Г, III C) IL IV D) IV
18.
19.
I sin 2xdx ni hisoblang.
Jo
A) -1 B) 1 C) j D)
31g4 + 3lg25
I- 1300 — 1g 13
ning qiymatini hisoblang.
A) 1,5 B) 6 C) 2 D) 3
10.	Qo’shni burchaklardan biri ikkinchisidan 12°
katta. Shu qo'shni burchaklarni toping.
A) 81°; 99е В) 82е; 98° C) 96°:84е
D) 804:100°
20.	Teng yonli uchburchakning balandligi 20 ga teng.
Yon tomoni asosidan 5 ga kam. Shu
uchburchakning asosini toping.
A) 40 B) 20 C) 24 D) 30
10
TEST 2006: Variant
105
Matematika
21-	ДАВС ning AB tomoui MN||AC to‘g:ri chiziq
yordarnida BM=2 va AM=4 boigan kesmalarga
ajratildi. Agar AMBN ning yuzi 18 ga teng
bo{lsa, ДАВС ning yuzi qanchaga teng bodadi?
A) 96 B) 162 C) 144 D) 108
, 22. To:glri burchakli parallelepiped asosining
tomonlari va balandligming qiymatlari 4:3:1,25
kabi nisbalda. Parallelepipedning diagonal! va
asos tekisligi orasidagi burchakiii toping.
A) 30° В) 45е C) arret $4 D) 60е
23.	Komis asosining radiusi 12\/3 ga teng. yasovchisi
asos tekisligi bilan 30° li burchak t ashkil etadi.
Asos markazidan yasovchigacha bo lgau masofani
toping.
A) 6?3 B) 8 C) D) 5
24.	(2 + со«г2о)(1 + <s2o) + 4sin2a ifodaning eng
kichik qiymatini toping.
A) 1.5 В) 2<5 C) 3 D) 2
25.	2siri1x — &in2r ~ 0 tengiarnani yeching.
A)	Ti;	+ k£Z
4
B)	xi; ~ 4- xk. k eZ
4
C)	irk; ~ 4- xk. k^Z
D)	J + rl, *•€?
Z *Z
26.	Тс к is barakatda muayyan masofani bosib o'tisb
uchim ketadigan vaqtni 30% ga kaniaytirish
uchun tezlikni necha foiz orttirish kerak?
A) 20 B) 42^ C) 30 D) Зз|
I	*J
31.	To g*ri krrtburchakning to'g'ri burchagi uchidan
uning diagonaiiga tushirilgan perpendikular
to‘g‘ri burchakni 3:2 kabi nisbalda bo4ladi. Shu
perpendikular bilan boshqa diagonal orasidagi
burchakni toping.
A) 72° B) 22,5° C) 18° D) 45°
32.	Vchlari A{2; 3:	B(3: 2: 1) va C(3: 4; 1)
nuqtalarda bo;lgan teng yonli uchburchakning
asosidagi burchagini toping.
I	2	x
A)	arccos-	B)	arccos- C)	-7
J	О	.	•	1
D) arccos”^
33.	у — yi -hiogj^cosr funksiya x (x E [0;2x])
ning qatiday qiymatlarida aniqlangan?
A) [04)U(-^:2r] B) [0;ir]
С) [офи&2«-1 D) [офи&г»]
z z	z z
34.	(2x+	> 0
tengsizlikuing buluo sonlardan iborat nechta
yechimi bor?
A) 1 В) $ C) 3 D) 2
35.	To'g'ri burchakli uchburchakning uzunligi 14 va
18 ga teng katetlariga tushirilgan medianalari uni
uchta uchburchakka va tolrtburchakka ajrat&di.
To'rtburchakning yuzini toping.
A) 64 B) 63 C) 42 D) 48
36	Teng lomonli silindming va teng tomonli
konusning balandhgi o zaro teng. Warning tola
sirt-iari nisbatini toping.
A) 3:8 B) 5:3 C) 3:2 D) 3:4
27.	p — —3x~ 4- 12z — 13 parabola uchining
koordinatlari yig’,indisini toping.
A) 1 B) -1 C) -2 D) 0
28.	x 4--—j- — — tenglamaning natural sonlardagi
У + ~
yechirnida у nimaga teng?
A) 4 В) 3 C) 2 D) 1
29.	\fx1 — 6x 4- 5 4- x2 — 6x -F 7 tenglamaning
ildizlari yig*indislni toping.
A) -3 B) 6 C) ~4 D) 3
30.	To‘gTi burchakli uchburchakning katetlari 48 va
14 ga teng. Kichik katetning gipotenuzadagi
proyeksiyasini toping.
4	92	R
A) 10 B) 6- C) 3~ D)
t	25	25
11
'J E5T 2006 : Variant
106
A/atem&tika
1
Matematika
12. Tekislikka tusbirilgan og’ma va perpendikular
1 15-2614 18 - 261 4-139 • 154-18 • 139 ni hisoblang
A) 14500 B) 13200 C) 16200 D) 15100
orasidagi burchak arcwn~~ ga teng. Og'maning
4b «7
uzunligi 58 ga teng. Perpendikularning
uzunligini toping.
2. 453,21 sonini standart shaklda yozing.
A) 4,5321-102 B) 4.5-103
C) <5321 103 D) 4,53-102
3.	n* soddalashtiring.
A) 6~2 В) 6"1 CJfe+l D) b2
4.
4 x ni soddalashtiring.
A) 80 B) 40 C) 42 D) 33
sin8fir-«nl2a ,, .	.
13. ------——~— ni soddalashtiring.
coslOcr - sin2o
А) 2«п’п2а B) —2 C) — 2sin2a
D) — 2cos2ot
14. x raqamining qanday eng katta qiymatida
(741 4- 2x2) son 3 ga qoldiqsiz bo‘Iinadi?
A) 8 B) 7 C) 2 D) 9
A) x B) z-1 C) x+1 D) 2x4-1
= 3 Uuglamani уeching.
A) 19§ B> c> 4 D) 19S
6. x2 — 13x + ^ = 0 tenglamaniug ildizlaridan biri
—14 ga Ung, Uning ikkinchi ildizini toping,
A) 27 B) -1 C) -27 D) 1
7 --------r—— > q tengsizlikni yeching.
x 4- 2
A) (2;oc) B) (-2;oo) C) <-=o;2]
D) (-oc;2)
8. 0.4(5) soni quyidagi sonlardan qaysi biriga teng?
A) 2.	в) —	C) —	D) ~
} 11	'90	' 90	} 90
(5 4
2	»’* I ni hisoblang.
A) 4 B) 9 C) 5 D) 3
10.	Ikki q</shni burchakning ayirmasi 28° ga teng.
Shu burchaklardan kichigini toping.
А) 78й В) 72е С) 76е D) 82°
11-	Quyidagi tasdiqlarning qaysilari to:g'ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi 7? = ~g\a,b,c— uchburchakning
tornonlari. 5— uchburchakning yuzi) formula
bilan hisoblauadi;
2)	radiusi R ga, rnarkaziy burchagi n- ga teng
doiraviy sektorning vuzi S ~ formula bilan
hisoblanadi:
3)	tomonl&ri a va 6 ga, ular orasidagi
burchaklaridan biri or ga Ung bo’lgan
parallelogramiuning yuzi S = -abfnnot formula
bilan hisoblanadi.
A) 2:3 B) 1;3 C) 1;2;3 D) 1:2
15.	Mehaat unumdorligi bir xil bo’lgan 8 kishi
malum hajmdagi ishni 15 kunda tugatishdi. 12
kishi o:shancha mehnat unumdorligi bilan
ishlasa. o‘sha hajmdagi ishni necha kunda
tugatishi munikin?
A) 8 B) 9 C) 12 D) 10
16-	(2a — l)(2a 4 1) 4- 36(36 — 4a) 4-1 niug eng kichik
qiymatini toping
A) 0 B) -1 C) 1 D) -2
г2
17.	----- < x — 4 UngsizHkni yeching.
x 4- 4
A) (-4:4) B) (—oo;—4) С) ф D) (0:4)
18.	J cosStdz ni hisoblang.
я
A) B) 1 C) | D) -1
О	v	v	V
19.	log^x — 4(о£3х 4-3 = 0 tenglainaning ildizlari
yig’indisini toping.
A) 10 B) 20 C) 30 D) 4
20.	Uchburchakning 7 ga teng bo’lgan bahndligi uni
perirnetrlari 18 va 26 bo^gan ikkita
uchburchakka ajratadi. Berilgan uchburchakning
perimetrini toping.
A) 31 B) 30 C) 36 D) 34
21.	To’g’ri to’rthurchakDing kat-ta tomoni 13 ga.
diagonaDarining kesishgan nuqtasidan katta
tomonigacha boMgan masofa 3 ga Ung. To‘g’ri
tcfrtburchakning yuzini toping.
A) 78 B) 96 C) 72 D) 48
22.	Muntazam tosrtburchakli piramidaning
balandligi 24 sm, apofernasi esa 26 sm. Piramida
asosining perimetrini toping.
A) 48 B) 40 C) 80 D) 96
12
2
TEST 2006 r Vari&nt
106
Matematika
23,	Konusning oLq kesimi teng tomonli uchburchak.
Agar konusuing toia sirti 192* ga teng bolsa,
konus asosning diametrini toping.
A) 24 B) 18 C) 21 D) 16
24.	Agar tga zs 3 bo'isa.	ning
0«m4ct+ lOcoarcr
qiymali qanchaga teng Wladi?
.> 18	R> 3	rt. 15	8
A) 29	B) 5	C) 32	DS 15
£
25.	2cos2~ = coax + cos2x + 2 tenglamani yeching.
..	*	.	.	n	r *fc	,	_
A)	-r-	+	rfc,	k € % B) j+~,	fr€#
2	4 t
C)	rt,	kez	D)	iez
26.	Agar tekis harakatda tc-iiik 30% ga ortsa.
ma’lurn masofaai bosib o’tish uchun ketadigan
vaqt necha foizga kamayadi?
A) 331 Б) 1б| C) 23-i D) 20
t>	ej	Im
34.	lg(x — 2) < 2 — lg(27 — x) tengsbdikning
yechimiwdan uechtasi butun sondan iborat?
A) 8 B) 9 C) 6 D) 7
35.	Uchburchaknmg burchaklari 45 va 60* ga. unga
tashqi chizilgan aylananiug radiusi R. ga teng.
Uchburchakning yuiini aniqUng.
.. Я2(3+ -У5)	3R--/3 jR’VS
A) ----- в) —j— C} —
о) ^у(Л+7з)
36.	O;q kesimi teng tomonli uchburchakdan iborat
komisga diantetri D ga teng sfera ichki chhilgaa.
Konusning to'la sirtini toping.
A) ^D2	B) jtD4 C) 5~tD-
2	4	4
D) YlP3
4
27.	у —	~ Ijxa 4- 2kx — -k va у — hr2 + kx — 4,5
4
funksiyalarning grafikhri kesishmaydigan £ ning
bareha butun qiymatten yig:indisirj toping.
A) 9 В) 0 C) 12 D) -2
28.	2 — 3j* — 4[ = —4 tenglarnaning ildizlari
yig;indisioi toping.
A) 7 B) 8 C) 10 D} 9
29.	Jjt2 — 3r| = 3x - x2 tenglamaning butun
soulardan iborat ildizlari yig'indisini toping.
A) 4 B) 5 C) 6 D) 3
I
30.	Asosi 8 smT balandligi 8 sns bo lgan teng yonli
uchburchakka tashqi chitilgan aylananing radiusi
necha sm?
А) И B) 10 C) 5 D) 12
31.	O’tmas burchagi 135е bcrigan paraHelogranmiga
ichki chizilgan doiraning yuzi 16* ga teng.
Parallelogrammning perimetrini toping.
А) 32Л B) 24 C) 24^/5 D) 32
32.	Agar a(l; —1; 3) va.b{4; 3; 0) bo’isa, a niug
qanday qiymatida 4n -I- crb vertex b — a vektorga
perpendikular boiadi?
A) 2,1 B) 1	C) |	D) -A
II «J	14
33.	\/3tg2* ~ 1 > 0 tengsizlikni yeching.
* т
А) (И; T]
c>
12
m
v:
D) +	+ *я).п€2Г
О	л
13
TEST 2006 : Variant	107
—	— ..	,	_it ;i i .. j ---- 	—
Matematika
Matemsliia
1 4 m5 3 dm2 4 лтп3 fiecha kvadrat santiirtetr
b»4adi?
A) 40244 B) 40304 Q 43004 D) 41034
2.	6,4; y\ -3,2 sonlarning o‘rta arifinetigi 0,8 ga
teng. у ni toping.
Л) -0,8 B) 1,2 C) —0,4 D) 0,4
I 11. Quyidagi tasdiqlarning qaysilari to‘g‘ri?
1)	uchburchakka tashqi chiziigan aylananing
radiusi ft = q^(a, ^.c- uchburchakning
tomotilan, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	tomonlari a va b ga, »lar orasidagi burchagi о
ga teng bo:lgan uchburchakuihg yuzi
S = ^abtfiua formula bilan hisoblanadi;
3)	crxsbash figuralar yuzlarining nisbati ularning
uios chiziqli clchovlarining nisbatiga teng.
Л) 2;3 В) 1;2 С) Г,2;3 O) 1;3
3.	16 — (2c - I)2 ni kolpaytuvchilarga ajrating.
Л (3-2e)(5-2r) B) (3>2r)(5-2c)
C) (2c-3)(2c-5) D) (3~2e)(5 + 2c)
4	(x~; + V 1) • ---r? Hi soddalashtiring.
(* + ?/)
A) a\ _fV_ o -J—
1 (x + y)3	' (l + s)’ M Х+»
m xV
12. Tekisiikka tushirilgan og’ma. va perpendikular
orasidagi bwrdjak arrsin^- ga teng. Og‘inaning
tizuuligi 122 ga teng. PerpeHdikw’arni’ng
uzunligioi toping,
A) 22 B) 120 C) 24 D) 90

13. tg(— — cr) = -- bo'Jsa. ctga ning qiyrnatini
toping.
A) 9 B) C) -4 D) |
5. (2z — 1)(x — 1,5) = 0 bo'lsa. 2x — i qanday
qiymatlar qabul qiladi?
A) faqat — ~	B) 2 yoki 0 C) 0 yoki 1,5
P) 0 yoki -i
5. x24 l!z + ^ = 0 tengfarnai ing iidizlaridan bin
— 12 ga teng. Uning ikkinchi ildizini toping.
Д) -23 B) 1 C) 23 0) -1
7. (r 4- 2)(jt — 3) < 0 tengsizlikni yeching.
A) (—co; —3) U (2; oo) B) (-2:3)
C) (-oc;-2)U(3;co)	0) (-3;-2)
8. Quyidagi sonlardan qaysj bin 0,8(1) ga teng?
B)
9
11
14. ------- ifoda natural son bo’ladigan я ning
natural qiyniatlari nechtA?
A) 7 B) 2 C) 5 D) 3
15.
A 38	47	56 U H 3	4	5
Agar « + 5l + ST = ° bo ls*’ 41 + M + 61
quyidagilardan qaysi biriga teng?
А) 4-е В) 3-a C) 3-| D) 5-a
16. у a 3x2 4 8z - 8 funksiyaning grafigi 4*ysi
choraklarda joylashgan?
A) barcha choraklaxda 8) 1?4 ill. IV
C) L IL Ш D) ill, LV
__ (7 + 3e> 5(x4 1)46	. .rv.
57’ < /	i /	.-П , irt tengsjzbkbr
(	2)~ — 8 < z(x - 2) + W
sistemasrm yeching.
A) [-2; 7) В) (-П: 2] C) [2; П)
D) (-7; -2]
9. x ning qanday qiymailarida у ~ 5r - 125
funksiya nomaiifiy qiyniailar qabul qiladi?
A) 2 < 3 x > 3 C) x < 2 D) x > 2
10. Ikkita to‘g‘ri cbiziqning kesishishnlan hosil
bo‘lgan qo‘sbni burchaklar 7 : 8 nisbatda bodsa,
shu burchaklami toping.
А) 75е: 105е B) 38’. 144* C) 38°; 142®
DO 84 е; 96°
18.	-T y;----- ning boshlang/ieh funksiyasini
swr(4x 4 I) ’
Loping.
I	1
A) -cty(4z-H)-frC B) -TCf?(4z 4-1)-Ь C
C) -bff(4x+l) + C ©) ltff(4x+l) + c
4	'4
19.	а == log^/вб, b ~ log1/e4 va c- lo&i/&4 sordarni
o’sish tartibida joylashtiring.
A) b < с < а $0 c < b < a C) 6 < a <
Г>) q < c < b
14
2
TEST 2006: Variant
107
Matcmatika
20.	Uzunligi -- ga teng aylana o4kir burchagi 30®
bo'lgan rombga ichki chizilgan. Rombning
perimetrini toping.
A) 16 B> 2 C) 4 D) 8
21.	ABC uchburchakda AB = AC, BMXAC,
BM == 18 va ЛМ = 24. ABC uchburchakning
yuzini toping.
A) 258 B) 254 C) 270 D) 262
22.	Teng tomonli uchburchakning tornonlari 3 m.
Uchburelink tekisligidan tashqarida uning
uchlarid&n 2>/3 in masofada yotuvehi nuqtadan
uchburchak tekisligigacha bo‘Igan masofani
toping.
A) V3 В) 1 C) 3 D) 1,5
23.	Ikkita sfera yuzlarining nisbati 2>/2 ga teng. Bu
sferalar diamet Hanning nisbatini toping.
A) В) У8 C) Л D) 8
izn36r 00*36°
sin 12°	co«12°
Л) 3 B) 2
D) //Г1
25. sinx + sin3x — 0 tenglama [0; 4x] oraliqda
uechta ildizga ega?
A) 7 B) 13 C) 8 D) 9
26. Korxonada mabsulot ishlab chiqnrish birinchi yili
/10% ga. ikkinchi yili 20% ga oshdi. Mahsulot
ishlab chiqarish ikki yil mobaynida necha foizga
ortgan?
A) 26 B) 25 C) 26,5 t) 32
л- . 13x + 8,5
27. у = fo(———
г + z
sohasini toping.
— 4) funksiyaning aniqlanish
•A) (-2; 5) B) (-oo;-2)U(i;=o)
X	X
C) (5:00) D) (—00;-2)
X
30-	Uchburchakning b va e ga teng tornonlari
orasidagi burchagi 30° ga teng. Uchburchakning
ucbinchi tomoni 16 ga teng bo‘lsa bant da uning
tornonlari c2 == b2 4- 166 4- 256 shartni
qanoatlantirsa, c ning qiymati qanchaga teng'
bo'ladi?
A) 1б\/3 В) 12Л С) 12Л .0) I6V?
/- 1
31.	у = \/3x + 2 va у ==	4- % tolg‘ri
v3
cbiziqlarniug kesishishidan hosil bo‘lgan o4kir
burchakni toping.
A) 75° B) 65° C) 90° D) 60°
32.	a(m — 1; v^5;4) vektorning uzunligi 5 dan katta
boiadigan m ning barcha qiytnatlarini toping.
A5 (~1;3) Bl (-oo;-2)U(2;oq)
C) (-oq;-DU(3;oq) D) (~2;2)
33.	у =	si or funksiya ж (x € [0; 2x])
ning qanday qtyrnatlarida aniqlangan?
A)	;т] B) [-: —]	C)
D) (0;£l
34.	(z 4-	< (x + 2)bK»,3*+{l) tengsizhk x
ning qanday qiymallarida o'rinli?
A) (-2;4) В) (-4,5;oc) О (-1;4)
D) (4:00)
35.	Radius! R ga teng bolgan dot rani ng markazidan
bir tomonda ikkita bir-biriga parallel vatar
o’tkazildi. Bu vatarlardan biri 120° !i, ikkinchisi
60° li yoyni tortib turadi. Parallel vatarlar
orasida joylashgan kesimnhig yuzini toping.
4	x/f2 ttR2	3r/i2	xft2
A	V B) -7-	C	—-	D)	—
4.0	0	3
36.	Sharga balandligi asosining diamet-riga teng
bo lgan konus ichki chizilgan. Agar konus
asosining yuzi 2,4 ga teng bo^sa, shar sirtining
yuzini toping.
A) 6 В) Ox C) 15 D) 12,5
28. in va n ning qanday qiyniatlanda
2x»n — 3ny = 12 va 3xrn 4- 2ny = 44 to'g‘ri
chiziqlar (2; 1) nuqtada kesishadi?
m =- 8, n = 6 B) nt = 6, n — 4
G) m=12,n = 2 D) m —4.n—10
29. 4fx 4- 4} = 3 4- (x 4- 4)2 tenglamaniug ildizlari
ko'paytma.sini toping.
A) 15 B) 105 C) -15 4>> —105
15
TEST 2006 : Variant
108
Matematika
1
Matematika
1.	279 ni 16 ga bo'lganda qokiiq 7 boiadi. Bo4inma
nechaga teng?
A) 12 B) 13 C) 11 D) 17
, 6,5-0.04-6.8 .	.	. .	.
2.	r * ё •T’TTTF пшй qtymatmi toping.
5.2-5,! -0.16
A)1 B)A C)1 D)|
3.	x2 4 r — 12 kvadrat- uchhadni chiziqli
ko'paytuvchilarga ajratihg.
A) (x- 3)(x + 4) B) (x + 3)(z-4)
C) (x-3)(4-x) D) (x + 3)(4-x)
4.	Agar P = -x - -y - (r 4- 2y) va
Q — ~x 4 ijr - (x 4 5t/) bo’lsa, P - Q ni toping.
A) 4» В) 2g С) ~-ц D) -4»
11.	Quyidagi tasdiqlarning qaysilari noto4g*ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi ^y(a,6.c— uchburchakning
tomonlari, S- uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga. markaziy burchagi о ga teng
doiraviy sektorning yuzi S = formula bilan
hisoblanadi:
3)	tomoni a ga. burchaklaridan biri a ga teng
rombning yuzi S — ^a2sina formula bilan
hisoblanadi.
A) 2;3 B) 1;2 C) 1;2:3 D) 1:3
12.	Tekislikka tushirilgan og4maning uzunligi 75 ga.
uning tekislikdagi proyeksiyasi esa 72 ga teng.
Og'ma va tekislik orasidagi burchakni toping.
24	7
B) nrcjun— C) orrstn--
25	24
A) arccos—
50
D) arc sin
25
13.	~—r--------------cos a ni soddalashtiring.
sin 2or 4 cos 2a
A) siu2a B) cos 2a C) —2 sin 2a
D) — cos2o
6x — m 7mx — 1
5. тп ning qanday qiyinatida —-— =----------
2	о
tenglamaning ildizi nolga teng bo‘ladi?
4	2	2	3
A) 5	B) -- C) i	D) -i
14.	5<x<109 tcngsizlikni qanoatlantiruvchi, 12 ga
karrali nechta natural son mavjud?
A) 10 B) 8 C) 9 D) 12
6.	X| va x> x" 4 2x — 12 = 0 tenglamaning ildizlari
ekanligi rna’lvni. x\ 4 z| ning qiymatini t-oping.
A) 12 B) 10 C) 28 D) 11
15.
842 sonining ovng tomoniga qanday raqam
yozilsa, hosil bo’lgau son 36 ga qoldiqsiz
bo'linadi?
A) 2 B) 4
D) 6
7.	----— > 0 tcngsizlikni yeching.
x 4 l
A) [~7; 5) B) (-oo: -7)
C) (~oe; —7)U[5: co) D) (-7; 5]
16.
у = у	~ funksiyaning aniqlanish
sohasini toping.	/
A) [2;3)U(4:5] B) (2:3)U(4;5)
8.	0. (7) 4 0. (5) — - ning qiymat.ini hisoblang.
8	12	1
A) B) 15 C) ig D) 1-
9.	/<?^2^pl00s ni hisoblang.
A) 4 В) 1 C) 2 D) 3
10.	Ikkita to'g'ri chiziqniug kesishiskndan hosil
boigan qo'shni burchaklarning gradus o’lchovlari
4 : 6 nisbalda bo'lsa, shu burchaklarni loping.
A) 60°: 120° B) 72°: 108° C) 50°; 130°
D) 30е:150°
17.	Quyidagi tengsizliklardan qaysi biri x va у ning
xy > 0 shartni qanoatlantiradigan barcha
qiymatlarida o'rinli?
*2
A)	+ £- + £> 2 B)(z-^>0
x~ 4 y~ xy
C) x2 - 6xy 4 9t/2 < 0 D) x2 — y2 > 0
,2r
18.	/ cos(0,25r)dx ni hisoblang.
A) 4~2y/3 B) —2 C) 2 D) -1
19.	2**	== 64 tenglatnani yeching.
A) 1 B) 1,5 C) 3 D) 2
16
TEST 2006: Variant
108
Matemat ika
20.	Teng yonli uchburchakning uchidagi tashqi
burchagi o sha uchdagi ichki burchagidan 5
maria katta. Uchburchakning asosidagi tashqi
burchagini toping.
А) 105е В) 100° С) 108е D) 95°
21.	Rasmda AfA/“||AC. MBN uchburchakning
perimetri 42 sm. ABC uchburchakning perimetri
84 sm. MBN uchburchakning yuzi 44 sm3.
ABC uchburchakning yuzini (sm2) toping.
A) 108 B) 99 C) 81 D) 176
22.	Pirarnidaning asosi to*g‘n burchakli uchburchak
boiib, uning gipotenuzasi uzunligi 20 ga teng.
Piramidaning barcha yon qirralari 26 ga teng
bcrlsa, lining balandligini toping.
A) 12 B) 24 C) 22 D) 20
23.	Silindr o'q kesimining diagonal! 8 ga teng va asos
tekisligi bilan 30° li burchak lashkil etadi.
Silindrning hajmini toping.
A) 48» В) 6» C) 16» D) 24»
24.	sin — • eos3-^ - stn3-^ • ni hisoblang.
lb lo 15 lb
A) 1 B) 1	C) |	D) Y
О	Z	о
25.	5sin4z — 8 = 3cos(^- 4- 4z) tenglarna [—2»; 2»]
kesniada nechta ildizga ega?
K)’l b) % С) Ь ТУ) *
26.	900 kg mevaning tarkibida 80% suv bor. Bir
nccha kundan keyin mevaning og irligi 500 kg ga
tushdi. Endi uning tarkibida necha foiz suv bor?
A) 68 B) 62 C) 64 D) 66
29.	(z2 4- 6z 4- 4)(z2 4- 6z 4- 6) = 120 tenglamaning
haqiqiy ildizlari yig'iudisini toping.
A) 5 B) -12 C) -5 D) -6
30.	Tokg;ri burchakli uchburchakning katetlari 5 va
7, 5 ga teng. To'g'ri burchak bissektrisasining
uzunligini toping.
A) Зх/2 В) 4\/2 C) 3 + 3>/2 D) 5\/2
31.	Parallelogram™ qo’shni toinonlarining yig’iudisi
10 ga, ayirmasi esa 8 ga teng, Shu
parallelogram™ diagonallari kvadratlarining
yig'indisini toping.
A) 144 B) 164 C) 121 D) 136
32.	5(3: —6; 6) vektorga kollinear va ab = 40,5
teuglikni qanoatlantiruvchi a vektorni toping.
А) a[3:6:9) В) аф-3;3) C) a(3:-6;6)
D)
33.	cost < sinx t-engsizlikni yeching.
A)	(7+»*:	kez
4	4
B)	(v + ’rt; + «*}. iez
4	4
C)	(2»Jt; » 4- 2»fc). k Z
D)	(т + 2т4;	+ k 6 Z
4	4
34.	cos2(x 4-1) • /0^4(3 - 2z — x2) > 1 tengsizlikni
yeching.
A)	В) [-l;0) С) Ы)
D) {-2;-l}
35.	Doiraga ichki chizilgan uchburchakning bir
tomoni uning diarnetriga teng. Doiraning yuzi
289» ga. uchburchak tomoni arid an birining
uzunligi 30 ga teng. Shu uchburchakka ichki
chizilgan doiraning yuzini toping-
A) 36» B) 16» C) 20» D) 64»
36.	Kesik kouusning yon sirti 10» ga, to:ia s’irti 18»
ga teng. Konusning to‘la sirti unga ichki
chizilgan shar sirtidan qanchaga ortiq?
A) 6» B) 14» C) 10» D) 8»
27. f(x) — ------ — I funksivaning qivmatlar
cosx
sohasini toping.
A) (-2; 2) B) (—1;1)	C) (-3:1)
D) [-2;0)U(0;21
28. У»2 — 4z + 4 » Ух2 — 16x4- 25 tenglamaning
ildizlari qaysi oraliqqa tegishli?
A) x < 3 B) 3 < x < 4 C) z < -2
D) x > 5
17
TEST 2006 : Variant
109
Matematika
1
Maternal ika
1 Quyidagi tasdiqtardan qaysi biri haruina vaql
to‘g‘ri?
Л) birorta ham qo'shifavchi П ga bo'linmasa,
yigindi ham 11 ga bo'lininaydi
B)	bar bir qo'shihivchi15 ga bodins a, yig'indi
barn 15 ga ho'Iinad)
C)	yig'indi 11 ga tw'linsa, bar bir qo*shiiuvchi
ham 11 ga bodinadi
D)	qo'shihivcbilardan kainida bittasi 12 ga
bo'hnsa, yig'indi ham 12 ga bo'linadi
II.	Quyidagi tasdiq taming qaysilari to'gVi?
I)	tomontari a, 6 va c bclgan uchburchakka ichki
diizilgan aylananing radiusi r = formula
bilan hisobtanadi;
2)	radiusi Л ga, markaziy burchagi a ga.teng
doiraviy sektorning yuzi S — 3^—-a formula bilan
hisobbnadi;
3)	tomontari a va b ga, nlar orasidagi
burchaklaridan biri a ga teng bodgan
paralielograrwrining yuzi S = absinct formula
bilan hisoblanadi.
A) 2;3 B) 1;2 C) 1;2;3 D) 1;3
1,6-0,7-1,8.....................
r7 TH Inng qiyrnat-im topmg.
t i *	/э • Vj v
A)
B)
2
3
1
24
D)
3. 16 — (2r — 3)2 ni ko‘paytuvchitarga ajratiug.
А) (2z- !)(7-2s) В) (2л + 1)(7 - 2x)
C) (2x-l)(2x+7) D) (2x 4-l)(2x - 7)
12.	Tckishkka tushirilgan og‘ma va perpendikular
16
orasidagi burchak arcminga teng. Og'maning
65
uzunligi 130 ga teng. Perpendikutarning
uzunligini toping.
A) 96 B) 64 C) 32 D) 126
13.
1 . , 2stncr 4- sin2o
Agar coso = — - bo lsa. ——-----------:——- m
7	2 sin л — mn 2o
h isobl ang.
4.	2n- — 3nn — 4n 4- 6a ko'phadni ko‘paytuvchilarga
aj rati ng.
A) (n-2)(2n~3a) B) (5 - n)(3a + 2n)
С) (2n-3a)(n-5) D) (3a-n)(5-2n)
14.
5.	(x 4- 4-) : 4- = 6 tenglarnani yeching.
У о
A) 215 B) 22j C) 20?	O) 22l-
V	J	J7	t>
15.
6.	ar - 7л 4- q = 0 Uu^taruaniu^ ildiztandan bid
-19 ga teng. Uning ikkinchi ildizini toping.
A) 8 B) -26 C) -8 D) 26
4
x D) 3
Quyidagi sontardan qaysi biri 15 ga qoldiqli
bo‘litiadi?
A) 3105 B) 6525 C) 6130 D) 4620

Proporsiyaning dasttabki uchta hadi yig'indisi 78
ga teng. Uning ikkinchi hadi birinchi hadining i
2 . .
qisnurn. urhinchi hadi esa- - qismmi tasbkil
etadi. Proporsiyaning uch’mchi hadini toping.
A) 18 B) 12 C) 24 D) 36
x *4* 3
7.		-- < 0 tengsizlikni yeching.
т — о
A) [-3; 5) B) (-co-. -3] C) (5; oo)
D) (-3; 5]
16.
17.
к ning qanday qiyrnatida у = kx 4- 2
funksiyaaing grafigi A(—4; 14) nnqt-adan o4adi?
A) -1 B) -2 C) -3 D) -6
z~ - bx -
x - 4
> x tengsizlikni yeching.
8.
0,(8)4-0,(3)-|
ning qiyinatini nisobtang.
C) (2; 4)
1	2	2
Л) *9 B) 4 C) 3
D) (-1; 3)
D) 0,(11)
0.	ni hisoblang.
A)'7 B) 3^/5 C) 15 D) 5
18.
Agar = sinz va /"(I) = 4 bo lsa, F(x) ni
toping.
A) 4 4- *«ml - sinx	B) 4 — cosl 4- eo.sr
C) 4 4- sVnl 4- sinx	D) 4 4- cosl — соях
10 Ikktta to4g‘ri chiziqning kesishishidan hosii
bcVlgan burchaklardan uchtasming yigkindisi 275°
ga long. Shu burchaklardan kichigini toping.
A) 45° В) 60е С) 85е D) 70°
19.
a = Iogj47189 ho*isa, Iog7 3 ni a orqali ifodalang.
2a ~ 1	R1 1 ~2tt	Гч a ~ 2
3 - a * a - 2	) 2a - 1
a — 2
1 —2a

18
TEST 2006: Variant
109
MAteitintik&
20, Teng yonli uchburchakning uchidagi burchagi
106°. Asosidagi burchaklarning bissektrisalari
kcsislrishidan hosil bo’lgan o'tkir burchakni
toping.
A) 43* B) 37° С) 47е D) 48°
21. Doiraga tashqi chizilgnn teng yonli
trapctsiyaning asoelari 8 va 32 ga teng. Shu
doirairing yuzim hisoblang.
А) 49% В) 64% С) 16% D) 36%
22. To’rtburchakli muntazam prizina asoeining yuzi
169 sm3, balandligt >/191 sm. Shu prizma
diagonalini toping.
A) 21 B) 23 C) 27 D) 22
30.	To'g'ri bnrchaklt uchburchakning gipotenuzasi 25
sm, kalBllaridan biriuing gipolenuzadagi
proyeksiyasi 23,04 sm. Usbbu uchburchakka ichki
rhizilgan ayUnaning radiusi necha sm?
A) 2,5 В) 3 C) 1,5 D) 2
31.	Asotdari 12 va 16 ga teng bo4gan teng yonli
trapctsiyaning diagonallari o’zaro perpcndikular.
Trapetsiyaning yon tomonini toping.
А)	В) 20 С) 10 D) 10v/5
32.	Agar a vektor b == $t—2j -4- k vektorga kollinear
va a ' b = 28 bo'Isa, a vektorniag uzunligini
toping.
A) — B) 14 С) 2VM D) ~
23.	Tomonlari 3 va 4 ga teng bo’lgan to'g’ri
to‘rtburcbak o’zining katta tornonLatrofida
aylanadi. Hosil bo’lgan jisnming fo'Ia sirtini
taping.
A) 48% B) 42% C) 36% D) 24%
24.	f(x) = 1 — 3cos2r — keos2x funksiya k ning
qanday qiymatida o'zgarmas bo ladi?
A) -2 B) -3 C) -1,5 D) -1
33. 1 — 2cos2x > ttin22x tengsizlikni yeching.
«)
C)
D)
25.	ros3x • xinx — cos3r = 0 tenglamani yeching.
a) (-i)‘4 + v*; l+2,rfc-i6Z
6	3	2
B) ? + £*, t€Z C) £ + »fc; xt, ieZ
D) J + ^i; 2xi, kez
6	3
26.	Bog’dagi daraxtlaruing 60% i teraklar. Qolgan
daraxtlarning 70% i chinorlar bo‘lsa, boshqaiari -
tollar. Bog’dagi daraxllarning necha foizini foliar
tasbkil etadi?
A) 18 B) 12 C) 24 D) 28
27.	у == kx2 — 2kx 4- 5 va и = 2 — hx funksiyalarning
grahklari к ning nechta butun qiymatlarida
kesishmaydi?
A) 2 B) 12 C) 4 D) 11
34.	3* 4- 3**3 > 84 tengsizlikni yeching.
A) (-cc; 0) B) (0; 1) C) (1; oo)
D) (0; 1)U(1; oo)
35.	Diagonal! orqali ikkita muntazam uchburchakka
ajraladigan rombga ichki chizilgan aylanauing
radiusi r ga teng. Rombning yttzini toping.
A) 4r5 B) 2^73 C) 4r’V2 D)
36.	Konusning o*q kesimi mutitazain uchburcbakdan,
silindroiki csa kvadratdan iborat. Agar learning
hajmlari teng bo’Isa, to'Ia sirtlarining nisbati
niuiaga teng?
Л) УЗ : ^2 В) У2 ; С) 1 : У5
D) 3:2
28. Qisqarmaydigan oddly kasrning maxraji
suratidan 18 taga ko'p. Agar kasrning suratiga
379 ni, tnaxrajiga I ni qo’shsak, berilgan kasrga
teskari kasr hosil boladt. Berilgan kasrning
rnaxrajini toping.
A) 19 B) 17 C) 14 D) 13
29.
t — 6 m ,	.	.
-----— = — tcnglarna in rung neciita natural
77! — ID t
qiymatida ildizga cga etnas?
A) 7 B) 5 C) 8 D) 28
19
7 h'S1‘ 2006 : Variant	110 Matematika	1
Matematika
1 Agar kajuayuvchini 26 ta va ayriluvchini 12 la
oittirilsa, ayirrna qanday o'zgaradi?
Л) 14 la ortadi B) 4 ta kamayadi
C) 4 ta ortadi D) 28 ta kamayadi
'2 Karitada ikki shahar orasidagi inasofa 3,5 sm ga
teng. Xaritadagi niasshtab 1:2000000 boisa,
shaharlar orasidagi baqiqiy rnasofa necha km
bo'ladi?
Л) 7 B) 140 C) 700 D) 70
3.	t~ — x — 6 kvadrat uehhadni chiziqli
ko4paylirvchilarga ajrating.
A) (x4-3)(s-2) B) (z-3)(z + 2)
C) (x + 3)(2-r) D) (x3-2)(8-x)
4.	(x2 4- l)(x4 - z2 4-1) - (x2 — 1 )2 4-r5 4- x3 4- .r ni
.wddalashtirgandan keyin hosil bo'lgan
ko'phadning nechla hadi bo’ladi?
A) 4 B) 5 C) 6 D) 3
5.	к parametrntng qanday qiymat-landa
| 3r - y^~~^ tenglamalar sistemasi yechimga
ega einas?
Л) 2 B) 9 C) 6 D) 3
6.	x- 4- 13x 4- q — 0 tenglantaring ildiziaridan biri
-11 ga teng. lining ikkinchi ildizini toping.
A) 2 B) -24 C) -2 D) 24
7.
x-2
j 4’1
< 0 tengsizlikni yeching.
11.	Quyidagi tasdiqlarning qaysilari noto‘g‘ri?
I)	radiusi R ga, markaziy burchagi ot ga teng
doiraviy sektorning yuzi S — ygro formula bilan
hisobianadi;
2)	tornonlari a va b ga, ular orasidagi
burrhaklaridan biri a ga teng bo’lgan
paraHelograrnrrming yuzi S = absino formula
bilan hisobianadi;
3)	diagonallari d\ va cf2 ga, ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
to'rthurchakmng yuzi S = d\dnsincx formula
bilan hisobianadi.
A) 2;3 B) 1,2 C) 1,2,3 D) l;3
12.	Tekislikkaogbna va perpendikular tushirilgan.
Og'rnaning tekislikdagi proyeksiyasi 63 ga,
perpendikulaming uzunligi 16 ga teng. Og'ma va
perpendikular orasidagi burchakni toping.
..	32	_	. 16	63
A) ar tews—;	B) arejnn-—r C) iircta~—
65	65
™ • 63
D) arc sin ~~
65
sin4 <r 4- sin” a • cos2 cr .	,, , ...
---------------------- ni soddalashtinng.
A)
D)
COS”
1 — tq2cr B) Uj2o/ G) 1 — clg-a
cos~ a
14. Agar avtornobil tekis harakatda3 soatda 324 km
ni bosib o tsa, 10 sekundda necha rnetr rnasofani
bosib ostadi?
A) 300 R) 200 C) 100 D) 600
15. a — 36 va 3, 36— a va 4 soniar proporsiyaning
a2 4- b J
ketrna-’ket hadlari bo'lsa, --;— kasrning
ab
qiymatjni toping.
A)[2;3) B) (-!; 2] C)(-3;2]
D) (2; 3]
8.	Arifmetik progressiva uchtin quyidagi
formulalardan qaysilari notc/g'ri?
i \ c _ «1 + (n - 1 )d «n - a< 4- d
I)	'	-it', 2)
2	n
3)	«1 4-«л = a-j 4- (tn-?
A) 1; 2 B) 2; 3 C) 2 D) 1
9.	4- io^jL.3 ni hisoblang.
A) -1 B) -3 C) 1 D) -0,5
10.	Qo'shni burcbakiardan biri ikkinchisidan 52° ga
katta. Shu btirchaklardan kattasiui toping.
A) 118* B) 106° C) 114° D) 116°
16.	f(x) ~ \/5 + \/4 4- x 4- x/5 4- funksiya
uchun quyidagilardan qaysi biri o'rinli bo'ladi?
A) toq ham. juft, ham emas B) toq ftinksiya
C) o(suvchi funksiya D) juft funksiya
4-	4)(3 _
n. ---------—----- > o tengsizlikning eng katta va
(x 4- 3)'
eng kichik butun yechindari yig'indisini toping.
A) -2 B) 1 C) 0 D) -1
4"	f/л»
18' / 0,25г+1 Bi hisoblan«-
A) 4/n(e + l) В) 2M(«+1) C)
D) /n(e4-2)
20
_ TEST 2006: Variant 110 
Matemat ikn
19.
a — log5<) ко hoTsa, )ogs 2 ni a nrqnli jforWang.
A)
D)
a ~ 3
1 — 2a
I — 2 л
a — 4
B)
Зд~ 1
2 a
20.
Muntazarn oltiburrhakka Uwhqi chiz'dgau
ay Jan an mg radiusi /2 bo’isa, unga ichki
chiziigan aylanamng radiusini toping.
21.
22.
24.
Yuzi 156 sm 2 . batandliklan 4 sm va 12 sm
bo lg.au paralMograinniniug perimetrini toping.
A) 73 B) 104 C) 96 0) 108
Muntazarn tortburchakli piramidaiHug
balandligi 12 ga, asosmhig Loinoui 7 ga teng.
Untng apofernasini toping.
A) 13.5	P/} 9 C) 12,5 D) 25
Asosining radiu si 16 sun va Lahmd’igi 8 »ш
boigan konus asosidan 3 sm masofada asosiga
parallel tekislik bilan kesdgau. Kesi tuning
ynzini (snr) toping.
А) 50* В) Збтг C) 100*	0) 25r
3
tj7O =: - • i(j'2tx
4	24	3
A) - В) 3 C) D) ~
30.	Tornonlari 16: 30 va 34 sm bo'lgan uchburchakka
tashqj chizitgan ayiauaning radiusi necha sm?
A) 18 В) 17 C) 19 O) 16
31.	Paralieiograinrnning burchaklaridan biri 150° ga
teng. (’ning 9 ga (nig bodgan diagonal!
ionioniga perpendikular. Paralielogramrmnng
perimetrini ioping.
A) 9(4+\/3) В) ЗСиЛ C) 9(3 4-/3)
!.)) 18(2 4 /3)
32.	AG-4; 1: 1), 7^(1; 4; 0) G(l; -2; 2) va_____
D( — 5: —5; 3) iju<|talar berilgan. AC va ZC2
vektorlar orasidagi burchakni toping.
А) 69е В) 'МГ С) 45й D) 30°
33.	у — y^i 4- IcgjTTslnx fimksiya х (z G [0:2?r])
ning qanday qiymatlariila aniqlangan?
A) (<>41	B) C) («;’)
6	' t)	0 Г)
Di
ildizl ari; i? ko’rsaiing.
34. -r 25^a	19 tenglaruani yeching.
A) 1 В) И) C) 5 D) ZW
35. Teng yonli trapeVsiyaga ichki cluzilgan
aylananing markazi ustkj asosining uchidau 3 ga.
pastki asosining uchidan 4 ga teng rnasofada
joylashgau. Shu trapet-siyaga ichki chizilgau
doiraniug yuzini toping.
A) .5,76x В) 2.56r C) 6.76% D) 3.24%
A) ~ + 2%£, k <= 7 B) 4.-.^+ 2*£. £ & 7
С»	5
C) 4:™ 4 2z£y k Q 7	0) ±-~ 4- 2*£. k € 7
V*	ЧЛ
3G. llapni 8\/3 ga teng bo'lgaij muntazam
let yard ruing balandlignu toping.
Л) 1 В) C) 3 D) 4i/3
26. Korxonada ruahsulct ish'ab chiqartsh birmchi yili
20% ga, ikkinchi yili 15% gaortdi. Mah.su lot
ishlab cbiqarish ikki yil mobaynida necba foizga
or* gon9
A) 28 B) 38 C) 32 D) 35
27. Agar Л(2; 7) nuqta /; ~ k-x~ 4-8/4- hi
parabolanmg urhi bcflsa, £ va m ning qiymatini
toping.
A) k — 2, m — I B) £ — 1. m “ —9
(;) A ~ --2^ rn..— —1 D) £ ~ - I, m ~ — 1G
28 — 4 --—г —" 4- — 4- -г —~ —• 6 tenglamani
3	15	35	63	09	143 b
yeching,
A) 13 B) 26 C) 16 D) 18
29. i«2 — 9r 4- 8- — —8 -4 &r — r2 tcnglani&ruttg
\ barcha natural yechhnlari yig4ndisini taping.
A) 40 B) 36 G) 28 D) 25
J EST Ж6 : Variant
111
M a tern at) ka
Matemat ika
12.
Tekisiikka tushirilgan og‘nia va perpeudikular
1 Agar kamayuvchint 30 ta va ayriluvchini 12 ta
knrnaytirilsa, ayinna qanday o^zgaxadi?
A) 24 ta ortadi E) 18 ta kainayadi
С) 12 fa kamayadi D) 12 ta ertadi
orasidagi burchak arcmin
]2
37
ga teng. Og'manmg
uzunHgi 74 ga teng. Perpendikularuing
uzunligini toping.
A) 70 B) 24 C) 54 D) 48
2.	2,014 : 0,19 4- 2,5 • 0,3 ni hisoblang,
A) 11,35 B) 9.85 C) 12,85 D) 8:85
3.	16 -- (8a — 3)2 ni ko’paytuvcbilarga aj rating,
A) (8a-l)(7 + 8a)	B) (8a + l)(8a - 7)
C) (8a —1)(7—8a)	D) (8a 4-1)(7 - 8a)
4.	2rrfr4 3a — 4ab2 — 66 kosphadni
ko‘paytuvchi]arga ajratiug.
A) (a - 2b)(2ab 4- 3)	B) (2ab - 3)(« - 56)
C) (2a2 4-6)(6 - 5a)	D) (3 4- 2ab)(a - 56)
5.	in ning qanday qiymatlarida }3 — :n| = m — 3
tenglik oxrirJi bo’ladi?
A) ineR B) rn > 3 C) rn > 3 D) rn ~ 3
6.	x\ va X2 t2 — 22x 4-8-0 tenglamaning ildizlari
bo‘lsa. 4- х2хо ning qiyrnatUH toping.
A) -176 В) -120 C) 176 D} 280
x — 1	.
7.	tengsizlikni yeching.
A) [1; 3) B) (-3; 1) C) (-2: 1)
D) (1; 3)
8.	Quyidagi ketma-ketiiklardan qaysilari geometrik
progressiyani tashkil etmaydi?
1) a„ = |-2"; 2) a„ = 3-2-“; 3) b„ = (-1)" + I.
A) 1:2 B) 1:3 C) 1 D) 3
9.	(ч/З)1*”*3 ui hisoblang.
A) 3 В) У13 C) 6
D) U
10.	Burchakmng bissektrisasi uning tomoni bilan 20°
П burchak tashkil etsa, burchakning o‘zini
toping.
A) 30° B) 45° C) 40° D) 60°
11.	Quyidagi tasdiq’arning qaysilari to'g’ri?
1)	tomonlari a va b ga, ular orasidagi
burdiaklaridan biri cr ga teng bo'lgau
parallelogranimning yuzi S = abftino formula
bilan hisoblanadi;
2)	tomonlari a va b ga, ular orasidagi burchagi о
ga teng bo‘lgan uchburchakning yuzi
S = kafaina formula bilan hisoblanadi;
3)	diagonallari di va d2 ga, uiar orasidagi
burchagi a ga teng ixtiycriy qavariq
to'rtburchakning yuzi S =s didvizna formula
bilan hisoblanadi.
Л) 2;3 B) 1;2 C) 1;2;3 D) 1;3
sin4cr 4- 2со.ч2<г co*-4o
13-------—------------------r-c— ni soddalasntiring.
I — .sinZo — CO.S4O-4- stnoo
A) 2sin2or	B) 2t^2o C) ct«/2o
D) 4tg2o
14.	420 : (60 — 1000 : r) — 12 dan x ni toping.
A) 1 B) 8 C) 35 D) 40
о
15.	O‘zaro teskari soiilarni aniqlang:
1) 3 - Л ra 3 + </2:
4)	\fl 4- 1 va y/2 - i.
A) 1;2;3 B) 1;3,4 C) 1:3 D) 2;3;4
16.	Quyidagi parabolalardan qaysi biri OX o‘qiga
urinadi?
1)	у = 2x2 — 5x 4- 8; 2) у = — 2x~ — 8x — 18;
3) у =	- 3x — 8:4) у = 4x2 — 6x 4-
A) 2 B) 1 C) 4 D) 3
17.	Quyidagi tengsizlikiardan qaysilari o'zaro teng
kuchli?
3)^-^>0;	4)r~3>0.
X“
Л) 1, 2; 4 B) 2; 3; 4 C) hammasi
D) 1; 3; 4
18.
ni hisoblang.
з
т ’> i « т -T
19.	Qayei javobda nianfiy son ko!rsatilgan?
А)	В) /од^З С) /0521,2
20.	Л(5:~-4) aylanadagi nuqta. C(12;20) nuqta
aylananing markazi boOsa, aylananing radiusini
toping.
A) 26 B) 15 C) 25 D) 17
22
TEST 2006 : Variant.
111
Matein a tifca
21.	Ikkit-a o‘xshash kcrpburcbak yuzlariuing nisbati
9:4 gateng. Kichik ko'pburchakning perimetri В
sm. Katta k</pburchakning perimetrim (oping.
A) 8 B) 9 C) 12 D) 6
22.	Prizrnaning asosi tomoni 3^5 htrlgan inuntaxam
oltiburchakdan. yon yoqlari kvadratlardan
iborat. Prizinainng katta diagonalini toping.
Л) 10 B) 15 C) 12 D) 7Л
23.	Kabmng bar bir yog’hn yuzi 27 maria, orttirilsa,
tining hajmi ucdia marta ortadi?
A) 54/5 B) Uy'S C) 27 D) И1/3
24.	Quyidagi ayirtualardan qaysi binning qiyrnat-i
i и anti у ?
A) coslO* - aw50* B) smW - .s-ml50°
C) ct</42° — ci #28° D) /</87° — /</85°
—	. 7ГХ
25.	\/3 — 2sm — 0 (7.5 < z < 13.5)
V
tenglamaning yechimini toping.
A) 10“ B) 8,5; 9,5 C) 8; 13
D) 10^ II
4
3
8
26.
Nodirda bor pulning
qisrni Jahongirrlagi
paining - qismiga teng. Nodir palming necha
** 4
foiziai 3ahnngirg,a bersa, uiarning pullari teng
bcrladi?
A) 37,5 B) 25 C) 17,5 D) 12,5
31.	ParaHelograrnmning tornonlari 20 va 7 ga teng.
lining katta tomoniga yopishgan burchaklarining
bissektrisalari qararna-qarshi tomonai nch
qisrnga ajratadi. Shu qisrnlardan eng kichigining
uzunligini topmg.
/\) 4 B) 2 C) 6 D) 5
32.	Agar a(—4; 2; 2) va 5(\/2: — V*2; 0) vektorlar
b
berilgaii bcrka, 2a va - vektorlar orasidagi
h u r chak 11 i to p i n g.
A) --jr B) arccos- Cl Г>) areco.s-
4	3	6	'	6
33.	cos"1 z — sin4 r. = G tenglamaning [0;2тг] kesmada
nechta ildizi boi?
j A) 1 B) 0 Cj -4 D) 3
34.	(t -	< (x -
tengsizlik x ning qanday qiymatlarida cfrinli?
Л) (2;4) В) (3;эс) C) (—00: 2) U (4:oa)
5 4~ \//5
D) (—"—; 4)
357 Radiusi УЗ bo’igan doiraga tashqi chizilgan teng
yonli trapetsiyaning asosfdagi burchagi 60°.
Trapetsiyaniijg yttzini toping.
!	.3
A) 3 B) 8/3	C) - D) 10
z
36. Sharga bonus ichki chizilgan. Konusning
yasovchisi asosiuing diametriga t-eng. Shar
hajrnining konus hajmiga msbatini toping.
A) 8:3 B) 32 : 9 C) 27 ; 4 D) 16 : 9
27. f(z} — — Z$(10cosx) funksiyaning qiyinatlari
1о<р1акиш toping.
A) {—oo.oo)	B) (“og:0] <3) \-V,0)
D) [— l;oc)
1	30	,	.
28. r 4------	~ tengiamanmg natural sonlardagi
1 Id
»+ -
У
A>
yeduniida r nirnaga teng?
A) 3 B) 4 C) 7 D) 2
k ning nechta natural cpymatida
tengiama ilduga ega bo'imaydi?
A) 6 B) 5 C) 8 D} 1
30. Gipotenuzasi 75 ga teng hodgan tc/g'ri burchakli
uchburchakning katetlari uisbati 4:3 ga teng.
Gipoteuuzaga tushirilgan balandlik uni qanday
kesmabrga ajratadi?
A) 50 va 25 B) 48 va 27 C) 40 va 30
D) 60 va 15
z - 8
6^10
23
TEST 9.006 : Variant
112
Matematika
1
Maternatika
1 2 680)3579 coni 9 ga bo'linishi uchun nuqtaning
o'rin^a qanday raqam qo'yilishi kerak?
Л) 4 В) 0 C) 8 D) 7
2 -1 - ga teskari sonni toping.
Л) -0,75 B) 1,5 С) I D) -?
II.	Quyidagi tasdiqlarning qaysilari ncto'g'ri?
1)	tomonlari atb va c bo'lgan uchburchakka ichki
cbizilgan aylananing radiusi r = —formula
bilan hisobianadi;
2)	tomonlari a va b ga. ular orasidagi burchagi a
ga teng bo‘lgan uchburchakning yuzi S ~ absina
formula bilan hisohlanadi;
3)	o'xshash figuralar yuzlarining nisbati ulainihg
mos chiziqli o'khovlari kvac rati arming nisbatiga
teng.
A) 2:3 B) 1;2 C) 1;2;3 D) 1;3
3 Uchburchakning birmchi tomoni x(r > 10) srn,
ikkinchi tomoni undan 6 sm qisqa, uchinchi
tornoni esa birinchisidan 4 sm uzun. Shu
uchburchakning perimetrini (sm) toping.
А) 3т+ 2 В) 3r-2 C) 3z4-3
D) 3x-3
12.	Tekislikka og'xna va perpendikular tusbirilgan.
15
Og‘rna va tekislik orasidagi burchak arccos-— ga,
17
og£rnaning tekislikdagi proyeksiyasi 30 ga teng
Perpendikularning uzunligini toping.
A) 16 B) 30 C) 32 Dj 23
r*5 4- 9x* 4- x .	,	. . .
4 —_-------------x hje sodaalasmirmg.
(* + I)2
А) г + 1 В) 2г C) 0 D) г-2
A gar (x — 5)(~з? — 4) = 0 bo'Isa, — 4 qanday
5	5
qiymatlar qabul qiiadi?
A) faqat —3 B) faqat 0 €) 0 yoki 3
D) 0 yoki —3
13.	tg(4 + a) = bo'isa, tgo ning qiymatini
4	5
toping.
A) 1 B) 6 C) D) 3
14.	.378 va 594 ning uniundy bo'luvchilari nechta?
A) 7 B) 8 C) 5 D) 9
e 4	4	15	7 15. 5—1,1 * 3 — 4* 1 1 : — 19	7	19 25	1 — 2- ni hisoblang.
1	,	2	1	a	2
A) 23i B) 23- О	*5	C) 24- D) 22- О	я>
6.	Xi va xq x2 — 14®-t- 9 = 0 tenglarnaning ildizlari
bo'lsa, Xi%2 + x?*2 ning qiyinatini toping.
A) 120 B) -92 C) -126 D) -144
<	i tengsizliklar sistemasining
! Z® —	— I) I
butun sonlardan iborat yeehimiari nechta?
A) 3 B) 5 C) 2 D) 6
16.	у — 4.5tnx - 1 funksiyaning [0; —] kesmadagi eng
b
katta qiymatini toping.
A) 1 В) 0 C) V^-1 D) 0,5
«л 5® 4- 8	.	. .
17.	2 > —----tengsizhkni Yeching.
4 — x
A) (-oo;-4)U(0;4) В) (-оо;0)Ц(4;оо)
С) Ф D) [-4;4]
8. 0, (8) 4- 0, (3) — - ning qiymatini hisoblang.
1	2	2
A)	lx	B>	’о	C>	ч	D)
V	<?	О
18.
a
В) Л C) -1 D)
<5
9. (v/7)u*^‘7 ni hisoblang.
A) 9 B) 3^/2 C) 18 D) 3
10. Qo'shni burchaklardan biri ikkmchisidan 40°
katta. Shu qo'sbni burchaklarni toping.
A) 110’; 70е В) 160°: 20° С) 140°; 40’
D) 20’; 160е
19.	loy^[x~— 9) 4- 9iog^(x — 9) < 4 tengsizhkni
yeching.
A) (5; 14) B) (6; 15) C) (9; 18)
П) (5; 81)
20.	Ucbburchak burchaklarining kattaliklari nisbati
1:1:2 kabi, katta tomonining uzunligi esa 24 ga
teng. Uchburchakning katta tomcniga tushirilgau
balandligim toping.
A) 12 B) 6,5 C) 6 D) 8
24
TEST 2006 : Variant
112
M&tematika
21.	A BCD to‘g‘ri to'rtburchakmng A burchagi
bisscktrisasi BC tomouni uzunliklari BM—16 sm.
va MC—9 sm boOgan ikki qisrnga ajratadi.
To'g’ri ro‘rtburchakning yuzini (sm2) toping,
A) 400 B) 500 C) 510 D) 480
22.	To'g‘ri parallelepiped asosining iomon’ari 9 va 12
ga, uiar orasidagi burchak 120° ga, yon qirrasi
Sx/3 ga teng, Paralleiepipedning kichik diagonal!
uzunligini toping,
A) 18 B) 5 C) 21 D) 15
23,	Shar katta doirasining yuzi 225^ ga teng.
Shaming markazidan qanday masofada
o^kazilgan tekislik shardan doirasining yuzi 161?r
ga teng bo‘lgan kesirn ajratadi9
A) 6 B) 7 C) 8 D) 3.5
24.	t ning q an day qiymatida
у = 1 — 3cos2r — /(1 4 cos2x) funksiyaning
qiyrnati o‘zgannas bo'ladi?
A) -3 В) 3 C) -1 D) -2
25.	2cos32x + .$rn22x — 1 tenglamani yeching
A) 4- эгп: — 4 n € Z
в)^г(2п + П, (6t-±i)^, n.^ez
z	v
c)(-i)n-t + irn, пег
О
_.	2тг
D) 7Г 4 2тт; ±-j- 4 4rn, n C Z
30.	Tolg‘ri burcbakji uchburchakning gipotenuzasi 25
sm, kateUarida.n binning gipatemizadagi
proyeksiyasi 1,96 sm. Ushbu uchburchakka ichki
chizilgan aylananing radiusi necha sm?
A) l В) 3 C) 2 D) 1,5
31.	MN(6; 7) va	6) vektorlar
parallelograminning tomonJari bo‘lsa, uning
diagonallari orasidagi burchakni toping.
A) 45° B) 30° C) 90° O) 60°
32.	Agar g(-6;3; 3) va 6(3;-3;0) bo‘lsa, 2a va -b
vektorlar orasidagi burchakni toping.
A] 60° В) 150й C) 135° D) 120°
33	cos 22: sin z. — cos 2г tenglamamng
90s < т < 180° shartni qanoadantiradigan
ildizlarini toping.
A) 110° B) 120° C) 135° О) 170е
34.	(1,25)1-* > (0. 64)2D+v4t) t^ngsizlikning
yechiinlari orasida nechta tub son bor?
A) 1 B) 5 C) 12 D) 9
35.	Teng yonli trapetsiyauiiig yuzi 60 ga, un.gi ichki
chizilgan aylananirig radios! 3 ga teng.
Trapetsiyaning asoslarini toping
A) 14; 6 B) 18; 2 C) 13; 7 D) 5: 15
3G. Konusning c/q kesimi irinntazarn uchburchakdan.
siHndrniki esa kvadratdan iburat, Agar ularning
hajrnlari teng bo'lsa, tu'la sirtiarining nisbati
nimaga teng?
А) УЗ : ^2 В) У2 : у/3 C) 1 : У5
Г)) 3:2
26.	Massasi 54 kg bo‘Igan mis va rux qotishmasining
tarkibida 45% mis bor. Qot'uhma tarkibida 60%
mis bo£lishi uchun unga yana necha kg mis
qcTshish kerak?
A) 24 B) 13,5 C) 25 D) 20,25
27.	у — x/8 —	~ 2ж funksiyaning eng katta
qiyinatini toping.
A) 4 B) 7 C) 3 D) 2
28.	To’rtta sonning yig’indisi 118 ga teng. Agar
birkichi va ikkinchi sonning nisbati 2 : 3 kabi.
ikkinchi va uchinchi sonning nisbati 3 . 5 kabi va
uchinchi va to'rtinchi sonning nisbati 5 : 6 kabi
bo'lsa, birinchi va to'rtinchi sonning yigSndisini
toping.
A) 62 B) 60 C) 59 D) 66
29.	kx2 4 3£z 4 2fc — 2 — 0 tcnglama yechimga ega
bo Irnaydig&n 1? ning butun qiymatiari o‘ita
artfmetigini toping.
A) -2 R) -3,5 C) -3 D) -4
I 1..5 Г 200G Variant-	113
Matematika
Matematika
l Bir nrthla natural sonning yig indisi 85 ga teng
Ag.it him scalar rung har biridan 2 ni ayirib,
indi hisoblansa. u 61 ga teng bo:ladi.
Yig'indida uecht-a son qatnashgan?
A) 7 B) 5 C) 8 D) 12
A) 1? BJ -0,6 C) -6 D) 0.4
11.	Quyidagi tasdiqlaming qaysilari notzyg'ri?
1)	tomoni a ga, btirchaklaridan biri о ga teng
rombning yuzi S — a'-sino formula bilan
hisoblanadi:
2)	tornonlari о va b ga, ular orasidagi
burchaklaridan biri a ga teng bo'jgau
paranelograrnmning yuzi S = \absina formula
bilan hisoblanadi:
3)	diagonallari a\ va d2 ga, ular orasidagi
burchagi о ga teng ixtiyoriy qovariq
to'rtburchakning yuzi 5 = didssina formula
bilan hisoblanadt.
A) 2:3 B) 1;2 C) 1;2;3 D) 1;3
3. а(Ь + c — be) — b(c 4- a — ас) — c{b — a) m
soddalashtiring.
Aj‘2d<.-26c B) — 2abc C) ab — ac
D) -26c
4- (y4 - y~ 4	+ 1) ~ (y ~ l)(j/ 4 2) -4 / + yz ni
soddalashtirgandan keyin hesil bo'lgan
ko'phadniug nechta hadi bo'ladi?
A) 4 BJ 3 C) 5 D) 6
5.	a ning qanday qiymatlarida |a 4- 41 = — a — 4
tengiik o;rinli boiadi?
A)	B) a = —4 C) a < -4
D)-a < -4
6.	i 4- 6 —---tenglamauing nechta haqiqiy Hdizi
x
bor?
A) 2 B) 1 C) iWiayo'q D) 3
7.	\/8r — 3 < -2 tengsizlikni yeching.
A)	B) x < 4 C) r > 4 D) z > |
8.	Quyidagi sonlardan qaysi biri 0.8(1) ga teng?
А) И	В) —	С) —	о) —
90	1 11	} 90	' 90
9.	у — 2<?т -- 3 funksiya grabgining Gy o’qi bilan
kesishish nuqtasi ordinatasini toping.
A) -1 B) -2 C) 1 D) 0
10,	ikki to'g'ri chiziqning kesishishidan hosil bo‘lgan
burchaklarning biri 40” ga teng. Qolgan
burchaklarni toping.
А) 110е, 110°, 110е В) 150% 150°, 30°
140°, 140е, 40° D) 60% 60% 30°
12.
Tekislikka og‘ma va perpendikular tushirilgan.
60
Og'rna va tekislik orasidagi burchak nrccos— ga.
og maning tekislikdagi proyeksiyasi 120 ga teng.
Perpendikularning uzunligini toping.
49
A) 12 В) C) 22
D)
' 25
13.	tg(— — a) = 4 bo^lsa, tga
ning qiyrnatini toping-
4
A} -3 B) | C) D) |
14.	------ifoda n ning nechta natural qiyrnatida
natural sou bo ladi?
A) 3 B) 6 C) 4 D) 5
19,5-.4^ 4-3^ 1,9
15.	-----—------------in hisoblang.
^-0.16
75
A) 16 B) C) 12 D) 7,45
*
16.	a ning qanday qiyrnatida у — z2 — 4x 4- 12 — a
parabolaning uchi Af(2; 5) nuqtada yotadi?
A) -2 B) 3 C) 5 D) 4
17.	—li < 0 tengsizlikni yeching.
r 4 2
A) (-2; 1)	(-oc; -3)U[-2; 1]
C) (-oc; -X]U’(-2; 1] D) (-oc; -3]
* x
18.	J*cos —dz ni hisoblang.
D) 2У2
19.	2  3c**r = 15 — 9co*r tenglamani yeching.
A) 2-jrn,n€Z В) -кл,п<Е 2
C) ±^+2»n,neZ D) ^ + 2m.nez
О	о
26
TEST '2006 : Variant
113
Mateinatibn
'20. Uchburchak tomonlarining uzunliklari zn; л va k j
tn- - 7?- 4- y/^nk teuglikm qanoatlantiradi. |
Uzunligi m ga teng lemon qarshisidagi burchakni
loping.
A) 150° B) 45° C) SO3 D) 135°
21 A BCD paralielogr.anunda OB± AC; AO—8.
OC—5 va BO-'4. Paralkdogrammning yuzirri
loping.
A) . 28 BL 50 C) 52 D) 56
2*2. Konusning yasovchisi 25 ga, uning asos tekisbgi
bilan tashkil qilgan burchagining sinusi 0.6 ga
teng. Konus o‘q kesimining perimetrini aniqlang.
M 80 B) 360 C) 90 D) 105
*23. Balandligi 12 ga, asosining radiusi 6 ga teng
bo‘]gan konusga yasovchisi 4 ga teng bo’igan
silindr ichki chizilgan. Silindr asosining radiusini
toping.
A) 4 B) 3 C) 2 D) 2,6
24.	Agar tgot ±ctgci =• 10 bo:lsa. sin2t» ni hisoblang.
A] 1	B) 1 C) |	D) 1
4	l	Э	3
25.	sin x • cos 'It. — cos r • sin2x = — - tenglamaning
2
ycchiimni toping.
A) irn , n e Z	B) ( — 1)” ~	, n e Z
O) ~n , Л e Z	D) ~-n , n e z,
V	Z
26.	Agar kubning qirrasi 20% ga karnaytirilsa, uning
hajrni necha foizga kamayadi?
A) 40 B) 48,8 C) 30,8 D) 60
27.	у — at1 4- bz 4- с(д > 0) funksiya z — 1 nuqtada 2
ga teng eng kichik qiymatga ega. Agar y(2) = 4
ЬоЪа. a,b va c larni toping.
A) a = 3,i--6,c=2 В) а = 4,6 = 2,c = 6
С) a — '2,b = —4, c = 4
D) .a = 6, b — —2. c = 4
23. rn ning qanday qiymatlarida
(?f) - 1 ).i?2 4- 2(m - 7)r 4-*2m 4* 2 kvadrat- uchhadni
to la kvadiat shaklida tasvir{af>h rnunikin?
Ai -17 B) -1.7: 3 C) 3 D) 2
30.	To*g4i bsHchakn uchburchakning katellari 30 va
4G ga teng. Katta katetning gipotenuzadagi
proyeksiyasini toping.
A) 14,5 Bl 32 C) 16.5 D) 16
31.	Aylanaga tashqi chiisilgan teng yonli
trapetslyaning asoslari 56 va W srn.
Trapetsiyaning balandligi necba sm?
A) 40 B) 28 C) 36 D) 35
32.	6(3; —6:6) vektorga kollinear va ab — 40 5
tenglikni qanoatlantiruvchi a vektorni toping.
A) r7(3;6,9j Bl J(|;-3:3) C) n(3;-6:6)
D) o(l;-1:1)
33.
iiriT > cost tengsizlikni yeching.
5
- т 4- 2 тп). n €.
4
A) (
y 4
>	- o-
- -Г 7ГП/, n G z

~ 4- тп). Ti £ Z

34 /оуьг(3 - 2z) > 1 tengshliknipg butun yechimlari
iiechta?
A) 3 B) 4 C) ] D) 2
35- Gipotenuzasi c ga va o‘tkir burchaklari
sinuslarining yig indisi q ga teng bolgan to’g ri
burchakli uchburchakning yuzini toping.
A) Lv-n Bl iC?(q2-ll
C) por + l) D) 1?V + 1)
36. Hajrni 8>/3 ga teng borlgan muntaxam
tetraedrning balandligini toping.
A) 4 В) 2ч/3 C) 3 Dl 4x/3
28. Agar I *5‘ S’ bodsa, z 4- 2y ning qivmatmi
к 4* у ~ 4
toping.
A) 1 В) 3 C) *2 D) 13
27
I'EST 2006 : Van ant____________114
Matematifca
Matematika-
1 Ikki shahar orasidagi inasofa 400 km bolsa.
i :a(K)0000 masshtabli xaritada bn masofa necha
mm ga teng bo'Jadi?
Л) 80 B) 100 C) 40 D) 20
2 (‘2. 01 - 3,81) • 3.8 ifodani hisoblang.
A) 5,82 B) 6,84 C) -5,82 D) -6,84
y” - X X -f у .	. .
3.	—-—— : —-— m soddaiashtaring.
2xy 2x
4.	*2n2 — Зап — 4n + ба koj>hadni ko*paytuvchilarga
aj rating.
А) (п-2)(2п-3а) B) (5 - n)(3fl 4-2n)
С) (2т? — 3a)(n — 5) О) (3a — n)(5 — 2n)
r- ,	\	.	. . . (2x - У — 5
5.	(r;y) sonlar jutti {	. sistemaning
L ox 4- 2y = 4
yechimi boisa, у — x ni toping.
A) -1 B) -3 C) 0 D) .3
6.	x2 - 1 lx 4- q — 0 tenglamaning ildiziaridan biri
—13 ga teng. Lining ikkinchi ildizini toping.
A) 2 В) -24 C) -2 D) 24
7.	4 > ж -V 1 tengsizlikni yeching.
A) {0: 15] B) [-1; 15) C) (-1; 15]
D) (0; 15)
8.	Arifrnetik progressiya uchun quyidagi
fotrnulalardan qaysilari to'g^ri?
1)	- 2e2 + a3 = 0;
2)	aj = а3 - <z2;
«	<4» — «1 + d
j) n -----------------.
а
A) 1 B) 2:3 C) 1;2 D) 2
9.	2 tengsizlikui yeching.
A) (1; I) B) (0; |) C) 00)
D) (0; 1)
4
10.	Markazly burchakka, rnos yoy aytananing -
a
qtsniiga teng. Shu rnarkaziy burchakni toping.
A) 144° B) 72° C) 216° D) 288°
II-	Quyidagi tasdiqlarning qaysilari to;g‘ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R =s ^(а.Ь,с— uchburchakning
tomonlari, S— uchburchakning yuzi) formula
bilan h isobl an adi;
2)	radiusi R. ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S = а formula bilan
hisoblanadi;
3)	tomonlari a va 6 ga, ular orasidagi burchagi o-
ga teng be'I fan uchburchakning yuzi
S — -absina formula bilan hisoblanadi,
A) 2;3 B) 1:2 C) 1:2;3 D) 1:3
12. Tekisiikka tushirilgan og!maning uzunligi 125 ga,
uning tekislikdagi proyeksiyasi esa 35 ga teng.
Oghna va tekislik orasidagi burchakni toping.
12 r, . 24
A) arccos~•	B) arcstn-— C) arctg~~~
25	25	48
ГЛЧ	.	7
D) атезшггг
25
, „ 1 + cos2a 4- cos4a 4- cos6ct .	...
Ij ------------—-------------- nj sodaalashtinng.
stnla 4- 2sin2aet>s4&
A.) tg'la B) ’2cig‘2ct C) ctg2a D) 2sm2o
14.	156 va 420 ning umumiy bcrluvchilari nechta?
A) 5 B) 7 C) 4 D) 6
15.	12 va 312 sonlarning urnumiy boJuvchilari
nechta?
A) 4 B) 2 C) 6 D) 3
16.	у = 2x2 - 2x + 7 funksiya grafigining abssissa
okqiga eng yaqin bo Igan nuqtasi koordinatlarun
toping.
A) (4,5; 0,5) B) (0,5; 4,5)
C) (-0,5;-4,5) D) (0,5;6,5)
17.	<0 tengsHdikning manfiy butun
yediimlari yig*indisini toping.
A) -4 В) -9 C) -6 D) -5
18.	I co$2xdx ni hisoblang,
J т
A) -2 В) 0 C) 1 D) -1
3
19.	log i (x -4-4) — /o^9(x 4-4) > —- tengsizlikni
yeching.
A) (-4;-l) В) (0;l) C) (-2;1)
D) (2:3)
20.	Teng yonli uchburchakning yon tomoniga
tushirilgan balandligi bilan ikkinchi yon tomoni
orasidagi burchak 26° ga teng. Teng yonli
uchburchakning asosidagi burchagini toping.
A) 48° В) 50е C) 58’ D) 55”
28
?
TEST 2006 : Variant
114
Matematika.
21.	Tomonlari 72 va 32 m boigan ro’g'ri
to rt burchakka. lengdosh kvadratuing tornonini
toping
A} 28 B) 36 C) 48 D) 24
22.	Muntazarn urrtburchakli piramidaning
balandligi 18 ga, asosining tomoni 15 ga teng.
Piramidaning apoferriasim hisoblang.
A) 13 В) 22.5 C) 19.5 D) 21
23.	Konus hajmining т ga nisbati 21 - ga teng boTib.
V
lining yasovebisi asos tekisligi bilan 45° li
burchak tashkil qiladi. Konusning baland’iigini
toping.
A) 7 В) 3 C) 4 D) 6
30.
AB=9 sin, DB—5.4 sm
ABC uchburchakka
tashqi chizilgan ayla-
naning radiusi
necha sm?
A) 9	E<) 6 C) 7,5 D) 6.6
31. Radiusi 3 ga teng BoHgan doiraga tashqi
chizilgan teng yonli trapetsiyanmg perimetri 40
ga teng. Trapetsiyaning kichik asosinl toping.
A) 4 B) 3 C) 2 D) 5
24.	i — eos323, q — sinVi'2s va k — tg235s son! arm
o'sish tartibida joy)ashtiring.
A) k < t < q B) q < t < k C) t < q < k
D) t < k < a
32. a(m - l:v5 4) vektorning uzunligi 5 dan knit a
bo ladigan m rung b.archa qiymatlarmi toping.
Al (-1:3) Bl (-oc:-2)U(2;oc)
C) (~oc-:-I)U(3;co) D) (-2:2)
25.	cost — sin^TcosT — 0 tenglamani yeching.
. . it . . IT 41T<- ,	„
A 2+^3+—^--
B) i+^;+^,t€z
.2	o
C) J +	(-i)‘ T + *k, k e z
Z	-3
D) ?<:; x + 2»i-,
£ z
26.	Ikki sex 230 ta kir yuvish mashiuasi ishlab
chiqarishi kerak. Birmchi sex ishlab chiqargan
mahsulotning | qismi ikkinchi sex ishlab
chiqargan mahsulotning 80% iga teng Birmchi
sex qancha mahsulot ishlab chiqargan?
A) 60 B) 50 C) 180 D) 80
1	к •	,,
zn(-arccos-) ni hisoblang.
2	9
I A> 49 B> 5 C) I 0) I
i
34.	z!-J~ 4- 9l/?r ~ 6 tengiamani yeching.
Л) 10 B) 1 C) 2 D) /16
35.	Tog'ri burchakli AC В uchburchakning katetlan
8 ga va 10 ga teng. Shu uchburchakning C tog'ri
burchagi uchidan CE mediana va CD bissektrisa
crtkazildi. CDE uchbuichakniug yuzini toping.
A) 4 В) С) з| ()) 2|
4	У	0	v
36.	Teng tomonli silindrning va teng tomonli
konusning balandligi o'zaro teng. Blaming to'la
sirtlari nisbatini toping.
A) 3 : 8 B) 5 : 3 C) 3:2 D) 3 : 4
/— 6т ч- 9
о,. J—-------------—
у 4 — r
sohasini toping.
funksiyaning aniqlanish
A) (—2;2)u{3) B) (-2:2)
C) (—00;—2)U{3)	D) (~2;3)
28. 15 —	= 2(2r — 5) bo‘lsa. Cfr ning qiyriiati
nechaga teng?
A) 7 B) 8 C) 11 D) 9
r5	x5
29. I—5— -----1 =------—г tenglamaning barcba
’ar4-1296*	1296 - x4
natural yechimlari yighndisini toping.
A) 1 B) 12 C) 10 D) 15
29
I KST 2006 : Variant
115
bfatematika
1
Matematika
i	ага ’	8 + 5п4+4я2
1.	n(n G AQuing ------------kasr butun son
n
boOadigan barcha qiymatlarini loping.
A) 1; 2 B) 1 C) 1; 2; 4 D) 2
, 0,4 0,15 1,6 .	•	. . л .
2	г л 6 г П? ning q^natim toping.
6, 4 • 2.5 • U. U3
A) | B) | C) 0,2 D) 2
5 о
3.	\A/56 4- 2\/10  х/>/56 - 2л/10 ni hlsoblang.
A) 6 B) 2 C) 4 D) 3
4.	2a26 + 3<x — 4аЬ2 — 6Ь ko‘phadni
kc/paytuvehilarga ajrating.
A) (a - 26)(2a6 + 3)	B) (2ab - 3)(e - 5b)
C) (2a2 + 6)(6 - 5a)	D) (3 + 2ab)(a - 55)
5.	m ning qanday qiymatlarida (jrt2 — l)y + 1 = m
tenglama yechirnga ega bo’lmaydi?
A) m = 0 B) rn = 1 C) m — 2
D) m- -1
4
6.	— — x + 1 tenglarnaning nechta haqiqiy iidizi
bor?
A) 2 В) 3 C) iidizi yolq D) 1
7.	(x + 3)(x — 2) < 0 tengsizlikni yeching.
A) (—oo;—3)U(2;oo) B) (—co;2) U (3:co)
C) (-3:2) D) (-oc;-2)U(3;oo)
8.	0,4(5) soni quyidagi sontardan qaysi biriga teng?
A> И в> Й C> Й D) Й
9.	> lag^l.2 tengsizlikni yeching.
A) (J; 1) B) (0; |) C) (1; oo)
D) (0; 1)
10.	Qcrshni burchaklardan bin ikinc.hisidan besh
marta kichik boisa, shu burchaklardan kattasini
toping.
А) 130е В) 150° С) 144° D) 140°
11.	Quyidagi tasdiqlarning qaysilari noto'g’ri?
1)	tomonlari a va b ga, ular orasidagi
burchaklaridan biri a ga teng bo’lgan
paralldogrammning yuzi S = -absina formula
bilan hisoblanadi;
2)	lomonlari a va b ga, ular orasidagi burchagi о
ga teng bo’lgan uchburchakning yuzi
5 = ^absina formula bilan hisoblanadi:
3)	o’xshash figuralar yuzlarining nisbati ularning
mos chiziqli o’lchoviarining nisbatiga teng.
A) 2;3 B) 1;2 C) 1;2;3 D) 1;3
12.	Tekidikka og’ma va perpendicular tushirilgan.
Og’maning tekislikdagi proyeksiyasi 45 ga,
perpendikularning uzunligi 28 ga teng. Og*ma va
perpendikular orasidagi burchakni toping.
..	14 n> .28	. 45
A) cjrcco-s— B) arcstn—-	C) arcstn —
ad	53	o3
45
D) arcctg —
13.	Agar cos2o — - bo'lsa, sin2 a
ni hisoblang.
A) I B) 1 C) | D) 3-
14.	43 • 15 • 25 - 37-4- 34 • 48 -77 yig‘indining oxirgi
raqamini toping.
A) 9 B) 4 C) 5 D) 0
15.	18 va 8 sonlari eng kichik umumiy karralisining
natural WVnvchilaji nechta?
A) 7 B) 12 C) 9 D) 8
16.	у = 4 — 2sinz funksiyaning [0;
kichik qiyniatini hisoblang.
kesmadagi eng
A) 2 В) 3 C) 1 D) 2 - x/3
17.	z ning qanday qiymatlarida у =
funksiyaning qiymatlari 3 dan kichik emas?
A) (~2;5] B) (-oo;-2)U[5;oo)
C) (-oc;-2) D) [5;oo)
18.	Joe sinAxdx ni hisoblang.
A)| B)-l C)| D)‘|
19.	— 5lpg$x + 6 = 0 tenglamaning ildizlari
yig'indisini toping.
A) 27 B) 36 C) 18 D) 12
20.	Aylananing 13^/2 ga teng vatari 90fl li yoyni
tortib turadi. Aylananing uzunligini toping
А) 20ж B) 24% C) 26% D) 22%
21.	Balandligi 32 ga teng bo’lgan rombga ichki
chizilgan doiraning yuzini toping.
A) 190% B) 196% C) 200% D) 256%
22.	Chiziqli o’lchovlari 3; 4 va 2>/14 sm bo’lgan
to’g’ri burchakli parallelepipedning diagonal!
necha sm?
A) 7 В) 11 C) 9 D) 10
23.	Radiusi 8 ga teng bo’lgan sharga balandligi 18 ga
teng bo’lgan bonus tashqi chizilgan Kouus
asosining radiusini toping.
A) 18 B) 12 C) 16 D) 24
30
2
TEST 2006 : Variant
115
MaCematika
. ir 3 *	. з * x 1 , тг .
24.	stn— -»o, - - «п й • cos^ ~ ~«n~ nt
hisoblang.
./7	x/5	a/?
A) В) 0 C) D) Y
о	b	4
25.	2sin2x — 1 — — tenglamani yeching.
A)	(-l)i+1£ + br;te Z
B)	C) ±^ + rE,-E£Z
u L	о
D) ±^+trE;i€Z
L ю
26.	Ishchining mehnat- unumdorligi 30% ortsa, uning
ish normasini bajarishga ketadigan vaqti necba
foizga qisqaradi?
A) 25 B) 20 C) 16? D) 23?-
«U	i
tJ2 — 4z -j-12
27.	у ~ —я----------- funksiyaning qivmatJar
r. - 4r + 5
to‘plamiga tegishli tub sonlar nechta?
A) 1 B) 4 C) 3 D) 2
5
33.	sin2 z--sinz~+-l<0 tengsizlik x (x G [0; 2rJ)
z
ning qanday qiymatlarida o‘rinli?
А) 1т,2т} B) (0;l)U&-;»J С) [0;-И
QU	O-
_ .т 5tfn
D
О 0
34.	г/#э +	" 6 t-englamani yeching.
A) 10 B) 1 C) 2 D) У16
35.	Doiraga ichki chizilgan muntazam
uchburchakning yuzi unga ichki chizilgan
kvadratning yuzidan 18,5 ga kam. Shu doiraga
ichki chizilgan muntazam oltiburchakniug yuzini
toping.
A) 9V3 + 6V2 B) 873+15 C) 27 + 24V5
D) 13,5+ 1273
36.	Asosi a ga, asosidagi burchagi a ga teng bo4gan
t-engyonli uchburchakni yon tomoni atrofida
aylantirishdan hosil bo:lgan jisrnning hajmini
toping.
7ra3«in2o xa^sina iraAcosn
A —---------- B)-------z--- C)
bcosa	a	O5tn dr
m *a *9°
28.	To‘rtta sonning yig‘indisi 118 ga teng. Agar
birmchi va ikkinchi sonning nisbati 2 :3 kabi,
ikkinchi va vchinchi sonning nisbati 3 : 5 kabi va
uchinchi va to'rtinchi conning nisbati 5 : 6 kabi
boHsa, birinchi va tcfrtinchi sonning yig‘indisini
toping.
A) 62 B) 60 C) 59 D) 66
29.	5x2 •+ bx — 15 = 0 tenglamauing ildizlari zi va i2
uchun 5rj 4- 2x2 — 1 munosabat o:rmli. Agar b
butun son ekanligi ma’lum bo'lsa, uning
qiyrnatini toping.
A) -10 B) 7 va —10	C) 10
D) -7 та 10
30.	Katetlarining nisbati 2:3 bo'lgan to‘g:ri burchakh
nchburchak balandligi gipotenuzasini
uzunliklaridan biri ikkinchisidan 0.6 ga karri
boMgan bo'laklarga ajratadi. Gipotenuzaning
bolaklarini toping.
A) 5 та 3 В) 2 та 4 С) 1.6 va 3,6
D) 1,08 та 0,48
31.	Teng yonli trapetsiyaning kichik asosi 3 ga,
perimetri 72 ga teng. Uning diagonaii o4mas
burchagini teng ikkiga boMadi. Trapetsiyaning
o‘rta chizig'ini toping.
A) 8,5 B) 13 C) 7,5 D) 12
32.	b vektor a (2; 4; 4) vektorga kollinear hamda bu
vektorlarning skalyar kf/paytmasi 144 ga teng. b
vektoruing uzunligini toping.
A) 16 B) 24 C) 18 D) 12
31
 TEST 2006: Variant
116	Matematika
Matematika.
1. Natural sonlar uchun quyida keltirilgan
rnulohazalardan qaysi bin noto^ri?
A) Agar ikki qo^sbiluvcbidan biri 11 ga bo‘Iinib.
ikjkinchisi 11 ga bo'h'nmasa, ularning
yig*indisi 11 ga bo'linmaydi.
Э) BenJgan sonlar bo'linadigan sonlaming eng
kattasi ularning eng katta umumiy
bo'luvchisi bo'ladi.
Q 3 va 5 ga bo'linadigan son 15 ga bo'linadi.
D) 3 ga bo‘Jingan son 6 ga ham bo'linadi.
11. Quyidagi tasdiqlaming qaysilari to‘g*ri?
1) uchburchakka tashqi chizilg&n aylananitig
radiusi Л= ^-(a,b,c— uchburchakning
tornonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
•2} tomoni a ga, burchaklaridan biri a ga teng
rombning yuzi S — a2sinot formula bilan
hisoblanadi;
3)	o'xshash figuralar yuzlarining nisbati ularning
mos chiziqli n’lchovlari kvadratlarining nisbatiga
teng;
n	1,6-0.159,2	.	.	...
2-	м~о;оз-мn,ng 4iymatmi ,oping-
A) I B) |	C)	|	D) 2
О	о	Z
3.	16 - (2 c — I)2 ni ko‘paytuvchilarga ajrating.
A) (3 —2e)(5 —2c)	B) (3 4-2c)(5 - 2c)
C) (2c-3)(2c-5)	D) (3 - 2c)(5 4-2r)
12. Tekislikka og‘nia va perpendikular tushirilgan.
Og‘manjng tekislikdagi proyeksiyasi 45 ga,
perpendikularning uzunligi 28 ga teng. Og‘ma va
perpendikular orasidagi burchakni toping.
л\	14 en - 28 гл - 45
A) arccos-^-	B) arcsm—-	С) агс&'гп-~г
ad	53	53
D) crcc<?28
4.	(x7 + 1)(х4 — x10 * 2 4-1) — (x2 — I)2 4- z5 4- x3 4- x ni
soddalashtirgandan keyin hosil bo'lgan
kcrphadnmg nechta badi bo£ladi?
Л) 4 B) 5 C) 6 D) 3
5.	n ning qanday qiymatlarida nx 4- 2 = n 4- 2x
tengiama cbeksiz ko‘p yechimga ega bosladi?
A) n - 1 B) n = 0 C) n f 1 D) n = 2
3
13- Agar cos2o = - bo'lsa, sin2 or ni hisoblang.
A) | B) 1 C) |	D) |
8	4	8	4
14. 198 va 630 ning umumiy bo^uvdulari rieqhta?
A) 6 B) 5 C) 7 ПУ 4 .
0,075-0,075 -6,4 . ..
1 □. ----------------ni hisoblang.
°'!75-s
6. Xi va z2 x2 — ax 4- 20 = 0 tenglaruaning ildizlari
1	1 q
boiib.----h — = —- t-englikni qanoatlantirsa, a
z? 20
ning qiymatini toping.
'A) 9 B) -1 C) 3 D) -3
A) 40,5 B) 4,05 C) 20,1 D) 20,25
7.
x-2
x + 3
< 0 tengsizlikni yeching.
16. у =	+ 4z - 8 funksiyaning grahgi q&ysi
choraklajrda joylashgan?
A) I, П. IIL IV B) IL III, IV С) I, Ц, III
D) I, Hl, IV
A) [2; 3)
D) [2; 3]
B) (-1; 2]
C) (—3;2]
8. Arifmetik progressiya uchnn quyidagi
fortnulalardan qaysilari noto'g'ri?
_aj4-(n-l)<Z	an-ai^d
1) эя —	——	’ n. 2)	—
z	n
3) ai -ban = аз 4- aR_j
A) 3; 2 B) 2; 3 C) 2 D) 1
17. -----rvr---zr > 0 tengsizlikni yeching-
\Z 4" 3)(x — 5)
A) (-3; -1)U(5; oo)	B) (3; -1]U[5; oo)
C) (-3; - 1]U(5; oo)	D) [-3: -l)u[&; oc)
18. f? sinSzdz ni hisoblang.
3
A) -7	B) |	C) -1 D) 1
0	5	W
Ф14-71
< 4 tengsizlikning eng katta butun
yechimini toping.
19. n ~	~ tne~" va
p = /о£1/з15 — /о^1/з5 sonlarni kamayish
tartibida joylashtiring.
A) 10 B) 6 C) 9 O) 11
A) m > n > p B) p > rn > n
C) m > p > n D) n> p > m
10. Qo:shni burchaklardan biri ikkinchisidan 12°
katta. Shu qo£shni burchaklarni toping.
A) 81°;99* В) 82°;98* C) 96°:84°
D) 80°; 100°
20.	Katta yon tomoni 6 sm. o‘tkir burchagi 30°
bo'lgan to’gri burchakli trapetsiyaga aylana
ichki chizilgan. Shu aylananing uzunligini toping.
А) т В) 2r С) Зтг D) 4ж
32
2
TEST 2006: Variant
116
Matematika
21.	Teng yordi trapetsiyaning yon tomoni va kichik
asosi 5 ga, balandligi 4 ga teng. Trapetsiyaning
yuzini toping.
A) 22 B) 32 C) 40 D) 20
22.	Muntazara to'rtburchakli piramidaning
balandligi 12 ga, asosining tomoni 7 ga teng.
Uning apofem asini toping.
A) 13,5 Bl 9 C) 12,5 D) 25
23.	Asosi rombdan iborat- to‘gcri prizmaning
balandligi 4,5 ga teng. Agar rombning
dioganahari 8 va 10 ga teng bo4sa, prizmanicig
hajrni qanchaga teng?
A) 320 B) 360 C) 240 D) 180
>	•	*	3 T . > Я- «”	. , .	, ,
24.	лгп Yq ‘ cos 15 ~ stn Jg ' cos уд ul “isoblang.
A) 1 B) | C) 1	D) ~
o	JL	о
25. sin 4a; < — cos4x tengsizlikni yeching.
26. Agar kubning qirrasi 20% ga kamaytirilsa, uning
hajrni necha foizga kamayadi?
A) 40 B) 48,8 C) 30,8 D) 60
qiymati nechaga teng bcrlishi mumkin?
A) 1,5 B) 1,8 C) 2,4 D) 1,4
T T	T T	T X
28-	3	+ 15 +	35	+ 63 +	99	+ 143	6 wo®lamani
yeching.
A) 13 B) 26 C) 16 D) 18
29.	у = 2x5 4- bz 4- c parabolaning uchi (—4; r-5)
nuqtada joylashgan. Bu funksiya nollarining
o‘rta arifmetigini toping.
A) -2 B) -4 C) 5 D) -3
30.
С к
\	AB—9 sm, DB=5,4 sm
\	ABC uchburchakka
\	tashqi chizilgan ayla-
\	nan mg radiusi
\ D necha sm?
A ----------------x В
A) 9 В) 6 C) 7,5 D) 6,6
31.	Teng yonli trapetsiyaning asosiari 30 va 50 ga.
balandligi esa 30 ga teng. Trapetsiyaning
diagonal!nt toping.
A) 56 B) 70 C) 60 D) 50
32.	m ning qanday qiymatlarida a(m — 1; m — 2; 2)
vekt-orning uzunligi 3 dan kichik bo'ladi?
A) -2<m < 1	B) 0< m < 3
C) — 1 < m < 2	D) — 1 < rn < 3
33 1 — 2$in4x < eo^4x tengsizlikni yeching.
A)	(-— 4- 2rfc; ~ 4- 2%£), fc € Z
B)	(rfc; + тгХ.-), k G Z
C)	+ +2Tk),keZ
,^k 7Г	_
D)	(^4 + Т},ке2
34.	(г + 2)’o8>(*'3+1) < (e + 2)1'«’<2x+s> tengsizlik x
ning qanday qiymatlarida o'rinli?
A) (-2;4) B) (-4,5;oo) C) (-1;4)
D) (4:oo)
35.	Muntazam uchburchakning yuzi 9\/5 ga teng.
Shu uchburchakdan eng katta yuzaga ega boigan
kvadrat qirqib olingan. Shu kvadratning
perimetrini toping.
A) 4873-72	B) 1873-12
C) 54-1673	D) 6473-96
36.	Kesik konusning yon sirti 10т ga. to‘la sirti 18r
ga teng. Konusning to4a sirti unga ichki
chizilgan shar sirtidan qanchaga ortiq?
A) 6x В) 14r C) l(hr D) 8x
33
TIS! 2006 Variant
117
Maternatika
1
Maternatika
1. Udi sut.ka nerha sekuuddan iborat?
A) 259200 В) 258400 C) 258300
P) 258200
2 5, 2: y; -2 sor.laruing u'rta arifrnetigi 1,2 ga teng.
у rn toping.
A) -0.8 B) 1.2 C) -0,4 D) 0,4
4. (4r — 3)2 — -r(-4* 4- 5) ko phadni staudarf
shakliga keltiring.
Л) 12/-25z4-9 B) 20/ - 29x 4- 9
C) 8/ -1 + 7 D) 2(1/ - 25x 4- 9
. . 6x — ?n 7rrtai — 1
a.	rn mng qaiiday qiymatida-----— =----------
tenglamaning iidizi no’ga veng boiadi?
л> B) -2 C) rt D) -5
О	о	о	Z
6.	X] va«2 / — 14x + 9 = 0 tengianiajHng ildlzlari
bo4sa, Tyx2 4- r2x2 ning qiyrnatini toping.
A) 126 B) -92 C) -126 D) -144
7.	(a? — l)(x 4- 2) < 0 tengsizlikni yeching.
A) (1;2) B) f-oo: 1) U (2?oo) C) (-2;1)
D) (-og;-2)U(1;oo)
8.	Quyidagi sonlardan qaysi biri 0;3(6) ga teng?
A> is B> 30 c> i D> ТГ
2'"*» 4‘ I m hisoblang.
A) 4 B) 9 C) 5 D) 3
4
10.	Markaziy burchakka tnos yoy ay I an an mg •p-
qisrniga teng Shu rnnrkaziy burchakni toping.
A) 144" B) 72° C) 216° D) 288°
11.	Quyidagi lasdiqlarning qaysilari noto'g'ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi ft —	uchburchakning
tomonlari. S— uchburchakning yuzi) formula
bilan lusoblanadi;
2)	radiusi ft ga, xnarkaziy burchagi n ga teng
doiraviy sektorning yuzi .S’ = ТДГ« formula bilan
hisoblanadi;
3)	tomoni a ga, burchaklaridan biri о ga teng
ronibning yuzi S = ka-sina formula bilan
h Isold an ad i.
A) 2:3 B) 1:2 G) 1;2,3 D) 1;3
12.	Tektslikka og‘rr.ta va perpendikuiar tushirilgan.
Og'nianing tekislikdagi proyelcsiyasi 11 ga,
perpendikularning uznnligi 60 ga teng. Og‘ma va
perpendikuiar orasidagi burchakni toping.
22 m • U	П
A)	arcc^r-	B) arcstn-—	G) arcctg--
Ы	61	60
• G0
B)	errszn —
01
13.		---------— ni soddaia.shtiring.
tg2o — ctg 2 о
A) —2tg4or B) cos4a C) — <g4o
D) tg4a
14.	Agar in > 1, n > 2 va k > 36 bo'Isa.
2 ; rn 4- 6 : n 4- 432 : k ifodaning eng katta
qiyinatini toping.
A) 7 B) 8 C) 17 D) 19
15. O'zaro teskari sonlarni aniqlang:
18, 7(4* - ))2(3= (1 -	tcnglik x
ning qanday qiyrnatlarida t.o;g4i bo'ladi?
A) 0,25<x<3 В) (-ос; 0,25]U{3}
C) -3 < x < 3 D) x < 3
.. f 9x - 1 > 7x 4- 3	.....
u. < .,n o “ .	, _ tengsjzhklar sistemast butnn
I 20 —	> 4r — 15
yechhidarimitg o'rta arifmetigini toping.
Л) 7 B) 3,5 C) 3 D) 4
1
18.	Agar f'(x) = sm3r 4- -----r bo'lsa, f(x)
x — 1
funksiyam toping.
A)	3ro.s3x 4- /ujx — ij 4- C
В)	солЗх 4- ln\x — 1| 4- C
C)	—-cos3x 4- tn\x — 1J 4- C
•J
D)	— cos'it + /«!»— 11 + C
34
TEST 2006 •Variant .	117
MaternA* ka
( I \	r
19.	a = / - 1	, 6 = v/3^ va c ~ ( \/3)° soniarni
\ о J
o’sish lartibida joy!ashtiring.
A) a < c < b B) b < с < a С) c < a <_ b
D ) c < b < d
20.	Balandligi 8 ga teng bo‘lgau. teng yonli
uchburchakning asosi yon toxnonidan 2 ga ortiq.
Uchburchakning asosini toping.
A) 15 B) 16 C) 12 D) 18
21.	Rastnda Л/ЛГЦАС. MBN uchburchakning
perimetri 42 sm, ABC uchburchakning perimetri
84 sm. MBN uchburchakning yuzi 44 sm2.
ABC uchburchakning yuzini (srit3) toping
A) 108
D) 176
27.	/(z) —	— 1} 4-	— 2| fiinksiyaning qiymatiar
sohasini toping.
A) (];oc) B) [0;oo) C) [3;oo) D) (2;oo)
28.	Qisqarmaydigan oddiy kasrning maxraji
surat idau 6 birlikka katta. Agar kasrnmg surat
va maxrajjga 5 ni qo'shsak, hosil bo'igan
.4
kasrnmg qiymati — ga teng bo'ladi. Berdgan
n
kasrning suraUni toping.
A) 7 B) 23 C) 13 D) 19
29,	5x* -t- bx — 15 = 0 tenglamaning ildizlari zq va x2
uchun 5#-, 4-2x2 — 1 rminosabat o'rinli. Agar b
butun sou ekanligi Hia’hirn bo‘lsa, uning
qiymatini toping.
A) -10 B) 7va-10 €) 10
D) -7 va 10
30.	IJ ch burchakni ng b va c ga long tomonlari
orasidagi burchagi 30° ga teng. Uchburchakning
uchinchi tomoni 16 ga teng ЬоЧаа haruda lining
tomonlari c~ — b2 4- 166 4 256 shartni
qanoatlantirsa, r. ning qiymati qanchaga teng
bo'ladi?
Л) 16^3 B) 12^ С) Г2УЗ D) 16>/2
22.	Tolg‘ri burchakli parallelepiped asosining
tomonlari 6 va 8 ga teng. lining diagonal! asos
tekisligiga 30е ii burchak ostida og‘ishgan.
Parallelepipedning hajmini toping.
Л) 8Ch/3 В) 20>Д C) 240 D) 160л/3
Rornbning o’Unas burchagi 120° ga, katta
a- u	о 1 •
diagouan - _ ga teng. Kombning yuzini
V 8
hisoblang.
А) 0.6</'-Уз В)	C) Irf’ D)
4	2
3d2
16
23.	Asosining radiusi 16 sm va balandligi 8 sin
bo'lgan konus asosidan 3 sm rnasofada asosiga
parallel tekislik bilan kesilgan. Kesimning
yuzini (sm2) toping.
А) 50т В) 36t C) WOx D) 25 tr
24.	t ning qanday qiymatida
у = 1 — 3cos2r — t(l 4- cos2ar) funksiyaning
qiyrnati o^garmas bo‘ladi?
A) -3 В) 3 C) -1 D) -2
25.	cos 3r cos т 4- 0,5 ~ sin 3x sin x tenglamaning
iklizlarini ko‘rsating.
. . X .	.	. r-r	x
А) - + 2vk^eZ В) 74T,*€2
n	4	2
О ±J + ^,iez D) I + ^,iez
o 2	о
*26. Nodirda bor paining qismi Jahongirdagi
8
paining - qismiga teng- Nodir palming necha
foizini Jahongiiga bersa, ularning pullari teng
bo'ladi?
A) 37.5 B) 25 C) 17,5 D) 12,5
32.	1; 1), B( 1; 4; 0) , C(l; -2; 2) va
Z>(—5; —5: 3) nuqtalar berilgan. AC va BD
vektorlar orasidagi burchakni toping.
A) 60° B) 90° C) 45° D) 30s
33.	sinx 4- f'osx - 1 tengiamanitig (—x; x] oraliqda
nechta iidizi bor?
A) i В) 0 C) 3 D) 2
34.	1од1ы ((0,25)'°й“>Н+1+и+-nj hisoblang.
A> I B) 7 CU D> П
I 35 Diagonal! orqali ikkita muntazam uchburchakka
ajraladigan rotnbga ichki chizilgan aylananing
radiusi r ga teng. Rombning yuzini toping.
A) 4r2 В) 2г2Л G) 4г2Л D)
36. Konusning o‘q kesimi mimtazam uchburchakdan,
silindrniki esa kvadratdan iborat. Agar konus
hajmining silindr hajtniga nisbati л/З : 2 kabi
bollsa, toia sirtlarining nisbatini toping.
A) ^3:^2 ’В) УЗ :х/2 C) ^9 :2
D) 3: 2
35
TEST 2006 : Variant
118
Matem&tika
1
Matematika
1. 1 soat 160 minut 5 sekundnecha sekunddan
iborat?
A) 12205 B) 106005 C) 13205	0) Ш05
o 2,60,71,8.....................
2‘ 7~2-'7 8 i 4 mng 4Watim ^ping.
A) I	В) 1	C) 2	D) 0,04
i>	2Л	1Z
y2x — x2*
3.	—_  ni qisq artin ng.
X 4- /
A) —Xх 4- y* B) r* 4- y*
D) x - у
C) /
II.	Quyidagi ta, fiqlarniug qaysilari noto’g*ri?
1)	tomcnlaxi a, b va c bo’lgan uchburchakka ichki
chizilgan ayUn&ning radiusi r ss formula
bilan hisoblanadi;
2)	tomonlari a va b ga, ular orasidagi
burchaklaridan biri or ga teng bo’lgan
parallelogrammning yuzi S = |a6stna formula
bilan hisoblanadi;
3)	o’xshash figitralar yuziarining nisbati ulaming
mos chiziqli o’khovlarining nisbat-iga teng.
A) 2; 3 B) 1;2 C) 1;2;3 D) 1;3
12.	Tekislikka tushirilgan og’maniitg uzunligi 75 ga,
uning tekislikdagi proyeksiyasi esa 72 ga teng.
Og’ma va tekislik orasidagi burchakni toping.
7	nx	24
A)	arccoeB)	arcsin~
50	25
- 1
D) arcstn—-
25
C) arcsine
24
4.	(x — 1)(2 — x) 4- (x — 3)2 ko'phadni standart
shaklga kelliring.
A) 3x24-15*4*7 B) -3*4*7
C) 12*4-4-*5 D) 9*4-7
1 4 cos'2ot 4- cos4ot 4- cos6o .	, , , ...
——-------------------------m soddalashtirmg.
stn4or 4- 2stn2crcos4a
A) tg2a B) '2ctg2a C) ctg2cr D) 2sin2a
5.	(2* — 1)(* — 1,5) = 0 bo’lsa, 2* — 1 qanday
qiymatlar qabul qiladi?
A) faqat — - B) 2 yoki 0 C) 0 yoki 1,5
D) 0 yoki
6.	x2 - 13* 4* q — 0 tenglamaning ildizlaridan biri
—14 ga teng. Uniag ikkinchi ildizini toping.
A) 27 B) -1 C) -27 D) 1
x — 5
7.	——- > 0 tengsizlikni yeching.
A) (-7; 5) B) (-oo; -7)
C) (-oo; -7)U[5; oo) D) (-7; 5]
8.	0,(7) 4 0, (5) - - ning qiymatim hisoblang.
<7
A) « В) !» C) 1| D) Q
9.	(-/б)1-**7* ni hisoblang-
A) 7 В) 3\/5 C) 15 D) 5
10.	Ikkita to'g*ri chtziqning kesishidan hosil bo’lgan
qo’shni burchaklarning ayirmasi 50° ga teng. Shu
burchaklardan kichigini toping,
А) 65е В) 60® С) 70® О) 50®
14.	24 sonining barcha natural bo’luvchilari
yig’indisini toping.
A) 48 B) 60 C) 124 D) 108
15.	51 • 6^ — 4^ - 5^ ni hisoblang.
4	4 co
A> B> ’°g c> l°g D)
16.	/(—2) — 5 va /(2) = 3 shartni qanoatlantiruvchi
chiziqli funksiyani aniqlang.
A) = B) /(«) = lr + 4
C) As) = ~^ + « D) A’) = 2« +1
17.	23 - 2* > (x 4~ 2)(x — 2) — 2(x — 1) tengsizlikni
yeching.
A) (0; 25] B) (-oo; 5] C) (-V21; -ДТ]
D) [--5; 5]
18.	J (cosxcos2x — fiinrsin2x)dT int-egralni
о
hisoblang.
1	1	2	л/2
A)	x	В)	-	C)	-	D)
О	о	о	и
4
19.	log<2(4 — 2х) — log^{4 — 2x) > - tengsizlikni
yeching.
A) (-oo; 1) B) (-oo; 0,5) C) (0; J)
’£>) (-4; -1)
36
2
TEST ’2006 : Variant
118
Matematika
*20. Uchburchakning asosiga tnshiriigan rnedianasi
uni pcrimelrlari 18 va 24 ga teng boMgan ikki
uchburchakka ajratadi. Berilgan uchburchakning
kichik yon tonioni 7 ga teng. Uning katta yon
tomonini toping.
A) 12 В) К) C) 13 О) 14
*21. To;g‘ri t.o’*rtburchakning katta tornoni 13 ga,
di agon al) acini ng kesisbgan nuqtasidan katta
tonionigacha boigan rnasofa 3 ga teng. T6‘g*ri
to'rtburchakning yuzini toping.
A) 78 B) 56 C) 72 D) 48
22. Muntazam tc/rtburchakli pirainidaning
balandligi 24 sm, apofernasi esa 26 sin. Piramida
asosiniug perimetrini toping.
A) 48 B) 40 C) 80 D) 96
*23. Yasovchisi *26 ga va balandligi 10 teng boMgau
konus asosimng yuzini toping.
Л) M4%" B) 144% C) 576% 0) 288%
24.	(2 4- ros-2a)(l 4- t$rcr) •+• 4$йго ifodaniiig eng
kichik. qiyniatnri toping.
A) 1.5	B).2.5 C) 3 D) 2
25,	sin 5x • co«2x — cos 5л - sin 2л 4 0,5 tenglarnaning
ildizlari ni koTsating.
A) ~ + ~тг~• t € 2 B) zt— 4- 2^k. k € 2/
г> л	.J
D) -* + ™'ktz
6	3
^6. 520 soni sb unday ikki bo‘lakka boMinganki,
ulardan btrining 80% i ikkinchisimug 24% ini
tashkil qiladh Bo’Iaklarni kichigini toping.
A) 120 B) 400 C) 460 D) 420
27.	/(x) = v^75 — x — x2 fnnksiyaning eng katta
qiyinatini toping.
A) 1,5 B) 72 C) 272 0) 3
28.	Qisqarmaydigan cddiy kasrning maxraji
snratidau 18 taga ko:p. Agar kasrning sural iga
379 ni, inaxrajiga 1 ni qo'shsak, berilgan kasrga
teskari kasr hosil bcrladi. Berilgan kasrning
rnaxrajini toping.
A) 19 B) 17 C) 14 D) 13
29.	Agar 4- x — 4 = 0 tenglamairrng ildizlari va
x-2 bo‘lsa, z’j + ning qiyrnati qanchaga teng
bo'Jadi?
A) 3 ,B) 1 C) -13 D) 2
30 Tt>‘g4ri burchakli uchburchakka ichki va tashqi
chizilgan aylanalar radiuslariuing nisbati 4:13
kabi. Kichik katet uzunligining katta katet.
uzuiiligiga nisbatiui aniqlang.
A) 5 : 1*2 B) 3:4 C) 4 : 13 D) 5 : 13
31. M{sty) nuqtaning koordin^t.lari yig'indisj 6 ga
teng. Bn nuqta va kourdinM boshi orasidagi eng
qisqa rnasofa qanchaga teng bo'ladt?
А) 2д/3 В) ЗУ2 C)	D) 1,5^2
32.
Agar a vektor b ~ 3z — 2j -T 2* vektorga kollinear
va « • b - 28 bo Isa, a vektc?rning uzunligini
toping.
B) 14 С) 2-/M D)
33. J.s/Tir 1| > 1,5 tengsizlik * rung (0;%) oraliqqa
tegishli qanday qiymatlarida o'rirdi bo'ladi?
f_____ f	J A n
34	\/5	— э?	| logi (2z —	4}	4- — r 1	> 0
>	\	4	iV/e>_r i* /
;	tengsizlikriihg butun sonlafdan iborat nechta
|	yechiini bar?
A)	1	B) 0 (?)	3	D) 2
35.	Doiraga ichki chizilgan uchburchakning bir
tornoni uning diainetriga teng. Doiraning yuzi
*289% ga, uchbtirchak toinoidaridan binning
uzunligi 30 ga teng. Shu uchburchakka ichki
chizilgan doiraning^yuzini toping.
A) 36% B) 16% C) 20% D) 64%
36.	Sharga kouus ichki chizilgan. Konusning
yasovchisi asosining diamctfiga teng. Shar
hajrnin’ntg konus hajmiga nisbatini toping.
A) 8:3 B) 32:9 C) 27:4 D) 16:9
37
TEST 2006 : Variant
119
Matematika
1
Maternal ika.
1 37 • 24 — 34 • 24 + 19 • И — 16 • 11 ning qiyrnatini
roping.
A) 90 B) 105 C) 100 D) 110
2.	3; y: 2,1 va 2.1 son lari ning crrta arifmeugi 2,55
ga teng. у ni toping.
A) 2,6 B) 2,1 Cl 3 D) 2
Tekislikka og-rna va perpendikular tushirilgan.
Og‘manmg tekislikdagi proyeksiyasi 12 ga,
perpendikularning uzunligi 35 ga teng. OgJma va
perpendikular orasidagi burchakni toping.
- 12	n-	24
Al	arcsm—-	B) атссо.ч-—
Л I	Si
u)	arc&in —
}	37
t 35
C) arci9^
3.	а(Ь — c) — 6(c — a) — c(b — a) ni soddalashtiring.
A) 2ab B) —2ac C) ‘2ab - 2bc D) 0
4	—---------------% ni soddaiashtiring-
(* + I)’
A) x 4-1 В) 2x C) 0 D) x - 2
5.	m ning qanday qiymatlarida |3 — rn| = m — 3
tenglik o’rinli bodadi?
A) rntR B) tn > 3 C) rn > 3 D) m = 3
6.	va *2 x~ — 22л 4-8 — 0 t-englarnaning ildizlari
bo’’lsa. 4- xfa ning qiyrnatini toping.
A) —176 B) -120 C) 176 D) 280
sin4 а 4- sin1 2 о < cos2 a .	.
13.	1 4------------5j---------- rn soddalashtirmg.
cos" о
A1 1 — tgJa B) tg2ot C) I — cto2o
1 ‘
О
14.	Agar ?n > 3, n > 5 va fc < 6 bo’lsa. 3m 4- 5n — 2k
ning eng kichik butun qiymatini toping.
A) 14 B) 23 C) 22 D) 13
15.	Qaysi juftlik o:zaro tub sonlardan iborat?
A).(11; 22) B) (8; 14) C) <12; 34)
D) (39; 44)
7.	— 3 < -2 tengsizlikni yeching.
A) x G 0
B) x < 4
C) x >4
D) X> I
/(r -3){x- 1)	.	.	.
16 у = 1/----t~ funksiyaning arnqlamsh
у x(4 — x)
sohasini toping.
A) (0;l)U[3;4) B) [0;l)U{3;4)
C) (-og;0)U(1;3]U(4:oq) D) (0;l]u[3:4)
8.	0,6(3} ш oddiy kasrga aylantiring.
дЧ 4	„.2	62	57
15	30	90	90
9.	(^7)^7? ni hisoblang.
A) 9 В) ЗЛ C) 18 D) 3
17.	--------------> 0 tengsizlikni yeching.
2x + 5
A) (-2„5;2) B) (-cc;-l,5)
C) (-2,5;-l?5) D) (-oc;-2,5)
10, Ikkila to4g*ri chiziqning kesishishidan hosil
bo‘!gan qo;shni burchaklar 7 : 8 nisbatda bo:lsa,
shu burchaklarni toping.
А) 75е; 105® B) 36°: 144° C) 38°; 142°
0) 84°;96°
1 1. Quyidagi tasdiqlarning qaysilari to:g:ri?
]) tornonlari a, 6 vac bolgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
radiusi R ga, rnarkaziy burchagi a ga teng
doiraviy sektorning yuzi S — о formula bilan
hisoblanadi;
31 tomoni c. ga, burchaklaridan biri о ga teng
rombning yuzi S ~ Еа^^па formula bilan
hisoblanadi.
A) 2;3 B) 1;2 C) 1;2;3 D) 1:3
20. Aylanaga tashqi chizilgan teng yonli
trapetsiyaning o’rta chizigsi 8 ga teng. Shu
trapetsiyaning yon tornonini toping.
A) 8 B) 4. C) 5 D) 7
38
TEST 2006 : Variant
119
Matemat 0л
21.	A BCD pavallelograminda OBI AC, A0=8.
OC=5 va BO=4. Parallelogrammning yuzini
toping.
A) 28 B) 50 C) 52 D) 56
22.	To4g’ri burchakli parallelepiped asosi ni rig
tornonlari va balandligining qiymatlari 4:3:1.25
kabi nisbatda. ParaHelepipedning diagonal! va
asos tekisligi orasidagi burchakni toping
А) 30е В) 45° C) arcctg4 D) 60°
23.	Ikkitasfera yuzlarining nisbati 2ч/2 ga teng. Bu
sferalar diametrlarining nisbatini toping.
А) В) У8 С) И? D) 8
. ,	."Л ч Я" . з 7Г	7Г 1.7Г.
24 sm—~	- sot,' —	— am —	 cos—-----sm —	ni
12	12	12	12	4	3
hisoblang.
A) Bl 0 C) 15)
О	о	4
25.	4sm22x = 1 tenglamani yeching.
A)	(—1)” “ + vn. Z
B)	± + uizz
i <L
С) + n GZ
D) ± д + -Г-, П € Z
У О
26.	IshchiuUg mehnat unumdorligi 30% artsa, uning
ish norrnasini bajarisbga ketadigan vaqti necha
foizga qisqaradi?
A) 25 B) 20 C) Ifw D) 23-L
ti	io
30.	To'g ri burchakli uchburchakning katetlari 5 va
7.5ga teng. To;g"ri burdiak bissektrisasining
uzuniigini toping.
А) ЗУ5 В) 4\/2 С) 3 + 3>/5 D) 5\/2
31.	Asoslari 8 va 14 ga teng bo;lgau teng yonli
trapetsiyaning diagonallari o’zaro perpendikular.
Trapetsiyaning yuzini hisoblang.
A) 64 B) 100 C) 121 D] 144
32.	Agar a(l; -1: 3) va 6(4: 3; 0) bo'lsa. a ning
qanday qiyrnatida 4n 4~a6 vektor b — a vektorga
perpendikular bo'ladi?
A) 2.1 B) 1 С) I D) 4
33.	cojs'2x — 5si’nr —3 = 0 tenglamani yeching.
A)	( — ly141 - +	€ Z
B)	(-1) T -b 7ГП.Г/ g Z
b
С)	(-1)и + ’| + 2тгп.п€^
D)	(“l)r'“ 4- '2irn. n € Z
о
34.	lg{x — 2) < 2 - Z^(27 — x) tengsizlikning
yechirnlaridan uechlasi butun sondan iborat?
A) 8 B) 9 C) 6 D) 7
35.	Rjadiusi 5 ga teng bo‘lgan doiraga to g'ri
burcliakli uchburchak ichki chizilgan. Shu
uchburchakka ichki chizilgan doiraning radiusi 1
ga teng. Uchburchakning yuzini toping.
А) 8У2 B) 12 C) 22 D) 11
36.	O:q kesimi teng tomonli uchburchakdan iborat
konusga diameter D ga teng sfera ichki chizilgan-
Konusning. to'la sirtini toping.
A) |»D2	B) ^D2	C) ^D2
2	4	4
D) -tD2
4
27.	у —--------------funksiyaning aniqlanish
x + 4
sohasiui toping
A) (-4; 4) B) (-4; 1] C) (-4: 1)
D) (-4; 2j
28.	Ух2 — 4x 4- 4 = Vx2 ~ lOr 4- 25 tenglamaning
ildizlari qaysi oraliqqa tegishli?
A) x < 3 B) 3 < x < 4 C) i < -2
D) x > 5
X	T
29.	I—j------1 =--------? tenglamaning barcha
r* - 1296	1296-r4
natural yechimtari yigindisini toping.
A) 1 B) 12 C) 10 D) 15
•9
39
TFJST 2006 : Variant
120
Matematika
1
Matematika
I 18-16- 15-16 + 36-24-33-24 + 17-11- 14 -11
ni hisoblang.
A) 155 B) 166 C) 153 D) 180
2. Xaritada ikki shahar orasidagi rnasofa 4,5 sm ga
teng. Xaritadagi masshtab 1:4000000 bolsa.
shaharlar orasidagi haqiqiy rnasofa веска km
boladi?
A) 270 B) 180 C) 900 D) 90
11.	Quyidagi tasdiqlarning qaysilari notzrg’n?
1)	tomonlari a, 6 va c bo’lgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S — formula bilan
hisoblanadi;
3)	diagonallari d\ va d2 ga, ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
to'rtburchakning yuzi S —	formula
bilan hisoblanadi.
3 a(6 + c — 6c) — 6(c + a — ac) — c(6 — a) ni
soddalashtiring. .*•
A) 2ac — 26c B) — 2abc	C) ab - ac
D) -26e
12.
у
4.	(x”1 + $T*) *-------=• ni soddalashtiring.
U + УГ
A)	Bl	Cl 1
(3.- + .C/)3	(x+.y)2	' x + y
D) т2у-
A) 2:3 B) 1:2 C) 1:2;3 D) 1:3
Tekislikka og'ma va perpendikular tnshirilgan.
40
Og'ma va tekislik orasidagi hurchak arccos-- ga,
41
og'maning tekislikdagi proyeksiyasi 80 ga teng.
Perpendikularuing uzunligini toping.
A) 36 B) 40 C) 30 D) 18
s/n8a — .srnl2a
c-oslOcr - sin2a
ni soddalashtiring.
A) '2sin‘2a B) —2 C) — '2siif'2cr
D) — 2cos2ot
5.	(8z + 1)  (z — -) — 0 bcrlsa, 8z + 1 qanday
qiymatiar qabul qilishi mumkin?
A) faqat - B) faqat — i C) 0 yoki 3
D) faqat 0
6.	x, va x2 — 13x + 12 — 0 tenglamaning
ildizlari boisa, + rfx2 ning qiymatini
toping.
A) 156 B) 94 C) -156 D) -152
f 3 + 4z>5
\2z - 3(z - 1) > 1
tengsizliklar sisternasining
butun sonlardan iborat yechimlari necbta?
A) 3 B) 5 C) 2 D) 6
8.	Quyidagi ketma-ketliklardan qaysilari geometrik
progressiyani tashkil etmaydi?
l)«TI=2xftJ(z^0);
2) Cn - GZn, (<KB 0);
3)6п = (5р.л“п60с + 1.
5
A) 3 B) 1:3 C) 2 D) 1
9.	x ning qanday qiymallanda у = 5х — 125
funksiya noman fiv qiymatlar Qabul qiladi?
A) x < 3 B) x > 3 C) x < 2 D) z > 2
10.	Qo'shni burchaklardan biri ikkinchisidan 40°
katta. Sbu qo’shni burchaklarni toping
А) 110е; 70° В) 160е; 20° С) 140°, 40е
В) 20°; 160е
14.	r raqamining qanday eng kichik qiymat.ida
(642 + 2z2) son 3 ga qoldiqsiz boTmadi?
A) 0 B) 5 C) 7 D) 2
15.	25 va 15 sonlari eng kichik umumiy karralisiamg
natural boMuvchilari uechta?
A) 4 B) 5 C) 7 0) 6
16.	Agar /(r + 1) = jt - 3z - 3 bolsa, J{x) ni
toping.
А) — 5z + 1 B) zz - 3z — 1 C) z2 —4
D) z2-5z + 6
17.	7 — r < (z — 2)~ + 3(x — 2) tengsizlikni yeching.
A) [-2; 1] В) (О;1]ЩЗ;0о)
C) (-00:-3] U [3; co) D) [-3;3]
18.	/ sin 3z cos3zdx ni hisoblang.
i 0
t
A) 7	B) 1 C) 1	D) 1
4	2 О
19,	a — hgi/^2t Ъ = /o^i/зЗ va с = /о?1/з4 sonlami
o’sish tart-ibida joy lashtiring.
A) c < 6 < а В) c < a < b C) 6 < a < c
D) a < b < c
20.	Radiusi R ga teng bo‘Igan aylanadagi nuqtadan
uzuniiklari Rxft ga teng bodgan ikkita vatar
o;tkazildi. Vatarlar orasidagi burchakni toping.
A) 60° B) 45° C) 120° D) 135°
21.	Tomoulari 4 va 8 m bo'lgan parailelogrammi»g
yuzi l6\/3 Parallelogramnxmng o4nias
burchagini toping.
A) 150° В) 120° C) 105° D) 135°
40
TEST 2006 : Variant
120
A/atematika
22.	Muntazam piramidaning yon sirti to;la sirtining
60% ini tashkil etadi. Piramidaning yon yoqlari
va asos tekisligi orasidagi burchakni toping.
A) arccos i B) 60° C) arccos |
™ 1
D) arccos ~
0
23.	Radiusi 8 ga teng boigan sharga balandligi 18 ga
teng bo’lgan konus tashqi chizilgan. Konus
asosining radiusini toping.
A) 18 B) 12 C) 16 D) 24
3
24.	tga = — • tg'2a —?
4
4	24
A) - В) 3 C) -
•J	i
25.
.	л
2siu2r < ctg — tengsizlikni yeching.
4
Ilf	7Г	.
—4- 47rn: - 4- 4rnj. n € Z
3	' 3
7Г 5?T	,	,	„
— 4- 27ГТГ. —- + 2xn], n € Z
б	о
7г	Г	_
~T2 +	12 + %П 1 П &
г	5тг	.	_
-- -h гп: — 4- гп, п 6 4
12	12	J
26. Agar tekis harakatda tezlik 30% ga ortsa,
ma’lum masofani bosib o‘tish uchun ket-adigan
vaqt nech a foizga kamayadi?
А) 331 B) 16^ C) 231 D) 20
27. у — —	-----===== funksiyaniog aniqlanish
i/x — 6 - >/9 — r
sohasiga tegishli barcha butun sonlar yig‘indisini
toping.
30. Katetlarining nisbati 3:2 kabi bo’lgan to‘g’ri
burchakli uchburchakning balandligi
gipotenuzasini uzunliklaridan biri
ikkinchisinikidan 3 ga ko;p bo’lgan ikki qismga
ajratadi. Berilgan uchburchakning gipotenuzasini
loping.
A) 7,8 B) 5,2 C) 8 D) 6
31 ABCD trapetsiyaning (ADJjBC, AD - katta
asos) ЯС diagonal! yon tomoniga perpendikular
hanida DAB burchakning bissektrisasida yotadi.
Agar ЛС — 16 va ZD A В = 60” bodsa.
trapetsiyaning o'rta <hizig:ini toping.
A) 1^3 B) 373 C) 8V3 D) 5v/3
32-	Udilari A(2; 3; I), B(3; 2; 1) va C(3; 4; 1)
nuqtalarda bo’lgan teng yonli uchburchakning
asosidagi burchagini toping.
1	2 7Г
- A) arccos-	B) arcrc<?S”	C) ~
D) arccos—
Уз
33.	[1 4-smz-J < | tengsizlikning [0; 2r] oraliqdagi
eng katta va eng kichik yechimlari ayirmasini
toping.
2x
A) 1,5г	В) r C) l,2x D) —
О
34.	co$-(x 4 I) • M^4(3 — 2z — t2) > 1 tengsizlikni
yeching.
A) [~2;-l] B) [-1:0) C) {-1}
D)
35.	Rasmda AE — 3 • ЕВ. AE FC, S^abc ~ 120-
BE FC tcfrt burchakni ng yuzini toping.
A) 28 B) 15 C) 30 D) 32
A) 75 B) 80 C) 40 D) 60
1	30	,	» , -
z -j----_ — tengiamaning natural sonlardagi
л I <5
УЧ- -
2
yechimida z nimaga teng?
A) 3 B) 4 C) 7 D) 2
36.	Komisuing orq kesirni muntazam uchburchakdan,
silindrniki esa kvadratdan iborat. Agar konus
t-o‘Ia sirtining silindr to4a sirtiga nisbati 1:3 kabi
bo'isa, hajmlarining nisbatini toping.
A) 2 : 9 B) 1 : 9 C) 4 : 9 D) л/2 : 9
29. (2|«1 — 3)2 = |«| tenglamaning barcha ildizlari
ko‘paytnia$ini toping.
a>4
c> D> tI
41
TEST 2006 : Variant
121
Mateiuafika
1
Matemat fka
I.	Bir nechta natural sonning yig'indisi 85 ga teng.
Agar shu sonlarning bar biridan 2 ni ayirib.
yigindi hisoblansa, u 61 ga teng bo’Iadi.
Yig'indida nechta son qatnashgan?
A) 7 B) 5 C) 8 D) 12
2.	— 1-ga teskari sonni toping.
A) -0,75 B) 1,5 C) |
3.	16 — (2x — 3)~ ni kcrpaytuvchilarga ajrating.
A) (2х-1)(7-2зг) B) (2x41)(7-2x)
C) (2r — l)(2z 4 7) D) (2i + l)(2z-7)
4 (/ - У2 + 1 )(1T + 1) - (y - l)(y 4 2) 4 ул 4 у3 ni
soddalashtirgandan keyin hosil bo'lgan
ko'phadning nechta hadi boiadi?
A) 4 В) 3 C) 5 D) 6
19	1
(2—- 4 x) : 4- — 5 tenglamani yeching.
22	5
1	IQ	3
A) 18^ B) 17- C) 21 D) 17^
6. x2 4 Ux 4 q — 0 tenglamaning iidizlaridan biri
—12 ga teng. Uning ikkinchi ildizini toping.
A) -23 B) 1 C) 23 D) -1
7. (r 4 2)(z — 3) < 0 tengsizliknt yeching.
Al (-oc;—3)U(2;oo)	B) (~2;3)
C) (-co; -2) U (3: dc) ,D) (-3;-2)
11.	Quyidagi tasdiqlarning qaysilari noto‘g£ri?
1)	tomonlari a, 6 va c bodgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi:
2)	diagonallari va ga, ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
to£rtburchakning yuzi S = |did2szna formula
bilan hisoblanadi:
3)	o'xshash figuralat yuzlarining nisbati ularning
mos chiziqli o'lchovlarining nisbatiga teng.
A) 2:3 B) 1;2 C) 1;2;3 D) 1;3
12.	Tekislikka tushirilgan og'ma va perpendikuiar
orasidagi burchak nresin— ga teng. Ognnaniug
uzunligi 58 ga teng. Perpendikularning
uzunligini toping,
A) 80 B) 40 C) 42 D) 33
„ „ cos ‘За sm За .	,, , , . .
13.	------ 4 —:---- ni sodaalashtinng.
COS O' sin о
A) 4cos2er B) 4 cos о C) —2
D} 2cos2o
14.
1
45
natural bo‘luvchilari soni nechta?
A) 7 B) 11 C) 13 D) 12
va kasr umumiy rnaxrajining barcha
ov
15. Qaysi juftlik erzaro tub soniardan iborat?
A) (22; 27) B) (21; 14) C) (10; 15)
D) (12; 15)
16.
/(x-3)^-1)
9 у x(4 - x)
sohasini toping.
funksiyaning aaiqlanish
A) (0;l)U[3;4) B) (0;l)U[3:4)
C) (-oo;0)U(l;3]U(4;<x) D) (0;l)u[3:4)
8.	Geornetrik progressiva uchun quyidagi
formulalard an qaysilari noto4g‘ri?
l)|>n = big-‘;2)^ = 6n_l-bn+>;
17. 2 - 3r > 2  (x — 1 )(z 4 1) —	4 3) tengsizlikni
yeching.
A) (-2; 2) B) (-oc; 2) C) (1; oc)
D) (0; 4)
A) 1 B) 1; 3 C) 3 D) 2
18.
cos(0,25z
ni hisoblang.
9.	x ning qanday qiymatlarida и — 3 — Igx funksiya
nomusbat qiymatiar qabul qiladi?
A) x > 1000 B) x > 100 С) x < 1000
D) z < 100
Л) 4-2з/3 В) -2 С) 2 D) -1
19.	log^x — 4/о#зХ 4 3 = 0 tenglamaning ildizlari
yig indisini toping.
A) 10 B) 20 C) 30 D) 4
10. Qo'shni burchaklardan biri ikkinchisidan
14е katta. Shu qo^shni burehaklarni toping.
A) 83’,-97*	В) 16е; 164° C) 82°;98°
D) 93е :87х5
20.	Vzunligi — ga teng aylana o4kir burchagi 30е
4
bo'lgan Tombga ichki chizilgan. Rornbning
perimetrini toping.
A) 16 B) 2 C) 4 D) 8
42
2
TEST 2006 : Variant
121
Matematika.
21.	Rombning balandligi 5 ga, diagonallarining
kcrpaytmasi 90 ga teng. Uning peri met rini
loping.
A) 16 B) 32 C) 28 D) 36
22.	Priznianing asosi tomoni зУб bo:lgan muntazam
oltiburchakdan, yon yoqlari kvadratlardan
iborat . Prizmaning katta diagonalini toping
A) W B) 15 C) 12 D) 7^5
23.	Shar katta doirasining yuzi 225т ga teng.
Shaming rnarkazidan qanday masofada
o'tkazilgan tekislik shardan doirasining yuzi 161тг
ga teng bolgan kesim ajratadi?
A) 6 B) 7 C) 8 D) 3,5
24.	/(r) = 1 — 3cos2ar — kccs'ir funksiya k ning
qanday qiymatida crzgarmas bo'ladt?
A) -2 B) -3 C) -1,5 D) -1
25.	cos 3т cos я 4-0. 5 = sin 3jj si az tenglamaning
ildizlarini kolrsating.
. \ T	> 1	r-»	tT i	„
A)	B) - +
6	4	2
C) ±? + т-^2 D) J + rt,te2
о 2	6
26.	Mahsnlotning narxi birinchi rnarta 20% ga..
ikkinchi marta yangi bahosi yana 10% ga
oshirildi. Mahsulotning oxirgi bahosi necha
foizga kamaytirilsa4 uning narxi dastlabki narxiga
teng bo‘Iadi?
A) 24^ B) 25 C) 33I D) 30
27.	f(r) = |i — 2| -H* + 8[ funksiyaning qtyntaUar
sohasini toping.
A) (3;oo) B) [10; oo) C) [6;oo)
D) [4;oo)
28. Ikki sonning ayirmasi 27 ga teng. Agar birinchi
sonni ikkinchisiga bo:Isak, bo{Hnma 4 ga va
qoldiq 3 ga tong chiqadi. Berilgan sonla ruing
yig'indisini toping.
A) 38 B) 31 C) 43 D) 29
* — 8 k
29. k ning nechta natural qiymatida ~—— =r -
tenglarna ildizga ega boimaydi?
A) 6 B) 5 C) 8 D) 7
30. Tomonlari 16; 30 va 34 sm bo'lgan uchburchakka
tashqi chizilgan aylananing radiusi necha sm?
A) 18 B) 17 C) 19 D) 16
31. Asoslari 12 va 16 ga tong bcflgan teng yonli
trapetsiyaning diagonallari o‘zaro perpendikuiar.
Trapetsiyauing yon totnonini toping.
А) 14>/2 B) 20 C) 10 D) 10У2
I
j
32.	Uchlari A(2; 3; 1), B(3; 2: I) va C(3; 4; 1)
nuqtalarda bo’lgan tong yonli uchburchakning
asosidagi burchagmi toping.
I J) arccoa-'
33.	4 cos' r -f- sin r cosx 4- 3 sin? x — 3
tenglamaning 90” < x < 180° sharini
qanoatlantiradigan ildizlari yig'indisini toping
А) 225е В) 150е С) 135” D) 210°
34.	3*4- 3*+3 > 84 tengsizlikni yeching.
A) (-oc; 0) B) (0: 1) C) (1; oo)
D) (0; 1)U(1: oo)
35.	Radiusi \/3 bo’igan doiraga tashqi chizilgan teng
yonli t rapetsiyaning asosidagi burchagi 60°.
Trapetsiyaning yuzini toping.
A) 3 B) C) J П) 10
36,	Konusniug о q kesimi teng lotnonli
uchburchakdan, silindrntki esa kvadratdan
iborat. Agar ulaming to4a sirtlari tongdosh
bo'lsa. hajmlarining nisbatini toping.
A) 1:3 B) 2 : 3 С) У2 : \/3 D) 1 : v/2
I
i
i
I
I
f
i
43
TEST 2006: Variant
122
Matematika
1
Matematika
1. Natural sonni 18 ga ba'lganda, bo4! inma 19 ga,
qcldiq 8 ga teng btrldi. BoTinuvchini toping.
A) 243 B) 263 C) 273 D) 350
2. Xaritada ikki shahar orasidagi masofa 4,5 sm ga
teng. Xaritadagi rnasshtab 1:4000000 bo'lsa.
shaharlar orasidagi haqiqiy masofa necba km
bo'ladi?
A) 270 B) 180 C) 900 D) 90
11.	Quyidagi tasdiqlarning qaysilari tolg*ri?
1)	tornonlari аЛ vac bo'lgan. uchburchakka ichki
chizilgan ayiananing radiusi г — -j^-- formula
bilan hisoblanadi:
2)	radiusi R ga, markaziy burchagi a ga teng
doiraviy sektoming yuzi S — ^ct formula bilan
hisoblanadi:
3)	tornonlari a va b ga. ular orasidagi
burchaklaridan biri o? ga teng bo:lgan
parallelogramrnning yuzi S = absina formula
bilan hisoblanadi.
A) 2:3 В) 1;2 C) 1;2:3 D) 1;3
3. x~ 4- £ — 12 kvadrat uchhadni chiziqli
ko;paytuvchilarga. ajrating.
A) (x - 3)(z 4- 4) B) {i4-3)(x-4)
C) (x-3)(4-z) D) (r+3)(4-z)
12.	Tekislikka og:ma va perpendikular tushirilgan.
15
Og’ma va tekislik orasidagi burchak arccos— ga,
og'maning tekislikdagi proyeksiyasi 30 ga teng.
Perpendikularning uzunligini toping.
A) 16 B) 30 C) 32 D) 23
4------------—5---£ 2 ni soddalashtiring.
1 - x 4- x“
А) P В) 0 C) 1-1 D) Д
X	X~
5. 12 • 1 X-x + - 1 ~ - tenglamani yeching.
\ 4	8/	2
A) ~ B) -1 C) -1| D) |
6. it va r2 x2 4* 2x — 12 = 0 tenglamaning ildizlari
ekanligi ma’lum. if 4 ning qiyrnatini toping.
A) 12 B) 10 C) 28 D) 11
8.	Quyidagi ketma-keUiklardan qaysilari geomet rik
progressiyani tashkil etmaydi?
1)	a„ = | 2“; 2) a„ = 3-2"”; 3) bn = (-1)" +1.
A) 1:2 В) 1;3 С) 1	0)3
9.	у = 5х — 1 funksiyaning grafigi koordinatalar
tekisligining qaysi choraklarida yotadi?
A) L II B) L Ш С) И, IV D) IV
10.	Qo'*sbni burchaklardan biri ikinchisidan besh
m&rta kichik bo4sa, shu bwrchakJaxdan kattasini
toping.
A) 130’ В) 150° С) 144е D) 140°
stn4cr 4- 2cos'2n • cos4tt ,, , , . .
13.	 ---r—:--------;------гт~ П! sodualashtimig.
1 — fnn‘2ot — cosia 4- smoa
A) 2s/n2a B) 2tg2a C) ctg2nr
D) 4f</2cr
14.	Agar m > 1. n > 2 va k > 36 bo isa.
2 : rn 4- 6 : n 4- 432 : k ifodaning eng katta
qiyrnatini toping.
A) 7 B) 8 C) 17 D) 19
15.	Agar 0 < к < in < n bo:lsa,
(n — m| — |n 4-	ni soddalashtiring.
A) 2k -2n В) -2n C) 2m-2fc
D) —2m
16.	t ning qanday qiyrnatida у = кх 4* 2
funksiyaning grafigi A(-4; 14) nuqtadan o‘tadi?
A) -1 B) -2 C) -3	D) -6
it /	4“ 1) 4" 6	’ I’t !
17-	| (x - 2)2 - 8 < r(i - 2) +10 wn«slzllklar
sistemasini yeching.
A) [-2; 7) B) (-11; 2] C) (2; 11)
D) (-7: -2]
18.	Agar f'{x) = sin3z + ——- bo’lsa. f(z)
X — 1
funksiyani toping.
A)	3cos3x 4- In\x — 11 4- C
B)	cosSx 4-	— 1| + C
C)	— icos3r 4- М|эг - 114- C
D)	—cos3i 4- M|z - 11 4- C
19.	a logo.28, b = /о$42, с = /о?о.»0»6,
d = 1<><7з0,8 va I = loga^i sonlardan qaysilari
musbat?
A) a} d va I B) b vac С) a, c va d
D) c va d
44
2
TEST 2006 - Variant
122
Matematika
20.	Teng yonli uchburchakning uchidagi burchagi
106°. Asosidagi burchaklarning btssektrisalari
kcsishishidan hosil bo'lgan o'tkir burchakni
toping.
z\) 43° B) 37° C) 47° D) 48°
21.	tkkita c/xshash ko'pburchak ytizlarining nisbati
9:4 ga teng. Kichik ko'pburchakning perimetri 8
sin. Katta ko^pburchakning perimetrini toping.
A) 8 B) 9 C) 12 D) 6
22.	Chiziqh odchovlarj 3: 4 va 2\/T4 sm bo'lgan
to’g’ri burchakli parallelepipedning diagonal!
necha sm?
A) 7 B) 11 C) 9 D) 10
23.	Konus asosi ning radiusi 12\/3 ga teng. yasovchisi
asos tekisligi bilan 30° П burchak tashkil etadi.
Asos markazidan yasovchigacha bo'lgan masofaui
toping.
A} 6x/3 В} 8 C) 3x/3 D) 5
Зжа
24.	Agar tga — 3 bo'lsa,-----•—-1^2----ning
5.s'ino lOcos (j
qiymati qanchaga teng bo'ladi?
18	m 3	ГЧ 15	ГЛ 8
} 29	} 5	5 32	> 15
25.	tgx 4-----= 2 tenglama (—Зтг; 3тг] kesmada
tgx
nechta ildizga eg a?
A) 5 В) 3 C) 6 D) 7
*26. Bog’dagi daraxtlarning 60% i teraklar. Qolgan
daraxtlarning 70% i chinorlar bodsa, boshqalari -
tollar. Bog‘dagi daraxtlarning necha foizini toBar
tashkil etadi?
A) 18 B) 12 C) 24 D) 28
30.	Gipotenuzasi 75 ga teng bodgan to'g'ri burchakli
uchburchakning katetlari nisbati 4:3 ga teng.
Gipotenuzaga tushirilgan balandlik uni qanday
kesmalarga ajratadi?
A) 50 va 25 B) 4$ va 27 C) 40 va 30
0) 60 va 15
31.	Koordinatalar boshidan 7x ^'24y~ 168 Wg’ri
chiziqqacha bo'lgan masofairi amqlang.
18	24	9
A) 5 В) 6— C) 6— D) 5 —
25	2 о	25
32,	Agar « vcktor 6 = 3t — 2j 4- £ vektorga kollmear
va а • b = 28 bodsa, a vektorning uzunligini
toping.
\/]4	г~	'Л
A)	4-	B) 14 С)	2у/й	D)	V
Z	Z
33.	sinx 4- cosx — I tenglamaning [-x: 2т] oraliqda
nechta ildizi bcr?
A) J В) 0 C) 3 D) 2
34.	lo(/j,7{3 “ 2z) > I tengsizlikning butuu yechimlari
nechta?
A) 3 B) 4 C) 1 D) 2
35.	Togri burchakli AC В uchburchaknmg katetlari
8 ga va 10 ga teng. Shu uchburchakning C to‘g‘ri
burchagi uchidan CC rnediana va CD bissektrisa
o'tkazildi. CDE uchburchakning yuzini toping.
A) 2z	B) 2^	С) з|	D) 2^
7	У	b	o
36.	Sharga balandligi asosining diametriga teng
bodgan konus ichki chizilgan. Agar konus
asosining yuzi *2,4 ga teng bo'lsa,shar sirtining
yuzini toping.
A) 6 В) 9т C) 15 D) 12,5
27. у = -zz-r- -----y=s=r— funksiyaning aniqianish
Vz — 6 — v9 — z
sohasiga tegishli barcha but-un sonlar yig‘indisini
toping.
A) 28 B) 15 C) 30 D) 32
*28.
f x - 3y - 5
Agar ( z + 2|y| = 3
toping
bo'lsa, x — 2y ning qiyrnatini
A) 2 В) 3 C) -1 D) 1
29. у ss 2z2 4- bx 4- c parabolaning uchi (—4; —5)
nuqtada joylashgan. Bu funksiya nollarining
cfrta arifmetigiiii toping-
A) -2 B) -4 C) 5 D) -3
45
TEST 2006 : Variant
123
Matematika
Matematika
1 1 scat 160 ridnut 5 sekund necha sekunddan
iborat?
A) 12205 B) 106005 C) 13205 D) 14205
2 3; y; 2J va 2.1 sonlarining о rta arifmetigi 2.3 ga
teng. у ni toping.
A) 2,6 B) 2,1 С) M .D) 2
3. ----------___ ni soddalashtiring.
1 — b 4- b~
А) Г 2	B) b~} (?) &4-I
12. Tekislikka tushirilgan og'nia va perpendikular
12	л
orasidagi burchak arcsin— ga teng. Og’maning
uzunligi 74 ga teng. Perpendikuiarning
uzunligini toping.
A) 70' B) 24 C) 54 D) 48
13. —:—r-------—r-----coso nJ soddalashl irmg.
sm 2a 4- cos 2с»
A) sin 2a B) cos 2a C) —2 sin 2a
D) —cos 2 a
14. 264 va 840 ning umurniy bo'luvchilari nechta?
A) 4 B) 9 C.) 8 D) 6
4.	(y2 - 1)- - (y2 - l)(t/* + y2 4-1)-+ у ni
soddalashtirgandan keyin nechta haddan iborat
bo'ladi?
A) 5	4 C) 3 D) 6
15.
Г1 Л3 л5 c?	kl
5 • 6 - — 4- -5- th hisoblang.
4	4	8	8
27	IQ	47	Q
А) В) 10-  С) 10- D) 11-
f>4	64	64	64
5.	(*+4-):4- = 6 teuglamani yeching.
У b
A) 215 B) 22j C) 20l D) 22|
V	У	У	<5
6.	x~ — 7z 4- q = 0 teiiglarnaning ildizlaridan biri
—19 ga teng. Uning ikkinchi ildizini toping.
A) 8 B) -26 C) -8 Q) 26
? 4- 3
7.	— < 0 tengsizlikni yeching.
A) [-3; 5) B) (-ce; -3] C) (5; oo)
0) (-3; 5]
8.	Quyidagi sonlardan qaysi biri 0.3(6) ga teng?
V Г» ® ё c> Й D> A
16.
Quyidagi parabolalardan qaysi biri OX o‘qiga
urinadi?
I) у — 2r2 — 5r 4- 8:2) у — — 2.x2 — 8x — 18;
3) у - x- - 3x - 8; 4) у = Az2 - 6x4-2-.
A) 2 B) I C) 4 D) 3
17. 23 — 2x > (x 4- 2)(x — 2) — 2(« — 1) tengsizlikni
yeching.
A) (0; 25] B) (-oo; 5] С) (-УН; v^T]
D) [-5; 5)
18' IM5JZI ni hisobUng-
A) 4/n(e4-l) B) 2Zn(e+l)
Q) ln(e 4- 2)
C)
9.	/og5/ne625 ni hisoblang.
A) Aye B) 5 C) 3
10.	Qo^shni burchaklardan. biri ikkinchisidan 52° ga
katta. Shu burchaklardan kattasini toping.
A) 118° В) 106й C) 114° ,Ь1 116й
11.	Quyidagi tasdiqlarning qaysilari to‘g‘ri?
1)	uchburchakka tashqi chizilgan aylanauing
radiusi R = ~(a, b, c— uchburchakning
tornonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi:
2)	tornoni a ga, burcbaklaridan biri о ga teng
rombning yuzi S’ = a^sinot formula bilan
hisoblanadi;
3)	o’xshasb figuralar yuzlarining nisbati ularning
mcs chiziqli o‘lchovlari kvadrailarining nisbatiga
teng;
A) 2:3 B) 1:2 C) 1;2;3 D) 1:3
19.	log i (x 4- 4) - log9[x 4- 4) > -- tengsizlikni
yeching.
A) (-4;-l) B) (0;I) C) (-2:1)
D) («)
20.	Teng yonli uchburchakning uchidagi burchagi 70°
ga teng. Yon tomonga o‘tkazilgan baiandlik va
asosi orasidagi burchakni t-oping.
А) 45й В) 35е С) 40е D) 306
21.	Rombning tornoni 6 ga, yuzi 18>/3 ga teng.
Rombning o^mas btirchagini toping.
А) 120е В) 135° С) 140° D) 150°
22.	.Teng tomonli uchburchakning tornonlari 3 m.
Uchburchak tekisligidan tashqarida uning
uchlaridan 2v/3 m masofada yotuvehi auqtadan
uchburchak tektsligigacha bo‘lgan masofani
toping.
A) x/3 B) 1 C) 3 D) 1,5
46
TEST 2006 : Variant
123
Matematika
23.	Konus asosining radiusi 2\/3 ga, yasovchisi va
asos tekisiigi orasidagi bnrchak 60° ga teng.
Konusning hajmini toping.
A)	B) 16% C) 8к/3 0) 24%
<5
co.sl2o — солЗа •	.. ,	. , - .
24.	---------------quyidagilardan qavsi binga
s-mlOo
teng?
Л) 2<w2a B} — 2sin’2fx	C) --stn2o
D) —2cos2a
25.	2ca$32x 4 sin22r — 1 t-englamani yeching.
. %	x	Itll	„
A)	±- 4 %n; - 4 —n G Z
6	4	2
B)	y(2n+l), (Ct± l)y, n>€Z
C)(-i)"j + »n, nez
о
2%
D) % 4 2%n; ±“ 4- 4%n. n € Z
3
26.	Korxonada mahsulot ishiab chiqarish birinchi yili
10% ga, ikkinchi yili 20% ga oshdi. Mahsulot
ishiab chiqarish ikki yil mobaynida necha foizga
origan?
A) 26 B) 25 C) 26,5 D) 32
27.	/(t) = [r — 2| 4 [x 4 81 funksiyaning qiymatlar
sohasini toping.
A) [3;oc) B) [10;oo) C) (6;oc)
D) (4;oc)
28.	|5 — x| — 2(2r — 5) bo'isa, 6 4 x ning qiymat!
nechaga teng?
A) 7 B) 8 О И О) 9
33.	cos4 r - sin4 r — Cl tenglainaning [0; 2т] kesrnada
nechta iidizi bor?
A) 1 В) 0 C) 4 D) 3
34.	(1,25)1-® > (0,64)-U+>/») tengsizlikning
yechirnlari orasida nechta tub son bor?
A) 7 B) 5 C) 12 D) 9
35.	Uchburchakning burcbaklari 45 va 60° ga, unga
tashqi chizilgan aylananing radiusi R. ga teng,
Uchburchakning yuzini aniqlang.
A> №(3 + >/3> з«2Л
A) ---------- В)	C) —-
R2 r -r
D) —(Л+>/3)
36.	Konusning o‘q kesimi muntazarn uchburchakdan.
silindrniki esa kvadratdan iborat. Agar konus
to!la sirtining silindr to4a sirtiga nisbati 1:3 kabi
bo'Isa. hajmlarining nisbatini toping.
A) 2 : 9 B) 1 : 9 C) 4 : 9 D) x/2 : 9
29.
jx2 - 9x 4- 8| = -8 4 9т - x2 tenglamaning
barcha natural yechirnlari yig;indisini toping.
A) 40 B) 36 C) 28 D) 25
30.	To'g'ri burchakli uchburchakning katetlari 30 va
40 ga teng. Katta katetning gipotenuzadagi
proyeksiyasini. toping.
A) 14,5 B) 32 C) 16; 5 D) 16
31.	Teng yonli trapetsiyaning kichik asosi 3 ga,,
perimetri 72 ga teng. Uning diagonal! o‘trnas
burchagini teng ikkiga bo’ladi. Trapetsiyaning
o’rta chirig'ini toping.
A) 8,5 B) 13 C) 7,5 D) 12
32.	3(m - 1; \/5;4) vektoming uzvnligi 5 dan katta
boMadigan m ning barcha qiymatlarini toping.
A) (-1;3) B) (-oo;-2) U (2; oo)
• С) (-ъс;-1)и(3;оо) D) (~2;2)
47
TEST 2006 : Variant
124
Aiatematika
Matematijka
1.	Uch sutka necha sckunddan iborat?
A) 259200 B) 258400 C) 258300
Ъ) 258200
2.	3; у; 2.1 va 2,1 son lari ning <rrta arifmetigi 2,55
ga teng. у ni toping-
A) 2,6 B> 2,1 C) 3 0) 2
3.	4-2\/П) • Va/Ss - 2л/Й ni hisoblang.
A) 6 B) 2 C) 4 D) 3
12.	Tekislikka og’nja va perpendikuiar tushirilgan
Og‘ma va tekislik orasidagi burchak arccoe — g »,
og:maning tekislikdagi proyeksiyasi 14 ga teng.
Perpendikularning uzimligini toping.
A) 14 $ 48 C) 28 D) 36
1 — cos4or 4- sin±'2a .	, . .
13.	-------------------m soddalashtinng.
A) 3ty22a В) 3dy*2a C) lg2tla
0) l,5cfp22o
4- x ni soddalashtiring.
A) x В) r - 1 C) x 4- 1 D) 2x 4-1
14.	5 < x < 109 tengsizlikni qanoatlantiruvchi, 12 ga
karra’i nechta natural son mavjud?
A) 10 B) 8 C) 9 D) 12
5. a ning qanday qiymatlarida -f 4j ~ — и - 4
tenglik o'rinli boiadi?
A) c € <p
D) a < —4
B)
a = — 4 Cy a < —4
6. x2 4- 13x 4- q = 0 tenglamaning ildizlaridan biri
—11 ga teng. Uning ikkinchi ildizini toping.
A) 2 JB) -24 C) —2 D) 24
15. a - 3b va 3. 3b — a va 4 sonlar proporsiyaning
a2 4- b2
ketma-ket hadlari bolsa. -----— kasrning
ab
qiymatini toping.
Al j B) | C) 9 D) у
16.
(z - 2)(4 - *)
funksiyaning aniqlanjsh
7. ------ < 0 tengsizlikni yeching.
r + u
A) [1; 3) B) (-3; 1) C) (-2; 1)
,D) (1; 3)
3. 0.6(3)ni oddly kasrga aylantiring.
А) А	В) —	C)	—	D)	—
1 15 f 30	'	90	}	90
9.	у = 5* — 5 funksiyaning grafigi koordinata
tekisligining qaysi choraklarida yotadi?
A) I III, IV В) I, Л' С) Ш, IV U? 7, II
10.	Ikki to’g'ri chiziqning kesishishidan hosil bo4gan
burchaklarning bin 40е ga teng. Qolgan
burchaklarni toping-
A) 110°, 110% ПО’ В) 150% 150% 30°
C) 140%. 140% 40° fD) 60% 60% 30°
11.	Quyidagi tasdiqlarning qaysilari tog!ri?
1)	uchburchakka tasbqi chizilgan aylananing
radiusi H = ^?(a,5te— uchburchakning
tomonlari, 5— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	tomonlari a,b va c bo Ogan uchburchakka ichki
chizilgan aylananing radiusi r = 7^7 formula
bilan hisoblanadi;
3)	diagonallari cfj va ga, ular orasidagi
burchagi ot ga teng ixtiyoriy qavariq
to‘rtburchakning yuzi S = |did2«ncr formula
bilan hisoblanadi.
AJ 2;3 B) 1;3 C) 1;2;3 D) 1;2
sohasini toping.
A) (~3;0)Up;4] B) f-3;0]U{2;4)
C) (—co; —3) U (О; 2) U (4; ос)
О) (-3;0J U [2; 4)
i «	.7^.0 о tengsizliklar sistemasi butun
I 2x 4~ 3 < 18 — Ззс
yechirnlanhing oJrla arifmet-igini toping.
A) 2,5 В) 3 О %5 D} 2
18. sin xdx ni hisoblang.
A) v	D> 5
Jfc*
19.
a = logi4r189 boTsa, ]og73 ni a orqali ifodalang
A)
D)
2a- 1
3— a
a — 2
1 -^a
1 — 2a
a - 2
a — 2
2a - 1
О
20.	Perimetri 28 bo‘Igan uchburchakning
bissektrisasi uni perimetrlari 16 va 24 bo'lgan
uchburchaklarga ajratadi. Berilgan
uchburchakning blssektrisasini toping.
A) 8 B) 5 C) 7 D) 6
21.	ABC uchburchakda AB = AC, BM-LAC,
BM 18 va MA = 24. ABC uchburchakning
yuzini toping.
Л) 258 Bl 254 C) 270 D) 262
48
2
TEST 2006 : Variant
124
Matematika
22.	Muntazam to'rtburchakli piramida asosining
tomoni 673 ga va apofemasi 6 ga teng. Piramida
hajmini toping.
A) 54 B) 10$ C) 162 D) 324
23.	Hadiusi 17 srn boJgan shar markasidan 8 sm
masofada tekislik bilan kesilgan. Kesirnning
yuzini (sm2) toping.
A) 225% B) 64% C) 54 D) 514%
24.	p = cetsSS0, q = c<?s42° va r ~ «тз222в sonlarni
kamayish tartibida yozing.
A] p > <? > r B) q> p> r
D) p > Г > q
C) q > Г > p
berilgan bo‘lsa. 2o va - vektorlar orasidagi
<V“
burchakni toping.
. x	3	.	2	5%	5
Al	-%	Bl	arccos-:	C)	-zr	t>)	arccos-^-
4	’	3	6	}	6
33. sin2 x — sm x + 1 <0 tengsizlik
ning qanday qiymMlarida o‘rinli?
. v r . ,	%, гЬя -1
—: %
6 J
%
6
6
7Г 07Г
6 6
X
25. 2cosr — = cost cos'lx 4- 2 tenglamani yeching.
A) J + irk.keZ B) - + ~-kiZ
2	4	2
С) %t, к e z D) к ez
26. Ikki sex 230 ta kir yuvish rnashinasi ishlab
chiqarishi kerak. Birinchi sex ishlab chiqargan
mahsulotning - qismi ikkinchi sex ishlab
4?
chiqargan mahsulotning 80% iga teng. Birinchi
sex qancha rnahsulot ishlab chiqargan?
A) 60 B) 50 C) 180 D) 80
34. f-yJ~
\V2 ~ 1
A)	В) /одб(Л+1)
С) Л+1 D) —
/2- 1
35. Doiraga ichki chizilgan rnuntazam
uchburchakning yuzi unga ichki chizilgan
kvadratning yuzidan 18,5 ga kam. Shu doiraga
ichki chizilgan muntazam oitiburchakning yuzini
loping.
1) n| soddalashtiring.
C) 27 + 2473
27. Agar B(2;7) nuqta у ~ kx2 4- 8т + m
parabolaning uchi bo‘lsa. k va ?n King qiymatini
toping.
A) k — 2, m = — 1 EH k — 1. гл = —9
C) k — —2. m — — 1 k — —1, m ~ —16
D) 13.5+1273
36. Asosi a ga, asosidagi burchagi a ga teng bo’Igan
t-eagyonli uchburchaktii yon tomoni atrofida
aylantirishdan hosil boclgan jisrnning hajrnini
toping,
3 - 2
m sin a
6cos&
та31 got
A)
3 .
TO. fyinot
3
rn COSOt
6stn2a
D)
28.	2 — 3]x — 4j = —4 tenglamaning ildizlari
yig'indisim toping.
A) 7 B) 8 C) 10 D) 9
29.	(x2 + 6z + 4)(x2 + 6r + 6) = 120 tenglamaning
haqiqiy ildiziari yig'indisim toping.
A) 5 B) -12	-5 D) -6
30.	Tolg'ri burchakb uchburchakning gipotenuzasi 25
srn, katetlaridan birining gipotenuzadagi
proyeksiyasi 1,96 sm. Ushbu uchburchakka ichki
chizilgan aylananing radiusi necha sm?
A) 1 B) 3 C) 2 O) 1,5
31.	Af (r, j/) nuqtaning koordinatlari yiglindisi 6 ga
teng. Bu nuqta va koordinat boshi orasidagi eng
qisqa masofa qanchaga teng Ь<У1ад&?
A) 273 B) 375 C) 4,572 D) l,5v^

49
TEST 2006 : Variant-
125
Mat-ernatika
1
Matemat, ika
1. Agar kainayuvchmi 30 t-a va aynluvchitii 12 ta
kamaytirilsa, aytrma qanday o’zgaradi?
A) 24 ta ortadi	B) 18 fa kainayadi
C) 12 ta kamayadi D) 12 ta ortadi
1.6 0,7-13.................
' -d n"^ ninS qiymatmi toping,
1.4- /.2-0,3
A) | B) 1 C) ± D) |
3. Uchburchakning birinchi tomoni x{x > 10) sm,
ikkinchi tomoni undan 6 sm qisqa, vchinchi
tomoni esa birinchisidan 4 sm uzun. Shu
uchburchakning perimetrini (sin) toping.
A) 3x4-2 В) 3r-2 С) 3x4 3
D) 3r-3
II.	Quyidagi tasdiqlarning qaysilari noto'g’ri?
1)	tornonlari e.i vac bo:lgan uchburchakka ichki
cbizilgan aylananing radiusi r ~ formula
bilan hisoblanadi;
2)	radiusi R. ga, markaziy burchagi q ga teng
doiraviy sektorning yuzi 5 — formula bilan
hisoblanadi;
3)	diagonaUari di va d-> ga. ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
tolrtburchakning yuzi S = did^sina formula
bilan Hsoblanadi.
A) 2;3 B) 1:2 C) 1;2;3 D) l;3
12.	Tekislikka tushirilgan og’ma va perpendikular
orasidagi burchak a resin — ga teng. Og'maning
61
uzunligi 122 ga teng. Perpendikularnmg
uzutiligini toping.
A) 22 B) 120 C) 24 D) 90
4.	Agar P - ~x - -y- (x + 2y) va
Q — -r 4-	— (x 4- 5v) bo’lsa, P — Q ni toping.
A) 4V B) 2y C) ~y D) -4S
1 I	у
5.	12- ; 2- = 16- : - tenglamaniyeching.
X X	v X
А) б| В) б!	С) б| D) Д
3	О	О	О
6,	х2 — Их 4- <? = 0 tenglamaning ildiziaridan biri
— 13 ga teng Uning ikkinchi ildizini toping.
A) 2 B) -24 C) -2 D) 24
4
13.		--------—- ni soddalashtiring.
ctg2o-tg2o
AJ sin4o B) 2tg4o C) cos4o D) tg4o
14.	O'lchamlari 22m x 15m bo’lgan zalni tomoni 20
sm bo’lgan kvadrat shaklidagi plitkaiardan
nechtasi bilan qoplash mumkin?
A) 18000 B) 1650 C) 8250 D) 9000
15.	Agar 0 < $ < p < k bo'Isa,
jp + + |k — q\ — |fc — pj ni soddalashtiring.
A) 2p4-2g -2k В) 2p C) 2p + 2fc
D) 2g
7.	16x2 — &r 4- 3 > 0 tengsizlikni yeching.
A) [0:oc) B) 0 C) (—oo;0)
D) (—oo; oc)
funksiyaning eng kichik qiyrnatini toping.
A) 5 B) 6 C) 10 D) 4
8.	Geometrik progressiva uchun quyidagi
formulalardan qaysilari noto'g'ri?
1) 6n =	2) 4J = br,-t b„+2;
.. „	Ml-»")
A) 1 В) I; 3 C) 3 D) 2
9.	t/ zz Tsx — 3 funksiya grafigining Oy okqi bilan
kesishish nuqtasi ordinatasini toping.
A) -1 B) -2 C) 1 D) 0
(x 4- 3)(x - I)	. , .	,.
1 /.----< 0 tengsizlikni yeebmg.
A) (-2; 1) B) (-oc; -3)U[-2; 1]
C) (-oo; -3]U(-2; 1] D) (-oo; -3]
18. I cos 2r dx ni hisoblang.
A) ~~ B) 1 C) D)
10.	Ikkita tefg^ri chiziqning kesishishidan hosil
bo‘lgan burchaklardan uchtasining yig’indisi 275°
ga teng. Shu burchaklardan kichigini toping.
A) 45° В) 60е C) 85” D) 70°
50
19. a — bgys 135 bo’lsa, loggS ni a orqali ifodalang.
A) -.31 A) a -2 ,	1 - 2a	B) —• a — i.	, а — 2 C> 2a A
D) G. — 3	4	
2
TEST 2006 : Variant
125
Matematika
20.	Uchburchak tomoniarin'mg uzunlikiari m\ n va k
in1 = n3 4- k2 + У3п£ tenghkni qanoatlantiradi.
Uzunligi m ga teng tomon qarshisidagi burchakni
toping.
А) 150е В) 45° С) 90° D) 135°
21.	Tornonlari 72 va 32 m bo'lgan to‘g4ri
to rtburchakka tengdosh kvadratning tomonini
toping.
A) 28 B) 36 C) 48 D) 24
22.	To'g^i parallelepiped asosining tornonlari 9 va 12
ga, nlar orasidagi burchak 120° ga, yon qirrasi
6 УЗ ga teng. Parallelepipedning kichik diagonal
uzunligini toping.
A) 18 B) 5 C) 21 D)“ 15
23.	Kubning har bir yog'ini yuzi *27 marta orttirilsa.
uning hajrni necha marta ortadi?
A) 54 УЗ В) 27 УЗ С) 27 D) 81 УЗ
30.	To’g'i i burchakii uchburchakning gipotemuasi 25
sm, katetlaridan binning gipotenuzadagi
proyeksiyasi 23.04 sm. Ushbu uchburchakka ichki
chizilgan aylananing radiusi necha sm?
A) 2,5 В) 3 C) 1,5 D) 2
31.	Parallelogramin qcrshni tomoolarining yig4ndisl
10 ga, ayirmasi esa.8 ga teng. Shu
parallelogramm diagonallari kvadratlarining
yig:indismi toping.
A) 144 B) 164 C) 121 D) 136
32.	Agar a(—6;3;3) va 6(3,—3,0) bo lsa, 2d va -6
vektorlar orasidagi burchakni toping.
А) 60е В) 150е С) 135° D) 120°
33	sinx > cosx tengsizlikni yeching.
A) (— Ч-2тп: ^тг+З'Я'л), n C Z
Д	4
24. t = cos32°, q — stn 112° va k ~ tglas6 sonlarni
o‘sish tartibida joylashtiring.
A) к < t < q B) q < t < k C) f < q < k
D) i < k < g
25. c&.fx — sItiSxcosx — 0 ten glam ani yeching.
_ . 7Г	л , Г	4?rk ,
A j — 4- 2тгк; —j k
i	о u
jt , т 2згк ,
В) т + T d-------к С И
Z	DO
C)	£ +	+ H-, keZ
£	о
D)	^k-. ~ + 2iri, k 6 Z
*26. Yig'indisi 38 va 62 sonlarining orta arifmetigiga
teng bo’lishi uchun 62 ning 60%i olinsa, 38 ning
necha foizini olish kerak?
7	1?	12
A) 17-^ B) 33- C) 33- D) 32
it?	1 У	1 i
27. Agar .4(1; —3) nuqta у — x2 4- px 4- q
parabolaning uchi bolsa, p va q ning qiyrnatini
toping.
A)	p = 4,g = 2 B) p = 2. ?=-l
C) p=l,Q--2 D) p=g = -2
34. у — log2 bgi/2 У4х — r2 — 2 funksiyaning
aniqlanish sohasini toping.
А) (2-У2;2 + У2)
В)	(2-У2:.1)и(3;2 + У2)
C)	(-oo;l)U(3;cc) О) (1;3)
35 ABC uchburchakning yuzi 12 ga teng. Uning В
uchidan BD = 3 mediana tushirilgan. Agar
LABD = 90й bodsa. AC toinonning uzunligini
toping.
А) У73 В) 2У73 C) 10 D) 8
36. Kesik konusning yon sirti 10?r ga. tola sirti 18 nr
ga teng. Konusning toia sirti unga ichki
chizilgan shar sirtidan qanchaga ortiq?
A) 6% В) 14т C) 10j D) St
28. m va n ning qanday qiymatlarida
2xm — 3ny = 12 va 3xm 4- '2ny 44 to‘g‘ri
chiziqlar (2; 1) nuqtada kesishadi?
A) m~8.n = 6 B) m — 6, n = 4
C) rn = 12,n = 2 D) m = 4,n—10
29. >n ning qanday qiymatlari<la
(m — l)r24-2(m —7)r-f-2nid-2 kvadrat ucbhadni
torla kvadrat shaklida tasvirlash murnkin?
A) -17 B) -17; 3 C) 3 D) 2
51
TEST 2006 : Variant
126
Matematika
Matematika
1.	Ikki shahar orasidagi rnasofa 400 km bo'lsa,
1:5000000 masshtabli xaritada bu masofa necha
mm ga teng boladi?
A) 80 B) 100 C) 40 D) 20
2.	3.3; x va —2.1 sonlarining o'*rta arifmetigi 0,6 ga
teng. x ni toping.
A) -0,6 &) 0,6 C) 2 0) 0.8
у — X~ X +-У
3.	——------:	m soddalashtiring.
.	£ — t/
A) Ю + у)
C) i D) 1-i
У	V
4.	2r(x — 1) — (2z 4- l)(r — 2) ko’phadni standart
shaklga keltiring.
А) 2x--3r B) 4z?- 1 C) -x+ I
D) r + 2
5.
U	1
Agar (x - 5)(-x - 4) — 0 bo‘lsa, ~x - 4 qanday
5	5
qiymatlar qabul qiladi?
A) faqat —3	B) faqat’O C) 0 yoki 3 ‘
D) 0 yoki -3
6	3 — x = — tenglamaning nechta haqiqiy iidizi
bor?
A) 2 B) 1 C) iidizi yo‘q D) 3
7.	Agar a > 6 va a6 / 0 bollsa. quyidagi
tengsizliklardan qaysi biri bar doim o‘rinli?
A) a2 > b2 B) 1 > | C) 2a > 3a - b
a b
D) 3a < 4a -b
8.	0,4(5) soni quyidagi sonlardan qaysi biriga teng?
A> П в> Й c> g D> S
9.	(\/3)u<is3 ni hisoblang.
A) 3 B) /13 C) 6
D) 13
10.	Ikki qo4shni burchakning ayirmasi 28° ga teng.
Shu burchaklardan kichigini toping.
A) 78’ В) 72® C) 76° D) 82°
11.	Quyidagi tasdiqlaming qaysilari noto'gW
1)	tomcnlari a, b va c bo4lgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
2)	tornonlari a va b ga, ular orasidagi
burchakiaridan biri a ga teng bcrlgan
parallelogramnming yuzi S = -absina formula
bilan hisoblanadi;
3} o'xshash figuralar yuzlarining nisbati ularning
mos chiziqli olchovl arming nisbatiga teng.
A) 2;3 B) 1;2 C) 1:2;3 D) 1;3
12.	Tekislikka og’ma va perpendikuiar tushirilgan.
Og'maiiing tekislikdagi proyekslyasi 63 ga,
perpendikularning uzurdigi 16 ga teng. Og’ma va
perpendikuiar orasidagi burchakni toping.
a\ 32	- *6	63
A) arccos— B) arcsm —	C) arctg —
65	65	65 •
- 63
1J) arcs in —
65
13.	tg(— + o) = bo:lsa, ctga ning qiymatini
toping.
A) 4 B) | C) |	D) |
2	5	t
14.	x raqaniining qanday eng kichik qiymatida
(G42 + 2x5) son 3 ga qoldiqsiz bo‘Iinadi?
A) 0 B’) 5 C) 7 D) 2
15.	MLehnat unumdorligi bir xil bo'lgan 8 kishi
ma lum hajmdagi ishni 15 kuuda tugatishdi. 12
kishi o^hancha mehnat unumdorligi bilan
ishlasa, o‘sha hajmdagi ishni necha kunda
tugatishi mumkin?
•A) 8 B) 9 C) 12 D) 10
16.	(2a — l)(2a 4-1) + ЗЦ36— 4a) 4-1 ning eng kichik
qiymatini toping
A) 0 B) -1 C) 1 D) -2
17.	2 - 3z > 2 - (x - l)(r + 1} — r(x + 3) tengsizlikni
yeching.
A) (-2; 2) B) (-oo; 2) C) (1; oo)
D) (0; 4)
*
' (Id- iyx)dx ni hisoblang.
n
A) 1 В) УЗ C) -1 D)
19.	Qaysi javobda manhy son ko’rsatilgan?
Л.) logj^/S В) 1одЛ C) /052I.2
, “1
D) /o5i-y==
’У45
20.	Teng yonli uchburchakning uchidagi tashqi
burchagi o‘sha uchdagi ichki burchagidan 5
marta katta.-Uchburchakning asosidagi tashqi
burchagini toping.
A) 105° B) 100° C) 108® D) 95°
21.	Yuzi 156 sm 2 , balandliklari 4 sm va 12 sm
bo'lgaa paraUebgrammning perimetrini toping.
A) 73 B) 104 C) 96 D) 108
22.	Piramidaning asosi to^ri burchakli uchburchak
bolib, uning gipotenuzasi uzunligi 20 ga teng.
Piramidaning barcha yon qirralari 26 ga teng
bo4lsa, uning baiandligini toping.
A) 12 8) 24 C) 22 D) 20
52
2
TEST 2006 : Variant
126
Matematika
23.	Balandligi 12 ga, asosining radiusi 6 ga teng
bodgan konusga yasovchisi 4 ga teng bodgan
silindr ichki chizilgan. Sihndr asosining radiusini
topingl
A) 4 В) 3 C) 2 D) 2,6
24.	rn = eas65°. n = «in45°,4 —' sin50Q va
p — cos80° sonlarni o’sish tartibida yozing.
A) m < n < p < q	B) p < ?n < n < q
С) p < 7П < q < n	D) q < n < p < m
25.	2 sin 2г < ctg — tengsizlikni yeching.
. . r 71Г	7Г ,
A)	L“-q- + 4xn; -- 4- 4T7ij. 71 € 7-
B)	[~ + 2ffn: ~ 4- 2irn]. n G 7
о	6
r	,	*	1
Cl Г7л + 7л + %nj-- n £ Z
А X»	lx.
E>) [io + TiTf, |t -t 777?]. П £ 2
it	12
26.	Massasi 54 kg bo’lgan mis va rux qotishmas'ming
tarkibida 45% mis bor. Qotishma tarkibida 60%
mis bo’iishi uchun unga у ana necha kg mis
qo’shish. kerak?
A) 24 B) 13.5 C) 25 D) 20/25
32. b(3: --6; 6) vektorga kollinear va ab = 40.5
tenglikni qanoatlantiruvchi a vektorni toping.
A) a(3;6:9) B) «("-"3:3) С) o(3:^6;6)
2
D)
| 33. у = ^/1 -j-Togj^TsHir fanksiya x (x G (0;2$rj)
ning qanday qiyinatjarida arxiqlangan?
A)	B) [i;^] С) (0;г)
D) (0:£
34.	(x _ 2yog3(r2-5r+5) <	2^J*—3)
tengsizlik x ning qanday giyniatlarida o'rinli?
A) (2;4) B) (3:^) C) (-oo; 2) U (4:oc)
D) (Ц^;4)
35.	To:g:ri burchakii uchburchakning uzunligi 14 va
18 ga teng katetlariga t ushirilgan medianalari uni
uchta uchburchakka va tc/rtburchakka ajratadi.
To:rfburchakning yuzini toping.
A) 64 B) 63 C) 42 D) 48
36.	Sharga balandligi asosining diarnetriga teng
bodgan konus ichki chizilgan. Agar konus
asosining yuzi 2,4 ga teng bodsa, shar sirtining
yuzini toping.
A) 6 В) C) 15 D) 12,5
27 у —----------------funksiyaning aniqlanish
x *b 4
sohasuii toping.
A) (—4; 4) B) (-4; I] C) (-4: 1)
D) (-4; 2]
28.	(k ~ 5)*i/ = fc- - 36 tenglamaning ildizlari manfiy
bo’ladigan k ning barcha butun musbat
q'tymatlari yigdndisini toping.
A) 13 B) 10 C) 8 D) 11
29.	Agar x2 — T, 4- q = 0 tenglamaning Xj va x-j
ildizlari =• 37 shartni qanoat-lantirsa, q
ning qiymatini toping
A) -II B) -5 C) -19 D) -12
30.	Tornonlari 13; 14 va 15 sm bo’lgan
uchburchakning eng katta balandligi necha sm?
A) В) C) D) 13
31,	Radiusi 3 ga teng bo’lgan doiraga tashqi
chizilgan teng yonli trapetsiyaning perimetri 40
ga teng. Trapetsiyaning kichik asosini toping.
A) 4 B) 3 C) 2 D) 5
53
TEST 2006 : Variant
127
Maternatika.
1
Maternal ika
I.	Agar karnayuvchini 26 ta va aynluvchiui 12 ta
orttirilsa. ayirma qanday cCzgaradi?
Д) 14 ta ortadi B) 4 ta kainayadi
C) 4 ta vrtaxii D) 28 ta kamayadi
2.	8 soniga teskari sonni toping.
A) 0.125 6) “0:8 C) 1.25 D) Ц
4
3.	x2 - x — 6 kvadrat uchhadni chiziqii
ко' paytuvchilarga. a j rati ng.
A) (x + 3)(x-2) B) (x-3)(x + 2)
C) (x + 3)(2 - x) D) (x + 2)(3 - x)
4-	(/ - y2 + iXy2 + 1) - (у - 1 )(y + 2) -r И -f у3 ui
soddalashtirgahdan keyin hosil bo‘lga.n
Wphadning nechta hadi bo'ladi?
A) 4 В) 3 С) о £>) 6
22	22	'	3	3
A) I9_ B) 20_. C) 18- D) 191
g
6. x + 6 ~ — tenglamaning nechta haqiqiy ildizi
x
bor?
A) 2 8) 1 C) ildizi yo‘q D) 3
_ x'~ ~ 4x4-5	.
i. ---?—-----> 0 tcngsizhkni yeching.
x — 3	~
A) (~oc; 3) В) [3; oo) C) (3; oo)
D) (-oo; 3]
8.	Quyidagi ket-ma-ketliklardan qaysilari geometrik
progressivani t-ashkil etmaydi?
l)a„ =2хл,(х#0):
2)	c„ = axn, (gx £ 0);
3)	br. = ф"  s»n60° +1.
A) 3 B) 1;3	> 2 D) 1
9.	tog x2 + ^^ 3 ni hisoblang-
A) -1	8) -3 C) 1 D) —0.5
10.	Ikki to'g'ri chiziqning kesishishidan hosil boJIgan
burcbaklarning kattaliklari nisbati 7:5 ga teng.
Shu burchaklardan kichigini toping.
А) 49е В) 63° С) <5° D) 54*
II.	Quyidagi tasdiqlarning qaysilari to4g:ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R — ~^(a. b.r— uchburchakning
tornonlari, S’— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi u ga teng.
doiraviy sektoruing yuzi S	formula bilan
hisoblanadi;
3)	tomonlari a va b ga. ular orasidagi
burchaklaridan biri a ga teng nodgan
parallelogrammning yuzi S — -absinv formula
bilan hisoblanadi.
A) 2:3 B) 1:3 C) 1:2:3 D) 1:2
12.	Tekislikka tushirilgan og maning uzunligi 75 ga;
uning tekislikdagi proyeksiyasi esa 60 ga teng.
Og'ma va tekislik orasidagi burchakni toping.
.3	3	3
A)	arcsin- B) arccos—- C) arcstn-
t>	10	4
4
D)	flresm-
з
13.	tg(— — <r)	4 boclsa, t.go ning qiymatini toping.
A) -3 B) | C) D) |
1	1	,
14.	--	va	—	kasr	umumiy maxrajining barcha
45	Ju
natural boUuvchilari soni nechta?
Д) 7 B) 11 C) 13 D) 12
it a	38	47	, ,T 3	4
15.	Agar - + - = a bo’lsa, - + -
quyidagilardan qaysi biriga teng?
A) 4 - a B) 3 - a C) 3 - D) 2 - a
16.	у = 2r2 + 4z — 8 funksiyaning grafigi qaysi
choraklarda joylashgan?
A) L II, IIL TV В) H, HL IV C) L IIT Ш
t)} L HL fV
— 3z2 4- 4z — 5
17.	----® tengsizlikni yeching.
A) (—2,5; 2) B) (-00;-1,5)
C.) (—2,5;-1,5) D) (—oo;-2.5)
18.	JI sinSxdx ni hisoblang.
A) B) 1 C) -1 D) 1
19.	2 • 3e<,,r = 15 - 9ee*x tenglamani yeching.
A) 2irn,n£Z B) m.n^.Z
С) ±^-+2тгп,пб2 Dj) — +2niji g Z
О	W
54
2
TEST 2006 : Variant
127
Matemaf/ka
20.	Balandligi 8 ga teng boUgan, teng yonli
uchburchakning asosi yon tomonidan 2 gaortiq.
Uchburchakning asosi ni toping.
A) 15 jB> 16 C) 12 D) 18
21.	Kat-etlarining nisbati 2:3 kabi bo'lgan to^ri
burchakli uchburchakning gipotenuzasi -/182 ga
teng Uchburchakning yuzini toping.
A) 24 B) 42 C) 36 D) 39
22.	Muntazam to'rtburchakii piramidaning
balandligi 18 ga, asosining tomoni 15 ga teng.
Piramidaning apofemasini hisoblang.
A) 13 B) 22.5 C) 19.5 D) 21
30.	To'g'ri burchakli uchburchakning katetlari 48 va
14 ga teng. Kichik katetning gipotenuzadagi
proyeksiyasini toping.
A? 10 В) б| C) D) 4^
i	x~-3	/3
31.	CVt-mas burchagi 135° bo'lgan paralleiogrammga
ichki chizilgan doiraning yuzi 1 Gtt ga teng.
Parallelogrammning perimetrini toping.
A) 32x/? B) 24 C) 24\/2 D) 32
32.	rn ning qanday qiymatlarida a(m - 1: m - 2:2)
vektorning uzunligi 3 dan kichik bo'iadi?
A) -2 < rn< 1	B) 0 < rn < 3
C) -1 < m < 2	0) — 1 < m < 3
23.
Konus hajmining л ga nisbati 21 - ga teng bo'lib,
uning yasovchisi asos tekisligi bilan 45е ft
burchak tashkil qiladi. Konusuing balandiigini
toping.
A) 7 B) 3 <C) 4 D) 6
.sin 36е	cg$36°
sin 12° cos!2°
A) 3 B) 2 C)	D) VTS-T
3x3. у ~ y/l - logj^sinz funksiya x (x € [0; 2-я-])
ning qanday qiymatlarida amqlangan?
.. tt, .5r , _a ,ir 5?г- {5тг
A) fO;-6-]U(-;Tj ,8) [gJ-g-l C) fy^)
D) (0:^1
О
34. (x - 2)lcg^-^’-Si+^ < (x -
tengsizlik x ning qanday qiymallarida o*rinh?
A) (2; 4) 8) (-oe;2)U(4:oo) C) (4;oc‘)
25. 4sin22x = 1 tenglamani yeching.
А)	+ *n. n € Z
Л. , 7Г тгп
е)±и + —, nez
С) (-1) -г + -г-, п €. Z
и
. .X тп „
D J:— + -r~, п Е 2
26. Tekis harakalda muayyan masofani bosib oftish
uchun ketadigan vaqtni 30% ga kamaytirish
uebufi tezlikni necha foiz orttirish kerak?
A) 20 B) 42® С) 30 О) Зз|
35. Gipotenuzasi c ga va o‘tkir burchaklari
siuuslarining yig'indisi q ga teng bodgan to gM
burchakli uchburchakning yuzini toping.
A) 1«V-D B) p(?2-l)
4	4
C.)^r(92 + 1) D) j<№ + !)
36. Konusning o‘q kesimi teng temonli
uchburchakdan, silindrniki esa kvadratdan
iborat. Agar ularning to’la sirtlari tengdosh
bodsa, hajndarining nisbatini toping.
A) I : 3 B) 2 :3 C) V2 : \/2 D) 1 : 72
27. у — (k - l)x2 4- '2kr - va у = kx2 + кт - 4,5
funksiyalarning grafiklari kesishmaydigan к ning
barcha butun qiymatlari yig;indisini toping.
A) 9 В) 0 C) 12 D) -2
28.. z +
55
= — tenglamaning natural sonlardagi
-
yechimida у nimaga teng?
A) 4 Я) 3 C) 2 D) 1
29. -----— — — tenglaina m ning nechta natural
m — 10 t
qiymatida ildizga ega emas?
A) 7 B) 5 C) 8 D) 28
55
TEST 2006 : Variant
128
Matem'atika
1
Matematika
l* 18-13-15-13+ 21-17-18-17+ 17-15- 15 14
ni hisoblang.
A) 135 B) 125 C) 180 D) 205
2.	Xaritada ikki shahar orasidagi masofa 3,5 sm ga
teng. Xaritadagi masshtab 1.-2000000 bodsa,
shaharlar orasidagi haqiqiy masofa necha km
bo’ladi?
A) 7 B) 140 C) 700 D) 70
3.	Uchburchakning birinchi tomoni i (z > 12) sin.
ikkincbi tomoni undan 7 sm qisqa, uchinchj
tomoni esa birinchisidan 5 sm uzun. Shu
uchburchakning perimetrini (sm) toping.
A) 3x — 1 В) 3z + 2 C) 3x + l
D) 3x-2
4.	2a26 + 3a — 4a62 — 66 ko'pbadni
ko‘paytuvchilarga ajrating.
A) (a - 2b)('2ab + 3) -0? (2a6 - 3)(a - 56)
C) (2a2 + 6)(6 - 5a) D) (3 + 2a6)(a - 56)
11.	Quyidagi tasdiqlarning qaysilari to'g+i?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R— ~g-(a, b.,!?- uchburchakning
tornonlari, 5— uchburchakning yuzi) formula
bilan hisoblanadi:
2)	tornonlari a va 6 ga, ular orasidagi burchagi a
ga teng bo4gan uchburchakning yuzi
S — -absina formula bilan hisoblanadi:
3)	o xshash figuralar yuzlarining nisbati ularnintg
jnos chiziqli o'lchovlarining nisbatiga teng.
A) 2:3 В) 1;2 С) 1:2;3 П} l;3
12.	Текislikka tushirilgan og:maning uzunligi 125 ga,
uning tekislikdagi proyeksiyasi esa 35 ga t-eng.
Og'ma va tekislik orasidagi burchakni toping.
A. 12	...	. 24	_	. 7
A) arccos—
25
7
D) arc sin —
25
В) arcsin— С) arctg~
13.
— - bo Isa. ct-ga ning qiyrnatini
toping.
A) 9 B) C) —4 D) 1
4	9
5.
k pararnetrning qanday qiymatlarida
3x —	tenglamalar sistemasi yechimga
ega emas?
A) 2 B) 9 C) 6 D) 3
6.	xi va r2 x2 — 17z + 6 = 0 tenglamaning ildizlari
boclsa. Xizl + &ing qiymat-ini toping.
A) -102 B) -32 C) 102 D) 77
7.	4 > \/x + 1 tengsizlikni yeching.
A) [0: 15] B) [-1: 15) C)
D) (0; 15)
(-1; 15]
8.	Quyidagi ketma-ketliklardan qaysilari gcometrik
progressiyani tashkil etmaydi?
1)	= | -2"; 2) a„ = 3 • 2->; 3) i>„ = (-1)" +1.
A) 1;2 B) 1;3 C) 1 D) 3
9.	Zo^-dplOO* ni hisoblang.
A) 4 B) 1 C) 2 D) 3
10.	Burchakning bissektrisasi uning tomoni bilan 20°
H burchak tashkil etsa, burchakning o{zim
toping.
А) 30е В) 45е С) 40° D) 60е
14.	Agar avtomobil tekis harakatda 3 soat-da 324 km
ni bosib o:tsa. 10 sekuudda necha metr masofani
bosib o+adi?
A) 300 B) 200 C) 100 D) 600
15.	12 va 312 sonlarning umumiy bo'luvchiiari ’
nechta?
A) 4 B) 2 C) 6 D) 3
- _ 2z з
16.	у = \/16 -	----- funksivaniag aniqlanish
x +1
sohasirii toping.
A) (-1; 4] B) [-4;	4}
C) [-4; «Г 0) [-4: -1)
17.	2 > -z----tengsizlikni yeching.
4 — x
A) (-oo;-4)U(0;4) B) (-oc;0)U(4;oc)
C) 4 D) t-4;4]
18.	J *sin3z cos3xdx ni bisoblang,
о
A) | 8) 1 C) J 0)1
19.	й =	h — togva с = sonlarni
o'sish tartibida joylashtiring.
A) c < 6 < a B) c<a<5 C) b < a < c
D) a <b < c
20.	Aylananing 13\/2 ga teng vatari 90° li yoyni
tortib turadi. Aylananing uzunligini toping.
A) 20r B) 24ir C) 26r D) 22r
56
2
Ma.tematika
TEST 2006 : Variant
128
21-	ДАВС ning AB tomoni MNJJAC to'g'ri chiziq
yordamida BM—2 va AM—4 bo‘lgan kesrnaiarga
ajratildi. Agar AMBN rung yuzi 18 ga t-eng
bo'lsa, ДАВС ning yuzi qanchaga t-eng bo'ladi?
A} 96 B) 162 C) 144 D) 108
22.	To'rtburchakli muntazam prizma asosining yuzi
169 sm2, balandligi x/191 sm. Shu prizma
diagonalini toping.
A} 21 B) 23 C) 27 D) 22
23.	Tornonlari 3 va 4 ga teng bo‘lgan to*g4ri
to*rt burchak o‘zining katta tornoni at rofida
ayianadi. Hosil bo'lgan jismnmg to'la sirtini
toping.
Л) 48% В) 42т C) 36% D) 24%
*24. Agar tgc* + cigot — 10 bo’lsa. sin'ia ni hisobtang.
A) |	B) 1 C) 1	D) 1
4	2 Э 3
25. co.sOz 4- cos4x — 0 tenglamani yeching.
A) (-1)* • ™	~~ 4- 2%fc, k e Z
10 э 2
10 + 5*’
V	1Г	ir
C) ±— +	-- + keZ
10	5	2
D) + ~k;	+ 2т*, t E Z
lu b Z
26- Korxonada mabsulot- ishlab chiqarish birinchi yili
*20% ga, ikkincbi yili 15% ga ortdi. Mahsulot
ishlab chiqarish ikki yil mobaynida uecha foizga
origan?
A) 28 B) 38 C) 3*2 D) 35
31.
Rombning o4mas burchagi 1’20° ga, katta
diagonal! —ga tong. Rombning yuzini
v 8
hisobiang.
A) 0.6d2\/5 В) “С^ч/з C) -d2 D) —
4	2	In
32.	Agar s(l: -1; 3) va 6(4: 3; 0) bo'*lsa, о ning
qanday qiyrnatida 4a 4- ob vektor b — a vektorga
perpendikular bo'ladi?
Л) 2,1 B) 1 С) I D)
33.	\/&д'2х - 1 > 0 tengsizlikni yeching.
r 1Г x
l12’ 4
4
A)
D) + тп; A 4- xnj.n € 2
b 2

34.	4- 25^T = 10 tenglamani yeching.
A) 1 B) 10 C) 5 D) /10
35.	Radiusi R ga teng bo'lgan doiraning rnarkazidan
bir tomonda ikkita bir-biriga parallel vatar
oRkazildi. Bu vatariardan biri Г20’ li. ikkinchisi
60° H yoyni tortib turadi. Parallel vatarlar
crasida joylashgan kesirnning yuzini toping.
mR- ^R2 3tR2	тг/?"
T B) T c) ~8~	~
36.	Teng tomonli silmdrning va teng tomonli
konusning balandligi o'zaro t-eng. Ularning to‘la
sirtlari nisbatini toping.
A) 2:8 B) 5:3 Cl 3.2 D) 3*4
27. у = ч/------т;— funksivaning aniqlanish
у 4 — x-
sohasini toping.
A) (-2;2)U{3} B) (-2:2)
C) (—oc;—2)U{3}	D) (-2;3)
28. Agar	Z 4' boslsa. r 4- 2y ning qiymatiru
toping.
A) 1 B) 3 C) 2 D) 13
*29. |x2 — ЗгI =	— x2 tenglamaning butun
sonlardan iborat ildizlari yig'indisinl toping.
A) 4 B) 5 C) 6 D) 3
30. Asosi 8 sm. balandligi 8 sm bo'lgan teng yonii
uchburchakka tashqi chizilgan aylananing radiusi
uecha sm?
A) 11 B) 10 C) 5 D) 12
57
TEST 2Ш : Variant
129
Matematika
1
Matematika
I.	Quyidagi tasdiqlardan qaysi biri hamma vaqt
to’g'ri?
A)	birorta ham qo'shiiuvchi 11 ga bo4inmasa,
yig'indi ham II ga boVinmaydi
B)	bar bir qo'shiluvchi 15 ga bo‘linsa, yig'indi
ham 15 ga bcfhnadi
C)	yig'icdi 11 ga boUinsa, bar bir qo'shiluvchi
ham 11 ga bo'Iinadi
D)	qo(shiluvchilardan kamida bittasi 12 ga
bcrtinsa, yig‘indi ham 12 ga ho'Iinadi
11.	Quyidagi tasdiqlaming qaysilari notolgri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi Я — ^y(a, b, c— uchburchakning
tomonlari, S’— uchburchakning yuzi) formula
bilan hisoblanadi-,
2)	radiusi Ft ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S ~ 7^* formula bilan
hisoblanadi;
3)	diagonailari dj va da ga, ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
to'rtburchaknmg yuzi S = ^d^d^sinot formula
bilan hisoblanadi.
A) 1.3 B) 1;2 C) 1;2;3 D) 2;3
2. 453,21 sonini standart shaklda yozing.
A) 4,5321-IO2 B) 4,5-103
C) 4,5321 IO3 D) 4,53-IO2
12.	Tekislikka og‘ma va perpendikular tushirilgan.
60
Og‘ma va tekislik orasidagi burchak arccos— ga,
3.	16 — (8a — 3)" ni ko'paytuvchilarga aj rating.
A) (8a-l)(7 + 8«) B) (Sa + l)(8a - 7)
C) (8a — 1)(7 — 8a) D) (8a + l)(7-8a)
og'maning tekislikdagi proyeksiyasi 120 ga teng.
Perpendikularning uzunligini toping.
49	168
A) 12 В) ~ C) 22 D)
. t+z+x + l	... ...
4.	-----------+ лш soddalashtinng.
A) x B) x - 1 C) x + I D) 2x +1
5.	m ning qanday qiymaiJarida (m2 — l)y + 1 == m
tenglama yechimga ega boimaydi?
A) m = 0 B) m — 1 C) m — 2
D) m = — 1
6.	xi va x2 x2 — Hr + 12 =: 0 tenglamaning
ildizlari bo‘Jsa, x\x\ + x2x-i ning qiymatini
toping.
A) 132 B) -78 C) -132 D) -168
7.	16r2 — 8z + 3 > 0 tengsizlikni yeching.
A) [0;oo) В) 6 C) (—oo;0)
D) (-oo;oo)
8.	0,(8) + 0,(3) — - ning qiymatini hisoblang.
A) 4	В) 1| С) | D) 0.(11)
V	v	о
.	1 , tl 2 sin a + sin 2с» .
13.	Agar cos a =. — - bo Isa, —--:—— ni
7	2 sin cr — sin 2a
hisoblang.
A) I B) 0,5 С) I D) J
14.	41  17 • 28  35 — 24 -12 • 87 ayirma qanday raqam
bilan tugaydi?
A) 2 В) 0 C) 6 D) 4
15.	O£zaro teskari sonlarni aniqlang:
1)УЗ-1Уа7§+1;2)
f
3)	д/ё - Уб va ч/б + y/5; 4) va
A) 2:3; 4 B) hammasi C) 1;2:4
0) 1;3;4
16.	/(-2) = 5 va /(2) = 3 shartni qanoatlantiruvchi
chiziqli funksiyani aniqlang.
А) Дх) = 2х-1 В) Я®)=|» + 4
C) /(z) = -|x + 4 D) /(r) = 2z+l
9.	(ТЗ)1"'’^ ni hisoblang.
A) 3 B) 713 C) 6
D) 13
(z — 4)(z + 2) л . ... .	,
И.	—i-—-2 — < 0 tengstzhkning eng katta va
(z; — 3)
eng kichik butun yechimlan ayirmasini toping.
A) 4 B) 3 C) 2 D) 5
10.	Ikkita to‘g*ri chiziqning kesishishidan hosil
bo'lgan qo'shni burchaklandng gradus 0‘lchovlari
4 : 6 nisbatda bc'isa, shu burchaklarni toping.
A) 60°, 120° В) 72е; 108° C) 50<>;130a
D) 30е; 150°
18.	/ sin 2xdx ni hisoblang.
Jo
A) -I B) I С) I D) -1
58
2
TEST 2006: Vknaflt
129
Matematika
19.	2foy23 • ^ЛУз2 • Zoffs—- ш hisoblang.
243
A) -9 B) -10 C) -g- D) -4
20.	Muntazam oltiburchakka tashqi chizilgan
aylananing radius) >/2 bo’lsa, unga ichki
chizilgan aylananing radiusini toping.
A) B) 1,5 C) 1,2 D) ~
21.	Balandligi 32 ga teng bo’lgan rornbga ichki
chizilgan doiraning yuzini toping.
А) 190тг В) 196* C) 200* D) 256*
29.	xZ 4- px 4- <j = 0 tenglamaning ildizlari
x2 - lx 4- 10 = 0 tenglamaning ildiziaridan ikki
maria katta. p + q ning qiymatini toping.
A) 26 B) -7 C) -14 I)) -46
30.	Katetlarining nisbati 2:3 bo’lgan tc>4g‘ri burchakli
uchburchak balandligi gipotenuzasini
uzunliklaridan bin ikkmchisidan 0,6 ga kam
bo’lgan bo’lakiarga ajratadi. Gipotenuzaning
bo‘faklarini toping.
A) 5 va 3 B) 2 va 4 C) 1,6 va 3,6
D) 1,08 va 0,48
31
R.ornbniug tornoni 6 ga, o’tkir burchaginiug
22.	Konusning yasovchisi 25 ga. uni ng asos tckisligi
bilan tashkil qilgan burchagining sinusi 0,6 ga
teng. Konus o‘q kesimining perimetrini aniqlang.
A) 80 B) 360 C) 90 D) 105
smusi
3
ga teng. Uning diagonallari
ko’paytmasini toping.
A) 18 B) 27 C) 48 D) 42
23.	Konus yasovchisi 4 ga teng va u asos lekisiigi
bilan 60° li burchak tashkil etadi. Konusiring
hajrnini toping.
24.	Quyidagi ayinnalardan qaysi birining qiyniati
manfiy?
A) соз10° — cos50°	.6) $tnl40° — sin 150°
C) clg42° - dg2S°	D) /587e-t385°
32. b vektor <7 (2: 4; 4) vektorga kollinear hamda bu
vektortarning skalyar ko’payt-masi 144 ga teng. b
vektorning uzunligini toping.
A) 16 B) 24 C) 18 D) 12
33 у — ^/T^Togj^, cos.? funksiya r (z € |0;2тг])
ning qanday qiymatlarida aniqtangau?
a) (—c-' Ьт:2,г и 0;Я1
•>	a Z	a	J
25.	sin 5x cos 2 т = cos5z • sin 2x 4- 0. 5 tenglamaning
ildizlarini koTsating.
A) ~ 4- k € Z B) i— 4- 2*A, k £ Z
о 3	4
C) + kez
10 о
26.	900 kg mevaning tarkibida 80% suv bor. Bir
necha kundan keyin mevaniug og’irligj 500 kg ga
tushdi. Endi uning tarkibida necha foiz suv bor?
Л) 68 B) 62 C) 64 D) 66
27.	у = az2 4-	4- c(a > 0) funksiya x =z 1 nuqtada 2
ga teng eng kichik qiymatga ega. Agar y('2) — 4
bo’Isa, «, i> va c iarni toping.
Л) а = ЗЛ-6.с=2 В) a~4,b~2,c~ 6
C) a = 2,b=-4,c = 4
D) a = 6, 6 = —2, c = 4
34.	3"? 4- 3^+3 > 84 tengsizlikni yeching.
A) (-00: 0) B) (0; 1) C) (1; oc)
D) (0; 1)U(1: do)
35.	Teng yonli trapetsiyaga ichki chizilgan
aylananing markazi ustki asosining uchidan 3 ga,
pastki asosining iichJdan 4 ga teng masofada
joylasbgan. Shu trapetsiyaga ichki chizilgan
doiraning yuzirii toping.
A) 5,76* B) 2,56* C) 6,76* D) 3,24*
36.	O'q kesirni teng tomorili uchburchakdan iborat
kcnusga diametri D ga teng sfera ichki chizilgan.
Konusning to’ta sirtini toping.
r.	q	г
Л) '^TD-	B) -^D'1	C) -x«2
D) jirP’
28. Qisqarmaydigan oddiy kasrning rnaxraji
snratidan 6 birlikka katta. Agar kasrniug sural
va maxrajiga 5 ni qo’shsak, hosil bo’lgan
4
kasrning qiymati £ ga teng bo’iadi, Bcrilgan
о
kasrning suratini toping.
A) 7 B) 23 C) 13 D) 19
59
TEST 2006 : Variant
130
Matematika
Matematjka
1. 15-261 + 18-261 +139 -15+18 • 139 ni bisoblang
A) 14500 B) 13200 C) 16200 D) 15100
2.
6,5-0.046,8
5,2-5,1-0,16
ning qiymatini loping.
A) i 3) C) 1 D) |
3.	Uchburchakning birinchi tomoni x(x > 13) sm,
ikkinchi tomoni undan 8 sm qisqa, uchinchi
tornoni esa birinchisidan 5 sm uzun. Shu
uchburchakning perimetrini (sm) toping.
A) 3r + 2 E) 3r-3 C) 3z + 3
D) 3г-2
4.	Agar P - -z - |y - (x + 2y) va
0=-г+|у-(г + 5y) bo4sa, P ~ Q ni toping.
A) 4y В) 2y C) D) -4y
5.	a ning qanday qiymatiar id a az = 3z + 1
tenglama yechimga ega boimaydi?
A) o = 2 B) a£l C) a~3 D) a £ 2
4
6.	= z + 1 tenglamaning nechta haqiqiy ildizi
bor?
A) 2 В) 3 C) iidkiyo'q D) 1
( 2x — 3(z — I) > 1 tenSs^^^ar sistemasining
butun sonlardan iborat yechimlari nechta?
8.	Ariftnelik progressiya uchun quyidagi
formulalardan qaysilari noto‘g5ri?
nc _as + (n-i)d	an-dr+d
i)	5Я — r • n, 2) —	-	— a,
z	n
3)	fii + On = аз + an-2
A) 1; 2 B) 2; 3 C) 2 D) 1
9.	x ning qanday qiymatlarida u = 3 - Igx funksiya
nomusbat qiymatiar qabul qiladi?
A) z>1000 B) z>100 C) x <1000
D) x < ICO
10.	Ikkit-a to'g+i chiziqning kesishishidan hosil
bo‘lgan qo'shni burchaklarning gradus o'lovlari
5 : 7 nisbalda bo^lsa, shu burchaklami toping.
A) 30ft;150e B) 75°; 105° C) 62°; 118°
D) 54е; 126е
11.	Quyidagi tasdiqlarning qaysilari noto‘g‘ri?
1)	radiusi R ga, markaziy burchagi о ga teng
doiraviy sektorning yuzi S ss formula bilan
hisoblanadi;
2)	tomonlari a va b ga, ular orasidagi
burchaklaridan biri a ga teng bo4gan
paraUelogrammning yuzi S = absinct formula
bilan hisoblanadi;
3)	diagonallari dy va dj ga, ular orasidagi
burchagi a ga teng ixliyoriy qavariq
to'rtburchakning yuzi S — d^sina formula
bilan hisoblanadi.
A) 2;3 B) 1;2 C) 1;2;3 <D) 1;3
12.	Tekislikka tushirilgan og^na va perpendikuiar
16	'
orasidagi burchak arcsin-- ga teng. Og‘snaning
65
uzunligi 130 ga teng. Perpendikularning
uzunligini toping.
A) 96 B) 64 C) 32 D) 126
7
13.	tg(~ + a) = — - bo'lsa, tga ning qiymatini
4	5
toping.
A) i B) 6 C) -| D) 3
14.	378 va 594 ning umumiy bo'luvchilari nechta?
A) 7 B) 8 C) 5 D) 9
15.	Agar r < z < у bo4sa, |z —-y| — \z —• — |z — r|
ni soddalashtiring.
A) 2y~2z В) 0 C) 2y-2z . D) 2z - 2y .
16.	у z= 3r2 + 8z — 8 funksiyaning grafigi qaysi
choraklarda joylashgan?
A) barcha choraklarda B) 1I; III, IV
C) ItII, 111 D) IILTV
iZ + 4ДЛ — X)	n . ... .	.
17.	-—-—"*~\2—L	G tengsizhkmng eng katta va
(г + 3)
eng kichik butun yechimlari yig*indisini toping.
A) -2 B) 1 C) 0 D) ~1
18.	I (1 + ctg2x)dx ni bisoblang.
A) 1 В) — C) -1 D) >/3-1
3
19.. а = log98 112 bo‘isa, log7 2 ni a orqali ifodalang.
A)
2 g- 1
3 — а
1 - 2а
а — 4
В)
а -3
2а -1
20. Teng yonli uchburchakning balandligi 20 ga teng.
Yon tomoni asosidan 5 ga kam. Shu
uchburchakning asosini toping.
A) 40 B) 20 C) 24 D) 30
60
Matematika 2006 уII
131		15	D	30	В	8	в	23	D	138		15	С	30.	D	8	D	23	с	145	
1	С	16	А	31	С	9	с	24	С - j	1	В	16	В	31	С	9	В	24	в	1	В
2	С	17	С	32	с	10	с	25	В	2	с	17	в	32	В	10	А	25	с	2	в
3	в	18	А	33	в	11	в	26	с	з 1	с	18	0	33	А	11	D	26	в	3	в J
4	с	19	А	34	D	12	А	27	с	4 1	в	19	А	34	А	12	А	27	с	4	в
5 b—				D	20	В	35	В	13	В	28	А	5	в	20	С ]	35	А	13	В	28	с	5	с
|6_	С	21	В :	36	В	14	А	29	D	6	С •	21	с	36	В	14	А	29		6 |	А
7	С ।	22	С	134		15	D	30	А	7	С	22	с	141		15	D	30	С	7 !	
8	А	23	Р	1	D	16	В	31	С	8	А	23	D	1	С	16	В	31	В	8	D
9	В	24	В	2	D	117	D	32	В	9	А	24	А	2	А	17	В	32	В	9	С
10	А	[25	D	3	А	18	С	33	D	10	А	25	А	3	А	18	А	33	D	10	С
11	А	26	D	4	В	19	0	34	В	11	в	26	С	4	А	19	А	34	А	Д1	В
12	А	27	С	5	С__	20	А	35	С	12	А	27	А	5	А	20	С !	35	А	12	в
13	С	28	В	6	D	21	С	36	D	13	С	28	С	6	В	21	в	36	А	13	с
14	D	29	В	7	В	22	D	137		14	D	29	D	7	А	22	с	144		14	в
15	D	30	в	8	С	23	D	1	D	15	В	30	А	8	D	23	А	1 8	В	15	А
16	А	31	с	,9	С	24	В	2	А	16	D	31	о	9	D	24	А	2	А	16	А
17	С	32	в	10	В	25	В	3	В	17	В	32	с	10	D	25	А	3	В	17	D
18	С	33	с	11	D	26	В	4	В	18	D	33	с	11	в	26	С	4	А ;	18	D J
19	В	34	с	12	С	27	В	5	D	19	в	34	в	12	с	27	А	5	В	19	в
20	А	35	D	13	А_	28	А	6	А	20	А	35	в	13	А	28	В	6	А	20	в
21	А	36	С	14	0	29-	С	7	D	21	С	36	с	14	А	29	В	7	В	21	в
Я2	В	133		15	А	зо	В	8	А	22	А	140		15.	А	30	D	8	D	22	р J
23	А	1	с	16	Л м	31	D	9		23	D	1	А	1.6	В	31	С	9	А	23	А
24	В	2	D	17	А	32	С	10	с	24	В	2	D	17	В	32	С	10	С	24	A j
25 г—	С	3	С	18	D	33	С	11	А	25	В •	3	А	18	С	33	В	11	D	25	В
26	D	4	С	19	В	34	D	12	D	26	D	4	С	19	в	34	с	12	В	26	В
27	А	5	с	20	С	31	0	13	С	27	А	5	В	20	А	35	с	13	0	27	В
28	D	6	с	21	D	36	С	14	В	28	В	6	А	21_	С	36	в	14	с	28|	D
29	В	7	в	22	С	136		15	Б	29	А	7	В	22	с	143		15	А	29	
30	В	8	А	23	С	1	А	16	А ’	30	В	8	D’	23	D	1	D	16	D	30	А _
31	D	9 J	В	24	в	2	D	17	С	31	с	9	D	24	В	2	А	17	В J	31	В j
32	В .	10	В	25	в	3	D	18	А	32	в	10	С	25	С	3	С	18	С	32	€ ;
33	D	11	В	26	А	4	А	19	С	,33	D	11	В	26	А	4	В	19	А	33	с ~
34	С	12	D	27	D	5	А	20	А	34	D	12	D	27	С	5	в	20	С	34	р 1
35J	В	13	В	28	В	6	С	[21	В	35	В	13	D	28	в	6	А	21	D	35	cj
36	А	14	С	29	с	7	С	!22	В	36	В	14	С	29	с	7	С	22	В	36	А !
132		15	в	30	с	8	А	23	0	139		15	D	30	А	8	А	23	С		
1	В	16	А	31	А	9	С	24	А	1	А	16	В	311	D	9	В	24	с		
2	С	17	С	32	С	10	В	25	В	2	А	17	А	32	В	10	В	25	в		
3 —„	в-	18	А	33	D	11	В	26	D	3	D	18	В	33	С	11	D	26	D		
4	А	19	В	34	D	12	р	27	D	4	О	19	С	34	0	12	В	27	в		
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6		А	21	с	36	С	14	А	29	В	|6	С	21	а'	36	А	14	А	29	С		
7	С	22	с	135		15	D	30	С	7	А	22	с	142		15	В	30	В		
8	А	|23	D	1 !	D	16	В	31	В	8	D	23	А	|1'	А		А	31	с		
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10	D	25	В	3	в	18	С	33	А	10	С	25	D	3	D	18	С	33	D		
11	О	26	D	4	в	19	D	34	D	11	А	26	В	4	D	19	в	34	С		
12	в	27	D	5	ЕЭ	20	£	35	А	12	С	27	В	5	С	20	D	35	А		
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Matematika 2006 yii
1X6		15	А	30	А	8	А ~	23.	С	123		15	В	30	В		А	23	в	130	
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6	A	21	D	36	В	14	D	29	А	6	D	21	С	36	в	14	D	29	С	6	с
7	C	22	D	11	19	115	Р	30	В .	7	А	22	D	: 126		15	D	30	С	7	с
8	D	23	С	1	В	16	А_	31	D	8	В	23	D	1	А	16	А	31	D	8	D
9	C	24	А	2	С	17	С	32	С	9	D	24	С	2	В	17	D	32	С	9	А
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12	C	27	А	5	в	20	А	35	В	12	А	27	&	5	D	20	С	35	В	12	D
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23	D	1	С	16	D	311	С	9	В	23	D	3»	в	16	А	31	А	9	D	23	D
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2b	В	3	А	18	А	33	D	11	D	25	А	3	В	18	D	33	В	11	В	25	В
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29	В	7	С	22	С	121		15	D	29	В	7	D	22	В	128		15	А	29	В
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33	D	11	А	26	D	4	D	19	В	33	с	11	А	26	0	4	А	19	В	33	D
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36	В	14	в	29	D	7	В	22	С	36	D ‘	14	с	29	D	7	В	22	С	36	А [
11	17	15	с	30	Д	8	D	23	А	124		15	в	30	В	8	D	23	D		
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[6	А	21	А	36	В	141	0	29	в	6	О	21	С	— 36	С	14	А	29	А			
(7 |	С	22	С	...		15	А	30.	в	7	0	22	0	127		,15	С	30	D	i	
8	В	|2Г	С	1	С	16	D	31	в	8	D	23	D	1	А	16	В '	[31	С		
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10	D	25	с	3	А	18	А	33	с	10	С	25	в	3	В		с	33	с		
11 :	А	26	А	4	В	19	С	34	с	11	А	26	в	4	О	19	А	34	в		
12	В	27	В	5	с	20	В	35	В 	12	В	27	D	5	с	20	С	35	А			
13	С	28	А	6	А	21	0	36	с	ДЗ	В	28	В	6	А	2.1	В	36	В		
j 14	CJ	29	С	7	С	22	в			14	С	29,	В	7	С	22	в	—_			
2
TEST 2006 : Variant
130
Matematika
21. Doiraga tashqi chizilgan teng yonli
trapetsiyaning asoslari 8 va 3'2 ga teng. Shu
doiraning yuzini hisoblang.
A) 49* В) 64* C) 16* D) 36*
.22. Agar kubning bar bir qirrasini 2 sm ga
uzaytirsak, uning hajmi 152 sm3 ga ortadi.
Berilgan kubning qirrasini toping.
A) 3 B) 2 C) 4 D) 1
23. Asosi rombdan iborat to‘gcri prizmaning
balandligi 4,5 ga teng. Agar rombning
dioganallari 8 va 10 ga teng bo'Isa. prizmauing
hajmi qanchaga teng?
A) 320 B) 360 C) 240 D) 180
5	6v^3 — 5
24. Agar tga Vtgfi ~ - va ty<xtg& - --=— ЬоЪа,
6	’	6V3
nimaga teng boiadi?
A) J +	B) ~ + i?Ck&Z
O	D
C) ?- + *k,k€Z D) ^L + vk,keZ
4	6
25. sin4т < — cos4x tengsizlikni yeching.
26. Maosh ikki mart a ketma-ket bir xil foizga
oshirilgach, maoehning 6*25 so'mi 900 so‘mga
aylandi. Maosh har safar necha foizdan
oshirilgan?
A) 12 B) 10 C) 14 D) 20
27.	= y/l, 75 - r — r2 funksiyaning eng katta
qiymatini toping.
A) 1,5 B) 72 C) 272 D) 3
30.
AB—18 sm, DB=10,8 sm.
ABC uchburchakka
ichki chizilgan ayla-
naning radiusi
necha sm?
31.	Paralielograrnmning tomonlari 20 va 7 ga teng.
Uning katta tomoniga yopishgan burchaklarining
bissektrisalari qarama-qarshi tomonni uch
qismga ajratadi. Shu qismlardan eng kichigining
uzunligini toping.
A) 4 B) 2 C) 6 D) 5
32.	A(-4; 1; 1), B(l; 4; 0) , G(l; -2j_2) va___
£>(—5; —5; 3) nuqtalar berilgan. AC va BD
vektorlar orasidagi burchakni toping.
A) 60° B) 90° C) 45° D) 30°
33.	cost < sinx tengsizlikni yeching.
A)	(— 4 тгк^ —— 4~*i), k € Z
4	4
B)	+	+ tez
С)	(2тк; T+2rfr), keZ
D)	(y + 2ffi; + keZ
4	4
34.	/оргэ(3 — 2г) > 1 tengsizlikning butun yechimlari
nechta?
A) 3 B) 4 C) 1 D) 2
35.	Teng yonli trapetsiyaning yuzi 60 ga, unga ichki
chizilgan aylananing radiusi 3 ga teng.
Trapetsiyaning asoslarini toping.
A) 14; 6 B) 18; 2 C) 13; 7 D) 5; 15
36.	Hajmi 873 ga teng bo‘lgan muntazam
tetraedrning balandligini toping.
A) 4 B) 273 C) 3 D) 473
28.
30	.	. i □
— tenglamanmg natural sonlardagi
yecbimida z nimaga teng?
A) 3 B) 4 C) 7 D) 2
29. 41г 4- 41 = 3 4- (г + 4)2 tenglamaning ildizlari
ko'paytrnasini toping.
A) 15 B) 105 C) -15 D) -105
61
TEST 2006 : Variant
131
Maternatika
1
Matemat ika
1.	18-16— 15-16+ 36-24- 33-244-17-11 - 14- И
ni hisoblang.
A) 155 B) 166 C) 153 D) 180
2.	1/25 songa teskari souni toping.
A) 8 B) -0.8 C) 0.8 D) --
4
3.	Uchburchakning birinchi tomoni x(x > 13) srn.
ikkinchi tomoni undan 8 sm qisqa. uchinchi
tomoni esa birinchisidan 5 sm uzun. Shu
uchburchakning perirnetrini (sm) toping.
A) 3z 4- 2 В) 3x- — 3 С) 3г 4- 3
D) 3г — 2
4.	(xJ 4- I)(z4 — x2 4- 1) - (x2 - I)2 4- z5 4- z3 4- x ni
soddalashtirgandan keyin hosil bodgan
ko'phadning necht a hadi bo'Iadi?
A) 4 B) 5 C) 6 D) 3
5.	n ning qanday qiymatlarida nz 4- 2 = n 4- 2x
tenglama cheksiz ko;p yechimga ega bo!ladi?
A) n = 1 B) n = 0 C) n # 1 D) n = 2
11.	Quyidagi tasdiqlarning qaysilari noto‘g:ri?
1)	tomoni a ga, burchaklaridan biri a ga teng
rombning yuzi S — crsinot formula bilan
hisoblanadi:
2)	tornonlari a va b ga, ular orasidagi
burchaklaridan biri a ga teng bodgan
parallelogrammning yuzi S = knbsina formula
bilan hisoblanadi;
3)	diagonallari dj va d'> ga, ular orasidagi
burchagi гл ga teng ixtiyoriy qovariq
to'rtburchakning yuzi S’ = d|d2sfno formula
bilan hisoblanadi.
A) 2;3 B) 1;2 C) 1:2:3 D) 1:3
Tekislikka tushirilgan og‘ma va perpendikuiar
orasidagi burchak arcsm— ga teng. Og!rnaning
nzunligi 74 ga teng. Perpendikularning
uzunligini toping.
A) 70 B) 24 C) 54 D) 48
, r, 1 - C0S4O 4- 41П"2о .	, ...
13. ---------:---------ш soddaiashtimig.
3cos"2ot
A) 3tflr22a B) 3ct<r2a C) ^22q
f)j l,5c^22cr
14.
Agar a € N bodsa. quyidagi ifodalardan qaysi
birinicg qiymati bar doim butun son bo ladi?
6. zj va z2 x2 - 17z 4- 6 - 0 tenglamaning ildizlari
bo!lsa. хгх^ + x^x? ning qiymatini toping.
A) -102 B) -32 C) 102 D) 77
A) B) ^±1
b	4
Di (°2 d-«)(« 4-2)
1	6
7. ----- > 0 tengsizlikm veching.
x 4- ч 
A) [—7; 5) B) (—oc; -7)
C) '(-co; -7)U[5; oc) D) (-7; 5]
15.
O’zaro teskari sonlarnl aniqlaug:
8. 0, (7) 4- 0, (5) - - ning qiymatini hisoblang.
я?
A> | B) l| C) D) 11
A) 1:2:3 B) 1;3;4 C) 1:3
D) 2:3; 4
16. i/ =
9. r ning qanday qiymatlarida - 5х — 125
funksiya nomanfiy qiymatiar qabul qiladi?
A) г < 3 R) x > 3 C) z < 2 D) x > 2
I(z - 5)(z - 2)
У (4 - x)(z - 3)
sohasini toping.
funksiyaning aniqlanish
A) .{2:3)U(4;5} B) (2;3)U(4;5)
C) (-oc;2]U(3;4)U[5;c«) D) (2;3]u[4;5)
10. Qo’shni burchaklardan biri ikkincbisidan
14° katta. Shu qo'shni burchaklarni toping.
A) 83°;97° В) 16е: 164° C) 82e;98°
D) 93°; 87°
17. —_— --------> x tengsizlikni yeching.
A) (1; 3) B) (-3; 1) C) (2: 4)
D) (-1; 3)
62
TEST 2006: Variant
Matezn&tika
ni hisoblang.
О) з7з~з
/ 7 \	*
19.	fl = ^ - 1	, 5 ~ 73* va r - (&$} sonlarni
o4sish tartibida joylashtiring.
A) a < c <b B) b < с < а С) с < а < b
D) c < b < а
20.	Radiusi R ga teng bo!lgan aylajuadagi nuqtadan
uzunliklari /?73 ga teng bodgan ikkita vatar
o‘tkazildi. Vatarlar orasidagi burchakni toping.
A) 60° В) 45й C) 120° D) 135°
21.	ABCD tog'ri to:rtburchakning A burchagi
bissektrisasi BC tomonni uzunliklari BM=16 sm
va MC=9 srn bo‘|gan ikki qismga ajratadi.
To:g‘ri to'rtburchakning yuzini (sm2) toping.
A) 400 B) 500 C) 510 D) 480
22.	Muntazam t-o‘rtburchakli piramida asosining
tomoni 673 ga va apofetnasi 6 ga teng. Piramida
hajmitii toping.
A) 54 B) 108 C) 162 D) 324
23.	Silindr o‘q kesimining diagonal! 8 ga teng va asos
tekisligi bilan 30е li burchak tashkii etadi.
Silindrning hajmini toping.
А) 48x В) 6т С) Збтг D) 24*
24. t = cos-32% q ~ Sinll2° va k — 1д'235й sonlarni
oSish tartibida joy lashtiring.
A) k <t <q B) q <i < k
D) t < к < q
C) i < q < k
25.	x/3-'2sm— = 0(7,5 < r< 13,5)
<z
tenglamaning yechimini toping.
A) io| B) 8,5,-9,5 C) 8; 13
D) io|;11
4
26.	Ishchining mehnat unumdorligi 30% ortsa, uning
ish normasirri bajarishga ketadigan vaqt-i necha
foizga qisqaradi?
A) 25 B) 20 С) 1б| D) 23-L
27.	A(l; 9) nuqta у — —®2 + ax +• 2 parabolaga
tegishli. Parabola uchining ordinatasini toping.
A) 18 B) 13 C) 2 D) 4
28.	|5 — x| = 2(2x — 5) bo'tsa, 6 + r ning qiymati
nechaga teng?
A) 7 B) 8 C) 11 D) 9
29.	у/x2 - 6т 4-54- x2 = 6т 4- 7 tenglamaning
ildizlari yigjndisini toping.
A) -3 B) 6 C) —4 D) 3
30.	Gipotenuzasi 75 ga teng bo'lgan to'g’ri burchakli
uchburchakning katetlari nisbati 4:3 ga teng.
Gipotenuzaga tushirilgan balandlik uni qanday
kesmalarga ajratadi?
A) 50 va 25 B) 48 va 27 C) 40 va 30
D) 60 va 15
31.	Paralielogramnining burcliakkridan biri 150° ga
teng. Uning 9 ga t-eng boHgan diagonal!
tomoniga perpendikuiar. Parallelogrammning
perirnetrini toping.
A) 9(4 4- 73) B) 36v/3 C) 9(3-tV3)
D) 18(2 + 73)
32.	rn ning qanday qiyrnatlarida a(rr* — l;m — 2;2)
vekt-ormng uzunligi 3 dan kichik bo:ladi?
A) —2 < ni < I B) 0 < m < 3
C) — l<m<2	D) — 1 < rn < 3
33.	1 - 2cos2x > s?n52x tengsizlikni yeching.
A)	G + 2xt; + 2тД * e Z
\	J у
В)	4~<Ь;т + тЛ:^,к e 7
C)	^-| +%!•; ^ +
_ /x . Зх Д .
D) i "т +	~—к	I, к € z
\ 4	4 J
34.	cos2{x + 1)  /034(3 — 2x — r2) > 1 tengsizlikni
yeching.
A) H;-l} B) H;0) C) {-1}
D) {-2;-!}
35.	Teng yonli trapetsiyauing yuzi 60 ga, unga ichki
chizilgan aylananing radiusi 3 ga teng.
Trapetsiyaning asoslarini toping.
А) И, 6 B) 18; 2 C) 13: 7 D) 5; 15
36.	Konusning o‘q kesimi muntazam uchburchakdan.
i rilindrniki esa kvadratdan iborat. Agar ularn’mg
hajmlari teng bo‘lsa, to‘la sirtiarining nisbati
nimaga teng?
A) 73 : 72 B) 7?: 73 C) 1 : 73
D) 3:2
63
TEST 2006 : Variant
132
Matematika
1
Matematika
1. 37 24 — 34 • 24 4- 19 11 — 16 • 11 ning qiymatini
toping.
A) 90 Bl 105 C) 100 D) 110
12. Tekislikka tushirilgan oghnaning uzunligi 125 ga.
uning tekislikdagi proyeksiyasi esa 35 ga teng.
Og'ma va tekislik orasidagi burchakni toping.
0.4-0,15-1,6
6.4-2.5-0,03
ning qiymatini toping.
, 4	12
A) arccos—
D) arc sin ~
B) <ircsm|| C) arctg^
A) ?•	B) | C) 0,2 D) 2
D	' c
1'3.
cos 3a	sin 3a .	.....
-----4----:--m soddaiashtmng.
cos a sm о
3.	16 - (2r •— 3)2 ni ko‘paytuvchilarga ajrating.
A) (2z-l)(7-2x)	B)‘(2x 4-1)(7--2x)
C) (2x — l)(2x + 7) D) (2z4-l)(2x-7)
4.	(у2 - I)2 - (y2 - l)(y4 5 * * * 4- jr 4* 1) 4- у ni
soddaiashrirgandan keyin nechta haddan iborat
bo'dadi?
A) 5 B) 4 C) 3 D) 6
/	\ i  e • 1	- у = 5
5.	(x: y) soniar jufti < $x 4- 2V — 4 sistemaning
yechimi bolsa. у — x ni toping.
A) -1 B) -3 C) 0 D) 3
6.	3 — x = - tenglamaning nechta haqiqiy ildizi
x
bor?
A) 2 B) 1 C) iMi2iyo‘q D) 3
—< 0 tengsizlikni yeching.
A)	[2; 3)
D) [2; 3]
B)	(-1; 2]
О (—3;2)
8. Quyidagi soniardan qaysi bin 0.8(1) ga teng?
A) Bl C) D)
' 90	'11	90	' 90
A) 4 cos 2a B) 4 cos a C) —2
D) 2 cos 2a
14.	24 soniniug barcha natural bo!luvchilari
yig'indisini toping.
A) 48 B) 60 C) 124 D) 108
15.	Qaysi juftlik o'zaro t-ub sonlardan iborat?
A) (11; 22) B) (8; 14) C) (12: 34)
DI (39: 44)
16.	Agar f(x 4-1) = x~ — 3x — 3 bo4sa. f(x) ni
toping.
A) z2-5x4-1 B) x2-3z-l C) x2 -4
D) x3 — 5x 4- 6
17.	7 — r < (x — 2)2 4“ 3(x — 2) tengsizlikni yeching.
A) [~2;1] B) (0;1]U[3;og)
Cl 4-00;-3] U[3;00) D) {-3:3]
18.	f(x) = 3x2 ~ 2 funksiya boshlang'ich
funksiya) arid an qaysi birining grafigi M (2; 10)
nuqtadan o4adi?
А) Г(х) = х3-2х4-6 Bl F(x) = r3-2x
C) F(r)-x3-2x + 8
D) F(r)~x3-2x4-5
19.	a — logbo80 bo*lsa. log52 ni a orqali ifodalang.
9. у ~ 'I*9* — 3 funksiya grafigining Oy o‘qi bilan
kesishish nuqtasi ordinatasini toping.
A) -1 B) —2 C) 1 D) 0
a - 3
1 -2a
1 -2a
a — 4
Bl
3a — 1
2-a
4
10. Markaziy burchakka mos yoy aylananing -
5
qismiga Ung. Shu markaziy burchakni toping.
A) 144° B) 72° C) 216° D) 288°
11. Quyidagi tasdiqlarning qaysilari noto*g'ri?
1) tomonlari. a,b va c bollgan uchburchakka ichki
chizilgan aylananing radiusi т = formula
bilan hisoblanadi;
2) tomonlaxi a va 6 ga, ular orasidagi
burchaklaridan biri a ga teng bo'igan
paraHelograrnrnning yuzi S — absina formula
bilan hisoblanadi;
3) o‘xshash figuralar yuzlarining nisbati ularning
mos chiziqli o4choviarimng nisbatiga teng.
A) 2;3 В) 1;2 О 1;2;3 D) 1,3
20.	Uchburchakning 7 ga Ung boUgan balandligi uni
perimetrlari 18 va 26 bo'igan ikkita
uchburchakka ajratadi. Berilgan uchburchakning
perimetrini toping.
A) 31 B) 30 C) 36 D) 34
21.	Teng yonli trapetsiyaning yon tomoni va kichik
asosi 5 ga, balandligi 4 ga Ung. Trapetsiyaning
yuzini toping.
A) 22 B) 32 C) 40 D) 20
22.	Agar kubning bar bir qirrasini 2 sm ga
uzaytirsak, uning hajmi 152 sm3 ga ortadi.
Berilgan kubning qirrasini toping.
A) 3 B) 2 Cl 4 D) 1
6И
2
TEST 200/) : Variant
132
Matematika
23.	Konusning o‘q kesimi teng tomoni i uchburchak.
Agar konusning tola sirti 192т ga teng bo‘lsa.
konus asosning diametrini toping.
A) 24 Bl 18 C) 21 D) 16
24.	f(x) — 1 — 3cos2r — kcos2x funksiya к ning
qanday qiymatida o'zgaxmas bo'ladi?
A) —2 B) -3 C) -1,5 D) -1
v3
25.	2sin2x — 1 = — tenglamaai yeching.
A) (-1)‘+^ + *ж;4е
6
в) +	C) ±^ + *t:kez
D) £~~ 4* xk; к C Z
26.	BogMagi daraxtiarning 60% i t-eraklar. Qolgan
daraxtlarning 70% i chinorlar bo‘lsa5 boshqaiari -
iollar. Bog'dagi daraxUanring necha foizim tollar
tashkil etadi?
A) 18 Bl .12 C) 24 D) 28
33. (sinx + 1| > 1,5 t-engsizlik r ning (0;t) oraliqqa
tegishlr qanday qiymatlarida o‘rinli bo'ladi? ...
34.	(z 4- 2)lo«»<xa+n <(x + 2)Io^(2^+9) tengsizlik x
aing qanday qiymatlarida o'rinli?
A) (-2:4) B) (—4.5:oc) C) (-1:4)
D) (4:oc)
35-	Radiusi 5 ga teng bodgan doiraga tcrg'ri
burchakli uchburchak ichki chizilgan. Shu
uchburchakka ichki chizilgan doiraning radiusi 1
ga teng. Uchburchakning yuzini toping.
A) 8v/2 B) 12 C) 22 D) 11
36.	Konusning o'q kesimi rnuntazam uchburchakdan.
siiindrniki esa kvadratdan iborat. Agar konus
hajmining silindr hajmiga nisbati x/3 : 2 kabi
bo'lsa. tola sirtlarining nisbatini toping.
А) УЗ :	В) УЗ : ?2 C) ^9 : 2
D ) 3 -.2
27.	f(r) =.	— I funksiyaning qiymatiar
sohasini toping.
A) (-2; 2) B) (—1; 1) C) (-3; 1)
DI [—2; 0) U (0; 2]
28.	Уг3 — 4т 4- 4 x: д/z2 ~ 10т + 25 tenglamaning
ildiziari qaysi oraliqqa tegishli?
A) r<3 B) 3<z<4 C) r < —2
D) z>5
29.	kx~ 4- 3kx + 21— 2 = 0 tenglama yechirnga ega
bo'lmaydigan k ning butun qiymatlari o'rta
arifmetigini toping.
A) -2 B) -3,5 C) -3 D) -4
30.	Tomonlari 13; 14 va 15 sm bo:lgan
uchburchakning eng katta balandligi necha srn?
a.) B) 1g C) D) 13
31.	ABCD trapetsiyauing (ADJ\BC, AD - katta
asos) AC diagonal! yon tornoniga perpendikuiar
hamda DAB burchakning bissektrisasida yotadi
Agar AC = 16 va LDAB = 60* bcrlsa,
trapetsiyaning oJrta chizig‘ini toping.
А) 41Д В) ЗЛ С) 8ч/3 D) 5/3
32.	A(-4; 1: 1), 13(1; 4; 0) , C(l; -2^2) va___
D(—5; —5; 3) nuqtalar berilgan. AC va В D
vektorlar orasidagi burchakni toping.
A) 60° B) 90° C) 45° D) 30°
65
______________ TEST 2006 : Variant__________________133
Matematika
Matematika
1. 392 ni qanday songa boiganda bo’linma 17 va
qoldiq I bo’ladi?
A) 21 B) 19 C) 23 D) 22
2. 5,2; y; -2 sonlarning o'rta arifmetigi 1,2 ga teng.
у ni toping.
A) -0,8 B) 1/2 C) -0,4 D) 0,4
11.	Quyidagi tasdiqlarning qaysilari noto’g’ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R = ^y(a, 5, c— uchburchakning
tomonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi q ga teng
doiraviy sektorning yuzi S = ^-cr formula bilan
hisoblanadi;
3)	tornoni a ga, burchaklaridan biri a ga teng
rombning yuzi S — |a2 sinct formula bilan
hisoblanadi.
A) 2:3 B) 1;2
C) 1;2;3 D) 1;3
4.
4- т
—— — - ---------x ni soddaiashtiring.
A) x -hl B) 2x C) 0 D) x-2
12.	Tekislikka ogcma va perpendikular tushirilgan.
Og’maning tekislikdagi proyeksiyasi 63 ga,
perpendikularning uzunligi 16 ga teng. Og'ma va
perpendikular orasidagi burchakni toping.
A x 32	. 16	63
A) arccos—	B) arcszn— C) urcfo-—
o5	65	65
. 63
D) arcszn —
65
5. (8r + 1)  (x — -) = 0 bo’lsa. 8r 4-1 qanday
qiymatlar qabul qilishi mumkin?
A) faqat у B) faqat -i C) 0 yoki 3
4	8
D) faqat 0
__ S2n8o - stnl2a .	,, . ...
13,	-----------— ni soddaiashtiring.
cos 10or • stnzor
A) 2$in2a B) —2 С) -2«п2о
D) — 2cos2a
14.	22 • 43 • 98 4- 16 -27-38 19 yig‘indiuing oxirgi
raqamini toping.
A) 6 B) 8 C) 2 D) 4
6-	x2 4* 13x 4- q ~ 0 tenglamaning ildizlaridan biri
-11 ga teng. Uning ikkinchi ildizini toping.
A) 2 B) -24 C) -2 D) 24
7.	(x 4-2)(r — 3) < 0 tengsizlikni yeching.
A) (—oc: — 3) U(2;oo) B) (-2;3)
C) (-oo;-2) U (3; oc) D) (-3; -2)
8.	Arifmetik progressjya uchun quyidagi
formulalardan qaysilari tosg‘ri?
1)	a5 — 2a2 4- аз — 0;
2)	О] — «з —
an — <*i 4- d
3)	n =---------d-----.
A) l В J 2;3 C) 1:2 D) 2
15.
16.
38	47	56	, u 3	4	5
А^гИ+51 + бТ = ЛЬО'ет'4Г+51 + €1
quyidagilardan qaysi hiriga teng?
A) 4-a B) 3-a C) 3 - D) 5 - a
t/ = 4sinr — 1 funksiyaning [0; —] kesmadagi eng
6
katta qiymatini toping.
A) 1 В) 0 C) %/2-l D) 0,5
17. x ning qanday qiymatlarida у =---—
x + 2
funksiyaning qiymallari 3 dan kichik emas?
A) (-2;5]	B) (-oo;-2)UI5;oo)
C) (-co;-2) D) [5: co)
9. у = 5T — 1 funksiyaning grafigi koordi natal ar
tekisligining qaysi choraklarida yotadi?
A) I, II В) I, III С) П, IV D) IV
10. Ikkita tolg‘ri chiziqning kesishishidan hosil
bo’lgan qo'shni burchaklar 7 : 8 nisbatda bo'lsa,
shu burchaklarni toping
A) 75°; 105° В) 36е; 144° C) 38°; 142°
D) 84°; 96°
2
18.	/ cos3xdx ni hisoblang.
>- ifj
2	12	1
A) -f В) - C) - D)
ООО	о
19.	— Ыодзх 4-6 — 0 tenglamaning ildizlari
yig'indisini toping.
A) 27 B) 36 C) 18 D) 12
66
TEST 2006 r Variant
133
Matematika
20.	4(5;—4) aylanadagi nuqta. C(12;20) uuqta
aylananing markazi b<ylsa. aylananing radiusini
toping.
A) 16 B) 15 C) 25 D) 17
21.	ABC uchburchakda AB - AC, BMA.AC.
BM = 18 va MA = 24. ABC uchburchakning
yuzini toping.
Л) *258 B) 254 C) 270 D) 262
22.	Muntazarn to‘rt burchakli piramidaning
balandligi 18 ga. asosining tornoni 15 ga teng.
Piramidaning apofemasini hisoblang.
A) 13 B) 22,5 C) 19,5 D) 21
23.	Tomonlari 3 va 4 ga teng bo’lgan to’g'ri
toTtburchak o’zining katta tornoni atrofida
aylanadi. Hosil bo’lgan jisrnning to’la sirtini
toping.
A) 48% B) 42% C) 36% D) 24%
24.	Quyidagi ayirrnalardaa qaysi binning qiymati
inanfiy?
A) coslO0 — cos50c	B) -rinl40° — s?n!50°
C) ctg423 - d.^28°	D) tg37° - tg№
25.	cn.$3r  star — cos3« = 0 tenglamani yeching.
A)	(-1 )* • ~ 4- ~k; J + 2%E к € Z
о 3 z
В)	4 + Jt, kez C) J + irk-, irk, tez
6	3	3
D) I + ^k- -ink. kez
b 3
i 31. Asoslari 8 va 14 ga teng bo’lgan teng yonli
trapetsiyaning diagonal! an o’zaro perpendikular.
Trapetsiyaning yuzini hisoblang.
A) 64 B) 100 C) 121 D) 544
32. Agar a vektor b = 3f — 2j 4- k vcktorga kolllnear
va d • b = 28 bodsa, d vektorning uzunliginj
toping.
,/V	v/T
A) ~ B) 14 С) 2\/И D) -y
.s/n(-arccos-) ni hisoblang.
34. (x -	<
tengsizlik .t ning qanday qiymatlarida oTinli?
35. Radius! \/3 bodgan doiraga tashqi chizilgan long
yonli trapetsiyaning asosidagi burchagi 60°
Trapetsiyaning yuzini toping.
A) 3 В) 8ч/3 €) | D) W
36. Sharga konus ichki chizilgan. Konusning
yasovchisi asosining diametriga teng. Sb ar
hajmining konus hajrniga nisbatini toping.
A) 8 : 3 B) 32 : 9 C) 27:4 D) 16 : 9
26.	Massasi 54 kg bo’lgan mis va rux qotishmasining
tarkibida 45% mis bor. Qotishma tarkibida 60%
mis bo'lishi uchun unga yana necha kg mis
qo4shish kerak?
A) 24 B) 13, <5 C) 25 D) 20,25
27.	/(x) — — /^(lOcosx) funksiyaning qiymat lari
tc/plamini toping.
A) (—co;oc) B) (-oq;0] C) (—1:0)
D)
28.	Ikki sonning ayirmasi 27 ga teng. Agar birinchi
sonni ikkinchisiga bo’isak. bo linina 4 ga va
qoldiq 3 ga teng chiqadi. Berilgan sonlarning
yig'indisini toping.
A) 38 B) 31 C) 43 D) 29
29.	m ning qanday qiymatlarida	(
(m - Г)г5 + 2(m — 7)x 4- 2rn 4- 2 kvadrat uchhadni !
to’la kvadrat shaklida tasvirlash mumkin?
A) -17 B) -17: 3 C) 3 D) 2	j
30.	To‘gxri burchakli uchburchakning katetlari 30 va
40 ga teng. Katta kat-etning gipotenuzadagi
proyeksiyasini toping.
A) 14,5 B) 3*2 C) 16,5 D) 16
67
TEST 2006 : Variant
134
Matematika
1
Maternatika
1.	Quyidagi rnulobazalarning qaysi biri natural
sonlarga nisbatan noto'g’ri?
A)	3 hamda 4 ga bo'ling&n son 12 ga ham
bo'linadi.
B)	Berilgan sonlarga bo'lmadigan sonlaraing eng
kichigi bu sonlarning eng kichik karralisi
bo'ladi.
C)	Oxirgi raqami 0 yoki 5 bo‘!gan son 5 ga
bo'iinadi.
D)	Oxirgi raqarni 6 yoki 9 bo‘Igan son 3 ga
bo'linadi.
2- ga tcs'kari sonni toping.
A) 1| B) -0.6 C) -6
О
D) <M
3. r2 + x — 12 kvadrat uchhadni chiziqli
ko'paytuvchilarga ajrating.
А) (ж — 3)(*4~4) В) (r + 3)(i-4)
C) (z-3)(4-x) D) (r + 3}(4-x)
— r~? ni soddalash tiring.
А) т’ В) 0 C) 1 - - D) ~
X	X~
5.	a ning qanday qiyrnatlarida |a 4- 4| ==• — a — 4
tengiik o'rinli bo'ladi?
A) a € ф В) а = —4 С) а < —4
D) a <—4
б.	z2 - 7x + q = 0 tenglamaning ildizlaridan biri
—19 ga teng. Uning ikkinchi ildizini toping.
A) 8 В) -26 C) -8 D) 26
7,	4 > y/x +1 tengsizlikni yeching.
A) {0; 15] B) [—1; 15) C) (-1; 15]
D) [0: 15)
8.	0,(8) + 0, (3) — - ning qiymatini hisoblang.
A) B) 1| C) | D) 0,(11)
v	iz	V
9.	(x)16	< 4 tengsiziikning eng katta butun
yechimini toping.
A) 10 B) 6 C) 9 D) 11
10.	Ikkita to‘gJri chiziqning kesishishidan hosil
bo'lgan qo’shni burchaklarning gradus o'lovlari
5 ; 7 nisbatda bo'lsa, shu burchaklarni toping.
A) 30°; 150° В) 75°;105c C) 62”:118°
D) 54°;126*
11.	Quyidagi tasdiqiarning qaysilari noto'g'ri?
1)	tomonlari a va b ga, ular orasidagi
burchaklaridan biri a ga teng bo'lgan
parallelogrammning yuzi S — ^ubsina formula
bilan hisoblanadi;
2)	tomoni ar i a va b ga, ular orasidagi burchagi а
ga teng bo'lgan uchburchakning yuzi
S = -absina formula bilan hisoblanadi;
3)	o'xshash figuralar yuzlarining nisbati ularning
mos chiziqh o'lchovlarining nisbatiga teng.
A) 2; 3 B) 1,2 C) 1:2;3 D) 1;3
12.
Tekislikka og'ma va perpendikuiar tushirilgan.
60
Og'ma va tekislik orasidagi burchak аггсоз— ga.
og'maning tekislikdagi proyeksiyasi 120 ga teng.
Perpendikuiarning uzunligini toping.
A) 12 В) - C) 22 D) -
2
13.	Agar cos2a = - bo'lsa, sin2 a ni hisoblang.
A) I B) 1 C) | D) |
14.	156 va 420 ning umumiy bo'luvchilaxi nechta?
A) 5 B) 7 C) 4 D) 6
19,5:4| + з1-1,9
15.	----------------- ni hisoblang.
— 0,16
A) 16 В) 4~ C) 12 D) 7,45
x + 1
16.	у = -—funksivaga teskari funksiyani toping.
2 —
	2^-1	2-3x
A)	W=3x + 1 B>	V~ z-f
	2i 4-1	__.	2 -3*
C)	^Зх + l D)	У - 1 i - r
17.	-— ------< 0 tengsiziikning rnanfiy butun
(r + 2)'
yechimlari yig'indisini toping.
A) -4 B) -9 C) -6	D) ^5
18.	Agar Ff(x) sinx va F(\) 4 bo'lsa, F(z) ni
taping.
A) 4 + rinl — sinz B) 4 — cosl + cosx
C) 4 4- rinl 4- sinx D) 4 4- cost — cosx
19.	Agar ioge 64 3 va Jog6 243 = 5 bo'lsa. ab ning
qiymatini toping.
A) 5 B) 12 C) 8 D) 6
20.	A(— 6; 1) aylanadagi nuqta, G(6; 10) nuqta
aylananing markazi bo'lsa, aylaning radiusini
toping. -
A) 13 B) 14 C) 15 D) 16
68
2
TEST 2006: Variant
134
Matematika
21.	Rasmda M7V||XC. MBN. uchburchakning
perimetri 42 sm, ABC uchburchakning perimetri
84 srn. Af В/7 uchburchakning yuzi 44 sm2.
ABC uchburchakning yuzini (sm2) toping
A) 108 B) 99 C) 81 D) 176
22.	Muntazam to'rt burchakli piramidaning
balandligi 12 ga, asosining tomoni 7 ga teng.
Uning apofemasini toping.
A) 13,5 B) 9 C) 12,5 D) 25
23.
1
Konus bajmining % ga nisbati 21- ga teng bo’lib,
О
uning yasovchisi asos tekisligi bilan 45° li
burchak tashkil qiladi. Konusning balandligini
toping.
A) 7 В) 3 C) 4 D) 6
29.	Agar x- + x — 4 = 0 tenglamaning ildizlari va
T2 bo'dsa, Ij 4- *2 ning qiyrnati qanchaga teng
bo'ladi?
A) 3 B) 1 C) -13 D) 2
30.	Asosi 8 sm, balandligi 8 sni bo'igan teng yonli
uchburchakka tashqi chizilgan aylananing radiusi
necha sm?
А) 11 B) 10 C) 5 D) 12
31.	Rombning kichik diagonal! УЗ ga, yuzi 1.5 ga
teng. lining o’tkir burchagini toping.
A) 60° B) 30° С) 70е D) 45°
32.	a{m — Г, a/5',4) vektorning uzunligi 5 dan katta
bo'ladigan ?n ning barcha qiymatlarini toping.
A) (-1;3) B) (—oo;—2)U(2:oc)
C) (—oc; — 1) U (3;oo) D) (-2,2)
33.	Agar |ci| < 1, }6| < 1 boMsa. arccosp — Aarcsinb
ifodaning eng katta qiymat-i qanchaga teng
bo'ladi?
A) 1 В) 2?г С) 5т D) 3it
34.	log\z& ^(0,25)1се1в^+* + ат+' ‘П ni hisoblang,
3	2	2	1
A> 8	7	C> 5	D> П
sin36” co$36e
2' ‘ .wnl2° ~ cos!2°
A) 3 B) 2 C)	D) 7/3 -1
25. 2sin2x — sin'2x = 0 tenglamani yeching.
A)	rfc; (-1)* • | + irk, k G Z
B)	irk; | + xfc, t G Z
C) »i; ’- + irk, keZ
О
D) 2 + rk, к G Z
35. To’g‘;ri burchakli ACB uchburchakning katetlari
8 ga va 10 ga teng. Shu uchburchakning C to‘g'n
burchagi uchidan CE median» va CD bissektrisa
o'tkazildi. CDE uchburchakning yuzini toping.
A) 2^	В) 2|	С) з|	D) 2j
f	У	о	<j
36. Konusning o‘q kesimi muntazam uchburchakdan,
•silindrniki esa. kvadratdan iborat. Agar konus
hajmining silindr hajmiga nisbati : 2 kabi
bodsa, to‘la sirtlarining nisbatini toping.
A) ^;^2 В) Л:\/2 C) ^9:2
D) 3:2
26. 520 soni shunday ikki ЬоЧакка bo'linganki,
ulardan binning 80% i ikkinchisining 24% ini
tashkil qiladi. Bo4aklarni kichigini toping.
A) 120 B) 400 C) 460 D) 420
27. у — ax^ -k b kubik parabolaniug grafigi
4(1; -52) va £?(—I; —56) nuqtalardan o’Udi.
Qaysi nuqtada bu funksiyaning grafigi Ox o'qini
kesib o'tadi?
A) (-3; 0)
D) (3; 0)
B) (2; 0) C) (-2; 0)
28.
f x — Sy — 5
Agar V + 2|»| = 3
toping.
bo’lsa, x — 2t/ ning qiymatini
A) 2 В) 3 C) -I D) I
69
TEST 2006 : Variant
135
Matematika
1
Matematika
l.	Natural sonlar uchun quyida keltirilgan
mulohazalardan qaysi biri noto‘g‘ri?
A)	Agar ikki qoshiluvehidan biri 11 ga bo'Hnib.
ikkinchrsi 11 ga boiinmasaf n laming
yig'indisi 11 ga bo'linmaydi.
B)	Berilgan son 1ar bo'linadigan sonlarni ng eng
kattasi и I anting eng katta utnumiy
bo'luvchisi bo'ladi.
C)	3 va 5 ga bo'hnadigan son 15 ga boTmadi.
D)	3 ga betilingan son 6 ga ham bo'iinadL
n 2,60.7-1,8.....................
2.	nin& q’yrnahni toping.
4)4-	» t К ’ * J •
л> I в) 54 C) B D) °’04
3.	Uchburchakning birinchi tornoni > 10) sm,
ikkinchi tornoni undan 6 sin qisqa, nchinchi
tomoni csa birinchisidan 4 sm uzun. Shu
uchburchakning perimetrini (sm) toping.
А) Зх + 2 B) 3z-2 C) 3*4-3
D) 3z-3
4.	(4® — 3)2 — !•(—4i- 4- 5) ko‘phadni standart
shakliga keltiring.
A) 12/- - 25* 4-9 В) 20*2 - 29* 4- 9
C) 8r-i + 7 D) 20*2 —25*4-9
5.
Agar (x — 5)(~x — 4) = 0 bollsa, ^-z — 4 qanday
5	о
qiymatlar qabnl qil&di?
A) faqat — 3 B) faqat 0 C) 0 yoki 3
D) 0 yoki —3
6.	Xi va i2 r2 — Hr 4 12 — 0 tenglamaning
ildizlari bo‘)sa, *(*2 4- zoning qiymatini
toping.,
A) 132 B) -78 C) -132 D) —168
I
xJ - 2x + 3 t . ... .
7	_________— > q tcngsiznkm yeching.
z 4* 2
A) [2;oo) В) (—2;oc) C) (—oo;2]
D) (—oo;2)
8.	Quyidagi sonlardau qaysi biri 0,3(6) ga teng?
4	11	9	4
A> >5 B) 30 C> 27 D) TT
9.	( yl)1**»*v ni hisoblang.
Л) 9 В) 3x/2 C) 18 D) 3
10.	Qo'shni burchaklardan biri ikkinchisidan 12°
katta. Shu qo:shni burchaklarni toping.
А) 81е; 99е В) 82°: 98е С) 96е; 84°
D) 80°; 100е
11.	Quyidagi tasdiqlarning qaysilari to‘g‘ri?
1)	tomontari a va b ga, ular orasidagi
burchaklaridan biri о ga teng bo'lgan
parallelograrnmning yuzi S = absinct formula
bilan hisoblanadi;
2)	tonionlari a va 6 ga, ular orasidagi burchagi o-
ga teng bo'lgan uchburchakning yuzi
.$* =. kabtsinot formula bilan hisoblanadi;
3)	diagonallari dj va d2 ga, ular orasidagi
burchagi о ga teng ixtiyoriy qavariq
to4rtburchakning yuzi S did^ina formula
bilan hisoblanadi.
A) 2;3 B) 1;2 C) 1;2;3 D) 1;3
12.
Tekislikka og'rna va perpendikular tushirilgaii.
15
Og'rua va tekishk orasidagi burchak arccos— ga.
og’maning tekislikdagi proyeksiyasi 30 ga teng.
Perpeiidikularning vzunligini t-oping.
A) 16 B) 30 C) 32 D) 23
13. tg(— 4- a) — - Ix/lsa. etger ning qiymatini
t-oping.
5	2	4
A) 4 B) |	C) ~	D) ~
14.
16.
l2-3n.r ,	,	, .
------ifotia n ning nechta natural qiymatiaa
n
natural son bo'ladi?
A) 3 B) 6 G) 4 D) 5
0,075 - 0.075-6,4 .
------  ——------ ш hisoblang.
0.175- i-
200
A) 40,5 B) 4,05 C) 20,1 D) 20,25
. - /(д - <)<2 - «)
S у (r + l)x
sohasini loping.
funksiyaning aniqlanisb
A)
C)
0)
|-l;0]U(2;4) B) (-l;0)U[2;4]
(-оо;-1)и(0;2]и[4;оо)
(-1;O]U[2;4)
(z — 7)(z 4.3)	.	.
’7- —ч----------7“ < 0 tengsizlikmug eng katta va
2z — z 4- 4
eng kichik butun yechimlari ayirmasini toping.
A) 9 B) 10 C) 7 D) 8
18. J cos’irdx ni hisoblang.
ч/ч — 2
A) -2 В) 0 С) ------------------- £>) -1
4
19.
31g4 4-3lg2b
Igl300- lg!3
ning qiymatini hisoblang.
A) 1.5 В) 6 C) 2 D) 3
70
TEST 2006: Variant
135
Matematika
20.	Uchburchak burchaklarining kattaliklari nisbati
1:1:2 kabi, katta tornonining uzunligi esa 24 ga
teng. Uchburchakning katta tornoniga tushirilgan
balandligini toping.
A) 12 B) 6,5 C) 6 D) 8
21.	Ikkita o'xshash ko'pburchak yuzlarining nisbati
9:4 ga teng. Kichik ko*pburchakrnng perirnetri 8
sm. Katta ko’pburchakning perimetrini toping.
A) 8 B) 9 C) 12 D) 6
22.	To’g’ri parallelepiped asosining tomonlari 9 va 12
ga, uiar orasidagi burchak 120s ga. yon qirrasi
ga teng. Parallelepipedning kichik diagonal!
uzunligini toping.
A) 18 B) 5 C) 21 D) 15
23.	Konusning o'q kesirni teng tomonli uchburchak.
Agar konusning to‘la sirti 192тг ga teng bo'Isa,
konus asosning diamctrini toping.
A) 24 B) 18 C) 21 D) 16
. я 3 ТГ . з %	T 1	. V
24	'505 р ~ S1n' j2 ’	4 П1
hisoblang.
А) В) 0 С) D>
Ъ	с	4
25. 5sin4r — 8 = Зса*(— 4- 4г) tenglama [—2*; 2г)
kesniada nechta ildizga ega?
-  A)“7-В)"0~~СУ 6' D) 8
26.
Nodirda bor paining ~ qisrni Jahongirdagi
8
pulping qisiniga teng. Nodir puhning necha
foizini J ahongirga bersa, ularning pullan teng
bo‘ladi?
A) 37.5 B) 25 C) 17,5 D) 12,5
30.	Tornonlari 16; 30 va 34 sm bo’lgan uchburchakka
tashqi chizilgan aylananing radiusi necha srn?
A) 18 B) 17 C) 19 D) 16
31.	Teng yonli trapetsiyaning asoalari 30 va 50 ga,
balandligi esa 30 ga teng. Trapetsiyaning
diagonaliui toping.
A) 56	8) 70 C) 60 D) 50
32.	Agar c7(—4; 2; 2) va 6(^2; —л/2; 0) ve к tor I ar
berilgau bo’Isa, 2а va - vcktorlar orasidagi
burchakni toping-
3	2
А) B) arccos-
4	Л
5%	5
—- D) arccos-
6	6
33.	sin* 4- cost — 1 tenglamauing [—я/Итг] oraliqda
nechta iidizi bor?
A) 1 В) 0 C) 3 D) 2
34.	(z - 2)3w^<ri"5r+5' < (x - 2)bKS(=«-3i
tengsizlik x ning qanday qiymatlarida o‘rinli?
C) (—oo:2) U (4;©o)
35.	Diagonal’: crqaii ikkita muntazam uchburchakka
ajraladigan rombga ichki chizilgan aylananing
radiusi r ga teng. Rombning yuzini loping.
A) 4r2 В) 2г2Л С) 4г2Л D)
36.	Sharga balandligi asosining diametriga teng
bo’lgan konus ichki chizilgan. Agar konus
asosining yuzi 2.4 ga teng bo'lsa, shar sirtining
yuzini toping.
A) 6 B) 9% C) 15 D) 12,5
27. у == — x2 -f- 6г — 10 funksiyaning eng katta
qiymatini toping.
A) 1 B) -1 C) 2 D) 0
28.
I 55
----p z= lenglamaning natural sonlardagi
?/4 ’
yechimida у uimaga teng?
A) 4 В) 3 C) 2 D) 1
29. 6zl 4- bx — 15 =: 0 tengiarnaning ildizlari x-f va
uchun 5xj 4- 2xa — 1 nnmosabat ohiidi. Agar b
butun son ekaniigi ma’iurn bo lsa, uning
qiymatini toping.
A) -10 B) 7 va —10 C) 10
D) -7 va 10
71
TEST 2006 : Variant
136
Mzlematika	1
Matemalika
1. 17  11 - 14  11 + 27  23 — 24 - 23 + 21 • 19 — 18 • 19
ni hisoblang.
A) 159 B) 165 C) 203 D) 143
2, (2, 01 — 3,81)' 3,8 ifodani hisobiang.
A) 5,82 B) 6,84 C) -5.82 D) -6,84
3. Uchburchakning birincbi tomoni x (x >12) sin,
ikkinchi tomoni undan 7 sm qisqa, uchiucbi
tomoni esa birinchisidan 5 sm uznn, Shu
uchburchakning perimetrini (sin) toping.
A) 3x- 1 B) 3x + 2 C) 3r + l
D) 3x-2
4. 2n2 — Зап — 4n 4- 6а ko'phadni ko’paylnvdrilarga
aj rati ng.
А) (п-2)(2п-3а)	B) (5 - n)(3a + 2n)
G) (2u — 3a)(n - 5)	D) (За — n)(5 ~ 2n)
5. l^l Лл	:21 z		t-englarnani yeching.
A)	4	B) g5	C) e| D) <1 6	b
6.	xj va xj x~ <- 22x 4-8 = 0 tenglamauing ildizlari
bo'lsa, Xi®? 4- ning qiyrnatini toping.
A) -176 B) -120 C) 176 D) 280
7.	(x ~ l)(x 4- 2) < 0 tengsizlikni yeching.
A) (1:2) B) (—oo; 1) U (2; oo) C) (-2:1)
D) (—co; — 2) U (1; oo)
8.	Quyidagi ketma-ketliklardan qaysilari geoinelrik
progressiyani tashkil etrnaydi?
1)*п-2хл, (z#0);
2)	= <ixn, (ax / 0);
3)	bn = (^)л • sm60° + 1.
5
A) 3 B) 1;3 C) 2 D) 1
9.	/о5«г6 >	tengsizlikni yeching.
A) (|; 1) B) (0; 1) C) (1; oo)
D) (0; 1)
10.	Ikkita tolg‘ri chisiqaing kesiahishidau hosil
boOgan qo*shni burchaklarning gradus o'kbovlari
4 : 6 nisbatda bo‘lsa, shu burcbaklarni toping.
A) 60°; 120° В) 72°;108° C) 50°;130°
D) 30°; 150°
11.	Quyidagi tasdiqlariting qaysilari to’g’ri?
1)	tornonlari a, b va c bo‘lgan uchburchakka ichki
chizilgan aylananiug radiusi г = ~ formula
bilan hisoblanadi:
2)	radiusi R ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S’ = formula bilan
hisoblanadi;
3)	tomoni a ga, burchaklari dan biri a ga teng
rombning yuzi S’ = -a^sina formula bilan
hisoblanadi.
A) 2:3 B) 1:2 C) 1;2;3 1>) !;3
12.	Tekhdikka og'ma va perpendikular tushirilgan.
40
Og‘ma va tekishk orasidagi burchak arcroti— ga.
41
og^naning tekislikdagi proyeksiyasi 80 ga teng.
Perpendikularning uzunligini toping.
A) 36 B) 40 C) 30 D) 18
. r. 14 sin 4а
14.	---------—- — cos о in soddalashtiring.
sin 2o + t os/а
A) sin2а- В) cos2а С) —2sin2а
О) — cos2o
14. 198 va 630 ning umurniy bo‘hivchilari neebta?
A) 6 B) 5 C) 7 D) 4
4	4	15 7	1
15. 0— . 3 - + 1 — : - - 2- ni hisoblang.
А) 2з1	В) 23;	С) 24;	D) 22?
<5	v	t5	<5
у = 4 — 2stnz funksiyaning [0; —] kesmadagi eng
6
kichik qiyrnatini hisoblang.
A) 2 В) 3 С) I D) 2-x/3
17.	Quyidagi lengsizliklardan qaysilari olzaro teng
kuchli?
.. x — 3 л x — 3
3)^—£>0;	4)i-3>o.
X"
A) I; 2; 4 B) 2; 3; 4 C) ha/nmasi
D) 1: 3; 4
18.	j0T ainAxdx ni hisoblang.
A) | B) 4 C) | D) 1
19.	а = Iog1/56, b = logi/e4 va c = log-»/5 4 sonlarni
o*srisb tartibjda joy lashtiring.
А) 6<с<а B) c<b<a C) b<a<c
. D) a < c < b
72
TEST 2006: Variant____________________136
Kfatcmatika
20.	Ikhburdiakning asosiga tushirilgau medianasi
uni perimetrlari 18 va 24 ga teng boMgan ikki
uchburchakka ajratadi. Berilgan uchburchakning
kichik yon tomoni 7 ga teng. Uning katta yon
torrwnini loping.
A) 12 B) 10 C) 13 D) 14
21.	Tornonlari 4 va 8 m bodgan paralleiograrnmning
yuzi 16\/3 nr. Parallelogramrrming o'tmas
burchagini toping.
A) 150° B) 120* C) 105° D) 135*
22.	Muntazam toMburchakli piramidaning
balandligi 24 sm, apofcniasi esa 26 sm. Piramida
asosining perimetrini toping.
A) 48 B) 40 C) 80 D) 96
23.	Asosi rombdan iborat to g‘ri prizrnauing
balandligi 4.5 ga teng* Agar rombning
dioganallari 8 va 10 ga teng boMsa. prizxnaning
hajmi qanchaga teng?
A) 320 B) 360 C) 240 D) 180
24.	(2 4* co*‘22nr)(l +	-f- 4«£n2c* ifodaning eng
kichik qiyrnatini toping.
A) 1,5 B) 2.5 C) 3 D) 2
. .% , .	.	.	\/3
25.	sin( — -b x)-Psjri(-- —-ar) = —	- tenglamaning
5	v	2
ildizlariui ko’rsating.
A) ~ + Ш,ке2 B) ±y+27rfc:fc€#
C) ±—4-2x1’, Jtcz D) + 2rfc, ke 7.
<S	*5
2G.
Ikki sex 230 la kir yuvish rnashinasi ishlab
chiqarishi kerak. Birinchi sex ishlab chiqargan
2
mahsulotning - qismi ikkinchi sex ishlab
chiqargan mahsulotning 80% iga teng. Birinchi
sex
qancha mans idol ishlab chiqargan?
60 B) 50 C) 180 D) 80
30.	To‘g‘ri burchakli uchburchakning katetlari 5 va
7.5 ga teng. Tb'g^ri burchak bissektrisasiniug
uzunligini toping.
А) Зх/2 B) 4v<2 C) 3 + 3\/2 D) 5\/2
31.	To'g'ri to'rtburchakning to'g'ri burchagi uchidan
tming diagonahga tushirilgan perpendiknlar
t.o‘g‘ri burchakni 3:2 kabi alsbatda bcfladi, Shu
perpendikular bilan hoshqa diagonal orasidagi
burchakni loping.
A) 72;> B) 22,5° C) 18° D) 45“'
32.	b vektor a (2; 4: 4) vektorga kollinear bamda bu
veklorlarning skalyar ko'paytrnasi 144 ga teng. b
vektorning uzunligini toping.
A) 16 B) 24 C) 18 D) 12
33.	p — ^/1 4- logi j2 cos x funksiya (0:2т])
ning qanday qiymatlarida aniqiangan?
1^’TJ	[0;%]
4	*
Q [O^My^] D) [0;Г)и(^:2?]
6л?б(\/2 4- 1)
34.	^c(V2 4- I) ni soddalashtiring
A)	B) ^6(x/2+l)
C) х/2 + l D) ----------
У2- 1
35.	ABC uchburchakning yuzi 12 ga teng. Uning В
uchidan LW = 3 mediana tushirilgan. Agar
AAI1D = 90* bodsa. AC toinonning uzunligini
toping.	•
Л) v/73 B) 2/73 C) 10 D) 8
s 36. Konusning o‘q kesirni muntazam nchburcbakdan.
silindrniki esa kvadraldan iborat. Agar kouus
to‘la sirtiuing silindr toda sirtiga nisbati 1:3 kabi
ho‘l$a, hajmlarining nisbatini loping.
A) 2 .9 B) 1 : 9 C) 4 : 9 D) 72 : 9
35
27.	*’ COS^V ifodaning eng katta
qiymati nechaga teng bodishi mumkin?
A) 1,5 B) 1,8 C) 2,4 D) 1,4
28 Qisqarmaydigan oddiy knsrniug rnaxraji
suratidan 18 taga ko'p. Agar kasrning suratiga
379 ni, rnaxrajiga 1 ni qo'shsak. berilgan kasrga
teskari kasr hosil bo'ladi. Berilgan kasining
rnaxraji rd toping.
Л) 19 B) 17 C) 14 D) 13
7 1 (x2 4- 6x + 4)(x2 + 6r 4- 6) = 120 tenglarnaniug
Uaqiqiy ildizlari yighndisini taping.
A) 5 B) -12 C) -5 D) -6
73
TEST 2006: Variant
137
Matematika
1
Matematika
1.	279 ni 16 ga bo'lganda qoldiq 7 bo'ladi. Boiinma
nechaga teng?
A) 12 B) 13 C) 11 D) 17
2-	2,014 : 0.19 4- 2.5 • 0,3 Bi hisoblang.
A) 11,35 B) 9,85 C) 12,85 D) 8,85
3.	r2 - x — 6 kvadrat uchhadni chiziqli
ko'paytuvchilarga ajraling-
A) (z + 3)(z--2) B) (x-3)(z4-2)
C) (z+3)(2-x) D) (t + 2)(3-x)
хз з
4.	(r”1 4-y-1) -------о ni soddalashtiring.
4-
Al Х?У' Bl	гл 1
(z 4- уУ (x 4- j/)2 z + у
D) x2y2
5.	n ning qanday qiymatlarida nx 4- 2 = n 4- 2x
tenglama cheksiz ko'p yechimgaega bo'ladi?
A) n = 1 В) n = 0 C) n / 1 D) n - 2
6.	T) va x2 — 13x 4- 12 = 0 tenglamaning
ildizlari bo’lsa, z^x^ + ning qiymatini
toping.
A) 156 B) 94 C) —156 0) -152
7.	Agar а > b va ab 0 bo'lsa, quyidagi
tengsizliklardan qaysi biri bar doim oVinli?
A) a2 > b2 B) — >C) 2a>3a — b
a b
D) 3a <_ 4 a — b
8.	0,4(5) soni quyidagi sonlardan qaysi binga teng?
A) IT B) 90 c) 90 D) 90
9.	у = 5r — 5 funksiyaning grafigi koordinara
tekisligining qaysi choraklarida yotadi?
A) I, III. IV B) I, TV С) III, IV D) I, II
10.	Ikki qo'shni burchakning ayirmasi 28° ga teng.
Shu burchaklardan kichigini toping.
A) 78° B) 72° C) 78° D) 82°
11.	Quyidagi tasdiqlarning qaysilari to'g'ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R = ~£(a.b. c— uchburchakning
tomonlari, S'— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi 5 = formula bilan
hisoblanadi;
3)	tomoniari a va b ga, ular orasidagi burchagi o'
ga teng bo'lgan uchburchakning yuzi
S ~ |a6sina formula bilan hisoblanadi.
A) 2:3 B) 1:2 C) 1:2:3 D) 1:3
74
12.	Tekislikka tushirilgan og'maning uzunligi 75 ga,
uning tekislikdagi proyeksiyasi esa 72 ga teng.
Og'ma va	tekislik orasidagi burchakni	toping.
7	24	7
A)	arccos—	B)	arcsin—	C)	arcsin-r-
oO	25	24
7
D) arcsin—
’	25
2
13.	— ---------—- m soddalashtiring.
tg 2a - cig 2a	°
A) —2tg4o B) cos4a C) — tg4a
0) tg 4a
14.	Agar m > 3, n > 5 va k < 6 bo'lsa, 3m 4- 5n — 2k
ning eng kichik butun qiymatini toping.
A) 14 B) 23 C) 22 D) 13
15.	842 sonining o'ng tomoniga qanday raqam
yozilsa, hosil bo'lgan son 36 ga qoldiqsiz
bo'linadi?
A) 2 B) 4 C) 8 D) 6
16.	\f(4z — 1)2(3 — r) (1 — 4х)л/3 — r t-englik x
ning qanday qiymatlarida to'g'ri bo’ladi?
A) 0,25<r<3 B) (-oo; 0,25]U{3}
C) -3 < x < 3 D) x < 3
. _ x 4* 1	.	.....
11. ;----------z-r > 0 teugsiziikm ycchmg.
(x 4- 3)(x - 5)
A) (-3: -J)U[5; oo)	B) (3; -1]U[5: oc)
C) (-3; -1]U(5: oo)	D) [-3; -1)U[5; oo)
I#, ----------njng boshlang'ich funksiyasini
co«2(~4- I)
toping.
A) «s(7 + l) + C B) ltff(£ + l) + C
4	4	4
C) -4<9(^ + l) + C D) -1<S(£+1) + C
19.	— 9) 4- 2/<?0уз(х — 9) < 4 tengsizlikni
yeching.
A) (5; 14) B) (6:15) C) (9; 18)
D) (5:81)
20.	A ABC da гВАС=45°, ZACB=x30’ va BC=16/2
ga teng. AB tomonning uzunligini toping.
A) 16 B) 12 C) 12^/2 D) 14
21.	Katellariniug nisbati 2:3 kabi bo'lgan to'g'ri
burchakli uchburchakning gipotenuzasi л/182 ga
teng. Uchburchakning yuzini toping.
A) 24 B) 42 C) 36 D) 39
22.	Prizmaning asosi tomoni Зл/5 bo'lgan muntazam
oltiburchakdan, yon yoqlari kvadratlardan
iborat. Prizmaning katta diagonalini toping.
A) 10 B) 15 C) 12 D) 7>/5
z
TEST 2006: Variant
137
Matematika
23.	Konus asosining radiusi 2\/3 ga. yasovchisi va
asos tekisligi orasidagi burchak G0° ga teng.
Konusning hajmini toping.
Ятгч/З	_
A)	B) 16% C) 8%^/3 D) 24%
*5
24.	Agar tga 4- cigar 10 bo'lsa, sm2ct ni hisoblang.
A) 1 B) 1 C) 1 D) |
sin x  cos 2x — cos x • sin 2x —
— — tenglanianing
yechimmi toping.
B) + vn , n e Z
n
D) ~n , n € Z
A) %n . n € Z
C) , n € Z
26. Korxonada inahsulot ishlab chiqarish birinchi yili
10% ga, ikkinchi yili 20% ga oshdi. Mahsulcrt
ishlab chiqarish ikki yil mobaynida necha foizga
ortgan?
A) 26 B) 25 C) 26.5 D) 32
27 у — kx2 — 2kx + 5 va u = 2 — кт funksiyalarning
grafiklari к ning nechta butun qiymatlarida
kesishmaydi?
A) 2 B) 12 C) 4 D) 11
?8- f + В + & + S + 55 + Пз = 6 te”Siarnani
yeching.
A) 13 B) 26 C) 16 D) 18
29. у = 2x2 4- bx + c parabolaning uchi (—4; -5)
nuqtada joylashgan. Bu funksiya nollarining
o'rta arifmetigini toping.
A) -2 B) -4 C) 5 D) -3
32 Agarafl; —1; 3) va 6{4: 3; 0) bo'lsa, a ning
qanday qiymatida 4a 4- ab vektor b — a vektorga
perpendikuiar bodadi?
A) 2,1 B) 1 C) | D) -A
33.	— Ssinx -3 = 0 lenglamam yeching.
A)	(~l)r‘+l у 4- ттг.п G Z
6
B)	(-l)"^ + irn,ne2
0
c) (~i)n+lJ+2»«.ng г
о
D) (~l)n| + 2m,n€Z
34.	x^9 4- 9^r = 6 tenglamani yeching.
A) 10 B) 1 C) 2. D) s/W
35.	Rasmda AE ~ 3 • EB, AF ~ FC, S&Abc = 120.
В EFC toM burchakning yuzini toping.
A
A) 75 B) 80 C) 40 0} 60
36.	Konusning o!q kesimi rnunt-azam uchburchakdan,
silindrniki esa kvadratdan iborat. Agar darning
hajmlari teng bo’lsa, to4a sirtlarimng nisbati
nirnaga teng?
А) УЗ:^ В) : т/3 C) 1 : УЗ
D) 3:2
11. Aylanaga tashqi chizilgan teng yonli
trapet-siyaning asoslari 56 va 14 sm.
Trapetsiyaning balandligi necha sm?
A) 40 B) 28 C) 36 D) 35
75
TEST 2006: Variant
138
Matematika,
Matematika
1. 4 nr 3 drn2 4 sm2 necha kvadrat santimetr
bo’Iadi?
A) 40244 B) 40304 C) 43004 D) 41034
2.
1,6-0,15-9/2................
4~6~~03-6.4 n’Bg qlyma‘‘nl ,OP‘ng
A) | B) | C) | D) 2
0	6	z
3.	a(b — c) — b(c — a) — c(b — a) ni soddaiashtiring.
A) Safe B) —2ac C) 2afe - 2bc D) 0
4.	(r - 1)(2 — t) + (x - 3)2 ko'phadni standart
shaklga kelt-iiing.
А) 3r2 4-15x4-7 В) —3x4-7
С) Г2г4-4-х2 D)’9x4-7
5.	к parametrning qanday qiymatlarida
1 3x — у — 4 len£0arna^ar sisternasi yechimga
ega ernas?
A) 2 B) 9 C) 6 D) 3
6.	= x 4- 1 tenglamaning nechta haqiqiy iidizi
bor?
A) 2 В) 3 C) iidizi yo^ D) 1
7.	—----“~з~~ — tengsizlikni yeching.
A) (-oo; 3) В) [3; oo) C) (3; oo)
D) (-oo; 3]
8. 0,(7) + 0,(5)-1
A) | B) d
*✓ «/
ning qiymatini hisoblang.
2	1
C) 1- D) 1-
9.	Zo^/plOO8 ni hisoblang.
A) 4 B) 1 C) 2 D) 3
10,	Qo'shni burchaklardan biri ikkinchisidan 40°
katta. Shu qoshni burchaklarni toping.
A) H0’;70e В) 160е;20° C) 140°:40е
D) 20° -,160е
11.	Quyidagi tasdiqlarning qaysilari noto;g‘ri?
1)	tomoulari a,b va c bo'lgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
2)	tomonlari a va b ga. ular orasidagi burchagi a
ga teng bo:lgan uchburchakning yuzi S ~ absina
formula bilan hisoblanadi;
3)	o‘5rshash figuralar yuzlarining nisbati ularning
mos chiziqli oichovlari kvadratlarining uisbatiga
teng.
A) 2:3 B) 1;2 C) 1:2:3 D) 1;3
12.	Tekislikka og'ma va perpendikular tushirilgan.
Og'maning tekislikdagi proyeksiyasi 12 ga,
perpendikularnmg uzunligi 35 ga teng. Og;ma va
perpendikular orasidagi burchakni toping.
*4	-	m	24
A) arcstn-- B) arccos —
Of	J (
35
D) arcsin —
35
?12
13.	tg( — — q) — 4 bo‘lsa., tgo ning qiymatirii toping,
x.
A) -3 В) | C) D) |
.5	5	3
14.	420 : (60 — 1000 : x) = 12 dan x ni toping.
A) 1 B) 8 C) 36 D) 40
О
15.	18 va 8 sonlari eng kichik umumiy karralisining
natural bo‘luvchilari nechta?
Л) 7 B) 12 C) 9 D) 8
16.	у = 2xs — 2x4-7 funksiya grafigining abssissa
o‘qiga eng yaqin bo'lgan nuqtasi koordinatlarini
toping.
A) (4,5; 0,5) B) (0,5; 4,5)
C) (—0,5;—4.5) D) (0.5;6,5)
17.	Agar a < — 1 bo‘lsa, quyida keltiriigao
ifodalardan qaysi birining qiymati eng katta
bo‘Iadi?
A) a"3 B) a~s C) a7 D) a“&
* x
18.	f cos— dx ni hisoblang.
A) -2 B) 2 C) 1 D) 2v/2
19.	n 5= ^i/24 4- ^i/22> m — /ne“2 va
p — /05j/з 15 — /0^1/35 sonlarni kamayish
tartibida joylashtiring.
A) m > n > p
C) m > p > n 0) n > p > m
20.	Aylanaga tashqi chizilgan teng yonli
trapetsiyaning o'rta chizig’i 8 ga teng. Shu
trapetsiyaning yon tomonini loping.
A) 8 B) 4 C) 5 D) 7
21.	Rombning tonnoni 6 ga. yuzi 18\/3 ga teng.
Rombning o4mas burchagini toping.
А) 120е В) 135° С) 140° D) 150*
22.	Teng tomonli uchburchakning tomonlari 3 m.
Uchburchak tekistigidan tashqarida uning
и ch lari dan 2>/3 m masofada yotuvehi nuqtadan
uchburchak tekisligigacha hoclgan masofani
toping.
А) л/3 В) 1 С) 3 D) 1,5
76
TEST 2005 : Variant
138
Matematika
23.	Radiusi 8 ga teng bo-lgau sharga balandligi 18 ga
teng bo’lgan konus tashqi chizilgan. Konus
asosining radiusini toping.
A) 18 B) 12 C) 16 D) 24
rosl2a — cos8a . .	.
/4. -----......... quyiaagilardan qavsi binga
sin 10 о
teng?
A) 2co5'2о В) — *2sin2a (?) —$m2cr
D) — 2cos2a
To sinz 4 sinSx = 0 tenglama [0; 4*] oraliqda
nechta ildizga ega?
A) 7 B) 13 C) 8 D) 9
26 Agar kubning qirrasi 20% ga kamaytirilsa. uning
hajmi necha foizga kamayadi?
A) 40 B) 48.8 C) 30.8 D) 60
27.	у — —3x2 4- 12x — 13 parabola uchining
koordinat-lari yigundisini toping.
A) 1 B) -1 C) -2 D) 0
28.	m va n ning qanday qiymatlarida
2rm — Зпу = 12 va 3xm 4 2ny = 44 to‘g‘ri
chiziqlar (2; 1) nuqtada kesishadi?
A) m —8,n“6 В) m = 6.n==4
C) rn= 12,n —2 D) m=4.n—10
29.	x2 4px 4$ = 0 tenglamaning ildizlari
x2 — 7x 4- Ю = 0 tenglamaning ildizlaridan ikki
marta katta. p4 q ning qiymatini toping.
A) 26 B) -7 C) -14 D) -46
30.	To’g’ri burchakli uchburchakning gipotemizasi 25
sm, katetlaridan birining gipotenuzadagi
proyeksiyasi 23.04 sm. Ushbu uchburchakka ichki
chizilgan aylananing radiusi necha sm?
A) 2,5 В) 3 C) 1,5 D) 2
31.	M>(6; 7) va MK(7: 6) vektoriar
paraUelogranimning tomontari bo: Isa. uning
diagonallari orasidagi burchakni toping.
A) 45° B) 30’ C) 90’ D) 60°
37. Agar a(—6;3;3) va 6(3; —3;0) bo’Isa, 2d va ^6
vektoriar orasidagi burchakni toping.
A) 60° B) 150° C) 135° D) 120е
33. |i 4s«nx| < ~ tengsizlikning [0;2x] oraliqdagi
eng katta va eng kichik yechimlari ayirm&sini
toping.
2ff
А) 1,5я В) т C) 1,2* D) —
J
34 (1,25)1 "* > (0,64)211+V«) tengsizlikning
yechimlari orasida nechta tub son bor?
A) 7 B) 5 C) 12 D) 9
35. Gipotenuzasi c ga va o4kir burchaklari
sinuslaxining yig;indisi q ga teng bo4lgan to!g;n
burchakli uchburchakning yuzini toping.
A)	B) pV-U
C) |c2(<?241) D) ~^(c24 1)
4	4
36. O q kesimi teng tomonli uchbutrchakdan iborat
konusga diametri D ga teng sfera ichki chizilgan.
Konusning to'la sirtini toping.
A) |rD2 B) ^D2 C)
П) jrD3
4
77
TEST 2006: Variant
139
Matematika
Matematika
1	/ m 8 4- 5n4 + 4n2 ,	,
I.	n(n G Ajning---------5---kasr butun son
n
bo‘ladigan bardha qiymatlarmi toping.
A) 1; 2 B) 1 C) 1; 2; 4 D) 2
2.	6,4; Vi —3,2 sonlarning o’rta arifmetigi 0,8 ga
teng. у ni toping.
A) -0,8 B) 1,2 C) “0,4 D) 0,4
3.	16 — (8c — 3)2 ni ko^aytuvchilarga ajrating.
A) (8a ~ 1 )(7 + 8a)	B) (8a + l)(8a - 7)
C) (8a — 1)(7 — 8a)	D) (8a 4-1)(7 - 8a)
4.	2r(x — 1) — (2x 4- l)(x — 2) ko‘phadni standart
shaklga keltiriug.
A) 2x2 “ 3r B) 4r2 — 1 С) —* 4-1
D) *4-2
5.	m ning qanday qiymatlarida (rn2 — \)y 4- 1 = m
lenglama yechimga ega bo'imaydi?
A) m — 0 B) m = 1 C) m = 2
D) m = — I
6.	va z2 r2 4- 2z — 12 — 0 tenglamaning ildizlari
ekanligi ma’lum. x{ 4- x2 ning qiyniat.ini toping.
A) 12 B) 10 C) 28 D) 11
7.	— 3 < — 2 tengsizlikni yeching.
A) x G 0 B) x < 4 C) x > 4 D) z > |
8.	Quyidagi ketma-ketliklardan qaysilari geometrik
progresstyani tashkil et-maydi?
I) a„ = |-2"; 2) <x„ = 3-2~”; 3) bn =	+
A) 1;2 B) 1;3 C) i D) 3
9.	ni hisoblang.
A) 7 В) Зл/5 C) 15 D) 5
10.	Ikki to‘g‘ri chiziqning kesishisbidan hosii bo'lgan
burchakiarning biri 40° ga teng. Qolgan
burchaklami toping.
A) 110°, 110°, 110° B) 150°, 150°, 30°
С) 140е, 140е, 40® D) 60е, 60°, 30®
11.	Quyidagi tasdiqlarning qaysilari noto4g'ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R'.= ^(а,Ь,с~ uchburchakning
tornonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi о ga teng
doiraviy sektormng yuzi S — formula bilan
hisoblanadi;
3)	tomoni a ga, burchaklaridan biri a ga teng
rombning yuzi S = ~a2sina formula bilan
hisoblanadi.
A) 2:3 B) 1:2 C) 1:2;3 D) 1;3
12.	Tekislikka tushirilgan og*ma va perpendikular
.. . .	. *	.20	л
orasidagi burchak a resin-— ga teng. Og mamng
uzunligi 58 ga teng. Perpendikularning
uzunligini toping.
A) 80 B) 40 C) 42
E>) 33
stn4a 4- 2cas2a - cos4a .	,, , , . .
13.	------r-r-----—?-------r-i1 nt soddalashtiring.
1 — sin2cr — cos4a 4-
A) 2srn2of 8) 2tg2a C) etg2a
D) 4tp2a
14.	—~—— ifoda natural son boladigan n ning
natural qiymatlari nechta?
A) 7 B) 2 C) 5 D) 3
15.	Proporsiyarnng dastlabki uchta hadi yigSndisi 78
ga teng. Uning ikkin.chi hadi birinchi hadining -
2
qismini, uchincbi hadi esa- - qismini tashkil
etadi. Proporsiyaning uchinchi hadini toping.
A) 18 B) 12 C) 24 D) 36
16.	/(*) = x/5 +-X+’t 4- \/5 4- V4 — x funk&iya
uchun quyidagilardan qaysi biri o^rinli bo‘Iadi?
A) toq ham. juft ham emas B) toq funksiya
C) o’suvchi fanksiya D) juft funksiya
x2
17.	—“ < x — 4 tengsizlikni yeching.
A) (~4; 4) В) (“oc;~4) C) d D) (0:4)
18.	J (cosxcos2x ~ sinxsin2x}dt integralni
0
hisoblang.
., 1	1	2	y/2
A> 3	B) e	C) 3	D) V
19.	Iog2(4 ~ '2x) “ log ^(4 — 2z) > - tengsizlikni
<5
yeching.
A) (“oo; 1.) B) (-oc; 0,5) C) (0; 1)
D) (~4; -1)
20.	Teng yonli uchburchakning yon tomoniga
tushirilgan balandligi bilan ikkinchi yon tomoni
orasidagi burchak 26е ga teng. Teng yonli
uchburchakning asosidagi burchagini toping,
A) 48® B) 50° С) 58й D) 55®
78
TEST 2006: Variant
139
Matematika
21.	ABCD paraJlelogratnmda OB± AC, A0=8,
OC=5 va BO—4. Parallelograrnrnning yuzini
toping.
A) 28 B) 50 C) 52 D) 56
22.	Chiziqlicrlchovlari 3; 4 va 2714 srn bo!lgan
10‘g‘ri burchakli parallelepipedning diagonal!
necha sm?
A) 7 B) 11 C) 9 D) 10
23.	Kubning bar bii yog2 ini yuzi 27 marts orttirilsa,
uni ng hajrni necha niarta ortadi?
A) 54\/3 B) 27 Л C) 27 D) 8! 75
5	6 \/3 — 5
24.	Agar tga + tgO = - va tgatgfi ~	bo'Isa.
О	6v3
ь + fl nirnaga tong bo’ladi?
A) J + ri, fc€Z B) J + rk. keZ
О	t
C) ~ + fcGZ D) —--Wk. fcEZ
4	6
25.	sin'2x 4- cos(~ 4-6*) ’x s»n4z tenglarnani
yeching.
A) ±— 4- am; -r-’ n C Z B) ~n£ Z
6	4	4
C) tti. n C Z D) -^+тп, n^Z
V
26.	Agar tekis harakatda tezlik 30% ga ortsa.
ma'him masofani bosib o'tish uchun ketadigan
vaqt necha foizga karnayadi?
А) зз!	В) 1б|	C) 23—	D) 20
л	a	la
27.	f(x) = |z — 1| 4-	— 2| funksiyaning qlymat-iar
sohasini toping.
A) (I;oc) В) [0: oo)
C) [3;oo) D) [2:00)
!• 30. Uchburchakning b va c ga tong tornonlari
orasidagi burchagi 30° gatong. Uchburchakning
uchiudu tomoni 16 ga tong boisa harnda uning
tornonlari c~ s= b~ 4- 16& + 256 shaft ni
qanoatlantirsa. c ning qiymati qanchaga teng
bo'ladi?
A) lev's В) Г2зД С) 12Л D) 1бЛ
31.	Teng yonh trapetsiyaning diagonal! 1673 ga teng
va u asosi bilan 30° li burchak tashkil etadi.
Trapetsiyaning o4rta chizigu nechaga teng?
A) 12 B) 16 C) 20 0) 24
32.	Uchlari A(2: 3; 1), B(3: 2; 1) vaC(3: 4; 1)
nuqt-alarda bolgan teng yonli uch.burciiak.ning
asosidagi burchagini toping.
A) arccofi^-	B) arccos^	C) ~
<5	u	ni
D) arccos—t=z
V3
33.	sinbx - 3cos2r = 4 tenglamani yeching.
A) — + 7rn,n€:Z B) -|+2fn,n€Z
^•4-27гп!п G Z D) r+ xn,n £ Z
34.	у = Iog2 log^ У4г — x- — 2 funksiyaning
xuiqlanish sohasini toping.
А) (2-Л;2 + ^/2)
В) (2-ч/2:1)и(3:2 + х/2)
C) (-oo;l)U(3:oo) D) (1;3)
35.	iladiusi R. ga tong bo'Igan doiraning markazidan
bir tomonda ikkita bir-biriga parallel vatar
o'tkazildi. Bu vatarlardan biri 120е U, ikkinchisi
60° li yoyni tortib turadi. Parallel vatarlar
orasida joylashgan kesimning yuzini toping,
кЛ= х-Я2 ЗтЯ1 . irR1
“ B' — C) ~ D) “
36.	Konusning o:q kesinii teng tomordi
uchburchakdan, silindrniki esa kvadratdan
iborat. Agar ulaming to'la sirtlari tongdosb
bo‘lsa, hajmlarining nisbatini toping.
A) } : 3 B) 2 : 3 C) 72 : УЗ D) 1 : 72
28. To‘rtta sonning yigdndisi 118 ga teng. Agar
birinchi va ikkinchi sonning nisbati 2 : 3 kabi.
ikkinchi va nchinchi sonning nisbati 3 : 5 kabi va
uchinchi va torrtinchi sonning nisbati 5 : 6 kabi
bo‘lsa, birinchi va to rtinchi sonning yig'indisini
toping.
A) 62 B) 60 C) 59 D) 66
29. (2}т| — 3)2 = |xj tonglamaning barcha ildizlari
ko'paytmasini toping.
A) -i B) i C) D)
TEST 2006 : Variant
140
Matematika
1
Matematika
1. 2.68013579 coni 9 ga bo'linishi uchun nuqtaning
o'rniga qanday raqam qo'yilishi kerak?
A) 4 B) 0 C) 8 D) 7
л И i *	- ' .
2. — 1- ga teskari sonm toping.
A) -0,75 B) 1,5 C) | D)
у2т — x2r
s-	П1 qisqartmng.
A) -жЧ yv B) x*+y* C)
D) x - у
4 ?... Л * x — f ni soddalashtiring.
(rd-1)
A) z-fl В) 2x C) 0 D) x~2
5. m ning qanday qiymatlarida |3 — rrz| = rn — 3
tenglik o'rinli bo'ladi?
A) meR B) rn > 3 C) m > 3 D) m = 3
12. Tekislikka tushirilgan og'ma va perpendikuiar
16
orasidagi burchak urcsin~~ ga teng. Og'maning
65
uzunligi 130 ga teng. Perpendikuiarning
uzunligini toping.
A) 96 B) 64 C) 32 D) 126
13.
• 4	. • 2	2
sm a 4 sm or • cos~ a.
-I-------------г---------- ni soddalashtiring.
cos or
A) 1 — tg2a B) tff2m C) 1 — dg2ot
D) —V
co-y"a
14.	Quyidagi sonlardan qaysi biri 15 ga qoldiqli
bo'linadi?
A) 3105 B) 6525 C) 6130 D) 4620
15.	9: 10; 15 va 27 sonlaridan nechta o'zaro tub
sonlar jufti hosil qilish mumkin?
A) 3 B) 4 C) 6 D) 2
16.	a ning qanday qiymatida у — x2 - 4z 4- 12 — а
parabolaning uchi M(2; 5) nuqtada yotadi?
A) 2 В) 3 C) 5 D) 4
6. x2 — 13r 4 q — 0 tenglamaning ildizlaridan biri
— 14 ga teng. lining ikkinchi ildizini toping.
A) 27 B) -1 C) -27 D) 1
x — 1
7. ""”'3 < 0 tengsizlikni yeching.
A) [1; 3) B) (-3; 1) C) (-2; 1)
D) (1; 3)
S. 0,6(3) ni oddiy kasrga aylantiring.
a\ 4 d\ JL c\ m
A) 15	) 30	90 °} 90
9.	log^ne623 ni hisoblang.
A) Aye B) 5 C) 3 D) 4
10.	Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan
burchaklarning kattaliklari nisbati 7:5 ga teng.
Shu burchaklardan kichigini toping.
A) 49° В) 63е С) 75е D) 54®
11.	Quyidagi tasdiqlarniug qaysilari noto'g'ri?
1)	tomoni a ga, burchaklaridan biri a ga teng
ronibning yuzi S = |o2sj7io formula bilan
hisoblanadi;
2)	diagonallari d\ va rf2 ga. ular orasidagi
burchagi or ga teng ixtiyoriy qavariq
to'rtburchakning yuzi S — d^d^stnot formula
bilan hisoblanadi;
3)	o'xshash figuralar yuzlarining nisbati ularning
mos chiziqli o'lchovlari kvadratlarining nisbatiga
teng.
A) 2;3 B) 1;2 C) 1:2.3 D) 1:3
80
17.	Quyidagi tengsizhklardan qaysi biri x va у ning
xy > 0 shartni qanoatlantiradigan barcha
qiymatlarida oTinli?
А) +	В) (x-y)2>0
x 4 У ТУ
C) x2 — 6xy + Oy2 <0 D) x2 — y2 > 0
18.	  -	....-r ning boshlang'ich funksiyasini
зт4(4х4-1)
toping.
A) icip(4x 4 1) +C B) — jct0(4r 4 1)4 C
C) -hs(4r + )) + C D) it?(4x + I) + C
19.	2?«:’'71+2х-4	£4 tenglamani yeching.
A) 1 B) 1,5 C) 3 D) 2
20.	Katta yon tornoni 6 sm. o'tkir burchagi 30c
bo'lgan to'g'ri burchakli trapetsiyaga aylana
ichki chizilgan. Shu aylananing uzunligini toping.
A) % В) 2r C) 3ir D) 4tt
21.	To'g'ri to'rtburchakning katta tomoni 13 ga,
diagonallarining kesishgan nuqtasidan katta
tomonigacha bo'lgan masofa 3 ga teng. To'g'ri
to’rtburcbakning yuzini toping.
A) 78 B) 96 . C) 72 D) 48
22.	Konusning yasovchisi 25 ga, uning asos tekisligi
bilan tashkil qilgan burchagimng sinusi 0t6 ga
teng. Konus b‘q kesimming perimetrini aniqlang.
A) 80 B) 360 C) 90 D) 105
TEST 2006: Variant
140
Mateinatika.
23 Siiindr o'q kesimining diagonal! 8 ga teng va asos |
tekisligi bilan 30° li burchak tashkil etadi.
Silindrning hajmini toping.
А) 48% В) 6% C) 16% D) 24tt
33.	4 cos2 г 4- sins cos r 4- 3sin2 x — 3
tenglamaning 90е < x < 180° shartni
qanoatlantiradigau ildizlari yig^ndisini toping.
A) 225° B) 150° C) 135° D) 210°
%	- 3	- i -	. ,
/1 sin-— • cos — sin~~ • cos -- ш hisoblang.
16	16	16	16	6
A) 1 B) 1 C) 1	D) ~
C	L	0
v3
cos 2 г sin 3r 4- sin 2x cos 3г = — tenglamani
yeching.
A) (-1)"	+ nez
•JU V
B) (-I)nоег C} ~n,n&z
20 a	30
D) (-1)"-^ + r«. nez
10 Э
?6. Tekis harakatda muayyan masofani bosib o'tish
uchun ketadigan vaqtni 30% ga kamaytirish
uchun tezlikni necha foiz orttirish kerak?
A) 20 B) 42^ C) 30 D) 33-
i	V
34.	IgLx — 2) < 2 - Ig(27 — x) tengsiziikning
yec him land an neehtasi butun sondan iborat?
A) 8 B) 9 C) 6 D) 7
35-	Teng yonli trapetsiyaga ichki chizilgan
aylananing markazi ustki asoslning u chi dan 3 ga.
pastki asosining uchidan 4 ga teng masofada
joylashgan. Shu trapetsiyaga ichki chizilgan
doiraning yuzini toping.
A) 5,76% B) 2,56% C) 6,76% D) 3,24%
36-	Sharga konus ichki chizilgan. Konusning
yasovchisi asosining diametriga teng. Shar
haj mining konus hajmiga nisbatim toping.
A) 8:3 B) 32:9 C) 27:4 D) 16:9
x — 4x *4“ Iz
Л. у — —й-----------funksiyaning qiymatiar
x ~ 4г -b 5
to‘plamiga tegishli tub sonlar nechta?
A) 1 B) 4 C) 3 D) 2
2Я 2 — 3jx — 4| — — 4 tenglamaning ildizlari
yig'indisini toping.
A) 7 B) 8 C) 10 D) 9
29. |x2 — 9r -b — —8 -+• 9z — r* tenglamaning
barcha natural yechimlari yig'indisini toping.
A) 40 B) 36 C) 28 D) 25
30. Katetlarining nisbati 2:3 bo’lgan to’g’ri burchakli
uchburchak balandligi gipotenuzasim
uzunliHaridan biri jkkinchisidan 0,6 ga karn
bo:lgan bo’lakiarga ajratadi. Gipotenuzaning
bo’laJdarini toping.
A) 5 va 3 B) 2 va4 C) 1,6 va 3,6
D) 1,08 va 0,48
31 - у V5x -b 2 va у — —4- 2 to'g'ri
V 3
chiziqlarning kesisbishidan hosil bo'lgan o'tkir
burchakni toping-
A) 75° B) 65° C) 90° D) 60°
32 6(3; —6; 6) vektorga kollinear va ab zz 40,5
tenglikni qanoatlantiruvchl a vektorni toping.
A) 5(3; 6; 9) B) S(|;-3;3) C) a(3;-6;6)
D)
III!
81
TEST 2006: Variant
141
Matematika
1
Matematika
1. 392 ni qanday songa bo‘lganda boOinuxa 17 va .
qcldiq 1 holadi?
A) 21 B) 19 C) 23 D) 22
2, 6,4; y: —.3,2 sonlarnmg o‘rta arifmetigi 0,8 ga
teng. у ni toping.
A) -0,8 B) 1.2 C) —0,4 D)>0.4
12. Tekislikka og‘ma va perpendikular tushirilgan.
Ogbnaning tekislikdagi proyeksiyasi 45 ga,
perpcndikularning uzunligi 28 ga teng. Og‘n»a va
perpendikular orasidagi burchakni toping.
14 • 28 ><’ • 45
A) arccos — B) arcstn — C) arcs tn —
м3	M	53
D) arccty —
3.	a(b + c — be) — Це 4- a — oc) — c(b — a) ni
soddaiashtiring.
.4) 2oc — 2bc B) — 2abc C) ab — ac
D) -26c
13.
.	1 ,	2 sin or + sin 2o .
Agar cos a = —- bo’lsa, —;----------------- ui
1	2 sm o — sin 2a
hisoblang.
A) 7 B) 0,6 C) I D) 3
hr	0
4.	2a26 4- 3a — 4ab2 — 66 ko’phadni
ko‘paytuvchilarga ajrating.
A)	+ 3) B) (2«6 - 3)(a - 56)
Q (2a2 + b)(b,~ 5a) D) (3 + 2a6)(a - 56)
14.	43 • 15 • 25 • 37 + 34 -48 • 77 yigindining oxirgi
jaqatrfin Г toping.
A) 9 B) 4 0) 5 D) 0
1
5.
(2 ^ + t) : 4
x-a
5 tenglamani yeching.
5
3	19	3
A)	18—	B)	17—	C)	21 D)	17^-
22	22	7	22
6.	x~ + Hjt 4- q — 0 tenglarnaning ildizlaridan biri
— 12 ga teng. Uning .ikkinchi ildizini toping.
A) -23 B) 1 C) 23 D) -1
,Д»
7.	----г < 0 tengsizlikni veching.
x — 5
A) [-3; 5) Й) (-00; -3] C) (5; oo)
D) (-3; 5)
8 Geometrik progressiva uchun quyidagi
fbrmulalardan qaysilari noto^ri?
l)4n = ti«”-';2)4’=i„_,.6„+2:
' M1-<C)
15..: Qaysi juftlik o'zaro tub sonlardan iborat?
A) (22; 27) B) (21; 14) C) (10; 15)
D) (12: 15)
16. a ning qanday qiymatida у — x2 — 4г 4- 12 - a
parabolising uchi M(2; 5) nuqtada yotadi?
A) 2 В) 3 C) 5 D) 4
, _	[ 9r — 1 > ~x + 3	-i-ii -	. ,
1/. s ~	tengsiziiklar sistemasi butun
I 20 - Sx > 4r - 15
yechimlariniog o‘rta arifmetigini toping.
A)-7 B) 3,5 C) 3 D) 4
• 18. I cos‘2xdx ni hisoblang.
T' *	'	’
A) -2 B) t> C)	О) -1
* A) l В) 1; 3 C) 3 D) 2 •
9.	+ iog^ ni hisoblang
А) -Г B) -3 C) 1 D) —0.5
10. Qo£shni burchaklardan bin ikkjnchisidan 52° ga
katta. Shu burchaklardan kattasini toping.
A) 118** B) 106* C) H4° D) 116*
11. Quyidagi lasdiqlarning qaysilari notocg<ri?
1) tomoni a ga, burchaklaridan biri о ga teng
rombning yuzi S = ±a2sina formula bilan
hisoblanadi:
2) diagonallari <T va d2 g*> ular orasidagi
burchagi о ga teng ixtiyoriy qavariq
to’rtburchakaing yuzi S == d^d^sina formula
bilan hisoblanadi;
3) o'xshash figuralar yuzlarining nisbati ulariung
moe chiziqli crlchoviari kvadratlarining nisbatiga
teng.	. .
A) 2;3 B) l;f C) 1;2;3 D) 1:3
19.	Agar loge 64 — 3 va logj, 243 = 5 bo‘lsih ab ni$g
qiymatini toping
Aj 5 B) 12 C) 8 D) 6
20.	Uchburchak tornonilining uzunliklari m; n va k
m2 = n* + P + \/3nk tenglikni qanoatlantiradi.
Uzunligi m ga teng tomon qarshisidagi burchakni
toping.
A) 156' B) 45° C) 90* D) 135° -
21.	Tomonlari 72 va 32 m bo’lgan tp’g’ri
to^rtburchakka tengdosh kvadraining tornonini
toping.
A) 28 B) 36 C) 48 D) 24
22.	Muntazarri piramidaning yon strti t-o’la sirtining
60% ini tashkil eladi. Piramidaning yon yoqlari
va asOs tekisligi orasidagi burchakni toping.
A) arccos- B) 60° C) arccos ?
4	3
D) arccos —
82
2
TEST 2006 : Variant
141
Matematika
2Л. Konus yasovchisi 4 ga teng va u asos tekisligi
bilan 60° H hutchak tashkil etadi. Konusning
hajrnini toping.
А) 8Л В)	C) D)
C	V	О
2d. p ~ c<?.s88°, q ~ cos42° va r = sin222e sonlarni
kamayish tartibidckyozmg.
A) p>q>,r B) q>p>r C) q > r > p
D) p > г > q
'25. tgr 4--= 2 tenglama [—Зтг: Зтг1 kesmada
tgx.
nechta ildlzga ef a?
A) 5 В) 3' C) 6 D) 7
34.	z?^-s 4- 25^x = 10 tenglamani yeching.
A) 1 В) C) 5 D) УТ6
35.	Muntazam uchburchakning yuzi 9\/3 ga teng.
Shu uchburchakdan eng katta yuzaga ega bcrlgan
kvadrat qirqib olingan. Shu kvadratning
perimetrini toping.
А) 48УЗ- 72 81 .1873- 12
C) 54 - 16V^ Д) 6473-96
36.	Hajmi 873 ga teng bodgan muntazarn
tetraedrning balandh®ini toping.
A) 4 В) 2-Л C) 3 D) 4^3
26 Mahsulotning narxi birinchi mart a 20% ga.
ikkinchi rnarta yangi bahosi у ana 10% ga
oshirildi. Mahsulotning oxirgi bahosi necha
foizga kamaytirilsa, uuing narxi dastlabki narxiga
teng bo!ladi?
A) 24-1 B) .25 с) 3з1 D) 30
«5*5	4
27. у — 78 — x2 — lx funksiyaning eng katta
qiymatini toping.
A) 4 Ъ) 7 C) 3 D) 2
Agar <
I
toping.
|z| 4- у =
3x4- у =
3,
4
bo Isa, x 4- 2y ning qiymatini
A) 1 B) 3 C) 2 D) 13
'29. ---— == -y tenglama m ning nechta natural
qiymatida ildizga ega emas?
А) f B) 5 C) 8 D) 28
30. To’gTi ourchakli uchburchakka ichki va tashqi
chizilgan aylanalar radiusrarining nisbati 4:13
kabi. Kichik katet uzunligining katta katet
uzunligiga nisbatini aniqlang.
A) 5:12 ‘B)’3:4 C) 4 : 13 D) 5 :13
31 Teng yonli trapetsiyaning diagonal, 16,/3 ga teng
Va u asosi bilan 30° li burchak tashkil et adi.
Trapetsiyaning o‘rta cbizig^i nechaga teng?
A) 12 B) 16z C) 20 D) 24
32 Agar a(—6;3;3) va 6(3;—3;0) bo:isa> 2c va ~b
vektoriar orasidagi Ьи»-факп1 toping.
A) 60ft B) ISO* (S 135^ D) 120°
r
3 3 cos 2x sin x	cos 2x tenglamaning
90° < r < 180* shartni qanoatlantiradigan
ildizlarini topingj . -
A) 110* . "B), 120* C) 135° D) 170*
83
TEST 2006 : Variant
14%	________ Matematika
Maternal ika
• 1
1.	Uch sutka necha sekunddan iborat?
A) 259200 B) 258400 C) 258300
D) 258200
. 1.6-0.7-1,8..............
2-	ГГ-ТУ-оз nmg <Wnat,ni toPlnS-
A) I B) 1 C) 1 D) |
3.	~C_.—— :	oi soddalashtiring.
A)
' у[1+у)
B) £—C) 1 D) 1 - -
У	У	У
x 4-xz4-x 4 1 ,	,	.
4.	-------------— у z ni soddalashtiring.
зг 4- 1
A) x B) x - 1 С) r + 1 I» 2x 4- 1
5.	a ning qanday qiymatlarida ax - 3x 4- I
tenglamayechiniga ega bo’hnaydi?
A) « ~ 2 B) a / 1 C) a = 3 D) а ± 2
6.	x2 — i lr 4- q = 0 tenglamaning ildizlaridan biri
—13 ga teng. lining ikkinchi ildizini toping.
A) 2 B) -24 C) -2 D) 24
7.	(зг 4 3)(r — *2) < 0 tengsizlikni yeching.
A) (~cc; —3) U (2;oo) B) (—oc: 2) U (3:ec)
C) (—3;2) D) (—oo;—2)U(3;oo)
Arifrnetik prcgressiya uchun quyidagi
formulalardan qaysilari noto'g‘ri?
n c ai+(n-l)d an-ai4-d
1)	Sn --------X-----n; 2)-----------
2	n
3) flj 4-Ол ~ аз + ап2‘2
A) 1; 2 B) 2; 3 C) 2 D) 1
/ \ 4
9.	I I ni hisoblang.
A) 4 B) 9 C) 5 D) 3
10.	Ikkita to'g'ri chiziqning kesishidan hosil boHgan
qo'shni burchaklaming ayirmasi 50° ga teng. Shu
burchakiardan kichigini toping.
A) 65° B) 60° С) 70е D) 50”
11.	Quyidagi tasdiqlaming qaysilari noto:g:ri?
1)	radiusi R ga, markaziy burchagi о ga teng
deiraviy sektonnng yuzi S ~ 7Sb'a formula bilan
hisoblanadi:
2)	tornonlari a va b ga, ular orasidagi
butch aklaridan bin er ga teng bo'lgan
p^rallelogrammning yuzi S — absina formula
bilan hisoblanadi;
3)	diagonallari d\ va d*> ga, ular orasidagi
burchagi л ga teng ixtiyoriy qavariq
to’rtburchakning yuzi S = did2s£ncr formula
bilan hisoblanadi.
A) 2:3 B) 1/2 C) 1/2:3 D) 1;3
12.	Ttfkislikka tushirilgan og‘manmg uzunligi 75 ga,
urdng tekislikdagi proyeksiyasi esa 60 ga teng.
Og'rna va tekislik orasidagi burchakni toping.
3	3	3
Д) nrcsm- B) arccosy- C) arcsin'-
D) arcstn-
13. tg(- + a)~ -j
toping-
A) | B) 6
bo'lsa. tg о ning qiyinat-ini
C) D) 3
14.	x laqamining qanday eng katta qiyrnatida
(741 4- 2r2) son 3 ga qoldiqsiz bo'linadi?
A) 8 B) 7 C) 2 D) 9
15.	25 va 15 sonlari eng kichik urnumiy karralisining
natural bo'luvchilari necht-a?
A) 4 Bl 5 C) 7 D) 6
2^ — 3
16.	— У16 — aT2 4----—— funksiyaning aniqlanish
x +1
sohasini toping.
A) (-1; *}	B) [-4; -1)U(-1; 4]
C) (-4; 4] D) [-4; -1)
{ 3x + 1 < 2z 4-11 ten^s’z^^ar sistemasining
butun yechimlari yig:indisini toping.
A) 5 B) 30 C) 21 D) 20
18.	/ cos(0,25r)dx ni hisoblang.
Jir
A) 4-273 B) -2 C) 2 D) -1
19.	2 ’ 3co,t* = 15 — 9C<>*X tenglnmani yeching.
Д) Srn.n^Z B)
С) + 2rn..n G £ D) ~ 4- 2жп,пб^>
<?	о
20.	Balandligi 8 ga teng bo^an, teng yonli
uchburchakning asosi yon tomonidan 2 ga ortiq.
llchburchakning asosini toping-
A) 15 B) 16 C) 12 D) 18
84
TEST 2006 : Variant
142
•Matematika
•)
21 ЛАВС ning AB tomoni MNjfAC to:g*ri chiziq
yordamida BM=2 va AM=4 bo’lgan kesmalarga
ajratildi. Agar AMBN ning yuzi 18 ga teng
bo‘isa. ДЛВС ning yuzi qauchaga teng bo’ladi?
A) 96 B) 162 C) 144 D) 108
'2'2 To'g'ri burchakli parallelepiped asosining
tornonlari va balandligining qiymatlari 4:3:1,25
kabi nishatda. Parallelepipedning diagonal! va
asos tekisligi orasidagi burchakni toping.
A) 39’ B) 45° C) arcctgt D) 60°
23. Konus asosining radiusi 1273 ga teng,.yasovchisi
asos tekisligi bilan 30° li burchak tashkil etadi.
Asos markazidan yasovchigacha bo;lgan masofani
toping.
A) 673 B) 8 C) 373 D) 5
.’4 t ning qanday qiyrnatida
у ~ 1 - 3cos2z — #(1 + co$2r) funksiyaning
qiymati o'zgannas bo’ladi?
A) -3 В) 3 C) -1 D) -2
2I>
3 яг
sin2x 4- cos(—y- + 6z) — stride tenglamani
yeching.
A) ±—4-xn:	n £ Z B) n^Z
о	4	4
C) in, n € Z D) — — 4-тп, n € Z
?(> 900 kg mevaning tarkibida 80% suv.bor, Bir
necha kundan keyin mevaning og’irligi 500 kg ga
tushdi. Endi uning^tarkibida necha fob? suv bor?
A) €8 B) 62 C) 64 D) 66
27
y~
3x 4" 8,5
r + 2
- 4) funksiyaning aniqlanish
30.
AB=18 sm, DB-10.8 sm,
ABC uchburchakka
ichki chizilgan ayla-
naning radiusi
necha sm?
31. MA'(6; 7)vaAff<(7; 6) vektorlar
parallelograinmning tornonlari boUsa, uning
diagonallari orasidagi burchakni toping.
A) 45° B) 30° C) 90° D) 60°
32. Agar a(l; —I; 3) va 6(4: 3; 0) bo’lsa, a ning
qanday qiyrnatida 4a 4- c?6 vektor b — a vektorga
perpendikular boiadi?
A) 2.1 B) L C) | 0) -A
33.
4
\tgx + ctgx\ — tenglamani yeching.
V 3
A) J + 2^;Jt€Z B) ±J + ^;teZ
3	V z
C) ±^ + rt;*e2 D) (-ljn£ + M-,k e z
m	U
tengsizlikning butun sonlardan iborat nechta
yechimi bor?
A) 1 B) 0 C) 3 D) 2
sohasini toping.
A) (-2;|) B) (-oo;~2)U(l;«>)
35. Doiraga ichki chizilgan muntazam
uchburchakning yuzi unga ichki chizilgan
kvadratning yusidan 18.5 ga кадп. Shu doiraga
ichki chizilgan mxmtazam oltiburchakning yuzini
toping.
A) 9\/3 + 6>/5 В) 8-Л+15 C) 27 + 24"/!
D) 13.5+ 12 Л
C) (|;<ю)
z»
D) (—oo;-2)
28 (k — 5)2y = k2 — 36 tenglamaning ildizlari manfiy
boS'adigan k ning barcha but-un musbat
qiymatlari yig^ndisini toping.
A) 13 B) 10 C) 8 D) ll
7‘J fcx2 + 3fez + 2k — 2 = 0 tenglama yechimga ega
bo‘lmaydjgan k ning butun qiymatlari o'rta
arifmetigini toping.
Л) -2 B) -3,5 C) -3 D) —4
36. Kesik konusning yon sirti 10т ga, toia sirti 1 Sa-
ga teng- Konusning to'la sirti unga ichki
chizilgan shar sirtidan qanchaga ortiq?
A) 6r B) 14% С) 10x D) 8%
85
TEST 2006: Variant
143_____________ _____Matematika
Matematika
1.	279 ni 16 ga bcrlganda qoidiq 7 bo'ladi. BoMinma
nechaga teng?
A) 12 B) 13 C) 11	0) 17
2.	-I- ga teskari sonni toping.
Л) -0,75 B) 1,5 C) I D)
3-	\Х*/56 4-”2>/10 • У-56 — 2 ./10 ni hisoblang.
A) 6 B) 2 C) 4 0) 3
11.	Quyidagi tasdiqlarning qaysilari noto‘glri?
1)	ucbburchakka tashqi chizilgan aylananing
radiusi R —	uchburchakning
tomonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga. markaziy burchagi a ga teng
doiraviy sektorning yuzi S = -fjj-o formula bilan
hisoblanadi;
3)	tomoni a ga. burchaklaridan biri a ga teng
rombning yuzi S — ~a2sina formula bilan
hisoblanadi.
A) 2,3 B) 1;2 C) 1;2;3 D) 1;3
12.
Tekislikka oglma va perpendikuiar tushirilgan.
...	7
Ogfrna va tekislik orasidagi burchak arecos-— ga,
Zx)
-C t/
4. (г-1 4- v":) --------т ni soddalashtirinc.
(г + У)
А)	Bj X'y~ Cl 1
(x + у)3 (x 4- у)2 X 4- у
D) x'V
og'tnaning tokislikdagi proyeksiyasi 14 ga teng.
Perpendikularning uzunligini toping.
А) И В) 48 С) 28 D) 36
4
13. ------------— ni soddalashtiring.
etg 2» — tg 2a-
A) sin 4a B) 2tg4a C) cos4o
D) tg4o
5. (2r ~ ])(x — 1.5) ~ 0 bo4sa, 2x — 1 qanday
qiymatiar qabul qiladi?
A) faqat — ~ B) 2 yoki 0 C) 0 yoki 1.5
D) 0 yoki — |
14.	43 * 15 • 25 *37 4- 34 • 48 * 77 уig‘indining oxirgi
raqamini toping.
A) 9 B) 4 C) 5 D) 0
6.	X] va x? x2 — ax 4- 20 =. 0 tenglamaning ildizlari
1	1	9
bo'lib,----h — = —- tenglikni qanoatlant-irsa, a
X’2	20
ning qiymatini toping.
A) 9 B) -1 C) 3 D) -3
15. 842 «mining o4ng tomoniga qanday raqam
yozilsa, hosil bo'lgan son 36 ga qoldiqsiz
bo'linadi?
A) 2 B) 4 C) 8 D) 6
7.	(x — l)(x 4- 2) < 0 tengsizlikfii yeching.
A) (1;2) B) (—oo; 1) U (2; oo)	C) (-2;1)
D) (—oo;—2) U (l;oo)
8.	Quyidagi sonlardan qaysi biri 0,8(1) ga Ung?
16.	у = 3x2 4- 8x — 8 funksiyaning grafigi qaysi
chorakiarda joy lashgan?
A) barcha.chorakfarda В) П, HL IV
C) L П? ill D) Щ; IV
f '2x — 4 x 4" 1	*	...
17.	j < 2я4 П tongsizliklar sistemasining
butun yechirnlari yig‘indisini toping.
Л) 5 B) 30 C) 21 D) 20
C) *1
• 90
D)
70
90
9. у = 2f*x — 3 funksiya grafigining Oy ocqi bilan
kesishish nuqt-asi ordinatasini toping.
A) -1 B) -2 C) 1 D) 0
10. Qo‘shni burchaklardan biri ikinchisidan besh
maria kichik bo4lsa, shu bnrchaklardan kattasini
toping.
A) 130° B) 150° C) 144° D) 140’
------j- ni hisoblang.
2-«n2 -
2
A) 3->/3 В) 3"2^ C) 373-3
19. Qaysi javobda rnaiifiy son ko’rsatilgan?
A) loy^y/3 B) loffa3 C) lt>321,2
D) ,o^ 7k
86
TEST 2006: Variant	143
Matematika
20 Muntazaru oltjburchakka tashqi chizilgan
aylananing radiusi л/2 bo'lsa, unga ichki
chizilgan aylananing radiusiai loping.
Л) ~ B) 1,5 C) 1,2 D)
2,
21. Balandligi 32 ga teug bo'lgan rombga ichki
chizilgan doiraning yuzini toping.
A) 190* B) I965F С) 200tt D) 256*
П. Piramidaning asosi to'g'ri burchakli uchburchak
bo'lib, uning gipotennzasi uzunligi 20 ga teng.
Piramidaning barcha yon qinalari 26 ga teng
bo'lsa, uning balandligini toping
A) 12 B) 24 C) 22 D) 20
23. Asosining radiusi 16 srn va balandligi 8 srn
bo'igan konus asosidan 3 sm masofada asosiga
parallel tekislik bilan kesilgan. Kesimnmg
yuzini (srn2) toping.
A) 50* B) 36* C) 100* D) 25*
21. rn — ew65°. n = sinlS*’, q — ftinbO* va
p =z cos8G° sonlarni o'sish tartibida yozing.
A) m < n < j> < q B) p < rn < il < q
C) p < m < q < n D) q < n < p <_ m
25. sin 5r - cos2x — cos 5z • sin 2x + 0.5 tenglatitaning
iidizlarini ko'rsatiug.
7Г	T\
A) z + -г-, к € Z B) + 2xb, k$Z
Ъ 3	л
c) (~0*7о + тр kez
io a
2x£ ,	„
D) kQZ
о о
26 Yig'indisi 38 va 62 soniarining o'rta arifrnetigiga
teng boiishi ucbun 62 ning 60%i oliusa, 38 ning
necha foizini otish kerak?
7	14	12
A) 17— B) S3- C) 33- D) 32
1*Z	1 Zz	ll
30.	To'g'ri burchakli uchburchakning katetlari 48 va
14 ga teng. Kichik katetning gipotenuzadagi
proyeksiyasini toping.
A) 10 B) & C) 3^	D) 4^
/	Zo	ZO
31.	M(z, t/) nuqtaning koordinatlari yig'indisi 6 ga
teng. Bu nuqta va koordinat boshi orasidagi eng
qisqa masofa qanchaga teng bo'iadi?
A) 2y/3	B.) 3V^ С) 4,5a/2 D) 1,5v^
32.	m ning qanday qiymatlarida а(тн — l;m.— 2, 2)
vektorning uztinligi 3 dan kichik bo'ladi?
A) — 2 < m < 1	B) 0 < m < 3
C) — 1 < m < 2	D) — 1 < m < 3
33.	ainx + соях = J lenglaTuaning {—ir; *] oraliqda
nechta ildizi bor?
A) 1 В) 0 Ci 3 D) 2
I 34.	— 2) < 2 - lg(27 — z) tengsiziikning
’ yechimlaridan nechtasi butun sondan iborat?
! A) 8 B) 9 C) 6 D) 7
i
35. Uchburchakning burchaklari 45 va 60° ga, unga
tasbqi chizilgan aylananing radiusi R ga teng.
Uchburchakning yuzini anjqlang.
A) + в) ЗД2у/5 С)' --Z1
О) -=-(г/2 + V5)
36. Asosi a ga, ascsidagi burchagi о ga teng bo'lgan
tengyonli uchburchakni yon tomoni atrofida
aylantirishdan hosil bo'lgan jismning hajmini
toping.
ч . •>	з •	a
*a	. та stria ха cos о
--	j}) —— ------ pi ---------—
Gcostjt	3	6 sin* a
та31оо
n\ ——
27. у = -y/gg------7===: funksiyaning aniqlanish
vz — 6 - v9 - x
sobasiga tegishli barcha butun sonlar yig'indisini
roping.
A) 28 B) 15 C) 30 D) 32
'H ikki sonning ayirrnasi 27 ga teng. Agar birinchi
sonni ikkinchisiga bo'lsak. bo'linma 4 ga va
qoidiq 3 ga teng chiqadi. Berilgan sonlarning
yig'indtsini t-oping.
A) 38 B) 31 C) 43	0) 29
xs	x5
’ H------ 7^7------------T tenglamaning barcha
x — 1296	1296 — x
natural yechfndari yig'indisini toping.
A) 1 B) 12 C) 10 D) 15
87
TEST 2006 : Variant
144
M&lerualika
1
Matematika
1.	Agar kainayuvchini 30 ta va ayriluvchini 12 ta
kamaytirilsa, ayirma qanday oJzgaradi?
A) 24 ta ortadi B) 18 ta fcaznayadi
C) 12 ta kamayadi D) 12 ta ortadi
2.	2,014 : 0,19 + 2,5 • 0,3 ni hisoblang.
Л) 11,35 B) 9,85 C) 12,85 D) 8,85
3.	16— (2c— I)2 ni kc/paytuvchilarga ajrating.
A) (3-2c)(5-2c)	B) (3 4-2c)(5 — 2c)
C) (2c - 3)(2c - 5)	D) (3 - 2c)(5 4- 2c)
4.	(у2 - I)2 - (y2 — l)(y4 4- y2 4- I) + у ni
soddalashtirgandan keyin nechta haddan iborat
bo4adi?
A) 5 B) 4 C)3 D) 6
12.	Tekislikka tushirilgan og‘ina va perpendikular
orasidagi burchak nrrsin— ga teng.
Og‘maning
uzunligi 122 ga teng Perpendikularning
uzuiiligini toping.
A) 22 B) 120 C) 24 D) 90
13.	tg(^ - o) =
toping.
4 , ,	•	-
- bo*lsa, ctgo ning qiyrnatim
A) 9 B> C) -4 P) 1
(ar, y) soular jufti
2z — у = 5
3т 4- 2y — 4
sistemaning
yechimi bo‘Isa. у — x ni toping.
A) -1 B) -3 C) 0 D) 3
6.	Tivazo x1 — 14т + 9 = 0 tenglnmaning ildizlari
bcrlsa, tjt2 + ®2X2 ning qiymatini toping.
Л) 126 B) -92,. С) -126 D) -144
7.	(x 4- 2)(x - 3) < 0 tengsizlikni yeching.
A) (—co;-3} U (2; co) B) (-2:3)
С) {-oo:-2)U(3;oo) D) (-3;-2)
14.	22 * 43 • 98 *4 16 • 27 • «38 19 yig‘indining oxirgi
raqajnini toping,
A) 6 B) 8 C) 2 D) 4
19,5:41 4-з|- 1,9
15	—'“п'ч----—------ n’ hisoblang.
^-0.16
(a
A) 16 B) 4| С) 12 D) 7,45
16.	и = </-——?P--	* - funksiyaning aniqlanish
У x(4 - x)
sohasini toping.
A) (O;1)U[3;4) B) (0;l)u[3;4)
C) <-oc;0)U(I;3]U(4;oc) D) ,(0:1] U [3;4)
8.	Arifrnetik progressiya uchun quyidagi
fornndalardan qaysilari to‘g4ri?
1)	gi — 2a3 4- ал ~ 0;
2)	«1 = а3 - a2;
ал - aj + d
3)	n =--------.
A) 1 В) 2;3 C) 1:2 D) 2
9.	Zoigr^u2 4- loffJL.3 ni hisoblang,
A) -1 B) -3 C) 1 D) -0,5
10.	Ikkita to‘g‘ri chiziqiring kesisinshidan hosil
bo4gan burchaklardan uchtasining yighndisi 275°
ga teng. Shu burchaklardan kicbigini toping.
A) 45° B) 60° C) 85° D) 70°
от 4" 8	.	.
17.	2 > —----- tengsizlikni vec.bing.
4 — £
A) (-^„4)^(0;4) B) (-oo;0)U(4;oo)
C) D) [-4; 4]
18.	Agar fix] = ягпЗх -I----—7 bojsa, f{x)
x — 1
funksiyani toping.
A)	3co.$3x 4- /n|z — 1| 4 C
B)	cos3x 4-	— 1| 4» C
C)	—-co«3x 4- /njr — 11 4* C
V
0) —co«s3r 4-	+ C
11.	Quyidagi tasdiqlarning qaysilari not-o'g’ri?
1)	tomonlarj a va b ga, ulnr orasidagi
burcbaklaridan biri a ga teng bol!gan
paralielograruninhjg yuzi S = ^absma formula
biJan hisoblanadi;
2)	tornonlari a va b ga, ular orasidagi burchagi а
ga teng bo‘lgan uchburchakning yuzi
S — ^ubftina formula bilan hisoblanadi:
3)	o‘xshash figuralar yuzlarining nisbati ularnmg
ivws chiziqli o'lchovlarining nisbatiga teug.
A) 2;3 B) 1;2 C) 1;2;3 D) 1;3
19.	a /<7S?i/43. b= ls>g\/3‘& va с —1од}/з4 sonlarni
o‘‘sish tartibida joylashtiring.
A) c < b < а В) с < а < b С) b < а < с
О) а < b < с
20.	Uchburchakning asosiga tushirilgan nicdianasi
uni perimetrlari 18 va 24 ga teng bo'lgan ikki
uchburchakka ajratadi. Berilgau uchburchakning
kichik yon tornoni 7 ga teng. Uning katta yon
tonion ini toping.
A) 12 B) 10 C) 13 D) 14
88
TEST' 2006 : Variant
144
Matematika
21.	Rornbning balandligi 5 ga, diagonallarining
lco‘paytmasi 90 ga teng. Uni ng perimetrini
toping.
A) 16 B) 32 C) 28 D) 36
22.	To'rtburchakli muntazam prizrna asosining yuzi
169 sin2, baJaudligi >/191 srn. Shu prizrna
diagonalini toping.
A) 21 B) 23 C) 27 D) 22
31.	A BCD trapetsiyaning (AD||BC, AD - katta
asos) AG diagonal! yon tonioniga perpendikular
harnda DAB burchakning bissektrisasida yotadi.
Agar AC = 16 va £DAB = 60° bo’Isa,
trapetsiyaning o'rta chizig'ini toping.
A) 4\/3 В) Зх/З C) 8?3 D) 5x/3
32.	Uchlari A(2; 3; 1), B(3; 2; 1) va 0(3: 4; 1)
nnqtalarda bo’lgan teng yonli uchburchakning
asosidagi burchagini toping.
23 Shar katta doirasining yuzi 225% ga teng.
Shaming rnarkazidan qanday niasofada
o’tkazilgan tekislik shardan doirasining yuzi 161%
ga teng bo^lgan ajratadi?
A) 6 B) 7 C) 8 D) 3.5
24 iqо = у • tff'2a —T
4
..	4	n x	л	xxx	24	__. о
А) ч	B)	3	C)	—	D) -
3	i 4
sin 4г < — cos4« tengsizlikni yeching.
’26 Maosli ikki rnarta ketma-ket bir xiJ foizga
oshirilgach, maoshning 625 so‘rni 900 so’rnga
aylandi. Maosh har safar necha foizdan
oshirilgan?
A) 12 B) 10 0) 14 D) 20
27 </ = — x2 + 6r — 10 Funksiyaning eng katta
qiymatini toping.
A) 1 B) -1 C) 2	0)0
1	2
Л) arccos— B) arccos-
D)
33.	1 - 2.«?zn4jr < cos24z tengsizlikni yeching.
A)	(-^ + 2%fc:^4-2%it)J'GZ
B)	(vk\ 4- тгк),к G Z
C)	( - ~ -b 7 -t- Ink). k G Z
4	4
T^, . nk r irk. .	„
("y’>	k G Z
34.	/о^хз(3 — 2^:) > 1 tengsizhkniug butun yecjiirnlari
nechta?
A) 3 B) 4 C) 1 D) 2
35.	Doiraga ichki chizilgan uchburchakning bir
tornoni uning diarnetriga teng. Doirauing yuzi
289зт ga, uchburchak tomonlaridan birining
uzunligi 30 ga teng. Shu uchburchakka ichki
chizilgan doiraning ytizint loping.
А) Зб5г B) 16% C) 20% D) 64%
36.	Teng tornonli silindming va teng tomonli
konusning baiandiigi o'zaro teng. Ularning to;la
sirtlari nishatini toping.
A) 3 :8 B) 5:3 C) 3 ; 2 D) 3 : 4
28. QisqarHiaydigan oddty kasrning inaxraji
suratid an 6 birlikka katta. Agar kasrning surat
va maxrajiga 5 ni qo'shsak, hosil bo’lgan
4
kasrning qiyniati - gateng bo’ladi. Berilgan
5
kasrning suratini loping.
A) 7 B) 23 C) 13 D) 19
2‘) Jz~ — ЗтI = 3г — x~ tenglarnanvng butun
soulardan iborat ildizlari yig'indisini toping.
A) 4 B) 5 C) 6 D) 3
to То^'п burchakli uchburchakning gipot-enuzasi 25
sin, katetlaridan birmiitg gipotenuzadagi
proyeksiyasi 1,96 em. Ushbu uchburchakka ichki
chizilgan aylananing radiusi necha sin?
A) 1 В) 3 C) 2 D) 1,5
89
TEST 2006 : Variant
145
Matematika
1
.Matema-tika
1. 37 24 — 34  24 + 19 • 11 — 16 • ll ning qiymatim
toping.
A) 90 B) 105 C) 100 D) 110
o 2,60,7’1.8 .	.	.	.
2. „	. nmg qxyniatmi toping,
i, 2 • i. b - 1,4
A) I c) T5 D) °'04
3,------—ni soddalashtiring,
1 - 6 + b2
А) Г2 В) Г1 C) 6+1 D) b2
4.----------—----x~2 ni soddalashtiring.
1 - X + X~
Al г2 В) 0 C)l-1 D) 4
.X	x~
5 (r + 3—) : 7- = 3 tenglamani yeching
25	3
99	99	3	3
A) 19^ B) 20- С) 18^ D) 19-
И. Quyidagi tasdiqlarning qaysilari noto'g'ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R = ^(a,6, c— uchburchakning
tornonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S = formula bilan
hisoblanadi;
3)	diagonallari dj va d2 ga, ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
to+tburchakning yuzi S — ~did2sina formula
biJan hisoblanadi.
A) 1;3 B) 1:2 C) 1;2;3 D) 2;3
12.	Tekislikka cg'ma va perpendikular tushirilgan.
Og:maning t-ekislikdagi proyeksiyasi 11 ga,
perpendikuhrning uzunligi 60 ga teng. Og'ma va
perpendikular orasidagi burchakni toping.
. ,	22 гл • 11	, 11
A) arccos— B) nrcsm — Q arcctg —
. 60
D) arc sin—-
61
1 + cos2a + cos4a + cos Oct .	.. . .. .
13.	----:--------------------m soddalashtiring.
stn^a + 2sin'2acos4(x
A) tg'lct B) 2dg'2cr C) ctg‘2& D) '2sin2nt
6.	x + 6 a-----tenglarnaning nechta haqiqiy ildizi
x
bor9
A) 2 R) 1 C) ildizi yo*q D) 3
7.	-----------> 0 tengsizlikni yeching.
x + 2
А) (2;oo) В) (—2;oo) C) (-oo;2]
D) (-сю;2)
8.	Quyidagi ketrna-ketliklardan qaysilari geometrik
progressiyani tashkil etmaydi?
1) a» = | -2"; 2)	= 2.2-; 3) i„ = (-1)" +1.
A) 1;2 B) 1;3	C) 1 D) 3
9.	log4r6 > 1o#4X1,2 tengsizlikni yeching.
A) (1; 1) B) (0; 1) C) (1; oo)
D) (0; 1)
10.	Burchakning bissektrisasi uning tomoni bilan 20°
li burchak tashkil etsa, burchakning olzini
toping.
Л) 30е В) 45е С) 40е D) 60°
{4,--------ifoda natural son. boiadigan n ning
n
natural qiymatlari nechta?
A) 7 B) 2 C) 5 D) 3
15.	Qaysi juftlik o‘zaro tub sonlardan iborat?
A) (22; 27} B) (21; 14) C) (10; 15)
D) (12; 15)
/(r — 2)(4 — x) r , .	• * • к
16.	у — J	~	aniqlanish
sohasini toping.
A) (-3;0)U[2;4] B) [-3;0]U(2;4)
C) (-cc;-3)U(0;2)U(4;<»)
D) (-3;0]U[2;4)
17.	--------------> 0 tengsizlikni yeching.
2r + 5
A)	(-2,5;2)	B)	(-oc;-l,5)
C)	(—2,5;—1,5)	D)	(-сю;-2, 5)
18.	J J sinbxdx ni hisoblang.
2	1	1
A)	__ B)	_	C)	-1 D)	-
19.	a — /0^0,28) b — logV2, с = /о$?ол0,6,
d =	8 va / - sonlardan qaysilari
musbat?
A) a, d va I B) b va с C) atcvad
D) c va d
90
TEST 2006 : Variant
145
Matematika
2() Uzunligi ga teng aylana crtkir burchagi ,30°
*
bo’lgan rornbga ichki chiziigan. Rombning
perimetrini toping.
A) 16 B) 2 C) 4 D) 8
21. Doiraga tashqi chizilgan teng yonli
irapetfiiyaning asoslari 8 va 32 ga teng. Shu
doiraning yuzini hisoblang.
A) 49* В) 64т C) 16* D) 36т
22. To‘g‘ri burchakli parallelepiped asosining
tornonlari 6 va 8 ga teng. Uning diagonal! asos
tokisligiga 30° li burchak ostida og!ishgan.
Parallelepipedning hajmini toping.
A) 80Л B) 20\/5 C) 240 D) 160-/!
2 I Radiusi 17 sm boigan shar markazidan 8 sm
rnasofada tekisfik bilan kesilgan. Kesimning
yuzini (sm2) topiiig.
А) 225т В) 64т С) 64 D) 514*
30.	Katetlarining nisbati 3:2 kabi bo'lgan to'gri
burchakli uchburchakning balandligi
gipotenuzasini uzunliklaridan biri
ikkinchisinikidan 3 ga ko'p boMgan ikki qisrnga
ajratadi. Berilgan uchburchakning gipotenuzasini
toping.
A) 7,8 B) 5,2 C) 8 D) 6
31.	Koordinatalar boshidan 7x 4~ 24y = 168 to*g’H
chiziqqacha boHgan masofani aniqlang.
( , r _ ^18	’ 24	_ 9
A) 5 В) 6™ C) 6—	D) 5—
25	25 2b
32.	Agar a vektor b 37 — 2j 4- £ vektorga kollinear
va a  b - 28 boMsa, a vektorning. uzunligini
toping.
A.) ~ B) 14 С) 2У14 D) у
33.	sinhs — 3cos2x =. 4 tenglamani yeching..
4- m. n E
B) —4- 2л-п, n € 2
Agar tgor = 3 bo:tsa,
3s? net
5>-?n3fr 4- 10co*-3o
ning
C) 4- 2xn, n G 2 D) * 4- *n. n g Z
qiymati qanchaga teng bo‘ladi?
1*	в) 2
29	1 5
34.	х':/Э 4- 9,9'x ~ 6 tenglamani yeching.
A) 10 B) 1 C) 2 D) /W
• > cos6x 4- cos4z — 0 tenglamani yeching.
A)	+ r + 2Tk, k^Z
IV 0	4
C) ±^+*fc; £ + 2%*. teZ
10 э 2
»)	+	5 + 2^, 4 ez
IO 5	2
35.	To'g'ri burchakli uchburchakning uzunligi 14 va
18 ga teng katetlariga tushirilgan rnedianalari uni
uchta uchburchakka va trrrtburchakka ajratadi.
To'rtburchakning yuzini toping.
A) 64 B) 63 C) 42 D) 48
36.	Hajrni 8\/3 ga teng boigan muntazam
tetraedrning balandligini toping
A) 4 B) 273 C) 3 D} 4^5
26 Korxonada mahsulot ishlab chiqarish birinchi yili
20% ga. ikkinchi yili 15% ga ort-di. Mahsulot
ishlab chiqarish ikki yil mobaynida necha foizga
ortgan?
A) 28 B) 38 C) 32 D) 35
1*2
2/ ,v - —5----------funksiyaning qiymatlar
x ’ - 4z -b 5
to'plamiga tegishli tub sonlar nechta?
A) 1 B) 4 C) 3 D) 2
•’8 |5 — x| - 2(2x — 5) bo:lsa, 6 4- x ning qiymati
nechaga teng?
A) 7 B) 8 C) 11 D) 9
•”» У r2 — 6r -r 5 4- x2 _ 6r 4- 7 tenglamaning
ildizlari yiglindisini toping.
A) -3 B) 6 C) -4 D) 3
91
TEST 2(Юв : Variant
146
Matematika
Matematika.
1. Bir nechta natural son ning yigbndisi 85 ga teng
Agar shu sonlarning har biridan 2 ni ayirib,
yig'indi hisobiansa, u 61 ga teng bo'Iadi-
Yig'indidn nechta son qatnashgan?
A) 7 B) 5 C) 8 D) 12
2. Xaritada ikki shahar orasidagi rnasofa 3,5 sm ga
teng. Xaritadagi masshtab 1:2000000 bo'lsa.
shaharlar orasidagi haqiqiy masofa necha km
bcdadi?
Л) 7 B) 140 C) 700 D) 70
11.	Quyidagi tasdiqiarning qaysilari to'g'ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R — ~(a.b,c— uchburchakning
tomonlari; S— uchburchakning yuzi) formula
bilan hisoblanadi,
2)	radiusi /7 ga. markaziy burchagi о ga teng
doiraviy sektorning yuzi S = formula bilan
hisoblanadi;
3)	tomonlari a va b ga, ular orasidagi
burchaklaridan biri a ga teng bo’lgaa
parallelogramnuiing yuzi S — -absinot formula
bilan hisoblanadi.
A) 2:3 B) 1:3 C) 1:2;3 D) 1;2
3.	r2 - x - 6 kvadrat uchhadni chiziqli
ко ‘ paуiu v c h i 1 at ga aj rat i ng.
A) (x + 3)(z-’2) B) (t-3)(x + 2)
C) (z + 3)(2-x) D) (X + 2K3-Z)
4.	(4a — 3)" — r(—4r 4- 5) kc'phadni standart
shakliga keitiring.
Л) 12r2 —25x4 9 B) 20x2 - -29i 49
C) 8z’ - x 4 7 D) 20г2 - 25г 4 9
5.
(я 44^) :4^
& u
- 6 tenglamam yeching.
12.	Tekislikka ogbna va perpendikuiar tushirilgan.
OgTnaning tekislikdagi proyeksiyasi 45 ga,
perpendikularning uzunligi 28 ga teng. Og‘ma va
perpendikuiar orasidagi burchakni toping.
A)	14 arccos — 5 u 45	,r	- 28 В j arcsin— 53	C) arcsm- d
D)	arectg — 28		
, „ 1 — ro,$4o 4 stn*2*> .	... ...
13.	-----------7--------ni sodoalasht-inng.
Л) 3t»722a B) 3cfg22o> C) tgJ'2et
D) 1. 5cfp22<y
7	2	7	1
A) 21-	B)	22-	C)	20-	D)	22-
У	У	У	3
С. x~ — 1 lx 4 4 ~ 0 tenglamaning ildizlaridaii biri
— 13 ga teng. Uning ikkinchi iidizini toping.
A) 2 B) -24 C) -2 D) 24
7. 16x~ — 8x4 3 > 0 t-engsizlikni yeching.
А) [0;оэ) B) 0 C) (—oc:0)
D) {—oo,oc)
14.	Quyidagi sonlardan qaysi biri 15 ga qoldiqli
bodinadi?
A) 3105 R) 6525 C) 6130 D) 4620
_1	r3	5	c3	.	,. ..	.
Io.	o-	•	6-	-	4-	• 5-	m	hisoblang.
4	4	8	8
•?7	10	47	* a
A) 11 £7 B) C> D) 10 11Й
64	64	64	64
16.	— j)*(3 — x) = (1 — 4s)\/3 — x tenglik x
ning qanday qiymatlarida to4gsri bo'ladi?
8. Arifmetik progressiya uchun quyidagi
formulalardan qaysilari noto‘g4i‘?
DS, = .“1+11^ . n: 2) a±Z.21±l = d:
2	‘	n
3) fl; 4 an = a3 4
A) 1; 2 D) 2: 3 C) 2 D) 1
9. ( /7)t n; hisoblang.
A) 9 R) 3s/2 C) 18 D) 3
10. Ikkita to'g'ri chiziqning kesishishidan hosil
bo'lgau qocshni burchaklarning grad us oMovlari
5 : 7 nisbatda bo'lsa, shu burchaklarni toping.
A) 30°: 150е В) 75°: 105’ С) 62°:И8°
D) 54°:126°
A) 0,25<r<3 B) (-oo; O,25]U{3)
C) -3 < x < 3 D) x < 3
17.	2 - Зз; > 2 (x — 1 )(x 4 1) -* x(x 4 3) tengsizlikni
yeching.
A) (-2; 2) B) (-oo: 2) C) (1; oo)
O) (0; 4)
*	x
18.	f cos — dx ni hisoblang.
c	4
A) -2 B) 2 C) 1 D) 2/2
19.	a ~ log75 1 35 bo'lsa, log$ 3 ni a orqali ifodalang.
A)
D)
2a - 1
1 — 2a
a — 3
1 -2a
a —2
92
>
TEST 2006 : Variant
146
Matematika
*r	1
2cos- — — co&x 4- cos'lx 4- 2 tenglam
’I) Perimetri 28 bo'lgan uchburchakning
lussektrisasi uni perilnetrlari 16 va 24 bo'lgan
uchburchaklarga ajratadi. Berilgan
uchburchakning bissektrisasini toping.
Л) 8 B) 5 C) 7 D) 6
1	Peng yonli trapeteiyaning yon tomoni va kichik
wsosi 5 ga, balandligi 4 ga teng. Trapetsiyaning
yuzini toping.
A) 22 B) 32 C) 40 D) 20
2	2 To'rtburchakli muntagain prizma asosining yuzi
169 sm2, balandligi x/191 sm. Shu prizma
diagonalini toping.
A) 21 B) 23 C) 27 D) 22
Л Ikkita sfera yuzlarining nisbati 2\/2 ga teng. Bu
sfcralar di ametrlarin in g nisbatini toping.
A) i/8 В) ч/8 C) v/2 D) 8
24 /(r) = 1 — 3ros2x — kcos'2z funksiya k ning
qanday qiymatida o'zgarmas bo'ladi?
A) -2 B) -3 C) -1,5 D) -1
ani yeching.
A) -r + trlr, k Z B) — 4- -7—, k € £
2	4 z
C) k$Z D) y, be 2
.’6 Massasi 54 kg bo'lgan mis va rux qotishmasining
tarkibida 45% mis bor. Qotishma tarkibida 60%
mis bo'lishi urban unga yaria necha kg mis
qo'shish kerak?
A) 24 B) 13,5 C) 25 D) 20,25
jt у (k — l)x3-k 2kx — ~k va у = kx2-k kx — 4,5
4
funksiyalarning grafikiari kesishmaydigau к ning
barcha butun qiymatlari yig'indisini toping.
A) 9 В) 0 C) 12 D) -2
X X X . X x x	,
M 5+ 15+ 35+ 63+ 99 +H3 = 6t"’g’amanl
yeching.
A) 13 B) 26 C) 16 D) 18
29 k ning nechta natural qiymatida ——— — - •
k 10 z
tcnglarna ildizga ega bo'lmaydi?
A) 6 B) 5 C) 8 D) 7
30 Katetlarming nisbati 3.2 kabi bo'lgan to'g'ri
burchakli uchburchakning balandligi
gipotenuzasini uzunliklaridan biri
ikkinchisinikidaa 3 ga ko'p bo'lgan ikki qismga
njratadi. Berilgan uchburchakning gipotenuzasini
toping.
A) 7,8 . B) 5,2 C) 8 D) 6
32.
33.
Asoslari 8 va 14 ga teng bo'lgan teng yonli
trapetsiyaning diagonallari o'zaro perpetidikular.
Trapetsiyaning yuzini hisoblang.
A) 64 B) 100 C) 121 D) 144
Agar a(—4; 2; 2) va	0) vektcrlar
berilgan bo'lsa, 23 va vektorlar orasidagi
burchakni toping.
3	2
A) rT B) nrccos-
4	3
5?r	5
D) nrecos—
6	6
4
9
.sin(~arccos—) ni hisoblang.
A.	V
1 C) I D
8
9
34.	у = log-, l°Si/2 'fax x1 ^2 funksiyaning
aniqlanish sohasini toping.
А) (2-Л;2+У2)
В) (2-Л; 1)U(3;2 + Л)
C) (-oo;l)U(3;oc) D) (1;3)
35.	Gipotenuzasi c ga va o'tkir bvrchaklari
sinuslarining yig’indisi q ga teng bo'lgan to'g'ri
burchakli uchburchakning yuzini toping.
A) jFfc3 - 1) В) |с2(г2 “ 0
C) p(?’ + l) D) 1?V + 1)
4	4
36.	Konusning o'q kesimi muntazam uchburchakdan,
silindrniki esa kvadratdan iborat. Agar uiarning
hajmlari teng bo'lsa, to'la sirt-larining nisbati
nimaga teng?
А) УЗ -. л В) л : Л С) 1 : Л
D) 3:2
93
TEST 2006 : Variant
147
Matematika
1
Matematika
1.	Natural sccni IS ga bo'lganda, bo'lwma 19 ga,
qoldiq 8 ga teng bolldi. Bo'Hnuvchini toping.
A) 243 B) *263 C) 273 D) 350
2.	453,21 sonini standart shaklda yozing.
A) 4,5321  Ю2 B) 4,5-lG3
С) 4,5321-103. D) 4,53-IO2
3.	16 — (2c — I)2 nt kospayttivchilarga ajrating.
A) (3-2e)(5-2c) B) (3 + 2c)(5~2c)
C) (2c -3)(2c-5) D) (3 - 2c)(5 4- 2c)
4.	2n2 — Зап — 4n -b 6а ko'phadni kcrpaytuvchilarga
ajrating.
A) (n-2)(?n-3a)
C) (2n - 3a)(n - 5)
B) (5 - n)(3a + 2n)
D) (За - n)(5 - 2n)
A)
11.	Quyidagi tasdiqlarning qaysilari tc<g‘ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi FL — c— uchburchakning
tomonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	toinonlari va c bodgan uchburchakka ichki
chizilgan aylananing radiusi r — formula
bilan hisoblanadi:
3)	diagonallari d-t va d2 ga, ular orasidagi.
burchagi <r ga teng ixtiyoriy qavariq
tr/nburchakning yuzi S = ~d\d2sinof formula
bilan hisoblanadi.
A) 2;3 B) 1;3 C) 1;2:3 D) 1:2
12.	Tekislikka og^na va perpendikular tushirilgan.
Og£mar«ing tekislikdagi proyeksiyasi 63 ga,
perpendikularning uzunligi 16 ga teng. Og'ma va
perpendikular orasidagi burchakni toping.
32 Т1Л	’ 16	-	63
arccos—r B) arcsm—r	ь) arctQ~
6p	60	65
. 63
65
5. 12*
, •> b
1 —t + -
2
2	1
5 B) -»
tenglamani yeching.
Agar cos2a — - bo‘lsa5 sin2 о ni hisoblang.
1? D) ?
21	‘ 3
A) i B) 1 С) I D) I
6.	«i var2 x2 - 13r + 12 .= 0 tenglamaning
ildizlari bo‘l$a, + x2X2 ning qiymatini
toping.
A) 156 B) 94 C) -156 D) -152
14. x raqamining qanday eng katta qiymatida
(741 + 2^2) son 3 ga qoidiqsiz bo‘linadi?
A) 8 B) 7 C) 2 D) 9
15.
15 7
19 ’ 25
— 2- ni hisoblang.
7.	>/8r — 3 < — 2 tengsizlikni yeching.
A) r € 0 B) x < 4 C) x > 4
D) *> |
V
8.	Arifmetik progressiva uchun quyidagi
formulalardan qaysilari totgtri?
1)	it] — 2a2 4" аз — 0;
2)	а: - аз — аз;
г,	«п-ai+d
3)п_-------------
А) 1 В) 2;3 С) 1:2 D) 2
9.	(^)16~2г < 4 tengsizlikning eng katta butun
«О
yechimini toping.
A) 10 B) 6 C) 9 D) 11
А) 23| B) 23? C) 24? D) 22?
о	о	J	3
16.	у ~ 2х2 - 2х + 7 funksiya grafigining abssissa
o'qiga eng.yaqin bodgan nuqtasi koorSinatlarini
toping.
A) (4}5;0,5) B) (0,5;4,5)
C) (-0,5;-4,5) D) (0,5;6;5)
17.	x ning qanday qiymatlarida у = -----—
x -F 2
funksiyaning qiymatlari 3 dan kichik emas?
A) (-2:5] B) (-oc;-2)U(5:=to)
C) (—cc;—2)	D) [5:oc)
f
18.	f cosZxdx ni	Hisoblang.
2	12	1
A)	-5	В)	- C) { D) -A
4J	О	о	о
10. Ikki qo‘shni burchakning ayirmasi 28° ga teng.
Shu burchaklardan kichigini toping.
A) 78* B) 72° C) 76’ D) 82°
19.
31g4+31g25
lg!300- lgl3
ning qiymatini hisoblang.
A) 1,5	8) 6 C) 2 D) 3
94
TEST 2006 : Variant	147
Matematika
Л) Teng yonli uchburchakning uchidagi burchagi
106°. Asosidagi burcbaklarning bisseklrisalari
kesishishidan hosil bo’lgan o’tkir burchakni
toping.
Л) 43е В) 37° C) 47a D) 48е
.'I ABCD to‘g4ri to’rtburchakning A burchagi
bissektrisasi BC tornonni uzunliklari BM=16 sm
va MC=9 sm boTgan ikki qismga ajratadi.
To’gTi LoTtburchaknirig yuzini (sm2) toping.
A) 400 B) 500 C) 510 D) 480
22. Konusning yasovchisi 25 ga, uning asos tekisligi
bilan tashkil qilgan burchagining sinusi 0.6 ga
teng. Ken us o’q kesimining perimetrini aniqlang.
A) 80 B) 360 C) 90 D) 105
73 Yasovchisi 26 ga va balandiigi 10 teng boTgan
konus asosining yuzini toping.
А) 144т2 В) 144% C) 576% D) 288%
s/n.36° cos36°
sznl2° cos 12°
A) 3 B) 2 C)
D) vM-1
.'b sin(— 4 x) 4 sin(~ - r) = —- tenglamaning
о	6	2
ildiziarini ko’rsating.
a) ~ + 2tk.kez в) ±^ + 2mt. kez
6	6
C) + kPZ D) ±^ + 2т*, keZ
t5	<>
7ti Agar tekis harakatda t-ezlik 30% ga ortsa,
inaJum masofani bosib o’tish uchun ketadigan
vaqt necha foizga kamayadi?
А) Зз| В) 1б| C) 23-L D) 20
о	о	1 <4
i 30 To’g'ri burchakli uchburchakning katetUri 5 va
7.5 ga teng. To’gTi burchak bissektrisasining
uzunligini toping.
А) Зх/2 В) 4x/2 C) 3 4 372 D) 5v/2
31.	Teng yonli trapetsiyaning kichik asosi 3 ga.
perimetri 72 ga teng. Uning diagonal! o*tmas
burchagini t-eng ikkiga bcrladi. Trapetsiyaning
o’rta chizig’ini toping.
A) 8,5 B) 13 C) 7,5 D) 12
32.	b veklor а (2; 4; 4) vektorga kollinear hamda bu
vektoriarning skalyar ko’paytmasi 144 ga teng. b
vektorning uzunligini toping.
A) 16 B) 24 C) 18 D) 12
33.	^^r^Togj^sin x funksiya x (x e (0; 2%])
ning qanday qiymatlarida aniqlangan?
. . , 7i . »5<r .	. . 7Г 3%_	_. .5%
A) !0;-!Uty;K] B)	C)
D) (0:r!
' '	0
34.	3* 4 3*+3 > 84 tengsizlikni yeching.
A) (-00; 0) B) (0: 1) C) (1; 00)
D) (0: 1)U(1; 00)
35.	Tosg’ri burchakli ACВ uchburchakning katet I an
8 ga va. 10 ga teng. Shu uchburchakning C to'g'ri
burchagi uchidan CE mediana va CD bisseklrisa
, oTkazildi. CDE uchburchakning yuzini toping.
A) 2?	B) 2^	C) 3~	D) 2?
J 7	9	5 b
36-	Konusning o'q kesimi teng tomouli
uchburchakdan, silindrniki esa kvadratdan
iborat. Agar ularning toTa sirtlari teugdosh
bo'lsa, hajndarining nisbatini toping.
A) 1 : 3 B) 2 : 3 C) s/2 : Л D) 1 : y/2
j
i
t
77. Agar 5(2; 7) nuqta у = kz~ 4 8x 4 »n
parabolaning uchi boTsa, к va m ning qiymatini
toping.
А) к = 2, m — — 1 В) к =z 1, m — — 9
С) к — -2. m — — 1 D) к — — 1, m ~ —16
'«’8 \fx* — 4x 4 4 —	— 10ж 4 25 tenglamaning
ildizlari qaysi oraliqqa tegishli?
Л) x<3 В) 3<x<4 C) x < —2
D) x > 5
2) Agar x- — r 4 q — 0 tenglamaning xj та хз
ildizlari 1’4 Zj x 37 shartni qanoatlantirsa, q
ning qiymatini toping.
A) -11 B) -5 C) -19 D) -Г2
95
TEST 2006: Variant
148
Matematika
1
Matematika
1.	2.68013579 coni 9 ga bodunishi uchun riuqtaning
c/rniga qanday raqarn qo\vilishi kerak?
A) 4 В) 0 C) 8 D) 7
2.	5. 2} y, —2 soldarning o'rta arifmetigi 1.2 ga <eng.
у ni toping.
A) -0,8 B) 1,2 C) -0,4 D) 0,4
3.	16 — (8a - 3)2 ni ko‘paytuvchilarga aiming.
A) (8a - i)(7 4-8a) B) (8al)(8a - 7)
C) (8a-])(7-8a) D) (8a + l)(7-8«)
4.	2z(z — 1) - (2x -f-1)(® — *2) ko*phadni standart
shaklga kehiring.
А) 2z2 - 3s B) 4a*2 — 1 C) —г 4- 1
D) z-4-2
,	.	. Or — in 7rnx -- 1
й. m ning qanday qiyrnatida -—-— =--------------
4	tJ
tenglamaning ildizi nulga teng bo'ladi?
6. s2 4 13r + q ~ 0 teng'amauing iidiziaridan biri
— Il ga uug. Uning ikkinchi ddizini toping.
A) 2 B) -24 C) -2 D) 24
‘ 7. Agar a > b va ab 0 bc/'sa, quyidagi
tengsizliklardan qaysi bin bar doira v’nnli?
A) a2 > B) . - > C) lu >3a-b
a b
D) 3q < 4a ~ b
8. Quyidagi sorilardan qaysi biri 0.3(6) ga teng?
d	ro	П	9	_	4
1 18	B-’	30	A) * C) * * * * * 1 27	°'	U
y—	_
9. (V3) ь<1з"л nj hisobiang.
A) 3 В) Из C) 6
D)
10. Ikkita to’g‘ri chtziqning kesishidan hosil boMgan
qo:shni burchakiarning ayirmasi 50’ ga teng. Shu
burchaklardan kichigini toping.
A) 65° B) SO3 C) 70° D) 50е
•’dd Quyidagi tasdiqlarning qaysilari to'g'ri9
1) tornonlari a, b va c bodgan uchburchakka ichki
chizilgan aylananmg radius/ r = 7^37-7 formula
bilan hisoblanadi:
2) radiusi R. ga. markaziy burchagi a ga. teng
doiraviy sektorning yuzi S = f°rrnula bilan
hisoblanadi;
3) tornonlari о va 6 ga. ular orasidagi
burchaklandan biri a ga teng bo‘igan
paraJlelogranvrrming yuzi S = absina formula
bilan hisoblanadi.
A) 2;3 В/ 1:2 C> 1:2:3 D) 1:3
12. Tekislikka og‘ma va perpendikular tushirilgan.
Og'ma va tekisbk orasidagi burchak access77 ga,
og^maning tekislikdagi proycksiyasi 120 ga teng.
Perpendikularning uzunligini toping.
49	168
A) 12 В) ~ C) 22 D)
...	.	4	,
1J. tg(-— a) — —- bo'jsa, ct« о mug qiymatun
4	5
toping.
A) 9	B) -j	C) -4 П) 1
14. 264 va 840 ning umumiy bo’iuvchilari nechta?
A) 4	B) 9	8 D) 6
J
15. Agar x < z < у bo’lsa, |t — y\ — |c\- y| - [2 —xrl
ni soddalashtiring.
! A) 2y-2z fcB) 0 C) 2y-2z D) 2z - 2y
i
i 46. f(r) — x/5 4- х/4~+ i + \/5 b Й - д: funksiya
i uchun quyidagilardan qaysi biri o^rinli bo‘ladi?
> A) toq ham. juft bam emas B) toq funh^i/a
j Cj o'suvchi funksiya D) juft fun ksiya
i '17. Quyidagi tengsizliklardan qaysi biri z va у ning
j zy > 0 shartni qanaafclantiradigaD barcha
qiymatlarida o‘rinli?
A) ^'— + —^->2 B) (e-y)»>0
X -r y- xy
С) я'2 -- 6.ry -t- 9y2 <0 D) x2 — y2 > 0
18.	Agar Ff(x) ~ siriZ va F(l) = 4 ЬоЪа, F(z) ni
toping.
A) 4 + sinl - sinx	B) 4 — cosl + cosz
C) 4 4- sinl 4- sinx	D) 4 + cosl - cost
19.	n = logij<A 4-	m = lne~2 va
p = /0^1/3! 5 ~ logyf-^ sonlarni kamayish
tart-ibida joylashtiring.
A) m > n > p	B) p > m > n
C) m > p > n	D) n > p > m
20.	Uchburchak burchaklarining kattaliklan nisbati
1:1:2 kabi. katta tomouining uzunligi esa 24 ga
teng. Uchburchakning katta tomoniga tushirilgan
bdandligini toping.
А) Г2 B) 6,5 C) 6 D) 8
21.	Yuzi 156 sm • . balandliklari 4 sm va 12 sm
bo‘lgan paraiielogrammning perimetrini toping.
A) 73 B) 104 C) 96 D) 108
22.	Chiziqli o'ichovlari 3: 4 va 2v/b4 sm bo‘lgan
to4g:ri burchakli parallelepipedning diagonal!
necha sm?
A) 7 B) 11 C) 9 D) 10
96
TEST 2006 : Variant
148
Matemat! кз
73 Balandligi 12 ga, asosining radiusi 6 ga teng
bo'Igan konusga yasovchisi 4 ga teng bo'lgan
silindr ichki chizilgan. Silindr asosining radiusini
loping
A) 4 В) 3 C) 2 D) 2,6
7 1 t — cos3'2°, q = sinl 12е va k t^235° sonlarni
o'sish tartibida joylashtiring.
A) к < t < q
D) t < к < q
Б) q < i < к C) t < q < h
2 sin2 - 1 — — tenglamani yeching.
А) (-1)‘+1~ + 17Г,-*е z
0
»)	+ 7'.. fc € Z C) + mt; k 6 Z
5ir
D) ±y^ + k e z
26 Mahsulotning narxi birinchi marta 20% ga;
ikkinchi rnarta yangi bahosi yana 10% ga
oshirildi. Mahsulotning oxirgi bahosi necha
foizga kamaytirilsa. uning narxi dastlabki narxiga
teng bo’ladi?
A) 24~ B) 25 C) Зз| D) 30
vU	<>
7 —-------------г co soy ifodaning eng katta
z" 4- 8x 4- 41
qiymati nechaga teng bo'Kshi mumkiri?
A) 1,5 B) 1,8 C) 2,4 D) 1,4
| 33. 1 — 2sin4r < cos24r. tengsizlikni yeching.
A)	(„1 + 2xt; + -2^k),k € Z
B)	(irZr; I "г 7ск).к G Z
C)	+ *2t£; ~ 4- 2rfc), fc G Z
4	4-
_.	.-xfc	7Г	xfc. ,	_
D)	(V:7 + V^fee7
Z	4	2.
34, logics ((0, 25)Jogi«(5‘+5+«+" ni hisoblang.
A)	В)	- C)	- D) —
7	8	j	7	-5	14
35. Doiraga ichki chizilgan muntazam
uchburchakning yuzi unga ichki chizilgan
kvadratning yuzidan 18,5 ga k&m. Shu doiraga
ichki chizilgan muntazam oltiburchakning yuzini
toping.
A) Sv'S + ev'? В) 8^3 + 15 С) 27 + 24у/3
О) 13,5M2v3
36. Asosi a ga. asosidagi burchagi a ga teng bo lgan
tengyonli uchburchakni yon tomoni atrofida
aylantirishdan hosil bo'lgan jismning hajmini
toping.
4 	3 •	3
5, тга sirro no sincr	„ ira соло
A) __.	B) —--------- Cl --------x—
6 coso	3	6 sin "a
o)
!	2
28.
30	.	.	. , .
=s teDglamanirig natural sonlardagj
yechimida z nimaga teng?
A) 3 B) 4 C) 7 D
‘24 4|r + 4| — 3 + (r 4- 4)3 tenglamaning ildizlari
ko‘paytmasini toping.
A) 15 B) 105 C) -15 D) -105
30. Tornonlari 16; 30 va 34 sm bo‘lgan uchburchakka
t-ashqi chizilgan aylananing radiusi necha sm?
A) 18 B) 17 C) 19 D) 16
31 To£g n to'Ttburcbakning to’g’ri burchagi uchidan
uning diagonaliga tushirilgan perpendikular
to‘gJri burchakni 3:2 kabi nisbatda bo'ladi. Shu
perpendikular bilan boshqa diagonal orasidagi
burchakni toping.
A) 72° B) 22,5° C) 18° D) 45°
.1? 6(3; —6; 6) vektorga koUinear va ofc — 40, 5
tenglikni qanoatlantiruvchi a vektocni loping.
Л) a(3;6:9) B) a(|;-3;3) C) a(3;-6;6)
I))
97
TEST 2006 : Variant
Matematika
Matematika.
1. ikki shahar orasidagi masofa 400 km bo'lsa.
1:5000000 masshtabli xaritada bu masofa necha
mm ga teng bo'ladi?
A) 80 B) 100 C) 40 D) 20
1,5-0,15-9,2 .	.	...
4лГЖЙ nins wnatm! topmg-
A) 7 «I | C) | D) 2
& S 2
3. Uchburchakning birinchi tomoni z (r > 12) sm,
ikkinchi tomoni undan 7 sm qisqa. uchinchi
tomoni esa birinchisidan 5 sm uzun. Shu
uchburchakning perimetrirri (sm) toping.
A) Зх-1 В) 3x4*2 C) 3x4-1
D) 3x-2
4. (г — 1)(2 — t ) 4 (x — 3)2 ko'phadni staiidart
shakiga keltiring.
A) 3r2 4-15x4 7 В) -3x4-7
C) Ш4-4-Х2 £>) 9i+7
-	. J
5. (2 — 4 г н 4 -
' 22	'	5
= 5 tenglamani yeching.
A) 18± B) 17 C) 21 D) 171
Zz	4Х
6 x2 4- Hr 4- g ~ 0 tenglamaning ildizlaridan biri
— 12 ga t-eng. Uiiiiig ikkinchi ildizini toping.
A) -23 B) 1 C) 23 D) — I
11.	Quyidagi tasdiqlaming qaysilari to'g'ri?
1)	tomonlari a va 6 ga, ular orasidagi
burchaklaridan biri a ga teng bo'lgan
paraHelogrammning yu?i 5 — absina formula
bilan hisoblanadi;
2)	tomonlari « va b ga, ular orasidagi burchagi o.
ga teng bo'lgan uchburchakning yuzi
S -- -absina formula bilan hisoblanadi:
3)	diagonallari r% va d? ga, ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
to'rtbnrchakning yuzi S — did^tno formula
bilan hisoblanadi.
A) 2:3 B) 1:2 C) 1;2;3 D) 1:3
12.	Tekislikka tushirilgan og'ma va perpendikuiar
orasidagi burchak arcsin— ga teng. Og'rnaning
61
uzunligi 122 ga teng. Perpen diku laming
uzunligini toping.
A) 22 B) 120 C) 24 D) 90
,. ,	i , C1 2 sin о 4- sin 2a
13.	Agar cos a — — bo Isa. —--------------- m
/	2 si n a — sin 2a
hisoblang.
A) B) 0,5 C) ? D) 3
4	3
14.	Agar avtornobil tekis harakatda 3 soatda 324 krn
ni bosib o'tsa. 10 sekundda necha metr masefani
bosib o'tadi?
A) 300 B) 200 C) 100 D) 600
15.	0‘zaro t eskari sonlarni aniqlang:
1) 3-V2 va3 4-/2;
7.	-—- < 0 tengsizlikni yeching.
x 4“ 3
A) [2; 3) B)(-l:2] C)(-3;2j
D) [2; 3]
у
8.	0. (8) 4- 0,(3) — ~ ning qiymatini hisoblang.
V5 3v5
2 _ va
3 a
A) 1;2,3 B) 1;3:4 C) 1:3
D) 2:3:4
A) 1| B) i| C) | D) 0.(11)
9.	/<5«7s?r^6-° ni hisoblang.
A) 4ye В) a C) 3
D) 4
(x — n)(x — 2) . , .	.	. . . ,
15. у =	-----—-------- funksiyaning amqlamsh
у 0 - x)<z — 3}
sohasini roping.
A) [2;3)U(4;5] B) (2:3)U(4;5)
C) (-oo:2]U(3;4)U|5;oc) D) (2:3}U[4:5)
10. ikki tcjg ri chiziqning kesishishidan hosil bo'lgan
burchakiarning biri 49’ ga teng. Qolgan
burchakiarni toping.
17.
(x - 4)(r 4-2)
(г-3р~
< 0 tengsiziikning eng katta va
А) 110е. 110°, П0в
C) 140*, 140'5, 40’
В) 150й, 150% 30°
D) 60’, 60% 30’
eng kichik butun yechimlari ayirmasini toping
A) 4 B) ’3 C) 2 D) 5
98
TEST 2006 : Variant
14Э
Matematika
IK ----------— ning boshlang’ich fnnksiyasini
t+1)
4
toping.
A) 4ig(^ + \) + C 8) lf9(i + l) + C
4	4	4
C) —4tg(---j-l)-Ь C D) ~-ig(~ 4 1) + C
4	4	4
va c — ( v^)5 sonlarni
a
o'sish tartibida joylashtiring.
20 Ayianaga tashqi chizilgan teng yonli
trapetsiyanmg o'rta chizig’i 8 ga teng. Shu
trapetsiyaniug yon tomoni ni toping.
A) 8 B) 4 C) 5 D) 7
21 Ikkita o’xshash ko'pbarchak yuzlarining nisbati
9:4 ga teng. Kichik ko’pburchakning perimetri 8
sm. Katta bypburchakning perimetri ni toping.
A) 8 B) 9 C) 12 D) 6
7? Piramidaning asosi to'g’ri burchakli uchburchak
bo’lib, uning gipotenuzasi uzunligi 20 ga teng.
Piramidaning barcha yon qirralari 26 ga teng
bo'lsa, uning baiandligini toping.
A) 12 B) 24 C) 22 D) 20
23 Ikkita sfera yuzlarining nisbati 272 ga teng. Bu
sferalar diametrlarining nisbatini toping.
A) 78 B) 78 C) 72 D) 8
24 Quyidagi ayirrnalardan qaysi binning qiymati
manfiy?
A) cos 10° — cos50ft
C) ot542e-^28°
B) sin 140’— sin 150°
D) f-p87° - t^85c
75. 5sin 4x — 8 — 3cos(— 4- 4z) tenglarna [—2tf; 2тг]
kesmada nechta ildizga ega?
A) 7 B) 0 C) 6 D) 8
26.	Bog’dagi daraxtlaming 60% 1 teraklar. Qolgan
daraxtlarning 70% i chinorlar bo’lsa, boshqalari -
toiler. Bog’dagi daraxtlarning necha foizini toll ar
tashkil etadi?
A) 18 B) 12 C) 24 D) 28
2Г /(x) — |x — 1] -b Iz — 2| funksiyaning qiymatiar
sohasini toping.
Л) [l;oo) В) (0;oc) C) [3;oo) D) [2:00)
29.	kx2 + 3kx 4 2k — 2 x 0 tenglarna yechimga ega
bc/lmaydigan k ning butun qiymatlari o’rta
arifmet-igmi toping.
A) -2 B) -3,5 C) -3 D) —4
30.	Katctlarining nisbati 2.3 bo’lgan to'g’ri burchakli
uchburchak balandligi gipotenuzasini
uzunltklaridan biri ikkinchisidan 0,6 ga kam
bo’lgan bo'laklarga ajratadi. Gipotenuzaning
bo'laklarini roping.
A’/ 5va3 B) 2 va 4 C) 1,6 va 3,6
D) 1. 08 va 0. 48
31.	Parallelograms qo’shni tornonlarining yig^ndisi
10 ga, ayirmasi esa 8 ga teng. Shu
parallelogramm diagonallari kvadratlanning
yig’indisini toping.
A) 144 B) 164 C) 121 D) 136
32.	A(-4; 1; I), B(l; 4; 0) , C(l; -2; 2) va__
D(—5; —5; 3) nuqtalar berilgan. AC va BD
vektorlar orasidagi burchakni toping.
А) 60е B) 90’ C) 45° D) 30s
33.	cos4 x — sin4 1 — 0 tenglamaning [0; 2tr] kesniada
nechta ildizi bor?
A) 1 В) 0 C) 4 D) 3
I og^l (72 + 1)
34.	( —-----^5«(T^d-l) ni soddalasfatiring.
\T2- 1/
A) 2<?g6(72~l) B) /o7e(T2 + l)
C) 72 + 1 D)
35.	Diagonal! orqali ikkita muntazam uchburchakka
ajraladigan rombga ichki chizilgan aylananing
radiusi r ga teng. Rombning yuzini toping.
А) 4г3 В) 2r5T§ С) 4r275 D)
36.	O’q kesimi teng lomonli ucbburchakdan. iborat
konusga diametri D ga teng sfera ichki chizilgan.
Konusning to'la sirtini toping.
A) |tD2 B)	С)
3
j D) -7tD2
{Ixl 4- u — 8
3J4- у — 4 ^°^sa’ x	qiyniatini
toping.
A) 1 B) 3 C) 2 D) 13
99
TEST 2006 : Variant	150
Matematika
1
Matematika.
. f .	8 4- 5n4 4 4?r ,	,
I.	nfn £ A)mng------------к-------kasr butun. son
rt
bo'ladigan barcha qiymat-larini toping.
A) 1: 2 В) I C) 1: 2: 4- D) 2
2.	(2.01 — 3,81) • 3, 8 ifodani hisoblang.
A) 5,82 B) 6,84 C) -5,82 D) -6,84
12. Tekislikka og‘ma va perpendikular tushirilgan.
Og‘maning tekislikdagi proyeksiyasi 11 ga,
perpendikularning uzunligi 60 ga teng. Oguma va
perpendikular orasidagi burchakni toping.
.	22	.11	11
A)	arccos-—7	B)	arcstn-—-	C)	arcctG—r
6i	61	60
. GO
D) urcstn - -
61
3.	v\/564-2-/10 * у//t>6 — 2/W ni hisoblang.
А) б B) 2 C) 4 D) 3
— a) = 4 bo‘isa, tga ning qiymatini
toping.
4-	(И У1 4 1 ){y~ 4 1) - (y - 1 )(y 4 2) 4 у* 4 гр ni
soddalashtirgandan keyni hcsil'boigan
ko'phadning nechta hadi bc/ladi7
A) 4 B) 3 C) 5 D) 6
5.	(2z — l)(.r — 1,5) ~ 0 bo* Isa, 2.г- -- J qanday
qiymatlar qabul qiladi?
A) faqat B) 2 yoki 0 C) 0 yoki 1,5
D) 0 yoki — i
6.	ar2 — 7x 4 q — 0 tengtamaning ildizlaridan biri
— 1$ ga teng. lining ikkinchi iidizini toping.
A) 8 B) -26 C) -8 D) 26
{3 4 4z 4 5
2x — 3(x — 1) > 1 tenSsl21’^ar sistemasining
butun sonlardaa iborat yecbimlari nechta?
A) 3 E) 5 C) 2 D) 6
8.	0,4(5) soni quyidagi sonlardan qaysi biriga teng?
5	4	45	41
А)	в) —	C) —	D) --
'11	7 90	7 90	' 90
9.	x ning qanday qiymatlarida у ~	— 125
funksiya nomanfiy qiymatlar qabui qiladi?
A) x < 3 B) x > 3 C) x < 2 D) x > 2
10.	Markaziy burchakka mos yoy aylananing -
qismiga teng. Shu markaziy burchakni toping'
A) 144° B) 72° C) 216° D) 288°
11.	Quyidagi Lasdiqlarning qaysilari to'g ri?
I)	tomontari a,i va <• bo:Igan uchburchakka ichki
chizilgan aylananing radiusi r ~ formula
bilan hisoblanadi:
2)	radiusi 7? ga. markaziy burchagi о ga teng
doiraviy sektorning yuzi S ~ formula bilan
hisoblanadi;
3)	tornoni « ga. burchaklaridan biri о ga teng
rornhning yuzi S ~ ka^sina formula bilan
hisoblanadi.
A) 2:3 B) 1:2 C) 1:2:3 D) 1:3
14.	41 • 17 • 28 < 35 — 24 12 -87 ayirma qanday m.qarn
bilan tugaydi?
A) 2 В) 0 C) 6 D) 4
15.	25 va 15 sonlan eng kichik umurniy karralisintag
natural boOuvchitari nechta?
A) 4 B) 5 C) 7 D) 6
16.	J(—2) — 5 va /(2) - 3 shartni qanoatlantiruvchi
chiziqli funksiyaui aniqiang.
Л) У(ж) —	- 1 B) f(r) ~ -г 4 4
C) /U)“-|r4 4 D) 7(~)-2я4 1
1 2*	3 T8 <3x	sisteniasi butun
yechunlanning o*rta anfmetigini toping.
A) 2,5 В) 3 C) 1,5 D) 2
18.	/(т) = Здг2 — 2 funksiya boshtaug‘ich
funksiyalaridan qaysi birining grafigi M(2; 10)
nuqtadan o'.tadi?
A) F(x) — j?3 — 2x 4 6 B) F(r) — xs — 2.T
C) F(x) — г3 — 2« 4 8
О) Г(зУ) x3 — 2x 4 5
19.	4 4) — /о<7д(х 4 4) > —tengsizlikni
yeching-
A) (-4:-1) В) (0;l) C) (-2;i)
D) (2:3)
20.	Radiusi Я ga teng bolgan aytanadagi nuqtadan
uzunliktari Rx/3 ga teng bo'lgaa ikkita vatar
o’tkazildi. Vatarlai orasidagi burchakni toping.
A) 60° В) 45G C) 120p D) 135“
21.	Teng yonli trapetsiyaning yon tornoni va kichik
asosi 5 ga, balandiigi 4 ga teng. Trapetsiyaning
yuzini toping.
A) 22 B) 32 C) 40 Dj 20
100
TEST 2006: Vanant
150
Matematika
?? Teng tomoidi uchburchakning tomonlari 3 in.
Uchburchak tekisligidan tashqarida uni ng
uchlaridan 2-\/3 m masofada yotuvchi nuqtadan
uchburchak tekisligigacha boigan masofani
toping.
A) x/3 B) 1 C) 3 D) 1,5
*3 Konus asosining radiusi 12\/3 ga teng, yasovchisi
asos tekisligi bilan 30® li burchak tashkil etadi.
Asos markazidan yasovchigacha bo’lgan masofani
toping.
А) 6У5 B) 8 C) 3/3 D) 5
'21. Agar tgtx + ctgor = 10 bo'lsa, stn'Zot ni hisoblang
A)	1 B) 1 C) 1 0)1
cos 2r sin 3л + sin 2л cos 3л =• ~ tenglamani
yeching.
Л) (—1)” •	+ —n. n G Z
OU Э
В)	(-1)” -s + f». C) in, n 6 z
/и О	dll
D) (-1)" - £ 4-I„. П G Z
76 520 soni shunday ikki bojakka bo’linganki,
ulardan birining 80% i ikkinchisining 24% ini
tashkil qiladi. Bo'laklarni kichigini toping.
A) 120 B) 400 C) 460 D) 420
J l у = кx2 — 2kx + 5 va у - 2 - b funksiyalarning
grafiklari к ning nechta butun qiymatlarida
kesishinaydj?
Л) 2 B) 12 ' C) 4 D) 11
1	55
28 x 4------j- = — tenglamaning natural sonlardagi
y+-
A*
yechimida у nimaga teng?
A) 4 В) 3 C) 2 D) 1
29 Agar x~ — x 4- q — 0 tenglamaning xi va xz
ildizlari xf 4*	~ 37 shartni qanoatlantirsa, q
ning qiymatini toping.
А) -И B) -5 C) -19 D) -12
10 Tog'n burchakli uchburchakning gipot-enuzasi 25
sm. katetlaridan birining gipotenuzadagi
proyeksiyasi 1,96 sm. Ushbu uchburchakka ichki
chizilgan aylananing radiusi necha sm?
Л) 1 В) 3 C) 2 D) 1,5
31 Teng yonli trapetsiyaning asoslari 30 va 50 ga,
balandligi esa 30 ga teng. Trapetsiyaning
diagonal!™ toping.
A) 56 B) 70 C) 60 D) 50
32.	S(m — I: \/5;4) vektoraing uzunligi 5 dan katta
bo'Iadigan rn ning barcha qiymatiarini toping.
A) (-t;3) B) (_«;-2)U(2;oo)
C) (-oo;-l)U(3;oo) D) (-2:2)
33.	1 — 2cos‘2x > sin22x tengsizlikni yeching.
A)	Q + 2irt;^+2Tit\t€Z
В)	f + rfc: г + tA , Jr € Z
("7Г e	« । .
^2 + *k: 2	c Z
D) + irk; +	€ Z
4	/
34.	(л + 2)1оеД**+О < (г + 2)1o^(^+9> tengsizlik x
ning qanday qiymatlarida oYmli?
A) (-2;4) В) (—4.5:oo) C) (-1:4)
D) (4;oo)
35.	Radiusi \/3 bo‘lgan doiraga tashqi chizilgan teng
yonli trapetsiyaning asosidagi burchagi 60®.
Trapetsiyaning yuzini toping;
A) 3 В) 8УЗ C) | D) 10
36.	Teng tornonii silindrning va teng tomonli
konusning balandligi oszaro teng. Ularmng to4a
sirtlari nisbatini toping.
A) 3:8 B) 5:3 C) 3:2 D) 3 :4
101
TEST 2006; Variant
151
Matematika	1
Matematika
1	18-13—15* 13 + 21 -17 — 18 17 + 17 • 15—15 14
ni h isobl a ng.
A) 135 B) 125 C) 180 D) 205
2.	3,3; x va -2,1 sonlarining o:rta arifmetigi 0,6 ga
teng. x ni toping.
A) -0,6 B) 0,6 C) 2 D) 0,8
3.	a(6 — c) - 6(e - a) — c(b — a) ni soddalashtiring.
А) 2аЬ В) —2ae C) 2ab~2bc D) 0
1	1
4.	Agar P = -z — -у - (л + 2y) va
X	Xr
Q = 1* + ly — (r + 5k) bo'lsa, P - Q ni toping.
A) 4S В) 2y C) -V D) -4»
u
5.	a ning qanday qiymatlarida [a + 41 = -a — 4
tenglik o‘rinli bo‘ladi?
A) a G ф B) a — -4 C) a < -4
D) a < —4
g
6.	x + 6 = — tenglamaning nechta haqiqiy ildizi
bor? *
A) 2 B) 1 C) xMiziyo'q D) 3
7.		- < 0 tengsizlikni yeching.
x — о
A) [-3; 5) B) (-oo; -3}
D) (-3; 5]
C) (5; oo)
8.	Quyidagi ketma-ketliklardan qaysilari geometrik
progressiyani tashkil etmaydi?
1)	a„ = 2zn, (z^ 0);
2)	cn -axn, (ax#0);
3)	bn = (I)" • swi60° + 1.
Э
A) 3 B) 1;3 C) 2 D) 1
9.	x ning qanday qiymatlarida u ~ 3 - Igx funksiya
nomusbat. qiymatlar qabul qiladi?
A) x > 1000 B) x > 100 C) x < WOO
D) z < 100
11.	Quyidagi tasdiqlarning qaysilari to‘g:ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R — ^(a,6.c— uchburchakning
tornonlari, S'— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	tornonlari a va b ga, ular orasidagi burchagi о
ga teng bo'lgan uchburchakning yuzi
S ss kabsinor formula bilan hisoblanadi;
3)	o'xshash figuralar yuzlarining nisbati ularning
mos chiziqli o'lchovlarining nisbatiga teng.
A) 2;3 B) 1:2 C) 1;2;3 D) 1:3
12.	Tekislikka tushirilgan og‘ma va perpendikular
., . ,	, ,	.20 л .
orasidagi burchak arestn— ga teng. Og’mamng
uzunligi 58 ga teng. Perpendikularning
uzunligini toping.
A) 80 B) 40 C) 42 D) XI
13.	1 +	TOdda]3shtirinS.
cosJo
A) 1 — tg2a B) tg2a C) 1 — ctg2a
D) -Д-
cos a
14.	O‘khamlari 22m x 15m bo'lgan zalni tomoni 20
sm boigan kvadrat shaklidagi plitkalardan
nechtasi bilan qoplash mumkin?
A) 18000 B) 1650 C) 8250 D) 9000
.	38	47	56	, 4	3	4	5
15.	Agar	—	+	*— + — = a	bo Isa. — +	+	—
*	41	51	61	41	51	61
quyidagilardan qaysi biriga teng?
A) 4 —a B) 3- a C)3-| D)5 —0
16.	(2a - l)(2a + 1) + 35(36 - 4a) + 1 ning eng kichik
qiyrnatini toping
A) 0 B) -1 C) 1 D) -2
(x + 4)(3 — z)
17.	-----———- > 0 tengsizlikning eng katta va
(i + 3)2
eng kichik bulun yechimlari yig‘indisini toping.
A) -2 B) 1 C) 0 D) -1
18.	---s—~—— ning bosblangJich funksiyasini
«n2(4z +1) b
toping.
A) ^c^(4z + l) + C B) -~c<5(4r + 1) + C
*r-	*
r
C) -|ts(4z + l) + C D) 1^(4т + 1) + С
10. Ikkits, tog'rl chiziqning kesishrshidan hosil
bo'lgan burchakiardan uchtasining yigindisi 275°
ga teng. Shu burchakiardan kichigini toping.
A) 45° В) 60е C) 85° D) 70°
19.
a = log347189 bo‘lsa, log73 ni a orqali ifodalang.
a \ 2a “*1	1 “ 2<J n a ~ 2
A)	C) 5ГЛ
_ , a — 2
D>
102
TEST 2006: Variant
151
Matematika
/() leng yonli uchburchakning balandligi 20 ga teng.
Yon tomoni ascsidan 5 ga kani. Shu
uchburchakning asosini toping.
A) 40 B) 20 C) 24 D) 30
2 1 Balandligi 32 ga teng bodgan rombga ichki
chizilgan doiraning yuzini toping.
Л) 190т В) 196ж С) 200т D) 256t
22 Muntazam t-o'rtburchakii piramidaning
balandligi 24 sm. apofemasi esa 26 sm. Piramida
asosining perimetrini toping.
A) 48 B) 40 C) 80 D) 96
23. Balandligi 12 ga, asosining radiusi 6 ga teng
bodgan konusga yasovchisi 4 ga teng bo’lgan
silindr ichki chizilgan. Silindr asosining radiusini
toping.
A) 4 В) 3 C) 2 D) 2,6
5	5
24 Agar igot + tgP = $ va tgcdgp —  —bo1 Isa.
a 4» 6 nimaga teng bodadi?
a) 2- + %fc,Aez B) J + Tfc, kez
•>	0
C) y + irk,k€Z D) -^ + *k,keZ
4	о
25.	4sm22r = 1 tenglamani yeching.
А)	(“1)п^ + тп, n e Z
о
T ТП	„
В)	+ “7Г> n € Z
X 4a
C)	(-i)"^ + v- neZ
, T ТП	_
D)	±— 4- —-5 n Q Z
У tJ
26.	Agar knbning qirrasi 20% ga kamaytirilsa. uning
hajrni necha foizga kamayadi?
A) 40 B) 48,8 C) 30,8 D) 60
29.------— = —- tenglama m ning nechta natural
rn — 10 i ”
qiyrnatida ildizga ega emas?
A) 7 B) 5 C) 8 D) 28
30.	Tornonlari 13; 14 va 15 sin bodgan
uchburchakning eng katta balandligi necha srri?
A) || В) C) D) 13
31.	Ascslari 12 va 16 ga teng bodgan teng yonli
trapetsiyaning diagonallari o'zaro perpendikular.
Trapetsiyaning yon tomonini toping,
A) 14^/2 B) 20 C) 10 D) 10Л
32.	Agar n(—6;3;3) va 6(3; —3;0) bo*Lsa, 2a va if
vektorlar orasidagi burchakni toping.
А) 60е В) 150° С) 135° D) 120°
33.	tri пт + cosx =• 1 tenglamaning [—rj oraliqda
nechta ildizi bor?
A) 1 В) 0 C) 3 D) 2
34.	cos2(3 4- 1) • /0514(3 - 2x - n2) > 1 tengsizlikni
yeching.	;
A) [-2;-l]	B) [-l;0) C) {-]}	\
D) {-2--1)
35.	Doiraga ichki chizilgan uchburchakning bir
tomoni uning diametriga teng. Doiraning yuzi
289ff ga, ucbburchak tomonlaridan binning
uzunligi 30 ga teng. Shu uchburchakka ichki
chizilgan doiraning yuzini toping.
A) 36r B) W C) W D) 64r
36.	Sharga balandligi asosining diametriga teng
bo'lgan konus ichki chizilgan. Agar konus
asosining yuzi 2,4 ga teng bo’lsa, shar si reining
yuzini toping.
A) 6 В) 9г C) 15 D) 12,5
. 3a- + 8.5	.	. . . ,
27 у — lg{----------4) funksiyaning amqlanish
f+ 7
sohasini toping.
A) (~2;1) B) (-oo;-2)U(l;t»)
C)	D) (—oo; —2)
28. To‘rtta sunning yig'indisi 118 ga teng. Agar
birinchi va ikkinchi sonning nisbati 2 : 3 kabi,
ikkinchi va tichinchi sonning nisbati 3 : 5 kabi va
uchinchi va to‘rtinchi sonning nisbati 5 : 6 kabi
bo;Isa, birinchi va to’rtinchi sonning yigindisini
toping.
A) 62 B) 60 C) 59 D) 66
103
TEST 2006 : Variant
152
Matematika
1
Matematika
I.	Agar kamayuvchini 26 ta va ayriluvchiui 12 ta
ort tirilsa. ayirma qanday o'zgaradi?
A) 14 ta or tadi	B) 4 ta kamayadi
C) 4 ta ortadi D) 28 ta kamayadi
n J
2.	2- ga teskan sonni toping.
A) 1| B) -0,6 C) -6 0) 0,4
11. Quyidagi tasdiqlaming qaysilari noto'g'ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R = ^(a.b,c— uchburchakning
tomonlari. 5— uchburchakning yuzi) formula
bilan hisoblanadi:
2)	radiusi R ga, markaziy burchagi or ga teng
doiraviy sektoming yuzi S ss formula bilan
hisoblanadi;
3)	tomoni a ga, burchaklaridan biri a ga teng
rombning yuzi S = ^ersina formula bilan
hisoblanadi.
A) 2;3 B) 1;2 C) 1;2;3 D) 1;3
3.	a[b + e — be) — b(c + a — ас) — e(b — я) ni
soddalashtiring.
A) 2ac — *2bc B) — 2abc	C) ab-ac
D) -2k
4.	(r3 + l)(x4 —z34- 1) —(z2- l)34-«54 *34-x hi
soddalashtirgandan keyin hosil bo'lgan
ko'phadning nechta hadi bo'ladi?
A) 4 B) 5 C) 6 D) 3
12.	Tekislikka tushirilgan og'maning uzunligi 125 ga.
uning tekislikdagi proyeksiyasi esa 35 ga teng.
Og*ma va tekislik orasidagi burchakni toping.
ал	10 * 12 d\ • 24 m 7
A) arccos— В) атапп— C) ardg—
n\ • 7
D) arcs in—
25
cos За sin За .
13.	1- —:-----------m soddalashtiring.
cos a sin or
A) 4 cos 2а B) 4 cos о- C) —2
D) 2 cos 2а
_ 6x — m 7mi — 1
5. m ning qanday qiymatida —-— = ——-------
tenglamaning ildizi nolga teng bo'ladi?
A) l В) -| C) | D)
14.	Agar N bo'lsa, quyidagi Hodalardan qaysi
birining qiyinati bar doim butun son bo'ladi?
л, B) £+1 C) irl
D) +	* 2)
6. Г] va xj z2 — 1 lx 4-12 = 0 tenglamaning
Odizlari bo'lsa, rjz2 4- z^zj ning qiymatini
toping.
A) 132 B) -78 C) -132 D) -168
> 0 tengsizhkni yeching.
A) [-7; 5) B) (-co; -7)
C) (-00; -7)U(5; 00) D) (-7; 5]
8. 0,6(3) ni oddiy kasrga aylactiiing.
4	_ 2	62	57
15	30	90	90
9. /o^lplOO3 ni hisoblang.
A) 4 B) 1 C) 2 D) 3
10. Ikki to'g'ri chiziqning kesishisbidan hosil bo'lgan
burchaklarniug kattalikUri nisbati 7:5 ga teng.
Shu burchaklardau kichigini toping.
А) 49е В) 63’ С) 75° В) 54°
15.	Mehnat unumdorligt bir xil bo'lgan 8 kishi
malum hajmdagi ishni 15 kunda tugatishdi. 12
kishi o'shancha rnehnat unumdorligi bilan
ishlasa, o'sha hajmdagi ishni necha kunda
tugatishi mumkin?
A) 8 B) 9 C) 12 D) 10
16.	к ning qanday qiymatida у = kx 4- 2
funksiyaning grafigi A(—4; 14) nuqtadan o'tadi?
A) -1 B) -2 C) -3 D) -6
17.	Agar a < — 1 bo'lsa, quyida keltirilgan
ifodalardan qaysi birining qiymati eng katta
bo'ladi?
А) а'3 В) (Г9 C) a7 D) a"5
18.	/ (1 4'Ciy2r)dz ni hisoblang.
A) 1 В) C) -1 D) V3-1
M
19.	R>02(4 — 2z) — log । (4 — 2x) > - tengsizlikni
yeching.
A) (-co; 1) B) (-co: 0,5) C) (0; 1)
D) (-4; -1)
104
TEST 2006: Variant
152
Matematika,
it Katta yon tomoni 6 sm, o'tkir burchagi 30°
bo'lgan tolg!ri burchakli trapetsiyaga aylana
к hki chizilgan. Shu aylananing uzunligini toping.
X) 7 В) 2% С) 3т D) 4т
‘ I To gri t-o'rtburchakning katta tomoni 13 ga.
diagouallarining kesishgan nuqtasidan katta
(ornonigacha bo5lgan masofa 3 ga teng. To'g'ri
to' rtburchakning yuzini toping.
Л) 78 В) 96 C) 72 D) 48
22 Muntazam to'rtburchakli piramidaning
balandligi 12 ga, asosining t omoni 7 ga teng.
lining apofemasini toping.
A) 13,5 B) 9 C) 12,5 D) 25
30о Gipotenuzasi 75 ga teng bo'lgan to'g'ri burchakli
uchburchakning katetlari nisbati 4:3 ga teng.
Gipotenuzaga tushirilgan balandlik uni qanday
kesmalarga ajratadi?
A) 50 va25 B) 48va27 C) 40 va 30
D) 60 va 15
31. Radiusi 3 ga teng bolgan doiraga tashqi
chizilgan teng yonli trapetsiyaning perimetri 40
ga teng. Trapetsiyaning kichik asosini toping.
A) 4 B) 3 C) 2 D) 5
32. f vektor а (2; 4; 4) vektorga kollinear hamda bu
vcktor laming skalyar ko'paytmasi 144 ga teng. b
vektorning uzunligini toping.
A) 16 B) 24 C) 18 D) 12
Konus hajmining % ga nisbati 21 - ga teng bo'lib,
uni ng yasovchisi asos tekisligi bilan 45° li
burchak tashkil qiladi. Konusning balandligini
toping.
D) 6
u i
„ . „ 3atna
Agar fgo = 3 ЬоЧза. ———---------5- ning
5stn « 4- 10cos a
qiymati qanchaga teng bo'ladi?
A) || B) j C) || D) A
33.
[1 4-<sinz| < ~ tengsiziikning [0; 2т] oraliqdagi
eng katta va eng kichik yechimiari ayirmasini
toping.
А) 1,5т В) jt С) 1,2т D) ~
0
34.	(1,2a)’-’ > (0.64)2 * *<1+^ tengsiziikning
yechimlari orasida nechta tub son bor?
A) 7 B) 5 C) 12 D) 9
35.	Rasmda AE = 3 • EBt AF =t FC, S^bc = 120.
BE FC to'rtburehakning yuzini toping.
/6 sin z - cos 2z — cos r • sin 2x = — - tenglamaning
yechimini toping.
A) 7rn , n € 2	B) ( —l)n — 4- im . n G 2
C) ~n t n€ Z	D) , n G Z
O	2
26 900 kg mevaning tarkibida 80% suv bor. Bir
necha kundan keyin mevaning ogurligi 500 kg ga
tushdi. Endi uning tarkibida necha foiz suv bor?
Л) 68 B) 62 C) 64 D) 66
2 A /(z) 3= -/g(10eo$z) funksiyaning qiymatlari
to'plamini toping.
A) (-00:0c) B) (-oo;0] C) (-1:0)
D) [—l;oo)
A) 75 B) 80 C) 40 D) 60
36.	Konusning o‘q kesimi muntazam uchburchakdan,
silindraiki esa kvadratdan iborat. Agar konus
to‘la sirtining silindr to'la sirtiga nisbati 1:3 kabi
boTsa, hajmlarining nisbatini toping.
A) 2:9 B) 1:9 C) 4 :9 D) xfi : 9
?S. (4 — 5)2y — b2 — 36 tenglamaning ildizlari nianfiy
bo‘ladigan k ning barcha butun musbat
qiymatlari yigundisini toping.
A) 13 B) 10 C) 8 D) 11
29. x~ 4- px 4- q — 0 tenglamaning ildizlari
z2 — 7r 4-10 = 0 tenglamaning ildizlaridan ikki
mart a katta- p4-<? ning qiymatini toping.
A) 26 B) -7 C) -14 D) -46
105
TEST 2006 : Variant
153
Matematika
1
Matematika
1. 15 • 261 + 18 • 261 + 139 -15 + 18 • 139 ni hisoblang'
A) 14500 B) 13200 C) 16200 D) 15100
12. Tekislikka og'ma va perpendikular tushirilgan.
Og‘maning tekislikdagi proyeksiyasi 12 ga,
perpendiku laming uzunligi 35 ga teng. Og‘ma va
perpendikular orasidagi burchakni toping.
2. 8 soniga teskari sonni toping.
A) 0,125 B) -0,8 C) 1,25 D)
A)
D)
. 12	.	24	_	35
arc sin—-	B) arccos-— Cj aretg-—
37	37	'	* 12
arcstn~
37
3. ----:—-я- ni soddaiashtiring.
1 - b + b2
А) Г 2 В) Г1 C) b+1
D) b2-
— x ni soddaiashtiring.
A) x + 1 В) 2x C) 0 D) x-2
5. a ning qanday qiymatbrida ar = 3x -+ 1
tenglama yechtmga ega bo‘lmaydi?
A) « = 2 B) a 1 C) a - 3 D) a / 2
13. —„	1 " ’ ni soddaiashtiring.
tg2a —ct.g2a
A) —2tg4or B) cos4o C) ~tg4o -
D) tg4cr
14. Agar m > 1, n > 2 va k > 36 bodsa,
2 : m + 6 : n -+ 432 : к ifodaning eng katta
qiymatini toping.
A) 7 B) 8 C) 17 D) 19
15.
Proporsiyaning dastlabki uchta hadi yig’indisi 78
1
2
6. zi va xj *2 ~ 22z + 8 = 0 tenglamaning ildizlari
bo^Isa. 2iX% *+ Xi*2 ning qiymatini toping.
A) -176 B) -120 C) 176 D) 280
x -1
x + 3
ga teng. Uning ikkinchi hadi birlnchi hadining
qismini, uchinchi hadi esa-
qismini t ashkil
etadi. Proporsiyaning uchinchi hadini toping.
7.
< 0 tengsizlikni yeching.
A) 18 B) 12 C) 24 D) 36
A) [1; 3) B) (-3; 1) C) (-2; 1)
D) (1; 3)
8. 0, (7) + 0, (5) — r ning qiymatini hisoblang.
A) | B) 4 C) 1|. D) 1|
(\ 4
2U«»16 ] ni hisoblang.
A) 4 B) 9 C) 5 D) 3
10.	Burchakning bissektrisasi uning tornoni bilan 20е
li burchak tashkil etsa, burchakning olzini
toping.
A) 30° В) 45е С) 40е D) 60°
11.	Quyidagi tasdiqlaming qaysilari noto'g’ri?
1)	tomontari a, b va c bo4gan uchburchakka ichki
chizilgan aylananing radiusi r = 3^7 formula
bilan hisoblanadi:
2)	diagonallari dj va d2 ga. ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
to‘rtburchakning yuzi S =	formula
bilan hisoblanadi;
3)	o‘xshash figuralar yuzlarining nisbati ularning
moe chiziqli o'lchovlariniug nisbatiga teng,
A) 2;3 B) 1:2 C) 1;2;3 D) 1;3
16. у = 2x2 -+ 4.r — 8 funksiyaning grafigi qaysi
choraklarda joylashgan?
A) I, Ц. Ill, IV В) II, III, IV C) 1, II, III
D) I, III, IV
17,		----— > x tengsizlikni yeching.
A) (1; 3) B) (-3; 1) C) (2; 4)
D) (-1; 3)
/ 3
18.	I sin 2xdx ni hisoblang.
A) -1 B) 5 С) I D) -1
/4	2
19.	a = bgi/56, b = log1/64 vac - log^s4 sonlarni
o'sish tartibida joylashtiring.
A) b < с < а В) с <Ъ < a C) b < a < c
D) a < c < b
20.	Teng yonli uchburchakning yon tomoniga
tushirilgan balandligj bilan ikkinchi yon tornoni
orasidagi burchak 26* ga teng. Teng yonli
uchburchakning asosidagi burchagini toping.
A) 48° ’ B) 50° C) 58’ D) 55е
106
TEST 2006 : Variant
153
Matematika
A BCD parallelograminda 0B± AC, A0=8,
(И;~5 va BO=4. ParaUelogramrrmmg yuzini
loping.
To‘gM burchakli parallelepiped asosining
tornonlari 6 va 8 ga teng. Uning diagonal! asos
t ekisligiga 30° li burchak ostidaoglshgan.
rarallelepipedning hajmini toping.
A) 80V5 B) 20</3 C) 240 D) 160a/3
Kanusning olq kesimi teng tomouli uchburchak.
Agar konusning to’iasirti 192т ga teng bolsa,
konus asosning diametrini toping.
A) 24 B) 18 C) 21 D) 16
/ ning qanday qiymatida
у — 1 — 3cos2x — i(l 4- c0$2z) funksiyaning
qiymat-i o‘zgarmas bo ladi?
A) -3 В) 3 C) -1 D) -2
cp»3z • sinx — cosix = 0 tenglamani yeching.
A) (-!)*• ? + ?*: $ + 2*i, i€2
t>	Z
и) т+t e z c) £ +%*; «ь, к e z
о о	S
0} ~ 4-	k e Z
о J
Ishchining mehnat unumdorligi 30% ortsa, uning
ish normasini bajarisfaga ketadigan vaqti necha
foizga qisqaradi?
A) 25 B) 20 С) 1б| D) 23^
<5	lu
A(l; 9) nuqta у ~ —x2 4- ax 4- 2 parabolaga
tegishli. Parabola uchining ordinatasini toping.
A) 18 B) 13 C) 2 D) 4
Qisqarmaydigan oddiy kasrning maxr&ji
suratidan 18 taga kofp. Agar kasrning suratiga
379 ni, maxrajiga 1 ni qcrshsak. berilgan kasrga
teskari kasr hosil bo’ladL BcriJgan kasrning
maxrajmi taping.
A) 19 B) 17 C) 14 D) 13
31.	O^m&s burchak 135е b<?‘lgan paralldograrrunga
ichki chizilgan doiramng yuzi 16т ga teng.
Paralleiograsurnmug perimetrini taping.
A) 32v/2 B) 24 C) 24v/2 D} 32
32-	a(zn — 1; 7^; 4) vektorning uzunligi 5 dan katta
bo ladigan m ning barcha qiymatlarini toping.
A) (-1:3) Б) (-oo;-2)U(2;oo)
C) (-oo;-I)U(3;cx>) D) (-2:2)
33.	4co^x 4* sin x cos x 4* 3 sin x- 3
tenglamaning 90° < x < 180’ shartni
qanoatlantiradigan ildizlari yig'indisini toping.
А) 225е В) 150е C) 135® D) 210®
34.	(r —	< (r -
tengsiriik t ning qanday qiymatlarida osrinli?
A) (2;4) B) (-oc;2) U (4;oc) C) (4;oo)
p) (Ц^,4)
<4*
35.	Teng yonli trapetsiyaga ichki chizilgan
aylananing гоахкш ustki asosining ucbidau 3 ga.
pastki asosining uchidan 4 ga teng masofada
joylashgan. Shu trapetsiyaga ichki chizilgan
doiraning yuzini.toping.
А) 5,76т В) 2,56% С) 6,76т D) 3,24т
36.	Kesik konusning yon sirti 10т ga._ to'lasirti 18т
ga Ung. Kohusning toia sirti unga ichki
chizilgan shar sirtidan qanchaga ortlq?
А) 6т В) 14т С) 10t D) 8t
(2|x| — 3)2 = jzi tenglamaning barcha ildizlari
ko'paytmasir.i toping.
1	r.\	л. 81	. 81
—16	) 16 c> —16	} 16
107
TEST 2006 : Variant	154	 Afatematika
— ~	--	-1	. r -t- -——w—Ж**»** «	11^—R«4 I —.	,. ...
Matematika *
1.	Quyidagi tasdiqlardan qaysi biri hamma vaqt
to'g'ri?
A) birorta bam qolshi!nvchi JI ga bo‘linmasa,
yig'indi ham IJ ga bo'Iinmaydi
B)	bar bir qo'shiinvchi 25 ga be'linsa. yig’indi
ham 15 ga. bo'linadi
C)	yig'indi 11 ga boTinsa, bar bir qo'^bihivchi
ham 11 ga bo'Iinadi
D)	qo^hilavchilardan kamida bittasi 12 ga
bt/hnsa, yig‘fodi ham 12 ga bolfoadi
11.	Quyidagi tasdiqlaming qaysilari noto'gW
1)	tomoni a ga, burchaklaridan bin or ga teng
rombning yuzi S = a?sin<* formula bitan
hisoblanadi;
2)	tornonlari a va b ga, ular orasidagi
burchaklaridan biri & ga teng Wigan
paraHelogr«running yuzi S = ^absina formula
bilan hisoblanadi:
3)	diagonallari d\ va tfj ga. ular orasidagi
burchagi a ga teng ixtiyoriy qovariq
to‘rtburchakning yuzi S — d^d^sina formula
bilan hisoblanadi.
A) 2;3 B) 1;2 C) 1,2;3 D) I;3
2. Xaritada ikki shahar orasidagi masofa 4,5 sm ga
teng. Xaritadagi masshtab 1:4000000 boslsar
sh&harlar orasidagi haqiqiy masofa necha km.
bo4adi?
A) 270 B) ISO C) 900 D) 90
12.	Tekislikka og‘ma va perpendikular tushirilgan.
7
Og:ma va tekislik orasidagi burchak arccos— ga,
og{maning tekislikdagi proyeksiyasi 14 gateng.
Perpendikularning uzunligini teping.
A) 14 B) 48 C) 28 D) 36
3.	x3 + r — 12 kvadrat uchhadni chiziqli
ko'paytttvchilarga ajrating.
A) (x-3)(x + 4) B) (x + 3)(*“4)
C) (x-3)(4-x) D) (z + 3)(4-x)
it + Г + 4 + 1
4.	-----~—--------$. x ni soddalashtiring -
r'f 1
A) x B) x- 1 C) z + 1 D) 2x4 1
13.	tg(y 4 a) = -- bo;lsa. tgor ning qiyrnatini
4	5
toping.
A) 1 8) 6 C) -4 D) 3
14.	Agar Tn>3tn>5va£<6 bo'lsa, 3m-4 5n— 2k
r.ing eng kichik butun qiyrnatini toping.
A) 14 B) 23 C) 22 £>) 13
b.
12 ^1 -x 4 -J = - tenglamani yeching.
A) -j B)-l C)-g D)|
6. Xi va xs-17z + 6 = 0 tenglamaning ildizlari
boisa, xixj 4 xjxj oing qiyrnatini toping.
A) -102 B) -32 C) 102 D) 77
15.	Agar_ + _=eWlsa,__ + _
quyidagilardan qaysi biriga teng?
A) 4-o B) 3—o C) 3-5 D) 2-o
16.	у = 4 - 2stnx funksiyaning [0; —] kesmadagi eng
6
kichik qiyrnatini hisoblang.
A) 2 В) 3 C) 1 D) 2-Л
7. 4 > \/r4 1 tengsizlikni yeching.
A] (0; 15] B) [-1; 15) C) (-1; 15]
D) [0; 15)
17.	f ?f "* 1	+ 3 tengsizliklar sistemasi bulun
120 - 3x > 4z — 15
yechimlarining oJrta arifmetigini toping.
A) 7 B) 3.5 C) 3 D) 4
8.	Quyidagi sonlardan qaysi biri 0,8(1) ga teng?
u 73	m 9	81	70
A) 90	11	C) 90	90
9.	v ~	— 1 funksiyaning grafigi koordinatalar
tekisligining qaysi cboraklarida yotadi?
A) L II B) I; III C) 11, JV D) IV
10.	Qo'shni burchakiardan biri ikkinchisidan
14е katta. Shu qc/shni burchaklarni toping.
A) 83°; 97* В) 16е; 164е С) 82°;98a
D) 93°:87’
18.	I sin rdx ni hisoblang.
A) В) C) -V2 D) у
19.	loy^x — 4fo^x + 3 = 0 tenglamaning ildizlari
yig4indisini toping.
A) ..10	B) 20 C) 30 D) 4
20.	A(5; —4) aylanadagi uuqta, <7(12; 20) nuqta
aylanarnng matkazi boslsa, aylananing radiusini
toping.
A) 16 B) 15 C) 25 D) 17
108
TEST 2006 : Variant
154
M&tematika
11 Rombning tomoni 6 ga, yuzi 18 Л ga teng.
Rombning o'tinas burchagini toping.
Л) 120° B) 135° C) 140’ D) 150’
< • Muntazam piramidaning yon sirti to‘la sirtining
60% ini tashkil etadi. Piramidaning yon yoqlari
va asos tekisligi orasidagi burchakni toping.
1	2
A) arccos — B) 60° C) arccos ~
4	3
D) arccos ~
73. Radiusi 8 ga teng boigaitsharga balandligi 18 ga
teng bo'Igan konus tashqi chizilgan. Konus
asosining radiusini toping.
A) 18 B) 12 C) 16 D) 24
21. p — eos88°, q ~ cos42° va r = sin’222* sonlarni
kamayish tartibida yozing.
A) p > q> r B) q> p> т C) q> r> p
D) p > г > q
25. cosx — sin3xcosx = 0 tenglamani yeching.
A) - +	-+ —, k € Я
£	О	о
в) т + —, Hz
4	О 3
с) £ + **:	£ + **, tez
*	о
D) jt; | + 2«i, teZ
32. Agar u(-4; 2; 2) va 6(x/2;	0) vektoHar
J
berilgan bo:lsa, 2u va - vektorlar orasidagi
burchakni toping.
А) ~т B) arccos-; CJ ~~ D) crceos~
4	3 o	o
33 у — y/i + logi sin X funksiya x (x € (0;2x])
ning qanday qiymatlarida aniqlangan?
A) (0;£u&r) В)	C) (0;«)
ou	bo
o) (o;|)
34.	oj/,<25 4- 25Zjr » 10 tenglamani yeching.
A) 1 B) 10 C) 5 D) x/W
35.	Radiusi 5 ga teng bo‘lgan doiraga to!g‘ri
burchakli uchburchak ichki chizilgan. Shn
uchburchakka ichki chizilgan doiraning radiusi 1
ga teng. Uchburchakning yuzini toping.
A) 8Л В) 12 С) 22 D) П
36.	Sharga konus ichki chizilgan. Konusning
yasovchisi asosining diametriga teng. Shar
hajmining konus hajmiga nisbatini toping.
A) 8.3 B) 32:9 C) 27:4 D) 16:9
26.	Tekis harakatda muayyan masofani bosib o4ish
uchun ketadigan vaqtni 30% ga kamaytirish
uchun tezlikni necha foiz orttirish kerak?
A) 20 B) 42^ C) 30 D) Зз|
•	*5
27.	у = —3x2 -b 12z — 13 parabola uchining
koordinatlari yig‘indisini toping.
A) 1 B) -1 C) -2 D) 0
28.	m van ning qanday qiymatlarida
2xm — Злу = 12 va 3xm + 2ny — 44 to‘g‘ri
chiziqlar (2; 1) nuqtada kesishadi?
A) m = 8,n=:6 B) m = 6,n = 4
C) n? = 12,n = 2 D) m = 4,n= 10
2У. jr2 — 3x| = 3x — tenglamaning butun
sonlardan iborat ildizlari yig'indisini toping.
A) 4 B) 5 C) 6 D) 3
30. Tolg!ri burchakli uchburchakka ichki va tashqi
chizilgan aylanalar radiuslarining nisbati 4:13
kabi. Kichik katet uzunligining katta kater
uzunligiga nisbatini aniqlang.
A) 5 : 12 B) 3 : 4 C) 4 : 13 D) 5 : 13
31. Rombning kichik diagonal! УЗ ga, yuzi .1,5 ga
teng. Uning o't-kir burchagini toping.
A) 60’ B) 30’ C) 70’ D) 45’
109
TEST 3006: Variant
155
Matematika
1
Matematika
1.	Quyidagi mulohazalarning qaysi biri natural
son I ar ga nisbatan uoto’g’ri?
A)	3 hamda 4 ga bo’lingan son 12 ga ham
bo'linadi.
B)	Berilgan sonlarga bo'Iinadigan sonlarning eng
kichigi bu sonlarning eng kichik karraiisi
bo'ladi.
C)	Oxirgi raqami 0 yoki 5 bo'lgan son 5 ga
bo^Iinadi.
D)	Oxirgi raqami 6 yoki 9 bo'lgan son 3 ga
bo'linadi.
2.	1,25 souga teskari sonni toping.
A) 8 B) -0.8 C) 0,8 D)
11.	Quyidagi tasdiqlarning qaysilari noto’g’ri?
1)	toman lari a, 6 va c bo’lgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
2)	tomonlari a va b ga, ular orasidagi
burchaklaridan biri a ga teng bo’lgan
parallelograxmnning yuzi S = -absinot formula
bilan hisoblanadi;
3)	o’xshash figuralar yuzlarining nisbati ularning
rnos chiziqli o’lcbovlarining nisbatiga teng.
Л) 2;3 B) 1;2 C) 1;2;3 D) 1;3
12.	Tekislikka og’ma va perpendikuiar tushirilgan.
15
Og’rna va tekislik orasidagi burchak arccos— ga,
og’maning lekislikdagi proyeksiyasi 30 ga teng.
Perpendikularning uzunligini toping.
у- ' —X . .
3.	—~---7- m qisqartinng.
X + у
A) -zT4-yT В) x* + y* C) z’-.y'
D) x-y
4.	(у4 ~ У2 4- l)(y2 + 1) - (!/ - l)(y + 2) 4- / 4- y3 ni
soddalashtirgandan keyin hosil bo’lgan
ко’ph ad ning nechta hadi bo’ladi?
A) 4 В) 3 C) 5 0) 6
5.	12^ : 2^ = 16“ : tenglarriani yeching.
•£ z о z .
А) б| В) б! С) б| D) 4
*>•>0	0
A) 16 B) 30 C) 32 D) 23
13.
sinSo — sinV2a
cosiOa • sin'2a
ni soddalashtiring.
A) 2sm2a B) —2 C) — ‘2sin2a
D) -2cos‘2o
14. 420 : (60 — 1000 : r) = 12 dan x ni toping.
A) i B) 8 C) 36 D) 40
О
15.
0,075 “0.075-6,4 . u.
---------------- ni hisoblang
0,175—
6.	xi va гз r2 - az 4- 20 = 0 tenglamaning ildizlari
119
bo’lib,---F — = —- tenglikni qanoatlantirsa, а
Zj 2v
ning qiymatini toping.
A) 9 B) -1 C) 3 D) -3
A) 40,5 B) 4,05 C) 20,1 D) 20,25
16. у = Asinx — 1 funksiyaning {0: —J kesmadagi eng
6
katta qiymatini toping.
A) 1 В) 0 C) лЛ-l D) 0,5
7.		-----------> 0 lengsizlikni yeching.
x — 3
A) (-oo; 3) В) [3; oo) C) (3; oo)
D) (-oo; 3]
8.	Geornetrik progressiva uchun quyidagi
formulalardan qaysilari noto’g’ri?
i)6n = 61<Г‘1;2) б2
П 1-7
A) 1 В) 1; 3 C) 3 D) 2
17.
/74-3r>5(z4-l) + 6
\(z-2)2-8<x(x-2)4-10
sistemasini yeching.
A) (-2; 7)
D) (-7; -2]
tengsizliklar
В) (-11: 2] C) [2; 11)
18.	J "I2 sin 3x cos 3xdt ni hisoblang.
о
A) |	B) 1	C) 1	D) 1
4	2	6
9. у = 5* — 5 funksiyaning grafigi koordinata
tekisligiiiing qaysi choraklarida yotadi?
A) I, III, IV B) I IV C) III IV D) I, II
10. Ikkita to’g’ri cbiziqning kesishishidan hosil
bo’lgan qo’shni burchaklarning gradus o’lchovlari
4 : 6 nisbatda bo’lsa, shu burchaklarni toping.
А) 60е; 120е В) 72°; 108° С) 50е; 130°
D) 30е; 150е
110
19.	— Slog-jT 4-6=0 tenglamaning ildizlari
yig’indisini toping.
A) 27 B) 36 C) 18 D) 12
20. Teng yonli uchburchakning nchidagi tasYiqi
burchagi o’sha uchdagi ichki burchagidan 5
mart a katta. Uchburchakning asosidagi tashqi
burchagini toping.
А) 105е В) 100е C) 108° D) 95°
TEST 2006 : Variant
155
Malem&tikA
I S uzi 156 sm 2 , balandliklari 4 sm va 12 sin
bo'lgan parallelogranmining penmetrini toping.
A) 73 B) 104 C) 98 D) 108
i Muntazam to+tburchnkli piramida asosining
tomoni 6г/3 ga va apofemasi 6 ga teng. Piramida
hajmini loping.
A) 54 B) 108 C) 162 D) 324
‘I Konus yasovchisi 4 ga teng va u asos tekisligi
lulan 60е li burchak tashkil etadi. Konusning
It a j mini toping.
I (} + cos22a)(l 4-	+ 4.$tn2o ifodatiing eng
kichik qiymatini toping.
Л) 1,5 B) 2,5 C) 3 D) 2
31. Aylanaga t-ashqi chizilgan teng yonli
trapetsiyaning asoslari 56 va 14 sm.
Trapetsiyaning balandligi necha sm?
A) 40 B) 28 C) 36 D) 35
t
32.
Uchlari A(2; 3; 1), B(3; 2; 1) va C(3, 4; 1)
nuqlalarda bo'lgan teng yonli uchburchakning
asosidagi burchagini toping,
A) ar eras-	B) arccos-	G) -r
3	3	4
1
D) arccos—=
' Уз
33.	\/Stj2x — I > 0 tengsiztikni yeching.
. it ж. , т тп т rrnx
A) ^12’4) B) 12 + T’4 +T)’"€ Z
D) + о
lz 4	о z
i > cos3xcosx + 0,5 = sin3xsinx tcuglarnaning
ildizlarim ko'rsating.
X ....	_	... X 7T^ .	_
A) ~ + 2Trk,keZ	B) - + --
b	4 z
,	. "Я" Тгк ,	_	_ T .	_
c) + —Jg2 d) - + irk,kez
6	2	о
Ml Ikki sex 230 ta kir yuvish mashinasi ishlab
chiqarishi kerak. Birinchi sex ishlab chiqargan
niahsulotning - qismi ikkinchi sex ishlab
У
chiqargau niahsulotning 80% iga teng. Birinchi
sex qancha mahsulot ishlab cbiqargan?
A) 60 B) 50 C) 180 D) 80
27 у = ---------------funksiyaning aniqlanish
x + 4
sohasini loping.
A) (-4; 4) B) {—4; 1} C) (-4; 1)
D) (-4; 2]
34.	(r -
teugsizlik x ning qanday qiymatlarida o‘nnli?
A) (2;4) R) (3;oo) C) (-00;2)U(4;00)
D) (Ц^Л)
35.	To'g'ri burchakli uchburchakning uzunligi 14 va
18 ga teng katetlariga tushirilgan rncdianalari uni
uchta uchburchakka va lo^tburchakka ajratadi.
To'rtburchakning yuzini toping.
A) 64 B) 63 C) 42	I>) 48
36.	Konusning o‘q kesimi muntazam uchburchakdan,
silindrniki esa kvadratdan iborat. Agar konus
hajrnining silindr hajmiga nisbati a/3 :2 kabi
bo'lsa. to‘la sirtiarming nisbatini toping.
A) ^3:^5 В) 1/3:л/2 C) ^9.2
D) 3:2
f x — 3y — 5
Agar X X + 2|sr| = 3
toping.
bo'lsa, x ~ 2y ning qiymatini
A) 2 В) 3 C) -1 D) 1
Л 5x2 4- bx — 15 = 0 tenglamaning ildizlari Xi va io
uchun 5r> +2^2 == 1 rnimosabat o'riuli. Agar 6
butun son ekanligi malum bo'lsa, uning
qiymatini toping.
A) -10 B) 7 va-10 C) 10
D) -7 va 10
l() To’g'ri burchakli uchburchakning gipotenuzasi 25
sm, katetlaridan birining gipotennzadagi
proyeksiyasi 23.04 sm. (Jshbu uchburchakka ichki
chizilgan aylananing radiusi necha sm?
Л) 2,5 В) 3 C) 1,5 D) 2
TEST 2006 : Variant
156
Matematika
Matematika
1.	Natural sonlar ijchim quyida keltirilgari
mulohazalardan qaysi biri noto'g'ri?
A)	Agar ikki qo'shiluvchidan biri J 7 ga bo’linib.
ikkinchisi 11 ga bolnunasa, ularning
yig4ndisi 11 ga bodinmaydi.
B)	Berilgan sonlar bo'linadigan sonlaming eng
kattasi ularning eng katta umumiy
bo'luvchisi bo'ladi.
C)	3 va 5 ga bo'hnadigan son 15 ga bo‘linadi,
D)	3 ga bollingan son 6 ga ham bc/Iinadi.
2.	3; y\ 2Д va 2,1 sonlarining o’rta ariftnetigi 2.55
ga long, у ni toping.
A) 2,€ B) 2,1 C) 3 D) 2
3.	Uchburchakning birinchi tornoni x(x > 10) sm,
ikkinchi tornoni undan 6 sm qisqa, uchinchi
tornoni esa birinchisidan 4 sin uzun. Shu
uchburchakning perimetriui (sm) toping.
А) Зт + 2 B) 3x —2 C) 3r + 3
D) 3x — 3
11.	Quyidagi tasdiqlarniiig qaysilari noto£g‘ri?
1)	tomonlari n, b va c boMgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
2)	tornoniari a va b ga, ular orasidagi
burchak laridan biri a ga teng bo‘lgan
parallelogrammning yuzi S ® absina formula
bilan hisoblanadi;
3)	o'xshash figuralar yuzlarining nisbati ularning
mos chiziqli o'lchovlarining nisbatiga teng.
Л) 2;3 B) 1;2 C) 1;2;3 D) 1;3
12.	Tekislikka tushirilgan og'tnaning uzunligi 75 ga,
uning tekislikdagi proyeksiyasi esa 72 ga teng.
Og‘ma va tekislik orasidagi burchakni toping.
A) arccos 50 D) arcein~ 2лЭ	24 B) arcsin— C)	arcsin—
4	ni soddaiashtiring. 2tg4a C) cos 4 a	
etg 2a - tg 2a A) sin 4a B)		D) tg4a
4.	(x — 1)(2 — r) + (r — 3)2 ko’phadni standart.
shaklga keltiring.
A) 3x2 4-15x4-7 B) -3r + 7
C) 12x + 4-x2 D) 9x + 7
14.	378 va 594 ning urnumiy bo^luvchilan nechta?
A) 7 B) 8 C) 5 D) 9
5. m ning qanday qiymatlarida |3 — m| = m — 3
tenglik o^inli bo‘ladi?
A) rncR В) rn > 3 C) m > 3 D) m = 3
15.	18 va 8 sonlari eng kichik umumiy karralisining
natural boMuvcbilari nechta?
A) 7 B) 12 C) 9 D) 8
6.	3 — z — - tenglamaning nechta haqiqiy iidizi
bor? *
A) 2 B) 1 C) iidizi yo^ D) 3
7.	{z 4- 3)(x — 2) < 0 tengsizlikni yeching.
A) (—oc;—3) U (2;oo)	B) (—oo; 2)U (3;oo)
C) (—3;2)	D) (—oo; —2) U (3; oo)
/(z - 4)(2 ~ x)	.	. , .
16. ?/= \ —— ---------- funksiyaning aniqlamsh
у (x 4- l)x
sohasini toping.
A) H;01U(2;4) B; (-l;0)U[2;4)
C) (—oo: —I)U (0;2] U [4;oo)
D) (-l;0}U[2;4)
17.
z2
—т < x — 4 tengsizlikni yeching.
8.	Geometrik progressiya uchun quyidagi
formulalardan qaysilari noto’g£ri?
1) fen = 6i<zn-5;2) h2=b^-bn^
18.
cos 2x dr ni hisoblang.
A) i В) 1: 3 C) 3 D) 2
9. (x/S)ni hisoblang.
A) 7 В) Зх/5 C) 15 D) 5
10. Qo'shiii burchaklardan biri ikkinchisidan 40’
katta. Shu qo‘slmi burchaklarni toping.
A) 110°; 70° B) 160’; 20° С) 140*; 40’
D) 20е; 160°
A) В) 1
D)
19.
n = log&080 bo‘lsa, logs 2 ni и orqali ifodalang.
А) ~-а B) C) ^4
1— 2a	2 — a	a — 3
_. 1 — 2a
D)
Ct ~~ 4
112
I
TOST 2000.* Variant
156
Matematika
4i Uchburchakning 7 ga teng bo’lgan balandligi uni
perimelrlari 18 va 26 bo’lgan ikkita
uchburchakka ajratadi. Berilgan uchburchakning
pcrirneUmi loping.
A) 31 B) 30 C) 36 D) 34
* I Tomonlari 4 va 8 m bo’lgan parallelogrammning
yuzi 16>/5 m\ Parallelogramnmirig o‘tmas
Burch agin i toping.
A) 150® B) 120° C) 105® D) 135°
<’/ Agar kubning bar bir qirrasini 2 stn ga
uzaytirsak, uning hajmi 152 sm3 ga ortadi.
Berilgan kubning qirrasini toping.
A) 3 B) 2 C) 4 D) 1
?3 Tomonlari 3 va 4 ga teng bo’lgan to'gTi
lo’rtburchak o’zining katta tornoni atrofida
aylanadi. Hosil bo’lgan jisinning to’la sirtini
toping.
Л) 48тг B) 42s- C) 36x D) 24tf
cosl2<> — co$8cr .. ..	...
Л1 —----r-—;-------quyidagdardan qaysi biriga
nnlOft
teng?
A) 2cos2a В) — 2ain'2<y	C) —sin2a
D) — 2cos2a
25.	2sin2r < etg tengsizlikni yeching.
4
A)	[—+ 4?rn; ~ 4- 4xn], n € Z
«J	«>
t	Sir
B)	hr 4 2згп;	4 2?rn]. n e Z
b	b
D) 4 *n; ~ 4- K«], n € Z
I £	*
26.	Korxonada mahsulot ishiab chiqarish birinchi yili
20% ga. ikkinchi yili 15% ga ortdi. Mahsulot
ishiab chiqarish ikki yil mobaynida necha foizga
origan?
A) 28 B) 38 C) 32	D) 35
. sin2x , „ . .	.	,
27.	=-------------I funksiyaning qtymatlar
cosx
sohasini toping.
A) (—2:2) B) (-1.1) C) (-3J)
D) [~2;0)U(0;2]
28.	2 - 3|x ~ 4| = —4 tenglamaning ildizlari
yig’indisini toping.
A) 7 B) 8 C) 10 0) 9
30. Uchburchakning b va e ga teng tomonlari
orasidagi burchagi 30° ga teng. Uchburchakning
uchtnchi tornoni 16 ga teng bo’lsa haruda uning
tomonlari c3 - 62 4 1664-256 sharin'»
qanoatlantirsa, e ning qiymati qanchaga teng
bo’ladi?
A) 16v/3 B) C) 12v<3 D) 16\/2
31.
Rombmiig о Unas burchagi 120® ga, katta
diagonal» —-j=- ga teng. Rombning yuzim
v 8
hisoblang.
А) 0,6<ЯУЗ В) ^d2%/3 C) D)
3rf2
16
32. 6(3; -6; 6) vektorga kotlinear va об = 40,5
tenglikni qanoatlantiruvchi a vektorni toping.
Л) «(3;6;9) В) оф-3;3) C) 5(3;-6;6)
о)
33. Jsi’nr 4 1| > 1,5 tengsizlik x ning (0; x) oraliqqa
tegishli qanday qiymatlarida o’rinli bo’ladi?
	?T	5т		^7Г
A)	-<г<	T	B)	
		2r	S’	. 2tt
C)	VI VI	T	D) -<	X<T
tengsizliknmg butun sonlardan iborat nechta
yechirni bor?
A) 1 Б) 0 C) 3 D) 2
35. Uchburchakning burchaklari 45 va 60° ga, unga
tashqi chizilgan aylananing radiusi Я ga teng.
Uchburchakning yuzini aniqlang.
R3(3 + \/3)	3R275 ff’Vfi
A | . .. .. ....i—~	H |  . —	t , i 
36. Konusning o‘q kesimi teng tonionli
uchburchakdan. silindmiki esa kvadratdan
iborat . Agar ularning to’la sirtlari tengdosh
boMsa. hajrnlarining nisbatini toping.
A) 1:3 B) 2:3 C) ^2 : ^3 D) 1 : У2
29. tn ning qanday qiymatlarida
(ш — 1)та-42(тП“ 7)zf2»n + 2 kvadrat uebhadni
to’ia kvadrat shaklida tasvjrlash mulukin?
A) -17 B) -17; 3 C) 3 D) 2
113
TEST 2006: Variant
157
Matematika
1
Materpatika
1. 17-11 — 14* 11 + 27-23 —24 «23 + 21 • 19 — 18 • 19
ni hisoblang.
A) 159 B) 165 C) 203 D) 143
„ 0,4-0,15-l,6 .
2 с л Vfn m nm« 4»ymatim toping,
v, » * <^3 0 * Vj VO
A) | B) | C) 0,2 D) 2
t> О
Я — X“ X + У
3. —-----: — ni soddalashtiring.
2xy 2x
A)	B) tZjL C) 1 D) !_f
уО+у) у у у
11.	Quyidagi tasdiqlarning qaysilari noto^ri?
1)	tornonlari a,b va c bo'lgan uchburchakka ichki
chizilgan aylananing radiusi r = formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S = 7^-0 formula bilan
hisoblanadi;.
3)	diagonallari d} va d2 ga, ular orasidagi
burchagi a ga teng ixtiyoriy qavariq
tohrtburchakning yuzi S = di drainer formula
bilan hisoblanadi.
A) 2;3 B) 1;2 C) 1;2;3 D) l;3
12.	Tekislikka tushirilgan ogcnianing uzunligi 75 ga,
uning tekislikdagi proyeksiyasi esa 60 ga teng.
Og‘ma va tekislik orasidagi burchakni toping.
1 — г + х "	, ...
4.		я----------х л ш soddalashtiring.
1 — х + х
А) »’ В) О С) 1-i О) X
X	X
3	3	3
A)	arcsin-	B)	arccos—г	О	arcsin-
7	5	10	4
D) arcsin-
5
I + cos2a + солист + cosGar .	... ...
----7-5—1	л------:----m soddalashtiring.
mn4o + 2stn2act>s4a
5.	Agar (х — 5)(—х — 4) = 0 bo'lsa, -х — 4 qanday
5	5
qiymatiar qabul qiladi?
A) faqat —3 В) faqat О С) 0 yoki 3
D) 0 yoki -3
Л) t^2cr B) 2ctg2& C) ctg2a D) 2sin’2a
14. 5 < x < 109 tengsizlikni qanoatlantiruvchi, 12 ga
karrali nechta natural son rnavjud?
A) 10 B) 8 C) 9 D) 12
6.	= х + 1 tenglamaning nechta haqiqiy ildizi
bor?
A) 2 В) 3 C) ildizi yo‘q D) 1
15. Agar 0 < q < ? < k bo‘lsa,
|p + $| 4- IA -	- |fc - p| ni soddalashtiring.
A) 2p + 2?-2fc В) 2p C) 2p + 2A
0) 24
x — 5	_	. ...	, .
f ----— > о tengsizlikni yeching.
x + 7
A) [-7; 5) B) (-oo; -7)
C) (-oo; —7)U[5; oo) D) (-7; 5]
8.	Arifmetik progressiya ucbun quyidagi
formulalardan qaysilari Co‘g‘ri?
1)	а\ — 2n2 + аз = 0;
2)	ai = a3 - a2;
. an — <5i + d
3)	„ =--------------.
A) 1 В) 2;3 C) lf2 D) 2
9.	x ning qanday qiymatlarida « — 3 — Igx ftmksiya
nomusbat qiyniatlar qabul qiladi?
A) x > WOO
t>) x < 100
B) x > 100
C) x < 1000
10.	Ikkita to‘g‘ri chiziqning kesislrishidan hosil
bo‘lgan qo’shni burrhaklar 7 : 8 nisbatda bo‘lsa,
shu burchaklarni toping.
А) 75е; 105° В) 36е; 144° С) 38е: 142°
D) 84°; 96°
16.	Agar /{r + 1) = x2 - 3z - 3 bo'lsa, /(®) ni
toping.
A) P-5r + l B) x2-3x-l C) x2-4
D) x2 - 5x + 6
(x + 3)(x — 1)
17,	i-----------L < 0 tengsizlikni yeching.
x + 2
A) (-2; 1) В) (-00; -3) U (-2; 1]
C) (-00; —3]U(—2; I] D) (-co; -3)
Г -------7 ni hisoblang.
I 0,25x+l
A) 4/n(e+l) В) 2/n(e + l) C) 2Z«t±J.
D) ln(e + 2)
19. 2/oy23ni hisoblang.
A) -9 B) -W C) -8 D) -4
20. ДАВС da ZBAC=45°, ZACB-3O0 va BC=WV2
ga teng. AB tomonning uzunligini toping.
A) 16 B) 12 C) 12^5 D) 14
114
TEST 2006: Variaflt
157
Matematifca
*1 Rasrnda Af/V’MAC. MBA? nchburchakning
perimetri 42 sm, ABC uchburchakning perimetri
84 srn. V BN uchburchakning yuzi 44 snr.
ABC uchburchakning yuzini (sm2) toping.
A) 108 B) 99 C) 81 D) 176
2'2. Prizmaning asosi tomoni 3\/5 bo’lgan muxitazam
oltiburchakdan, yon yoqlari kvadratlardan
iborat. Prizmaning katta diagonalini toping.
A) 10 B) 15 C) 12 D) 7T§
73, Yasovchisi 26 ga va balandligi 10 t-eng bo’lgan
konus asosining yuzini toping.
Л) 144т2 B) 144% С) 576% D) 288%
24. tga =	• tg2a
4	24	3
A) |	В) 3 С) у	D) £
25 ^3- 2sin -y = 0 (7,5 < x < 13,5)
tenglarnaning yechimini toping,
A) 10- B) 8,5,9,5 C) 8; 13
D) 10-11
4
9G. Yig'indisi 38 va 62 sonlarining o‘rta arifrnetigiga
teng bo’lishi uchun 62 ning 60%) olinsa, 38 ning
necha foizini olish kerak?
7	13	12
A) 17^ B) 33^ C) 33- D) 32
1У	4 У	1 I
30. Asosi 8 str», balandligi 8 sm Ьс/Igan teng yonli
uchburchakka tashqi chizilgan aylananing radiusi
necha sm?
A) 11 B) 10 C) 5 D) 12
31.
у = x/3x 4- 2 va у = --	4 2 to’g'ri
v3
chinqlarning kesishishidan hosil bo’lgan o’tkir
burchakni toping.
А) 75* B) 65* С) 90е D) 60*
32.	rn ning qanday qiymatlarida a(m — l;m — 2;2)
vektorning uzunligi 3 dan kichik bo’ladi?
A) —2 < m < 1 B) 0 < m < 3
С) -1 <m<2 D) -1 <m<3
33.	cos 2x sins = cos2z tenglarnaning
90* < z < 180* shartni qanoatlantiradigan
ildizlarini toping.
A) 110* B) 120* C) 135* D) 170*
34.	(log. (-2x - 4) + 7-1— ) > 0
X 5	bg« 3) —
tengsizlikning but-un sonlardan iborat nechta
yechirni bor?
A) 1 B) 0 C) 3 D) 2
35.	Radiusi R. ga teng bo'lgan doiraning markazidan
bir tomonda ikkita bir-biriga parallel vat-ar
o’tkazildi. Bu vatarlardan biri 120* li, ikkinchisi
60* H yoyni tortib turadi. Parallel vatarlar
orasida joylashgan kesimning yuzini toping,
A) — В) C)	D)
36.	Sharga balandligi asosining diarnctriga teng
bo’lgan konus ichki chizilgan. Agar konus
asosining yuzi 2,4 ga teng bo’lsa, shar sirtining
yuzini toping.
A) 6 B) 9%’ C) 15 D) 12,5
27.	f(x) =	— 2| + |x 4- 8| funksiyaning qiyniatlar
sohasini toping.
A) (3;oo) B) [10;oo) C) [6; oo)
D) [4: <x>)
28.	m va n ning qanday qiyniatiarida
2гтп — Зпу — 12 va 3zm + 2ny — 44 to'g’ri
chiziqlar (2; I) nuqtada kesishadi?
A) m = 8, n = 6 B) rn ~ 6, n = 4
C) m = 12, n = 2 D) m^.4,n-lG
29.	у = 2r2 4 bx + c parabolaning uchi (—4, —5)
nuqtada joy lash gan. Bn funksiya nollarining
o’rta arifinetigini toping.
A) -2 B) ~4 C) 5 D) -3
115
TEST 2006 : Variant
158
Matematika
1
Matematika
1. 1 soar 160 minut 5 sekund necha sekunddan
iborat?
A) 12205 B) 106005 C) 13205 D) 14205
2. 3; y\ 2,1 va 2,1 sonlarining o'rta ariftnetigi 2,3 ga
Ung. у ni toping.
A) 2,6 B) 2,1 C) 3,4 D) 2
ni qisqartiring.
4. Agar P =	- |y - (x 4- 2y) va
1	1
Q = ?г 4 -y - (ar 4- 5y) bo'lsa, P — Q ni toping.
X	X
A) 4y В) 2y C) —y D) -4y
11.	Quyidagi tasdiqlarning qaysilari to'g’ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R = c~ uchburchakning
tomoniari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	radiusi R ga, markaziy burchagi a ga teng
doiraviy sektorning yuzi S’ = formula bilan
hisoblanadi;
3)	tomonlari a va b ga, ular orasidagi burchagi а
ga teng bo'lgan uchburchakning yuzi
S = ^absincx formula bilan hisoblanadi.
A) 2:3 B) 1;2 C) 1;2;3 D) 1;3
12.	Tekislikka tushirilgan og'ma va perpendikuiar
16
orasidagi burchak a resin—- ga teng. Og‘maning
u%>
uzunligi 130 ga teng. Perpendikuiarning
uzunligini toping.
A) 96 B) 64 C) 32 D) 126
13.
1 4- sin 4a
sin 2or 4- cos 2a
— cos q ni soddalashtiring.
A) sin 2a B) cos 2a C) —2sin 2a
D) — cos 2a
j2 —* Зп.
14. —------ifoda n ning nechta natural qiymatida
natural son bo‘Iadi?
5.	(x 4- 4-) : 4- = 6 tenglamani yeching.
A) 211 в) 22§	C) 2o£ D) 22^
W	У	<7	V
A) 3 B) 6 C) 4 D) 5
15- Agar 0 < k < m < n bo'lsa,
|n — m| — |n 4- Jt| — |m — k| ni soddalashliring.
A) 2fc-2n В) -2» C) 2m-2fc
D) -2m
6.	z2 — 13s4^=0 tenglamaning ildizlaridan biri
—14 ga teng. Uning ikkinchi ildizini toping.
A) 27 B) -1 C) -27 D) 1
7.	(z4- 2)(x — 3) < 0 tengsizlikni yeching.
A) (—oo; —3)U (2; oo)	B) (-2;3)
C) (—oo;-2) U (3; oo) D) (-3;-2)
8.	0, (8) 4 0, (3) — - ning qiymatini hisoblang.
•7
A) 11	B) 12	C) |	D) 0,(11)
i)	v	U
9.	x ning qanday qiymatlarida у - 5* - 125
funksiya nomanfiy qiymatiar qabul qiladi?
A) x < 3 B) x > 3 C) z < 2 D) x > 2
16.	Quyidagi parabolalardan qaysi biri OX o'qiga
urinadi?
1)	у = 2z2 — 5z 4- 8; 2) у — —2r2 — 8z - 18;
3)	у = x3 - 3z — 8;4) у — 4z2 — 6r 4 2^.
4
A) 2 B) 1 C) 4 D) 3
(z - 7)(z 4-3)	_	. ... .	,
17.	---5—---------< 0 tengsiziikning eng katta va
2x£ - x 4-4
eng kichik butun yechinilari ayirrnasini toping.
A) 9 B) 10 C) 7 D) 8
18.	sirtAxdx ni hisoblang.
A) | В) 4 C) | D) 1
19.
yeching.
10. Qo'shni burchaklardan bin ikkinchisidan 12°
katta. Shu qo'shni bvrchaklarni toping.
А) 81е; 99* В) 82*; 98° С) 96’; 84°
D) 80"; 100°
A) (5; 14) B) (6; 16) C) (9; 18)
D) (5; 81)
20. A(—6:1) aylanadagi nuqta, C(6: 10) nuqta
aylananing markari bo'lsa, aylaning radiusini
toping.
A) 13 B) 14 C) 15 D) 16
116
TEST 2006 : VariAnt
158
Matematika
'/I ЛВС uchburchakda AB = AC\ BM±AC,
UM = IS va MA = 24. ABC uchburchakning
yuzini toping.
A) 258 B) 254 C) 270	0) 262
i Muntazam to’rtburchakli piramidaning
balandligi 18 ga, asosining tomoni 15 ga teng.
Piramidaning apofemasini hisoblang.
A) 13 B) 22,5 C) 19,5 D) 21
73 Radiusi 17 sm bo’lgan shar markazidan 8 sm
masofada tekislik bilan kesilgan. Kesimning
yuzini (sm2) toping.
А) 225т В) 64x C) 64 D) 514rr
32.	Agar a vektor 6 — 3г — 2j 4- k vektorga kollinear
va a • b ~ 28 bo’lsa, a vektoming uzunligini
toping.
A) ~ B) 14 C) 2Vi4 D)
33.	соях < sinx tengsizlikni yeching.
A)	(~4-xk; — 4-xk),
B)	^4-тк), k^Z
С) (2%Ь; * 4- 2rfc), k € Z
D) (^4-2rfc: ~4-2t1j),
4	4
.	*	-<”	- з *	*	. . . . ,
24.	Stn~— ‘ cos-— — sin -- • cos-- HX hisoblang.
16	16	16	16	b
A) 1 8} A	C) 1	D) ~
О	Z	C
25.	sinx 4- sin&e = 0 ten glam a (0; 4т] oraliqda
nechta ildizga ega?
A) 7 B) 13 C) 8 D) 9
26.	Korxonada mahsulot ishlab chiqarish birinchi yili
10% ga, ikkinchi yili 20% ga oshdi. Mahsulot
ishlab chiqarish ikki yil mobaynida necha foizga
ortgan?
A) 26 B) 25 C) 26,5 D) 32
34.	x^25 4- 25/,x = 10 tenglamani yeching.
A) 1 B) W C) 5 D) VW
35.	Muntazam uchburchakning yuzi 9%/3 ga teng.
Shu ucbburchakdan eng katta yuzaga ega bo’lgan
kvadrat qirqib ohngan. Shu kvadratning
perirnetrini toping.
A) 48^3-72	В) 18^5-12
C) 54-16^3	D) 64УЗ-96
36.	Teng tornonh silindming va teng t-omonli
konusning balandligi o’zaro teng. Ularning to'la
sirtlari nisbatini toping.
A) 3:8 B) 5:3 C) 3 : 2 D) 3 : 4
27.	у — \/8 — x5 — 2x funksiyaning eng katta
qiymatini toping.
A) 4 B) 7 C) 3 D) 2
28.	Qisqarrnaydigan oddiy kasrnmg maxraji
suratidan 18 taga ko’p. Agar kasrning suratiga
379 ni, maxrajiga 1 ni qo’shsak, berilgan kasrga
teskari kasr hosil bo'ladi. Berilgan kasrning
maxrajini toping.
A) 19 B) 17 C) 14 D) 13
29.	|x2 — 9x 4- 8] = —8 4- 9x - r2 tenglamaning
barcha natural yechirnlari уig’indisini toping.
A) 40 B) 36 C) 28 D) 25
30.	To’g’ri burchakli uchburchakning katetlari 30 va
40 ga teng. Katta kaxetning gipolenuzadngi
proyeksiyasini toping.
A) 14,5 B) 32 C) 16,5 D) 16
Rornbning tomoni 6 ga, o‘tkir burchaginmg
sinusi ga teng. Uning diagonallari
ko'paytmasmi toping.
A) 18 B) 27 C) 48 D) 42
117
TEST 2006 : Variant
159
Matematika
1
Matematika
1.	4 m2 3 dm2 4 sm2 necha kvadrat santimetr
bo‘Jadi?
A) 40244 B) 40304 C) 43004 D) 41034
„ 6,5-0,04’6,8 .	...
2-	c o'iTi л i'k mnS «Pymatni toping.
5,2 • o, 1 • U, lo
A) 5 B) A
1	2
6 D> 3
3.	Uchburchakning birinchi tornoni r(z > 13) sm,
ikkinchi tornoni undan 8 sm qisqa, uchinchi
tornoni esa birinchisidan 5 sm uzun. Shu
uchburchakning perimetrini (sm) toping.
A) 3x4 2 В) 3z-3 C) 3z + 3
D) 3z-2
4.	(4z - 3)2 — z(—4z 4- 5) ko’phadni standart
shakliga keltiring.
A) 12^-25x4-9 B) 20z2-29x4-9
C) 8z2-x4-7 P) 20z2- 25r + 9
5.	(z;y) scalar jufti | Зх4-2у=^4 ®5*етап*п&
yechimi bo’lsa, у — x ni toping.
A) -1 B) -3 C) 0 D) 3
6.	zi va x? x2 4 2z — 12 = 0 tenglamaning ildizlari
ekanligi ma’lum. z2 4- z2 ning qiymatini toping.
A) 12 B) 10 C) 28 D) И
< 0 tengsizlikni yeching.
11.	Quyidagi tasdiqlaming qaysilari notocg*ri?
1)	tomonlari a, b va c bo‘lgan uchburchakka ichki
chizilgan aylananing radiusi r e formula
bilan hisoblanadi;
2)	tomonlari a va b ga, ular orasidagi burchagi a
ga teng bo‘lgan uchburchakning yuzi S — absint*
formula bilan hisoblanadi;
3)	o‘xshash figuralar yuzlarining nisbati ularning
mos chiziqli o’lchovlari kvadrat lari ning nisbatiga
teng.
A) 2;3 B) 1;2 C) 1;2;3 D) 1;3
12.	Tekislikka tushirilgan og*ma va perpendikular
12
orasidagi burchak arcsin— ga teng. Og‘maning
uzunligi 74 ga teng. Perpendikulaming
uzunligini toping.
A) 70 B) 24 C) 54 D) 48
13.	tg(~ + o) = j bo‘lsa, ctgor ning qiymatini
toping.
A) 4 B) |	C) 1	D) |
£	V	I
14.	24 sonining barcha natural bo4uvchilari
yig’indisini toping.
A) '48 B) 60 C) 124 D) 108
15.	12 va 312 sonlarning umumiy bo‘luvchilari
nechta?
A) 4 B) 2 C) 6 D) 3
16.	у = -—r- funksiyaga teskari funksiyani toping.
2 — «JZ
2-3r
x — 1
2-3z
1 — x
A) [1; 3) B) (-3; 1) C) (-2; 1)
D) (1: 3)
17. Quyidagi tengsizliklardan qaysilari o‘zaro teng
kuchli?
8.	0, (7) 4- 0, (5) — - ning qiymatini hisoblang.
A) | B) 11 C) 11 D) 11
3)^-4>0;	4)r —3>0.
X'
A) 1; 2; 4 B) 2; 3; 4 C) hammasi
D) 1; 3; 4
9. fotjj/ne625 ni hisoblang.
A) 4y« B) 5 C) 3 D) 4
10. Qo'shni burchaklardan bin ikinchisidan besh
marta kichik bo4sa. shu burchaklardan kattasini
toping.
A) 130° B) 150° C) 144° D) 140°
18. / (cosxcos2z — 3inxsin2x)dx integralni
о
hisoblang.
1	1	2	x/2
A)	|	В)	-	C)	i	D)
3	b	3	о
19. 2к-Л4-2г-4 = tenglamani yeching.
A) 1 B) 1,5 C) 3 D) 2
118
i
TEST 2006: Variant
159
Matematika
JO Teng yonli uchburchakning uchidagi burchagi 70е
ga teng. Yon tornonga o'tkazilgan balandlik va
asosi orasidagi burchakni toping.
/V) 45° B) 35° C) 40’ D) 30°
21 ДАВС ning AB tomoni MN||AC to‘grri chiziq
yordamida BM—2 va AM=4 bo’lgan kesmalarga
ajratildi. Agar AMB7J ning yuzi 18 ga teng
bo‘lsa. ДАВС ning yuzi qanchaga teng bosIadi?
A) 96 B) 162 C) 144 D) 108
22 To:gTi parallelepiped asosining tomonlari 9 va 12
ga. ular orasidagi burchak 120° ga, yon qirrasi
бл/З ga teng. Parallelepipedning kichik diagonal!
uzunligini toping.
A) 18 B) 5 C) 21 D) 15
23. Asosi rombdan iborat to'g‘ri prizmaning
balandhgi 4,5 ga teng. Agar rombning
dioganallari 8 va 10 ga teng boisa, prizmaning
hajmi qanchaga teng?
A) 320 B) 360 C) 240 D) 180
29. y/r2 —6г4-5 4- x~ - 6л 4- 7 tenglamaning
ildizlari yig indisini toping.
A) -3 B) 6 C) —4 DJ 3
30. To‘g‘ri burchakli uchburchakning katetlari 48 va
14 ga teng. Kichik katetning gipotenuzadagi
proyeksiyasini toping.
A) 10 В) б| С) з||	D) 4—
i	zO	zo
3L Parallelograrnmning tomonlari 20 va 7 ga teng.
Uning katta tomoniga yopishgan burchaklarinlng
bissektrisaiari qarama-qarshi tomonni uch
qismga ajraladi. Shu qismlardan eng kichigining
uzunligini toping.
A) 4 B) 2 C) 6 D) 5
32. Л{—4; 1; 1). B(l; 4; 0) , C(l; -V2) va
D(~5: —5; 3) nuqtalar berilgan. AC va BD
vektoriar orasidagi burchakni toping.
A) 60° B) 90° C) 45° D) 30е
4
33. |/gr 4- dgx| — -y= tenglamani yeching.
»3
24. m — cos&)*t n ~ згп45’, q ~ stn50’ va
p = cos80e sonlarni o'sish tartibida yozing.
A) < n < p < Q B) p<m <n <q
C) p < m < q < я D) q < n < p < m
A) ^ + 2mfc;t62 B) ±^ + ^--,keZ
3	6	2
C) +	D) (-1Г7 + 2rt;*ez
3	о
25. 2sin2x — sin2® — 0 tenglamani yeching.
A)	rk; (-1)* • ri, fc € 2
B)	Tit; j + »*. fc G Z
С) тк; J+ fk, keZ
a
r>) xfc; 7 + rfc, *e^
аМ	л
26.
3
Nodirda bor pulning - qismi Jahongirdagi
О
pulning ~ qismiga teng. Nodir pulixring necha
foizini Jahongirga bersa, ularning pullari teng
bo'ladi?
34.	(ls‘25)1-x > (Q,64)2^1+v^ tengsizlikning
yechimlari orasida nechta tub son bor?
A) 7 B) 5 C) 12 D) 9
35.	Teng yonli trapetsiyaning yuzi 60 ga, unga ichki
chizilgan aylananing radiusi 3 ga teng.
Trapetsiyaning asoslarini toping.
A) 14; 6 B) 18; 2 C) 13; 7 D) 5; 15
36.	Konusning o‘q kesimi muntazam uchburchakdan,
silindrniki esa kvadraldan iborat. Agar ularning
hajinlari teng bo'lsa, to'la sirtlarining nisbati
nimaga teng?
А) УЗ : t/2 B) 72 : ч/З C) 1 : 73
D) 3:2
A) 37,5 B) 25 C) 17,5 D) 12,5
27. Дж) =s >^/1,75~ л — r2 funksiyaning eng katta
qiymatini toping.
A) 1,5 В) 72 С) 272 D) 3
28.
Qisqarmaydigan oddiy kasrning maxraji
suratidan 6 birlikka katta. Agar kasrning surat
va maxrajiga 5 ni qo’shsak, hosil bo'lgan
4
kasrning qivmati — ga teng bo ladi. Berilgan
5
kasrning suratini toping.
A) 7 B) 23 C) 13 D) 19
119
TEST 2006: V&riwt
160
Matematika
1
Matematika
1.	18 16-15-15 + 36-24-33-24+ 17-11- 14-11
ni hisoblang.
A) 155 B) 166 C) 153 D) 180
12. Tekislikka og‘ma va perpendikular tushirilgan.
Og‘ma va <ekislik orasidagi burchak arccos— ga,
41
og'maning tekislikdagi proyeksiyasi 80 ga teng.
Perpendikularning uzunligini toping.
A) 36 B) 40 C) 30 D) 18
2.	—Irga teskari sonni toping.
<5
A) -0,75 B) 1,5 C) | D) -(
V	V
3.	16 - (2z — 3)2 ni ko*paytuvchilarga ajraling.
A) (2z- l)(7-2r) B) (2j+1)(7-2z)
C) (2z - l)(2z + 7) D) (2л + 1)(2г - 7)
sin4a + 2cos2a • cos4a	. .
7----------------------г—— ni soddalashtiring.
1 — sin2a — coslot + stn6a
A) 2sin2oc B) 2tg2a C) ctg2a
D) 4iy2a
14. 156 va 420 ning umumiy bo‘luvchilari nechta?
A) 5 B) 7 C) 4 D) 6
4. (z2 +l)(z4 - z2 +1) - (z2 - I)2 + z5 + z3 +z ni
soddalashtirgandan keyin hosil bo‘lgan
ко' ph ad ning nechta hadi bo'ladi?
A) 4 B) 5 C) 6 D) 3
5. m ning qanday qiymatlarida (m.2 — l)y + 1 • » m
tenglama yecbimga ega boimaydi?
А) гл - 0 B) m = 1 C) m = 2
D) m = -1
6. ri va z2 x2 — 14r + 9 = 0 tenglarnaning ildizlari
bo‘lsa, + x2tq ning qiyrnatini toping.
A) 126 B) —92 C) -126 D) -144
7. vz8z — 3 < —2 tengsizlikni yeching-
A)zd B) 2 < 4 C) z>4
D) z>|
8. 0,4(5) soni quyidagi sonlardan qaysi biriga teng?
A> и B> c> Й D> S
9.	у —	— 3 funksiya grafigining Oy osqi bilan
kesishish nuqtasi ordinatasini toping.
A) -1 B) -2 C) 1 D) 0
10.	Qo’sbni burchakiardan bin ikkinchisidan 52° ga
katta. Shu burchakiardan kattasini toping.
A) 118° B) 106° C) 114° D) 116°
11.	Quyidagi tasdiqlarning qaysilari to:g‘ri?
1)	uchburchakka tashqi chizilgan aylananing
radiusi R’ = ^(aj, c— uchburchakning
tornonlari, S— uchburchakning yuzi) formula
bilan hisoblanadi;
2)	tomoni a ga, burchaklaridan biri a ga teng
rombning yuzi S = a2sina formula bilan
hisoblanadi;
3)	o'xshash figuralar yuzlarining nisbati ularning
mos chiziqli c/lchovlari kvadratlarining nisbatiga
teng;
A) 2; 3 B) 1:2 C) 1;2;3 D) 1:3
12U
15.
a — 35 va 3t, 3b — a va 4 sonlar proporsiyaning
u2 + b2
ket-ma-ket- kiadlari ЪоЧза, ——— kasrnmg
qiyrnatini toping.
A) 5 B> I c) | D> T
16. у — —-r + 1 -
Л . 18
funksiyaning eng kichik qiyrnatini toping.
A) 5 В) б C) 10 D) 4
17. 23 — 2z > (z + 2)(z — 2) — 2(z — 1) tengsizlikni
yeching.
A) (0; 25] B) (-oo; 5] C) [-V21; x/21)
D) M: 5}
г f
18. / (1 + ig^x)dx ni hisoblang.
Jq
19.
a = logse 112 boMsa, logr 2 ni a orqali ifbdalang.
A)
D)
2g- 1
3 — a
a — 3
2«-l
B)
a
2a-1
1 -2a
a — 4
20. Aylananing 13д/2 ga teng vatari 90° li yoyni
tortib turadi. Aylananing uzunligini toping.
A) 2(hr В) 24тг C) 26x D) 22x
21. Tornonlari 72 va 32 m bodgan to'g'ri
to^tburchakka tengdosh kvadratning tomonini
toping.
A) 28 B) 36 C) 48 D) 24
22. To'g'ri burchakli parallelepiped asosining
tornonlari va balandligining qiymatlari 4:3:1.25
kabi nisbatda. Parallelepipedning diagonal! va
asos tekisligi*orasidagi burchakni toping.
A) 30° B) 45° C) arcctg4 D) 60°