• МДТЕМАТ1КА
F Ж® '
jk YOt
YAROAKlYt
1 1 гГН *Л»ЖП*РН t	plrj



2010 yilning testlar. 101 varianti.	Matematika
VARIANT № 101	Ал — 9
. 1,60,7-1,8	. 1-	i й 7, no nin9 Q'ymatini toping. 1,4  f,d  U,O А) —	В) —	С)— D) — 5	'24	12	3 2.1,2 va 3 raqamlari yordamida yozilgan turli raqamli barcha uch xonali sonlar yig'indisini toping. A) 1233 B)2133 C) 1332 D) 2331 3. (ax + 2y)(3x + (3y) = yx2 + 6-xy + y2 4 ayniyatdagi noma’lum koeffitsentlardan biri a ni toping. A)4	B)|	C)3	D)|	9.	Umumiy hadi an =	(n C N) bo'lgan 3n +1 ketma ketlikning nechta hadi (1,7; 2,2) oraliqqa kirmaydi? A) 8	B) 10 C) 4	D) 6 10.	ДАВС da Z В = 90°, Z C = 60°. BB, balandlik 2 ga teng. AB ni toping. A) 4	B) 2	С) 2Л D) 2^2 11.	Agar x > u va z > t bo’lsa, quyidagi tengsizliklardan qaysi biri har doim o'rinli bo'ladi? A) x-z > y-t	B) — >y 0 (x + y)4 > (z +1)4 D) x - z > у -1 12.	Berilgan beshta sonning har biri 3 ga
4. m (2; 3; x) va n (-1; 4; 2) vektorlar perpendikulyar bo'lsa, x ning qiymati qanchaga teng bo'ladi? A) 0	B)-5 C)T5 D)sT5	ko'paytirilib, so'ngra hosil bo'lgan sonlarning har biriga 2 qo'shildi. Hosil bo'lgan sonlar yig'indisi 76 ga teng bo'lsa, berilgan sonlar уig'indisi nechaga teng bo'lgan? A) 15 B) 24 C) 20 D) 22
№ 5.	/(x) = -x+—funksiyaning (6; 2) nuqtadan o'tuvchi boshiang'ich funksiyasini toping. №	№	x^ A-^+±--18	B)-—- + —-16 2	6	2	6 У2	v2	y3 0-±-+£-+18	D)_r+r+16 d о	do 6.	Agar jf(x) = x-sin2x bo'lsa, /'(n) + /(it) + 2 ni hisobiang. А)2тг B) 2	C)2+2tt D)2-2n 7.	Quyidagi sonlardan qaysi biri 1 dan katta? a = O,72'3 O,30'8; b = 3,2~*2-1,2^e; c = 0,6°'4-0,3°'e; d = О.Г’^-О.б-0-4; e = 0,4°-3,5'1'3. А) с	В) e	0 a	D) d Jfff + yfi 8-	-	ni qisqartiring. Д)?7 + уЛ	0 л ту A Ту	13.	Perimetri 28 bo'lgan uchburchakning bissektrisasi uni perimetrlari 16 va 24 bo'lgan uchburchaklarga ajratadi. Berilgan uchburchakning bissektrisasini toping. A) 8	B) 5	C) 7	D) 6 14.	Katetlarining nisbati 2:3 kabi bo'lgan to'g'ri burchakli uchburchakning gipotenuzasi 2^26 ga teng. Uchburchakning yuzini toping. A) 39 B) 6-i/l3	C)5i/l3 D) 36 15.	Agar x-y = 5 vaxy = 14 bo'lsa, x3y + xy3 ning qiymati qancha bo'ladi? A) 354 B) 273	C)742 D) 216 16.	Arifmetik progressiyada as - a, = 6 bo'lsa, ae - a5 ning qiymati nechaga teng bo'ladi? A) 12	B)10	018	0 9 17.	Teng yonli trapetsiyaning diagonal'! uning o'tkir burchagini teng ikkiga bo'ladi. Agar trapetsiyaning perimetri 48 ga, katta asosi 18 ga teng bo'lsa,uning o'rta chizig'ini toping. A) 16 B) 13	0 14 D) 12
1
2010 yilning testlar. 101 varianti.
Matematika
18.	M ta sonning o'rta arifmetigi 14 ga,
boshqa N tasinikl - 28 ga teng. Shu M + N ta
sonning o'rta arifmetigini toping.
A)^	B)W
1 42	' M
_. 14M + 28A/	Di 14N+-28M
M + N	Г M + N
1	2	5
19.	7—: 6— = 5— : x proporsiyaning noma’lum
2 5	8
hadini toping.
А)з|	B)41
э	о
C)41	D)51
О	о
20.	Muntazam to'rt burchakli piramidaning
balandligi 9 ga, diagonal kesimning yuzi 54
ga teng. Piramidaning hajmini toping.
A) 216 B) 206	0128 D) 648
21.	(x + 2)(x - 3) < 0 tengsizlikni yeching.
A) (-»; -3) U (2; ») B) (-2; 3)
O(-“i-2)U(3;-~) D) (-3;-2)
22.	Teng yonli uchburchakning uchidagi
tashqi burchagi o'sha uchdagi ichki
burchagidan 4 marta katta. Uchburchakning
asosidagi tashqi burchagi necha gradus?
A) 100 B) 102	0 96 D) 108
23.	Grafigi rasmda tasvirlangan funksiyaning
qiymatlari x ning qanday qiymatlarida manfiy
bo'lishini tengsizlik yordamida ifodalang.
A) x > 0 B) x г О О x г -1 D) x > -1
24.	Uchlari A(2; 3; 1), B(3; 2; 1) va C(3; 4; 1)
nuqtalarda bo'lgan teng yonli uchburchakning
asosidagi burchagini toping.
1	2
A) arccos —	B) arccos —
3	3
C) —	D) arccos -L
4	V3
25.	Hadiari musbat bo'lgap geometric
progressiyaning birinchi va uchinchi hadi
ko'paytmasi 4 ga, uchinchi va beshinchisiniki
esa64 gateng. Progressiyaning ikkinchl,
to'rtinchi va Oltinchi hadiari yig'indisini toping.
A) 42 B) 38 C) 40 D) 46
26.	Quyidagi mulohazalardan qaysi biri to'g'ri?
A) Ikkita parallel to'g'ri chiziqni uchinchi to'g'ri
chiziq bilan kesganda hosil bo'lgan ichki bir
tomonli burchaklar yig'indisi 180° dan kichik.
B) Teng yonli uchburchakning balandiiklari
hamda medianalari bir nuqtada kesishadi.
О Teng tomonli uchburchakning balandiiklari
kesishish nuqtasida 4:3 nisbatda bo'linadi.
D) Ikkita, to'g'ri burchakli uchburchakning
gipdtenuzalari va bittadan o'tkir burchaklari
bir - biriga teng bo'lsa bunday uchburchaklar
tengdir.
27.	^+—_ 6 - 724 ni hisoblang.
V5-V24
A)-3	B)-1	0-8 D)-7
28.	Ikki shahar orasidagi masofa 200 km
bo'lsa, 1:5000000 masshtabli xaritada bu
masofa necha mm ga teng bo'ladi?
A) 20 B) 200 О 100 D) 40
5	1
29.	Agar tga + tgP =— va tgcrtgp =- bo'lsa, a
6	6
+ p nimagateng bo'ladi?
A)-- + nk, kSZ	B)^ + trk,kCZ
6	3
C)-\+Ttk,kCZ	D)- + TTk,kCZ
6 \	4
30.	Quyidagi mulohazalardan qaysi biri to'g'ri.
A) Ikkita^parallel to'g'ri chiziqni uchinchi to'g'ri
chiziq bilan kesganda hosil bo'lgan ichki bir
tomonli burchaklar yig'indisi 180 dan kichik.
B) Teng yonli uchburchakning balandiiklari
hamda medianalari bir nuqtada kesishadi.
C) Teng tomonh uchburchakning balandiiklari
kesishish nuqtasida 4:3 nisbatda bo'linadi.
D) Ikkita to'g'ri burchakli uchburchakning
gipotenuzalari va bittadan o'tkir burchaklari
bir biriga teng bo'lsa, bunday uchburchaklar
tengdir.
31.	cos2x a-ltengsizlikning [0; 1 ,5tt]
kesmadagi yechimini toping.
A)[0;
ООО	о о
C)[^;2n]	D)[0;^]U[^x]
о	о о
2
2010 yilning testlar. 102 variant!.
Matematika
32.	392 ni qanday songa bo'lganda bo'linma
17 va qoldiq 1 bo'ladi?
A) 21 B) 19	C)23 D) 22
33.	Xo'jal ikda paxta ishlab chiqarish har yili
10% ga ortsa, 3 yilda paxta ishlab chiqarish
necha foizga ortadi?
A) 30 B) 32	0 33 D) 33,1
34.	у = 4-VlOx-1 funksiyaninggrafigigaXo =
1 nuqtada o'tkazilgan urinma va koordinat
o’qlari bilan chegaralangan uchburchakning
yuzini toping.
a)§ b)| o4
35.	Passajir va yuk poyezdi bir-biriga tomon
harakatlanmoqda. Uiar orasidagi masofa 275
km. Yuk poyezdining tezligi 50 km/soat
passajir poyezdining tezligi yuk poyezdining
tezligidan 20% ortiq. Uiar necha soatdan
keyin uchrashadi?
A) 3 B) 2	02,5 D) 4
36.	Hadlarining yig'indisi 2,25 ga, ikkinchi hadi
0,5 ga teng bo'lgan cheksiz kamayuvchi
geometrik progressiyaning maxrajini toping.
A)l;- B)1 O-i- D)-;-
'3 6	'4	'34	' 3 3
VARIANT №102.
1.	m ning qanday qiymatida a (1; m; -2)
va b (m; 3; -8) vektorlar perpendikulyar
bo'ladi?
A) 4 B) -2 C) 2 D) -4
2.	Agar 0 < q < p < к bo'lsa, Ip + ql + Ik - ql -
Ik - pl ni soddalashtiring.
A) 2p + 2q - 2k B) 2p
C) 2p + 2k	D) 2q
3.	Uchburchak tomonlarining uzunliklari m; n
va к m2 = n2 + k2 + Тзлк tenglikni
qanoatlantigadi. Uzunligi m ga teng tomon
qarshisidagi burchakni toping,
A) 150° B) 45°	0 90° D) 135“
4.	(У2- 1)2-(y2- ^(y’ + y2* 1) + У ni
soddalashtirgandan keyin nechta haddan
iborat bo'ladi?
A) 5 B) 4 C) 3 D) 6
5.	Qaysi javobda sin(-790)°,cos600° va
tg475° laming ishoralari, yozilish tartibida
berilgan?
A)-,-, + B)+,-, + 0+.-.- D)-, -
6.	Agar 2<xS5va3<y<6 bo'lsa, xy - x
ning qiymati qaysi oraliqqa tegishii bo'ladi?
A) (1; 28)	B)(2; 25)
C) (6; 30)	D) (4; 25)
7.	1Д/56 +2-/To у75б"-2-Ло' ni hisoblang.
A) 6 B) 2 C) 4 D) 3
8.	Aylanaga tashqi chizilgan teng yonli
trapetsiyaning asoslari 56 va 14 sm.
Trapetsiyaning balandligi necha sm?
A) 40 B) 28 C) 36 D) 35
9.	(m2 -	• — —) ni soddalashtiring.
m -1 m-1
A)----—	B)-—
m+1	1-m
C) m - 1	D) 1
10.	(x2 - 9) V*+1 = 0 tenglamani yeching.
A)-1;3	B)±3	0±3;1 D)	2
11.	Arifmetik progressiyaning birinchi va
to'rtinchi hadi yig'indisi 26 ga teng, ikkinchi
hadi esa beshinchi hadidan 6 ga ko'p. Shu
progressiyaning to'rtinchi va sakkizinchi hadi
yig'indisini toping.
A) 10 B) 20	0 12 D) 22
12.	Quyidagi mulohazalardan qaysi biri to'g'ri?
A) Ikkita to'g'ri burchakli uchburchakning
gipotenuzalari va bittadan o'tkir burchaklari
bir-biriga teng bo'lsa, bunday uchburchaklar
tengdir.
B)	Teng tomonli-uchburchakning balandiiklari
kesishish nuqtasida 4:3 nisbatda bo'linadi.
C)	Ikkitadan tomoni, bittadan burchagi o'zaro
teng bo'lgan uchburchaklar tengdir.
D)	Ikkita parallel to'g'ri chiziqni uchinchi to'g'ri
chiziq bilan kesganda hosil bo'lgan ichki bir
tomonli burchaklar yig'indisi 180° dan kichik.
13.	A-2 +12 • 3~3 + (-^-)"! ni hisoblang.
5	10
1	9
A)4^ В) 0	C)2	0)3-=-
J
3
2010 yilning testlar. 102 varianti.
Matematika
14.	Muntazam to'rtburchakli piramidaning
balandligi 24 ga, asosining tomoni 14 ga
teng. Uning apofemasini toping.
A) 25 B) 28	C)18	0 32
15.	p ning qanday qiymatida x2 - px + 5 = 0
tenglamaning ildizlaridan bin boshqasidan 4
ga katta?
A) 6 B) 4 C) -4 D) ±6
16.0,0000087 sonini standart ko'rinishda
yozing.
A) 8,7-10’5	B) 8,7-107
0 8,7-10-®	D)8,7-10’7
._ 2	4	,	. 7n ,	,
17.	— x— = Jsm30 +sin—tenglamani
3	5 V	4
yeching.
A) 2-’	B)0	0 2	D)| 
18.	Quyidagi mulohazalarning qaysi biri
natural sonlarga nisbatan noto'g'ri?
A)	Oxirgi raqami 0 yoki 4 bo'lgan son 4 ga
bo'linadi.
B)	Faqat o'ziga va birga bo'lingan son tub
son bo'ladi.
О Berilgan sonlarga bo'linadigan sonlaming
eng klchigi bu sonlaming eng kichik karralisi
bo'ladi.
D) Oxirgi raqami 0 yoki 5 bo'lgan son 5 ga
bo'linadi.
19.
0,2'-2 -0.06+0,3*
0,05 0,9-0,05
ning qiimatini
hisoblang.
A)-0,2	B)-1	0 0.2	D)-2
20.	a ning qanday qiymatlarida ax + 2y = 3 va
3x - у = -1 tor'g’ri chiziqlar kesishadi?
A) a i 2 B)a = 0 -C)a#-6 D)a6R
21.	n ning qanday qiymatida a (n; -2; 4)
vab (n; 3n; 1,25) vektorlar perpendikulyar
bo'ladi?
A) 6 B) 3	02	01; 5
22.	Quyidagi muiohazalardan qaysi biri
noto'g'ri:
A) To’g'ri chiziqdan tashqarida yotgan
nuqtadan bu to'g'ri chiziqqa faqat bltta
perpendikular to'g'ri chiziq o'tkazish mumkin.
B) Agar bir uchburchakning uch tomoni
ikkinchi uchburchakning uch tomoniga mos
ravishda teng bo'lsa, bu uchburchaklar
tengdir.
C) Agar ikkita teng tomonli
uchburchaklarning balandiiklari teng bo'lsa,
bu uchburchaklar tengdir.
D) Uchburchakning barcha tashqi burchaklari
yig'indisi 180° gateng.
23	.4-7 + 8-11 + 12-15+ ... + 96-99
yig'indini hisoblang.
A) -75 B) -80 C) -72 D) -S3
24.	-4,8:lal = -0,5 tengiikni qanoatlantiruvchi
a ning barcha kiymatlarini toping.
A) 9,6 va -9,6	B) 0
О 2,4	D) 9,6
25.	(-^++¥-)(y2 - 3|y| + 2) = 0 tenglamaning
manfiy ildizlari nechta?
A) 1 B) 2	0 3	0 4
26.	Agar x = 256
. „	X-1 X2 + X4 I „ ..
bo Isa, —5---5----7--1 x* +1 riing
x‘+x2 z*+1
qiymatini hisoblang.
A) 14 B) 15	016	013
27.	Boshlang'ich funksiyani topish uchun
quyida keltirilgan formulaiardan qaysilari
to'g'ri?
1)f(x) = xp,p#-1 F(x)= —+0
P+1
2)	f(x) = —-—, к 5* 0, kx + b>0 F(x) = kln(kx
kx+b
+ b) + C;
3)	f(x) = екх*ь, к # 0 F(x) = 1 ekx+b + C;
4)	f(x) = sin(kx + b), к F(x) = - cos(kx +
b) + C;
5)	f(x) = e ’ + sin3x F(x) = - e ’ + 3cos3x + C.
A)1;4;5
B) 1; 2; 3
О 11 3; 5
D) 1;3;4
4
2010 yilning testlar. 102 variant!.	Matematika
28.	Teng yonli ABC uchburchakning (AB = AC) A uchidan uchburchak tekisligiga uzunligi 32 ga teng bo'lgan AD perpendikulyar o'tkazildi. D nuqtadan BC tomongacha bo'lgan masofa 40 ga teng. ABC uchburchakning BC tomoniga o'tkazilgan balandligi qanchaga teng? A) 12 B) 24 C) 20 D) 14 (-№+x-ll(№-3x'+2).-i	.... . 29.	4	7Х+12	L 2 0 tengsizliknmg butun sonlardan iborat yechimlari nechta? A) 1	B) 4	C)3	D) 2 30.	Natural sonni 18 ga bo'lganda, boTmma 19 ga, qoldiq 8 ga teng bo'ldi. Bo'linuvchini toping. A) 243 B) 263 C) 273 D) 350 31.	у = 5х -1 funksiyaning grafigi . koordinatalar tekisligining qaysi choraklarida yotadi? A) I, II В) I, III С) II, IV D) IV 32.	2n2 - Зап -10n + 15a ko'phadnl ko'paytuvchiiarga ajratlng. A) (5-n) (За-2n) B) (5 + n) (2n - 3a) C)(3a-n)(5-2n) D) (2n + 3a) (n + 5) 33.	Agar tg(x + y) = 5 va tgy = - bo'lsa, tgx ni 8 toping. A) 8	B)-|	C)3	D)1 34.	(x + 2)(x - 3) < 0 tengsizlikni yeching, A) (-»; -3) U (2; ») B)	(-2; 3) C)	(-»; -2)U(3; -») D)	(-3; -2) 35.0,(328); x va 0,(671) sonlari arifmetik progressiyani tashkil qiladi. x ning qiymatini toping. A) 0,(532)	B) 0,50 C) 0,(45)	D) 0,(523)	VARIANT № 103 1.	a ning nechta qiymatida x2 + y2 = 1 va (x - a)2 + y2 = 4 aylanalar urinadi? A) 4	В) 3	C) 2	D) 1 2.	Dastlabki beshta hadining yig'indisi -124 ga va maxraji 2 ga teng geometrik progressiyaning birinchl hadini toping. A)-3	B)-1	C)-2 D)-4 3.	Agar sina = -, sinp = —< a < tt va — < s	5	13 2	2 p<n bo'lsa, sin(a - p) ning qiymati qanchaga teng? A) —	B)-—	C)-— D)- — 65	' 13	' 65	' 65 1	? 1	я 4.	(б — 8 — ):~ + 11 — ni hisoblang. A)-7| В)б| С)-б| D)-7y _	+ 7э8_75? гт . .. .. 5,	л	2L—л	<8 ni hisoblang. V72 А) ^2	В)	0,9988207 С)2	D)	1 6.	Natural a sonni natural b songa bo'lganda, bo'linma c ga va qoldiq d ga teng bo'ldi. Agar bo'linuvchi va bo'luvchi 3 marta orttirilsa, d qanday o'zgaradi? A) 2 taga ortadi	B) 3 marta ko'payadi C) o'zgarmaydi	D) 2 marta ko'payadi 7.	F(x) = ex —1 sin3x - etgx + S funksiya quyidagi funksiyalardan qaysi binning boshlang'ich funksiyasi? A)	f(x) = ex - cos3x + —~ sm2x B)	f(x) = ex - cos3x	V- COS2X C)	f(x) = ex - cos3x	
36.4cos5x = 6 + 3cos +tenglama [~tt; 2tt] kesmada nechta iidizga ega? A) 1	B)o	C) 3	D) 2	sinx D) f(x) = ex + cos3x + —1— sin2x
5
2010 yilning testlar. 103 variant!.	Matematika
. 0,28 0,23	0,9 ... .	c  8. 084 + 'ооз " 005 l oaanln3 q|'/rnatinl t°Plng- 32 A)-10 B) 25	C)10	D)y	18. (y+3X-¥.~'l)< q tengsizlikni yeching. x+2 A)(-2; 1) B)(-;-3)U[-2;1]
9, (0,98 — 0,312:0,3) 25 +^ni hisobiang. A)-14|	B)-lA O-t-L	D)_10±	C)(-~;-3]U(-2; 1] D) ( —;-3] 19. Teng yonli uchburchakning asosidagi burchak uning uchidagi burchakning 75% iga teng. Uchburchakning uchidagi burchagini toping. A) 90° B) 120° C) 135° D) 72°
10. Maxraji 2 ga teng bo'lgan geometrik progressiyaning dastlabki oltita hadi yig'indisi 126 ga, dastlabki beshta hadi yig'indisi 62 ga teng. Progressiyaning birinchi hadini toping. A) 6	B) 5	C) 4	D) 2 11. ABC uchburchakning yuzi 12 ga teng. Uning В uchidan BD = 3 mediana tushirilgan. Agar Z ABD = 90° bo'lsa, AC tomonning uzunligini toping. A) >/73	B)2>/73 C)1°	D>8 12.5,4; y; -2,2 soniarning o'rta arifmetigi 0,8 ga teng, у ni toping. A) 0,4	B)3	C)1,2 D)-0,8 13.	(x2 + x^1^+5xt4)gotengs.z|ik|ling x + 5x + 6 butun sonlardan iborat yechimlari nechta? A) 4	B) 5	C) 2	D) 3 14.	ЛАВС da Z В = 90°, Z C = 60°. BB, balandlik 3 ga teng. AB ni toping. A) 12	B)6	C)6>/2	D)6>/3 15.	Muntazam uchburehakli piramidaning yon qirrasi 20 ga, asosining tomoni 16 >/з ga teng. Piramidaning balandligini toping. А)8>/з B) 12 C) 8	D)16 16.1 dan 71 gacha bo'lgan toq sonlar yig'indisi qanday raqam bilan tugaydi? A) 4	B) 9	C) 0	D) 6 17.5x2 + bx - 15 = 0 tenglamaning ildizlari x, va Xj uchun 5x, + 2x2 = 1 munosabat o'rinli. Agar b butun son ekanligi ma’lum bo'lsa, uning qiymatini toping. A)-10	B)7va-10 C)10	D)-7va10	20. Agar A,B,C va D soniarning nisbati 2:3:4:2 kabi bo'lsa,	nin9 qiymatini aniqlang. А) —	В)—	C)-	D)- ' 4	27	5	9 21. Muntazam piramidaning yon sirti to'la sirtining 60% ini tashkil etadi. Piramidaning yon yoqlari va asos tekisligi orasidagi burchakni toping. 1	B) 60° A) arccos — 4 2	1 C) arccos —	D) arccos— 3	5 22.4cos22x - 2,5 = cos4x tenglamani yeching. A) + —+ —,nCZ	B)-+^,nCZ 7 12 2	4 2 C)£ + ^,nCZ	D)- + —,nCZ 3 2	6 2 23.	- 2>/2  ^6 + 4>/2 ning qiymatini toping. A) 2	B) 1	C) 3	D) 4 24. ^-JsAlb^nisoddalashtiring. 28-16V3 A)|	B) 1 C)1	D)2->/3
6
2010 yilning testlar. 104 variant!.
Matematika
25	1	| x-2x*	+ y
( х-У xi	4y!
soddalashtiring.	
м Jy-4x	Q, 77+77
477 + 77)	’2(77-77)
c) 77+77	o)-i
5	5
26. xy = — va 36 < — < 84 bo‘lsa, x ning
butun qiymatlari ko'paytmasini toping.
A) 120 B) 60 C) 90	0) 180
27.434 sonini 13 va 18 ga teskari
proporsional sonlarga ajrating.
A)192va242	B)224va210
C)150va284	D)252va182
5
28. Agar x - 5, 5x + — m = 0 tenglamaning Xi
8
va xa ildizlari uchun 3xi - 2x2= 14 munosabat
o'rinli bo'lsa, m ning qiymatini toping.
A) 6 В) 3 C) -4  D) 4
29, у=у—r funksiyaning grafigiga x0 = 1
nuqtada o'tkazilgan urinma va koordinat
o'qlari bilan chegaralangan uchburchakning
yuzini toping.
А)—	В)—	С)— D) —
4	'2	8	' 6
30.	x ning qanday qiymatlarida lx2 - 36l = 36
- x2 tenglik o'rinli bo'ladi?
A) x 2 6	B) x < -6
C) x 2 -6	D) —6 s x 5 6
31.	AH; 1; 1), B(1; 4; 0), C(1; -2; 2) va D(-5;
-5; 3) nuqtalar berilgan. AC va BO vektorlar
orasidagi burchakni toping.
A) 60° B) 90’ C) 45’ D) 30’
32.	cosx < sinx tengsizliknl yeching.
А) Г — +	+ ^,kez
Ч4 4 J
B)^+^—+ffkjkez
C) (2uk; it + 2тгк), к C Z
D)f- + 2?ric—+2nk\ kez
I4 4 J
33.	у = log (6 + x - x2) funksiyaning
aniqlanish sohasidagi butun soniarning
yig'indisini toping.
A) 0 B) 3 C) 2 D) 5
34. Agar tga = -—bo'lsa,
2 cos2 a-sin 2g
2sin2a-sin2a
ni
hisobiang.
A)1	B)2
C)-4' D)-l
35. Agar lai < 1, Ibl < 1 bo'lsa,
arccosa-4arcsinb ifodaning eng katta
qiymati qanchaga teng bo'ladi?
A) 1 В) 2тг C) 5tt D)3tt
36. Asoslari 12 va 16 ga teng bo'lgan teng
yonli trapetsiyaning diagonallari o'zaro
perpendikular. Trapetsiyaning yon tomonini
toping.
А) 1477 B>20 c) 10	D)1077
VARIANT № 104
1. To'g'ri burchakli uchburchakning katetlari
24 va 7 ga teng. Kichik katetning
gipotenuzadagi proyeksiyasini toping.
2	4	04
A)3- B) 5	C)2— D)l|-
/	do	2b
2.14 - xl < 5 tengsizlikning butun sonlardan
iborat yechimlari nechta?
A) 5	B)10	C)11 D) 9
3.	To'g'ri to'rtburchakning to'g'ri burchagi
uchidan uning diagonaliga tushirilgan
perpendikular to'g'ri burchakni 3:2 kabi
nisbatda bo'ladi. Shu perpendikular bilan
boshqa diagonal orasidagi burchakni toping.
A) 72’	B) 22,5°	C) 18°	D) 45’
4.	Тб ni hisobiang.
A) 1	B)1,2	C) 1,25	D)1,5
5.	(a + b)(a + b + 1)- (a-b)(a-b -1) ni
ko'paytuvchllarga ajrating.
A)4a(b + 1) B) 2(a + b)(6+1)
C)2a(2b + 1)	D)2a(b-1)
7
2010 yilning testlar. 104 variant).	Matematika
6. To'g'ri burchakli uchburchakning gipotenuzasi 25 sm, katetlaridan birining gipotenuzadagi proyeksiyasi 1 ,.96 sm. Ushbu uchburchakka ichki chizilgan aylananing radiusi necha sm? A) 1	B)3	C) 2	D) 1,5 7. x2 - 3|xj - 28 = 0 tenglamaning ildizlari ko'paytmasini toping. A)-36 B) -49 C) -64 D)-32 8.	To'g'ri burchakli uchburchakning burchaklaridan biri 60° ga, gipotenuzaga tushirilgan medianasi 15 ga teng. Kichik katetning uzunligini toping. A) 7;5	B)10,5 C) 15 D) 12 9.	Geometrik progressiyaning dastlabki 6 ta hadi 2, b2, b3, b4, b5 va 486 bo'lsa, b2 + b3 + b4 + b6 ni hisoblang. A) 230 B) 240 C) 200 D) 260 10.	у = kx - 7 to'g'ri chiziq va у = ax2 -13x + 17 parabola absissalari 4 va 2 ga, teng bo'igan no'qtalarda kesishadi. к - a ayirmaning qiymatini toping. A) 2	B) -2 C) 3	D) -3 11.	Balandiigi 8 ga teng bo'lgan, teng yonli uchburchakning asosi yon tomonidan 2 ga ortiq. Uchburchakning asosini toping. A) 15 B) 16 C) 12 D) 18 12.	(3z - x)3 + (x - 2y)3 - (3z - 2y)3 ko'phadni ko'paytuvchilarga ajrating. A) 3(3z-x)(x-2y)(3z-2y) B) To'g'ri javob keltirilmagan. C) -3(3z - 2y)(3z - x)(x - 2y) D) Ko'paytuvchilarga ajralmaydi. 13.	—— < 1 - x tengsizlikni yeching. x-1 A)	(-1; D B)	(-«; i) C) (-~;-1)U(0; 1) D)0	14.	yla-Za'^b^ + b—^rr+4^bni a/: - b/s soddalashtiring (a > 6). A) -2b1'2	B) 2a1'2 - 2b1ffl C) 2b1ffl	D) -2a1'2 15.	Д ABC ning tomonlari’MNIIAC to'g'ri chiziq bilan kesildi. ABC va MBN uchburchaklarning perimetrlari 3:1 kabi nisbatda. ABC uchburchakning yuzi 288 ga teng. MBN uchburchakning yuzini toping. A) 32 B) 56 C) 16 D) 64 16.	/(х)=ф1,/(1) = ? A) aniqlanmagan	B) 2 C)1	D)1 17.	Uchburchakli piramida asosining tomoniari 9,10 va 17 teng. Uning barcha yon qirralari asos tekisligi bilan 60° burchak tashkil qiladi. Piramidaning baiandligini toping. A)§ B)	C)^ D)^ 16	16	8	24 18.	Arifmetik progressiyada a4 - a2 = 4 va a7 = 14, Shu progressiyaning to'rtinchi hadini toping. A) 7	B)6	C)12 D) 10 19.	Burchagi 60° ga, katta asosi 10 ga teng bo'lgan teng yonli trapetsiyaga aylana ichki chizilgan. Trapetsiyaning kichik asosi uchi va aylana markazi orasidagi masofani toping. А)з| В) 4-1	C)±/2	D)31 5	0	з	O 20.	m ning qanday x,	[x-y=m-1 ,	,	, qiymatlanda^tenglamalar sistemasining yechimi koordinat tekisligining 1 choragiga tegishli bo'ladi? A) (2; °°)	B) (-“l ") C)(|;2)	D)(-»;|) □	о
8
2010 yilning testlar. 105 variant!.
Matematika
21.	Agara(1;-1; 3) vab(4; 3; 0) bo'lsa, a
ning qanday
qiymatida 4a+ab vektor b - a vektorga
perpendikular bo'ladi?
A) 2,1 B)l. C)|	D)-^
22.	cosxcos2x = cos3x tenglama [0; 2тг]
oraliqda nechta ildizga ega?
A) 3	B)1 C) 5 D) 2
f sin 100° +sin 20° У  u, u,
23.	----:-------- ni hisoblang.
I sin50° J	a
A)|	B)1	C)3	D)|
24.	V2000-1998-1997-2001+ 5 ni hisobiang.
A) 2	B)3	C)Vt7	D)4
25.	Bir ishchi buyurtmani 6 soatda, boshqasi
esa 10 soatda bajaradi (tugatadi). Uiar •
birgalikda 3 soat ishlaganlaridan keyin
ishning qancha qismi bajarilmay qolgan
bo'ladi?
1112
A)1	B)1	C)1 D)f
26.	Muntazam to'rtburchakli piramidaning
balandiigi 24 ga.asosining tomoni 14 ga teng
Uning apofemasini toping.
A) 25 B) 28	C)18 D) 32
27.	Qaysi tenglik qoldiqli bo'lishni ifodalaydi?
1) 43 = 9-5 - 2; 2) 43 = 7-5 + 8; 3) 43 = 8-5 +
3; 4) 43 = 21-2 + 1.
A) 2; 4	B) hammasi
C) f; 2; 4	D) 2; 3; 4
28.	a = 4b va c + 6b = 0 (b # 0) bo'lsa, — ni
c
toping.
2	2	1	1
А)Ц	B)-4	0-1	D)-11
О	О	J	\j
3
29.	tg(2arcsin —) ni hisoblang.
4
A)-77 B)-3,/7 оз77 0)2^7
30.	2—-f—zn-3^-1—f—tf7-6^ni
3 (7 J 3 1.5 J
soddalashtiring.
A) 4	B)m-2 0 3 D)m + 3
31.	Agar f(x) = (1 +•! )(7 + 4x) bo'lsa, f(-l)
ni toping.
A) 9	B)-3 C) 15	D)-5
A) 4 B) 2	0 3 D) 1
33.	Goometrik progressiyaning maxraji 3 ga,
dastlabki to'rtta hadiari yig'indisi 80 ga teng.
Uning to'rtinchi hadini toping.
A) 24 B) 32 О 54 D) 27
34,	m ning Vm-1;V5m-1;Vl2m+1;... lar
ko'rsatilgan tartibda arifmetik progressiya
tashkrl qiladigan qiymatlari yig'indisini toping.
A)	8
B)	m ning bunday qiymatlari yo'q
О 12
D) 15
35.
3 . 4
’ 41' 51
38 47	34
Agar—+ — = a bo'lsa, —+— quyidagilard
'll	51	7,1
an qaysi biriga teng?
A) 4 - a B) 3 - a
ОЗ-1 D)2_a
36. Uchburchakning tashqi burchaklaridan biri
120° ga, shu burchakka qo'shni bo'lmagan
ichki burchaklarining ayirmasi 30° ga teng.
Uchburchakning ichki burchaklaridan
kattasini toping.
A) 75° B) 70° C) 90° D) 85°
VARIANT № 105
1. 10-2l:3-l+^2l-1-lj-6ni hisobiang.
A)15| B) 17 О1б| О1б1
О	о	о
2. Agar bo'luvchi х - 2 да, bo'linma х -1 да,
koldiq 4 да teng bo'lsa, bo'linuvchi nimaga
teng?
A) )c + x - 1
9
2010 yilning testlar. 105 variant!.	Matematika
B)	x2 - 6 C)	x2 - 3x + 6 D)	x2 - 5x 3. m ning qanday qiymatida у = mx + 2 to'g’ri chiziq va у = 5X2 parabola abssissasi x = -1 bo'lgan nuqtada kesishadi? A)-7 B) 5	C)3	D)-3	агссо5(х-2)+уГ7 y	log3(5-2x) aniqianish sohasiga tegishli butun sonlar nechta? A)	3 B)	Bunday sonlar yo’q C)4
4.	+ 2л^ ni hisoblang A) 2 B) 1,5 C) 0,5 D)1 5.	n ning qanday qiymatida a (n; -2; 1) va b (n; 3n; 8) vektorlar perpendikulyar bo’ladi? A) 2	B) 4	C) 3	D) 4; 2 6.	a = logv23; b = log, /43 va c = logi/25 bo’lsa, a, b va c sonlar uchun quyidagi munosabatlarning qaysi biri o’rinli? A) b < c < a В) a < c < b C) a < b < c D) b < a < c 7.	у = x2 - 3x + 2 parabolaga abssissasi Xo = 2 bo’lgan nuqtada o’tkazilgan urinmaning burchak koeffitsiyenti nimaga teng? A) 1	B) 2	C) -3 D) 3 8.	m ning Vm-1;V5m-1;Vl2m+1;... lar ko'rsatilgan tartibda arifmetik progressiya tashkil qiladigan qiymatlari yig'indisini toping. A)	8 B)	m ning bunday qiymatlari yo’q C)	12 D)	15 Y-|_ 1 9. у = g—— funksiyaga teskari funksiyani toping. ..	2x-1	_.	2-3x A)y =	 B)y =	 '	Зхч-1	'	x-1 2x + 1	n.	2-3x С) у =	 D) у =	 1 3x + 1	1-x	D)1 11.	к parametrning qanday ,	., [kx-3y = 6.	.	. qiymatlanda Д4 tenglamalar sistemasi yechimga ega emas? A) 2	B) 9	C) 6	D) 3 12.	Agar x < у < z bo’lsa, lx - yl - Iz - yl - Iz - xl ni soddalashtlring. A) 2z - 2y	B) 2y - 2z C) 2x	D) 2y 13.	Cheksiz kamayuvchi geometrik progressiyaning birinchi hadi 2 ga, hadlarining yig’indisi esa 5 ga teng. Shu progressiyaning hadlari kvadratlaridan hadlari progressiyaning hadiari yig'indisini toping. A) 6,25 B) 6,5 C) 5,75 D) 6,75 14.	Quyidagi ifodalardan qaysi biri -1 ga teng? A) ((-1)2)3	B) H-1)2)3 C)((-1)3)2	D) (-(-1)3)3 15.	Agar f*2" 2xy+y ~ 9 bo'lsa, lx + yl ni a |xy = 6,75 hisoblang. A) 5	B) 4	C) 7	D) 6 16.	у = x2 parabolani a (-3; 2) vektor bo'yicha parallel ko'chirganda, uning tenglamasi qanday bo'ladi? A) у = x2 + 6x + 11 В) у = x2 + 5 С) у = x2 -1	D) у = x2 + 9 17.	(x- 1)’ V8-2X-X2 £ 0 tengsizlikning yechimini ko'rsating. A)[-2;3] B)[-4;1]U{2} C) [2;~) D) [-2; 1]U{3)
10
2010 yilning testlar. 105 variant!.
Matematika
18. Agar kamayuvchini 26 ta va ayriluvcnini
12 ta orttirilsa, ayirma qanday o'zgaradi?
A) 14 ta ortadi B) 4 ta kamayadi
C) 4 ta ortadi D) 28 ta kamayadi
19. To'g'ri burchakli trapetsiyaning diagonal!
uni tomoni 20 ga teng bo'lgan teng tomonli
uchburchakka va to'g'ri burchakli uchburchakka
bo'ladi. Trapetsiyaning o'rta chizig'ini toping.
A) 15	B)18	C)10 D) 16
20.2x(x - 1) - (2x - 1 )(x + 1) ifodani
ko'phadning standart shakliga keltiring.
A) 4X2 - 1	В) 2X5 - 3x
C) 3x + 1	D) -3x + 1
21. arccos(sin(-41 °)) necha gradus?
A) 41° B)-41°	C)139° D) 13Г
22. (a + b)(a-b + 1) + (a-b)(a + b-1)-26
ni soddalashtiring,
A)	2a-2b	B) 2b
C)2a2-ab2	D)2a
23.4cos5x = 6 + 3cos^+5xj tenglama [-it;
2tt] kesmada nechta ildizga ega?
A)1
B)	a
C)3
D) 2
24.	Agar avtomobil tekis harakatda 3 soatda
324 km ni bosib o'tsa, 20 sekundda necha
metr masofani bosib o'tadi?
A) 200	B)300	C)600 D) 1000
25.	ABC uchburchakda Z A = 30°, AB = 7з ,
AC = 4. A uchidan tushirilgan balandiik
uzunligini toping.
A)|V2T B)l,/2i C)|V21 D)|T2i
26.	F(x) =£ x2- cosx + C funksiya у = Дх)
funksiyaning boshlang'ich funksiyasi, у = /(x)
funksiyaning hosilasini toping.
A)1 + 2cosx
B)	1 + 2sinx
x
C)	2cos2 2
x
D)	2sin2 2
27.	Arifmetik progressiya uchun quyidagi
formulalardan qaysilari to'g'ri?
1) a> - 2a2 + a3 = 0; 2) a, = a3- a2;
3) n = -^ + d..
d
A) 1 B) 2; 3 C) 1; 2 D) 2
28.	To'g'ri burchakli ACB uchburchakning
katetlari 8 ga va 10 ga teng. Shu
uchburchakning C to'g'ri burchagi uchidan
CE mediana va CD bissektrisa o'tkazildi.
CDE uchburchakning yuzini toping.
A)2|	B)2|	C)3|	D)2|
/ 1 у
29.	2Ьэ’” ni hisoblang.
A) 4 B) 9 C) 5 D) 3
30.	Geometrik progressiyaning dastlabki
uchta had! yig'indisi -26 ga, dastlabki
to'rttasiniki esa -80 ga teng. Agar shu
progressiyaning birinchi had! -2 ga teng
bo'lsa, uning maxraji qanchaga teng bo'ladi?
A) 3 B) -3 C) -2 D) 2
31.	Agar (x-5)(—x+ 4) = 0 bo'lsa,-x +4
5	5
qanday qiymatlar qabul qiladi?
A)	0 yoki 5
B)	-20 yoki 0
C)	faqat 0
D)	0 yoki 8
32.	/(x) = 0,5x2 - x - 1,5 funksiya grafigining
abssissasi 2 ga teng bo'lgan nuqtasiga
o'tkazilgan urinmaning burchak
koeffitsiyentini toping.
A) 2 B) 1	C)4 D) 3
33.	Uchburchakli piramida asosining tomonlari
4, 8 va 9 ga teng. lining barcha yon qirralari
asos tekisligiga — burchak ostida og'ishgan
6
Piramidaning hajmini toping.
A) 24^3	В)4-Л С) 8-Уз D)16i/3
34.	(2 + cos22a) (1 + tg2a) + 4sin2a ifodaning
eng kichik qiymatini toping.
A) 1,5 B) 2,5	C)3	D) 2
11
2010 yilning testlar. 107 variant!.
Maternatika
30	. Muntazam oltiburchakka tashqi chizilgan
aylananing uzunligi 4тг ga teng. Shu
ko'pburchakning yuzini toping.
A) 6 В)л/з С)6-Уз О)4-Уз
ix
31	, /(x) = - -y- x2 + 1 funksiyaning grafigiga
-—nuqtada o'tkazilgan urinmaning OX
Xo =
o'qi bilan tashkil qilgan burchagini toping.
A) 60°	B)30’	C)150o D) 120’
32	.11 + sinxl < tengsizlikning [0; 2tt]
oraliqdagi eng katta va eng kichik yechimlari
ayirmasini toping.
А) 1,5п B) it	C)1,2n	D)^-
33.	Uchburchak burchaklarining kattaliklari 2;
3 va 10 sonlariga proporsional.
Uchburchakning burchaklarini toping.
A) 24°; 36”; 120”	B) 20°; 46°; 120"
C) 10°; 50’; 120’	D) 30”; 40’; 110’
34.	^9+ 31/3 -^Э-За/з -^7+ 4^3 ni
soddalashtiring.
А)л/з-1 В)3->/з С)2-Тз D)2 + Vs
35.	Ikki sonning ayirmasi 27 ga teng. Agar
birinchi sonni ikkinchisiga bo'lsak, bo'linma 4
ga va qoldiq, 3 gateng chiqadi. Berilgan
soniarning yig'indisini toping.
A) 38	B)31	C)43	D)29
36.	Tekisiikka og'ma va perpendikular
tushirilgan. Og'maning tekislikdagi
proyeksiyasi 11 ga, perpendikularning
uzunligi 60 ga teng. Og‘ma va perpendikular
orasidagi burchakni toping.
22
A)	arccos —
61
B)	arsin
61
C)	arcctg—-
oU
60
D)	arcsm —
VARIANT № 107
1.	n ning qanday qiymatida a (n; -2; 4)
va b (n; 3n; 1,25) vektorlar perpendikulyar
bo'ladi?
A) 6 В) 3 C) 2 D) 1; 5
2,	ax2 + bx + c = 0 tenglamaning
koeffitsiyentlari b - a +. c tenglikni
qanoatlantiradi. Agar Xi va x2 berilgan
kvadrat tenglamaning ildizlari
bo'lsa, — + — - 2 ning qiymatini hisobiang.
2(a + c)
ac
(a-c);
3.	Boshlang'ich funksiyani topish uchun
quyida keltirilgan formulalardan qaysilari
to'g'ri?
1)f(x) = xp, p #-1 F(x) = pxp+1 + C;
2)	f(x) =—!— , к # 0, kx + b > 0 F(x)
kx+b
=-lln (kx + b) + C;
3)	f(x) = екх+ь, к 0 F(x) = | el“+l’ + C;
4)	f(x) = cos(kx + b), к 5s 0 F(x) = ksin(kx + b)
+ C;
5)	f(x) = e2* - cos— F(x) = -^ e2* - 3sin +
3	2	3
0.
A) 2; 4; 5	B) 1; 2; 3
C) 2; 3; 4	D) 2; 3; 5
Jx>3
у%-з|£1
tengsizliklar sistemasini yeching.
A)	2 £ x £ 3
B)	-2 £ x £ 4
C)	3 £ X £ 4
D)	X £ 4
14
2010 yilning testlar. 107 variant!.
Matematika
5.	To‘rtburchakli muntazam piramida
asosining tomoni 2 marta kattalashtirildi,
balandligi esa 2 marta kichiklashtirildi. Hosil
bo'lgan piramida hajmining dastlabki
piramida hajmiga nisbatini toping.
A) 4:1	B)1:2 C) 1:1 D) 2:1
6.	Qaysi javobda manfiy son ko'rsatilgan?
А)1од^7з
B)log23
3
С) 1одг1,2
D) log, -jL-
7 v45
7.	AE = 4, EB = 10, CE = 2, DE = ?
A) 15 B) 16 C) 18 D) 20
8.	x2 < x + 15 tengsizlikmng butun sonlardan
iborat yechimlari yig’indisini toping.
A)	9
B)	4
C)5
D)7
9.	Agarr#; —+aj=— bo'lsa, tga ning
qiymatini toping.
А)-—	В)—	С)—	D)~—
60	60 'll	'11
10.	Quyidagi ifodalardan qaysi biri 1 ga teng?
A) (-(-1)t	B)((-1)3)3
C)(-H)4)3	D)((-1)3)4
11.	y=lx2-4l + x2-2 funksiyaning qiymatlari
to’plamini toping.
A) [-2; -°)	B) [2; »)
C) [4; »)	D) (0; «)
12.	ax + 5 = 7x + b tenglama yechimga ega
bo'lmasa, quyidagilardan qaysi biri to'g'ri?
A)	a = 7; b # 5
B)	a # 7; b = 5
C)a = 8;b=12
D)a = 13;b= 13
13.7 + 5v2 + 	_ ni soddalashtiring.
V3-V6
A) 2	B) -1
0 2V2 + 1 D> ~2
14. Uchburchakli piramida asosining tomonlari
11,13 va 20 ga teng. lining barcha yon
qirraiari asos tekisiigi bilan 60° burchak
tashkil qiladi. Piramidaning balandligini
toping.
A)65£ B)g c)6573	65^
12	12	' 6	' 18
4 — ¥
15.1 + logx = (Iglg2 - 1 )logx10 tenglama
nechta ildizga ega?
A) 2 B) 1 C) 3 D) 4
16.	Quyidagi mulohazalardan qaysi biri
noto’g'ri?
A) Qavariq beshburchak ichki burchaklarining
yig'indisi 540° ga teng.
B) Agar bir uchburchakning bir tomoni va shu
tomon qarshisidagi burchagi, ikkinchi
uchburchakning bir tomoni va shu tomon
qarshisidagi burchagiga mos ravishda teng
bo'lsa, bu uchburchaklar tengdir.
C) Teng tomonli uchburchakning balandliklari
uchidan boshlab hispblanganda kesishish
nuqtasida2:1 nisbatda bo'linadi.
D) Ikki qo'shni burchakning yig'indisi 180° ga
teng.
17.	Yig'indisi 35 ga teng bo'lgan uchta son
o'suvchi geometrik progressiyaning dastlabki
uchta hadlaridir. Agar shu sonlardan mos
ravishda 2; 2 va 7 sonlarni ayrilsa, hosil
bo'lgan sonlar arifmetik progressiyaning
ketma-ket hadlari bo'ladi, Arifmetik
progressiyaning dastlabki 10 ta hadining
yig'indisini toping.
A) 245 B) 275 C) 255 D) 265
18.	Muntazam olti burchakka tashqi chizilgan
aylananing radiusi 7з bo'lsa, unga ichki
chizilgan aylananing radiusini toping.
A) 1,5
Bl —
15
2010 yilning testlar. 107 varianti.	Matematika
C)f D) 1,2 19. <810 ! 675 > <162 + 225 J (810,675 +1,11 + 0,19.-1,г.? n| hisobj <162 225 J 2,06 + 0,54 A) 15,5 B) 15 C) 14,5 D) 16 20.	Tekislikka tushirilgan Og'ma va 12 perpendikular orasidagi burchak arcsln — ga teng. Og'maning Io uzunligi 26 ga teng. Perpendikularning uzunligini toping. R A) 10— B) 12	C)10 D) 20 6 21.	Agar bo'luvchi x - 2 ga, bo'linma x -1 ga, qoldiq 4 ga teng bo'lsa, bo'linuvchi nimaga teng? A) x2 + x - 1	B) x2 - 6 C) x2 - 3x + 6	D) x2 - 5 22.	Teng yonli uchburchakka ichki chizilgan aylananing markazi uning balandligini 17:15 kabi nisbatda bo'ladi. Uchburchakning asosi 60 ga teng. Shu doiraning yuzini toping. А) 900тг	В) 64tt C) 56,25rr	D) 15rr 23.	AN ABC uchburchakning bissektrisasi. Agar AB = AN va z C = 30° bo'lsa, В burchak necha gradusga teng? A) 40° B) 50°	C)60° D) 70° 24.	Qaysi javobda sln(-790)°,cos600° va tg475° laming ishoralari, yozilish tartibida berilgan? A)-,-,+ B)+,-,+ C)+,-,- D)-,-,- 25.	(x + 3) (x - 2) < 0 tengsizlikni уeching. A) (-»; -3) U (2; «) B) (-«; 2) U (3; ~) C)(-3;2)	D)(-«;-2)U(3;»)	„„ 0,215-1,6-0,215 ... , 27. —	1—— ni hisobiang. 3,45-3^| A) 4,3 B) 0,45	C)-0,43 D)-4,2 19	r~~ 28. -=	2 <5 + 4 ni soddalashtiring. V20-1 A)	5 B)	6 04 D) 2 V5 + 4 29.	To'rtburchakli muntazam piramida asosining tomoni 4 marta kattalashtirildi, balandligi esa 4 marta kichiklashtirildl. Hosil bo'lgan piramida hajmining dastlabki piramida hajmiga nisbatini toping. A) 1:1 B) 4:1	C)1:16 D) 1:4 30.	cos2(x + 1)-lg (9 - 2x - x2) a 1 tengsizlikni yeching. A)[-1; 0) B)[-1;1) C)(-»:-i] D){-1} 3	7	3 31.	3— :2— = 3—: x proporsiyaning noma'lum hadini toping. Al2£ Bl2§ 031 32.	з/з + 2cos2x = 0 tenglamani yeching. A)±—+aMeZ 12 B)(-l)*’‘qy+-^-,*<=Z 12	2
2a”'3	a2'3	_	a+1	. а3'3-За-1'3 a5'3-a3'3 a3-4a + 3 soddalashtiring. A) 0	B)1	C)-1	q <3+1	C)±-+nk,keZ 6 D) (-!)“- +—,keZ 6 2
16
2010 yilning testlar. 108 varianti.
+ v3 =5
33.	Г y , 2xy = ?
A) 3 B) 2	C)4 D) 1,5
34.	^8 + Зл/2-^8-3>/2-v/6 + 4V2 ni
hisoblang.
A)2-V2
B)3-T2
C)1 + a/2
D)2 + V2
35.	Agar olti hadli geometrik progressiyaning
dastlabki uchta hadining yig'indisi 112 ga va
oxiridagi uchta hadining yig'indisi 14 ga teng
bo'lsa, birinchi had! nechaga teng bo'ladi?
A) 56 B) 81 C) 72 D) 63
36.	5/9+5V3-^/б + эТэ+д/7 + 4Тз ni
soddalashtiring.
А)1+Тз	В)2+Тз
С)2-7з	D)i/3-1
VARIANT № 108
1. a - 3b va 3,3b - a va 4 sonlar 
proporsiyaning ketma-ket hadiari
a2 + b^
bo'lsa,-----kasrning qiymatini toping.
ab
A)I C)l D)T
о	о	о	3
2. Teng yonli uchburchakka ichki chizilgan
aylananing markazi uning asosiga tushirilgan
balandligini, uchidan boshlab
hisobiaganda, ^-va 2 ga teng kesmalarga
О
ajratadi. Uchburchakning asosini toping.
A)	10
B)	12
C)	8
D)	14
3. 12~4n ifoda n ning nechta natural
qiymatida natural son bo'ladi?
A) 5 B) 2 C) 6 D) 4
 Maternatika
4. Muntazam to'rtburchakli piramida asosining
tomoni 5 ga, tola sirti 65 ga teng. Piramida
yon yog'ining asos tekisligiga og'ish
burchaginl toping.
A)	arcsin -
8
5
B)	arccos —
8
C)	arcsin —
16
D)	arccos —-
16
5. cosa = —, 0 < a < — bo'lsa,
18	2
6cos qanchaga teng bo'ladi?
A) 3 B) 5 C) 6 D) 4
6. Aylanaga tashqi chizilgan teng yonli
trapetsiyaning o'rta chizis'i 8 ga teng. Shu
trapetsiyaning yon tomonini toping.
A)	8
B)	4
C)5
0)7
7. Ja-2a''W’ + b--£^ni
soddalashtiring (a > b).
A) 2bV2 B)2a’/2	C)-2b,Q D)-2a1'2
8. MN (6; 7) vaMK (7; 6) vektorlar
parallelogrammning tomonlari bo'lsa, uning
diagonallari orasidagi burchakni toping.
A)	45°
B)	30°
C)	90"
D)	60’
9. n ~8,1+7 ni qisqartiring.
Л — I
A) —	B)—	C)— D)—
n + 1	4-1	' n+l 4-1
10. a ning qanday qiymatlarida a(3x - a) = 6x
- 4 tenglama bitta musbat yechimga ega?
A) (-2; 2)	B> (-2; •>)
C) (-2; 2) U (2; »)	D?(2;«)
17
2010 yilning testlar. 108 variant!.	Matematika
11.-0,25; 0,5;... geometrik progressiyaning hadiari 10 ta. Shu progressiyaning oxirgi 7 ta hadi yig'indisini toping. A) 83 B) 86 C) -43 D) 56 12.Tomonlari 11,12 va 13 gateng bo'lgan uchburchakning katta tomoniga tushirilgan medianasi uzunligini toping. A) 10 B) 9	C) 8,5 D) 9,5 13. To'g'ri burchakli uchburchakning katetlari 32 8 va — gateng. Kichik katetning gipotenuzadagi proyeksiyasini toping. A) 5.4 В)б| C)6	D) 4,8	17. b~1*-~-ni soddalashtiring. 1 -b + b A) b"2	B)b"1	C)b+1 D)b2 18.7,10,13,... arifmetik progressiyaning nechta hadining har birini qiymati 99 dan katta. 212 dan kichik bo'ladi? A) 34 B) 33 C) 38 D) 39 19. 3--- + .. 3—— jfodaning eng katta 5+cos/? tg2y+ctg2y qiymatini toping. A) 4,75 B) 6,25 C) 2,75 D) 3,45 f -л	A	4	.	. . 20. tg — - a = — bo'lsa, ctga ning qiymatini (4	)	5
(71	19 14. Agartg —+ « = — bo'lsa, ctga ning V 4	)	5 qiymatini toping. A)-— B) — C) —	D)-— -12	12	7	7	toping. A) 9	B)--l	C)-4	D)1 f2V’	Г2Г 21.1— I +2-4’’-ljl nihisobiang.
15. Boshlang'ich funksiyani topish uchun quyida keltirilgan formulalardan qaysilari to'g'ri? 1)	f(x)=xp, p *-1 F(x)=—+ C; p+1 2)	f(x)=l,x>0F(x) = lnx + C; 3)	f(x) = ebtb, к *0 F(x) = ke |“+ь + C; 4)	f(x) = cos(kx + b), к r 0 F(x) = ksin(kx + b) + C; 5)	f(x) = e f + sin3x F(x) = 2e ’ - cos3x + C. A) 2; 3; 5	B)1;2;4 C) 1; 2; 5	D) 1; 3; 5	A) 2	B)3±	C)4y D)	2,5 22. Iloggxl - log3x - 3 < 0 tengsizlikni	yeching. A)(1;~)	В)(з?з;м) C)(0;1)	°)[777;ю) оу О 23. к ning qanday ..	[(кг-/г-25)х-г2,5-12,5 = 0, .. qiymatlanda f	sist [2x + y + /r = 0 emsning birorta ham yechimi bo'lmaydi? A) 3	B) -5	C) -2 D) 6
16. tg(x-—) 2-1 tengsizlikni yeching 4 A)[^-+2nn;- + 2nn],neZ В)[^ + ттп;| + ттп], nGZ C) [-—+ тгп; —+ тгп), n C Z 2	4 D) (-^ + тгп; nn], nCZ	24. Agar/(x) = e’’2x-cos(2x- 1) bo'lsa, /'(1) ning qiymatini toping. A) 0	В) -2e C) 2e D) -2 25.520 sonini shunday ikki bo'lakka bo'lingki, ulardan birining 80% i ikkinchisining 24% ini tashkil qilsin. Bo'laklarni kattasini toping. A) 400 B) 120 C) 420 D) 460 26.2n2 - Зап - 4n + 6a ko'phadni ko'paytuvchilarga ajrating. A) (n - 2) (2n - За)	B) (5 - n) (3a + 2n) C) (2 - 3a) (n - 5)	D) (3a-n)(5-2n)
18
2010 yilning testlar. 109 variant!.	Matematika
f№ + y! =6 27. Agar J'	bo'lsa lx - yl ning |x + y = V11 qiymatiki toping. A) 6	B)0	C) 1	D)-S „ 7з + 2л/2+7з-2,/2+72 ... 28. 					— ni hisoblang. A) 0,5	B)-^ C) 0,75 D)^y 29.3x2 < 16x - 5 tengsiziikning butun yechimlari ko'paytmasini toping. A) 120 B) 12 C) 24 D) 30 30. Uchburchakning tomonlari 12:18 va x ga teng. Uchburchakning yarim perimetri qaysi oraliqqa tegishli bo'ladi? A) (9; 15)	B) (18; 30) C)(15;24)	D) (30; 48)	35.1Idizlari 5 + 7? va 5 - 7? bo'lgan keltirilgan kvadrat tenglamaning barcha koeffitsiyentlari yig'indisini toping. A) 29	B) 10	C)9	D)-7 36. 71024-108 + 0,5- 732 -243 ni hisoblang. A) 48	B) 45	C) 51	D) 49 VARIANT № 109 1. cos 930° ning qiymatini aniqlang. A)-O,5 B)^	C)1	D)-^ 2. To'g'ri burchakli trapetsiyaning diagonal! uni tomoni 20 ga teng bo'lgan teng tomoni! uchburchakka va to'g'ri burchakli uchburchakka bo'ladi. Trapetsiyaning o'rta chizig'ini toping. A)	10 B)	12
,, 1э + Тб5	/э — Тб5 ... 31. ,—-— + J—— ni hisoblang. A)9-Tio	B)7l3 C)7-V2	0)75	C) 15 D) 16 3-Teng yonli trapetsiyaning asoslari 30 va 50 ga, balandligi esa 30 ga teng. Trapetsiyaning diagonalini toping. A) 56 B) 70 C) 60 D) 50
32. у = tep** g’5 ~ funksiyaning aniqlanish sohasini toping. A) (-2-1)	B)(—;-2)u[|;^ O^l;”]	D)(-M;-2)	4.	= о tenglamaning [0; 6n] sin 2 kesmada nechta ildizi bor? A)	4 B)	12 C)	8
33. Uchburchak burchaklarining kattaliklari nisbati 2:3:1 kabi, kichik tomonining uzunligi esa 5 ga teng. Uchburchakning katta tomoni uzunligini toping. A) 10 В)12Тз C)13 D)ST2 34.To‘rtburchakli muntazam piramida asosining tomoni 3 marta kattalashtirildi, balandligi esa 3 marta kichiklashtirildi. Hosil bo'lgan piramida hajmining dastlabki piramida hajmiga nisbatini toping. A) 9:1	B)1:1 C) 3.1 D) 1:9	D)6 5. Agar x2y + xy2 = 12 va x2y - xy2 = 84 bo'lsa, 1 ning qiymatini hisobiang. A)1	B)1	C)-l D)1 6. Arifmetik progressiyada аю = 56 bo'lsa, uning dastlabki 19 ta hadiari yig'indisini toping. A) 1024 B) 1032 0 Ю56 D)1064
19
Matematika
2010 yilning testlar. 109 variant!.
7. Boshlang'ich funksiyani topish uchun
quyida keltirilgan formulalardan qaysilari
to'g'ri?
1)f(x) = xp,p#-1 F(x)=-^ + C;
2)	f(x)=-,x>0F(x)=--l- + C;
3)	f(x) = ekx+tl, к # 0 F(x) = 1 elo'+b + C;
4)	f(x) = sin(kx + b), к 5s 0 F(x) = -kcos(kx +
b) + C;
5)	f(x) = e2* - cos F(x) = ~ e2* - 3sin у + c-
A) 3; 4; 5	B) 1; 3; 4
C)1;3;5	D)1;2;5
3. AB va CD vatarlaming kesishish nuqtasi О
nuqta AB vatami AO = 4 va OB = 12 ga. CD
vatami esa uzunliklarining nisbati 1:3 bo'lgan
kesmaiarga ajratadi. CD vatarning uzunligini
toping.
A) 12	B)15	C)18	D)16
. x+2 1-№ . 1 x . -
9.----------r  (---r--------г) ni
1-x 1 + № (x-1) 1-*
soddalashtiring.
A) —
i-x
B)^D1
1-x
C) 1
D)_4
x-1
10.
,	1
ni soddalashtiring.
A)2Va
C)1
11.	(1 + cosx)tg ^ + 1=0 tenglamani
yeching.
A)--| + 2nk, kCZ В) тг + 2тгк, к 6 Z
Onk.kCZ D) tt + ттк, кCZ
4
12.	Itgx + ctgxl =-= tenglamani yeching.
y3
Tt
A)	(-1)" б’+ 2тгк; к G Z
B)	—+ trk;kez
C)±- + —;kCZ 
6	2
D)±^ + trk;keZ
13.	Agar ft/) = 2x3х bo'lsa, /(0) ni toping.
A) -1 B) 2 C) -2 D) 3
14.	~~ kasmi qisqartiring.
-9/ + №
A)——	8)——
x-3y	x+3y
C)——	D)----?—
x+3y	x+3y
15.	To'rtta sonning yig'indisi 36 ga teng. Shu
sonlardan chetki hadlarining yig'indisi 18 ga
va o'rta hadlarining ayirmasi 4ga teng
proporsiya tuzildi. Proporsiyaning o'rta
hadlari yig'indisini toping.
A) 18 B) 77 C) 12	D)16
16.	m ningi/m-1;V5m-1;Vl2m + 1;... lar
ko'rsatilgan tartibda arifmetik progressiya
tashkil qiladigan qiymatlari yig'indisini toping.
A) 8
B) m ning bunday qiymatlari yo'q
C)12
D) 15
5	1
17.	a = 2log25, b = 4log , —, c = 3log, —
4 26	6 23
sonlarni o'sish tartibida joylashtiring.
A)a<b<c	B)b<a<c
C)c<a<b	D)b<c<a
18.	Tomonining uzunligi 24+12-Уз ga teng
muntazam uchburchakka ichki chizilgan
kvadratnlng yuzini toping.
A) 324 B) 864 C) 648 D) 432
20
Matematika
2010 yilning testlar. 109 varianti.
19.	Konusining o'q kesimi teng tomonli
uchburchakdan, silindrniki esa kvadratdan
iborat. Agar ularning tola sirtlari tengdosh
bo'lsa, hajmlarining nisbatini toping.
A) 1:3	B) 2:3
C) 72:73	D)1:T2
20.	Arifmetik progressiyada a2 = 12 va a? = 3.
Shu progressiyaning o'n oltinchi hadini
toping.
A)-12	B)-15	C)-6	D)-30
21.	m ning qanday qiymatida a (1; m; -2)
va b (m; 3; -8) vektorlar perpendikulyar
bo'ladi?
A) 4 B)-2 C) 2 D)-4
22.	37-24 - 34-24 + 1911 -16-11 ning
qiymatini toping.
A) 90 B) 105 C) 100 D) 110
23. Tekislikka og'ma va perpendikular
tushirilgan. Og‘ma va tekislik orasidagi
40
burchak arccos — ga, og'maning tekislikdagi
proyeksiyasi 80 ga teng. Perpendikularning
uzunligini toping.
A) 36 B) 40 C) 30 D) 18
24. —- - ifoda n ning nechta natural
n + 5
qiymatida butun son bo'ladi?
A)	2
B)	hech bir qiymatida
C)4
D)1
27.	a ning qanday qiymatlarida 2x - у = 11 va
x - ay = 18 to'g'ri chiziqiar kesishadi?
А)яД	B)a = —	C)o = — D)o* —
2	'	2	'	11	'	11
28.	Agar olti hadli geometrik progressiyaning
dastlabki uchta hadining yig'indisi 112 ga va
oxiridagi uchta hadining yig'indisi 14 ga teng
bo'lsa, birinchi hadi nechaga teng bo'ladi?
A) 56 B) 81 C) 72 D) 63
29.	Teng yonli trapetsiyaning kichik asosi 3
ga, perimetri 72 ga teng. lining diagonali
o'tmas burchaglni teng ikkiga bo'ladi.
Trapetsiyaning o'rta chizig'ini toping.
A) 8,5 B) 13 C) 7,5 D) 12
30.	Quyidagi mulohazalardan qaysi biri
noto'g'ri?
A) Agar ikkita teng yonli uchburchakning
asoslari va asoslaridagi burchakiari teng
bo'lsa, bunday uchburchaklar tengdir.
B) Teng tomonli uchburchakning balandliklari
uchidan boshlab hisoblanganda kesishish
nuqtasida 2:1 nisbatda bo'linadi.
C) Agar bir uchburchakning bir tomoni va shu
tomon qarshisidagi burchagi, ikkinchi
uchburchakning bir tomoni va shu tomon
qarshisidagi burchagiga mos ravishda teng
bo'lsa, bu uchburchaklar tengdir.
D) Qavariq beshburchak ichki burchaklarining
yig'indisi 540° ga teng.
31.	2X2 - 14x + c = 0 tenglamaning ildizlaridan
biri 0,5 ga teng. Shu tenglamaning ikkinchi
ildizini toping.
A) 3 B) 4 C) 6,5 D) 0
2S- hisoblang-
A)-il В)-б| 0-8^ D)91
4	4	4	4
X— 1
32.	——- < 0 tengsizlikni yeching.
A)[1;3)	B)(-3;1)
C) (—2; 1)	D)(1;3)
26. у = (tg—)"’-*"1 funksiyaning qiymatlar
6
sohasini toping.
A)[-4=-:73]
73
В) (0;7з)
C)(0; 3]
D) (-«; 3]
33.
9
11--7,4
3
1	2
:5—+1— ni hisobiang.
A) 2,2	B)2^	C)2 D) 3,2
4
34. -—= x+1 tenglamaning nechta haqiqiy
ildlzi bor?
A) 2	B)3
C) ildizi yo'q	0) 1
21
2010 yilning testlar. 110 varianti.
Matematika
35. у = lx2 - 41 + x2 - 2 funksiyaning qiymatlari
to'plamini toping.
A) [-2; «)	B) [2; ~)
C) [4; -°)	D) (0; «)
36.8 soniga teskari sonni toping.
A) 0,125 B)-0,8	C)1,25	D)-|
VARIANT №110
1.	a ning qanday qiymatlarida 3(x + 1) = 4 +
ax tenglamaning ildizi -1 dan kata bo'ladi?
A) (0; «)	B) (4; ->)
C) 0)	D) (-«o; 3) и (4;-°)
2.	2-Уз +5 —— ni soddalashtiring
V12-1
A) -4	B)6
02^3-4	D)-6
3.	log,2 + log4,4 = 1 tenglama ildizlarining
ko'paytmasini toping.
A) 2 B) 4	01	0 8
4.8 va 18 sonlari eng kichik umumiy
karralisining natural bo'luvchilari nechta?
A)	8
B)	12
0 6
D) 9
5,	Agar a - p = - bo'lsa, —ning
2 coso+cos/?
qiymatini toping.
A)1 В)7г O^ D)1
6.	Uchlari A(3; -2; 1), B(3; 0; 2) va C(1; 2; 5)
nuqtalarda bo'lgan uchburchakning BD
medianasi va AC tomoni orasidagi
burchakning kattaligini toping.
A) 60°
B) arccos —
3
C) 45°
л/2
D) arccos —
3
7.	V2 + 2sin2x = 0 tenglamani yeching.
A)(-l)‘*'-+«:eZ
8
о 2
C)(-l)"' —+ fflt,*eZ
8
,keZ
8 2
8.	(x + 3)2 - 2lx + 3I - 3 = 0 tenglama
ildizlarining yig'indisi nechaga teng?
A)-6	B)-5	C)—4	0)4
9,	Uchburchak ikkita burchagi yig'indisining
kosinusi --iga teng. Uchinchi burchagining
kosinusini toping.
«I
0-1
d>5
10.	Konusning o‘q kesimi muntazam
uchburchakdan, silindrniki esa kvadratdan
iborat. Agar konus to'la sirtining silindr tola
sirtiga nisbati 1:3 kabi bo'lsa, hajmlarining
nisbatini toping.
A) 2:9	B)1:9 C) 4:9	D)v£:9
11.	160 dan katta bo'lmagan 7 ga karrali
barcha natural sonlarning yig'indisini toping.
A) 1617 B) 1470 C) 1624 D)1771
12.	3B) * 10 + 2” yig'indining oxirgi raqamini
toping.
A) 3 B) 5	• C)1	D)7
13.	'(~4)-2-(-3)_ sonining uchdan bir
9715	a
qismini toping.
A) 3 B) 6 C) 9	0) 2
14.	Raqamlarining yig'indisidan 8 marta katta,
raqamlari kvadratlarining yig'indisi esa 53 ga
teng bo'lgan ikki xonali sonning kvadratini toping.
A)729 B) 5184 C)6561 D) 529
22
2010 yilning testlar. 110 varianti.	Matematika
15.	Quyidagi ketma-ketlikiardan qaysilari geometrik progressiyani tashkil etadi? 1) an = 2xn; 2) c„ = ax" + 1; 3) bn = a (| )"sin60. A) 1; 3	B) 2; 3 C) hech biri	D)1;2;3 16.	ABC uchburchakda Z A = 30°, AB = i/з , AC = 4. A uchidan tushirilgan balandlik uzunligini toping. A)^72? B)1^T C)|^T D)2^L 17.	Teng yonli trapetsiyaning kichik asosi 3 ga, perimetrl 66 ga teng. lining diagonal! o'tmas burchagini teng ikkiga bo'ladi. Trapetsiyaning o'rta chizig'ini toping. A) 12	B)10 C) 8	D)7,5 18.	Quyidagi tenglamalardan qaysi biri ildizga ega emas? A)	10x2-24x + 16 = 0 B)	6x2-11x + 3 = 0 С) 27X2 + 18x + 3 = 0 D) бх2 - 13x + 6 = 0	f(x-2)2 + lyl = 4 22. Agar J , ,	bo'lsa, x + у ning [|x-2| + |y| = 2 qiymatini toping. A) 4 yoki 2 yoki 0	B) 0 yoki 3 C) 2 yoki 4	D) 0 yoki 4 23. Agar F'(x) = 2x - 1 va F(1) = -2 bo'lsa, F(x) funksiyani aniqlang. A)	F(x) = x2 + x - 4 B)	F(x) = 2x2-x+ 1 C)	F(x) = Зх2 - 3x + 2 D)	F(x) = x2-x-2 24.	JiW?+3 ni hisoblang. Л/2+1 A) 1,5	B)1	C)|	D)0,5 25.	Arifmetik progressiyada ад - a2 = 4 va a? = 14. Shu progressiyaning to'rtinchi hadini toping. A) 7	B)6	C) 12 D) 10 26.	Uchburchak ikki burchagi yig'indisining 1
19. у = ^7 - |x - 2| +	funksiyaning aniqlanish sohasini toping. A) [-7;-1,5)	B)(-5;1,5) C)(-«;-1,5)	D)(-1,5;9] 20. Uchburchakli piramidaning asosidagi barcha ikki yoqli burchaklar 30° ga teng. Agar piramidaning balandligi 6 ga teng bo'lsa, uning asosiga ichki chizilgan doiraning radiusini toping. A) 2n/3 B) 6^3 C) 2	D) 3	siriusi — bo'lsa, uchinchi burchagining sinusi qancha teng bo'ladi? B>1	=>1	O>| 27. Boshlang'ich funksiyani topish uchun quyida keltiriigan formulalardan qaysilari to'g'ri? 1) f(x) = xp, p + -1 F(x)= — + C; p+1 2)’ f(x) = --- -, к 10, kx + b > 0 F(x) = kinfkx kx+o
J2 21. sinxosx <— tengsizlikni yeching. 4 А)^-+ттк<х< —+ ттк, kCZ 4	4 В)-— + пк<х<— + nk, kCZ 8	8 С)£ + пкйх<:— + rrk,kCZ 8	8 D)£ + тгк < x <— + тгк, к C Z 8	8	+ b) + C; 3)	f(x) = e10"0, к # 0 F(x) = 1 екх+ь + C; 4)	f(x) = sinfkx + b), к t 0 F(x) = cos(kx + b) + C;	‘ 5)	f(x) = ef + sin3x F(x) = ef + 3cos3x + C. A) 1; 4; 5	B) 1; 2; 3 C)1;3;5	D)1;3;4
23
2010 yilning testlar. 111 variant!.
28. Ikki sonning yig'indisi 6 ga, kvadratlarining
ayirmasi esa 12 ga teng. Shu sonlaming
ko'paytmasini toping.
A) 7 B) 12	C)8 D)-8
30.	у = 6 - Vwx+5 funksiyaning grafigiga x0
= 2 nuqtada o'tkazilgan urinma va koordinat
o'qlari bllan chegaralangan uchburchakning
yuzini toping.
q	p7	07
A4	C>T 0)9
Z	4	О
31.	Quyidagi formulalardan qaysilari to'g'ri?
1)	sin(x + y) = cosx-cosy - sinx siny;
2)	tg(x + y) =	x у x + у jc £ + nn
1-fgxfgy’	2
n£Z;
-. . 2— 1+COSX
3)	sin2 2 =—-—;
4)	slnx + siny = 2sin cos i
5)	tgx+tgy= sin(*+y) , Xi у ?s£ + тгп, n S
cosx-cosy 2
Z.
A) 3; 4; 5	B) 2; 3; 5
C) 2; 4; 5	D) 1; 2; 5
32.	sin( 1 arccos ) ni hisoblang.
А) —	В) —	С)-	□)-
' 9	' 3	4	9
33.	Uchburchakning tomonlari 7 va 11 ga,
uchinchi tomoniga tushirilgan medianasi 7 ga
teng. Uchburchakning uchinchi tomonini
toping.
A) 14	B)13	C)12 D) 10
Matematika
34,	x, у - raqamlar; xy va 8y esa ikki xonali
sonlar. Agar xy-6 = 8y bo'lsa, x + у ning
qiymati qanchaga teng bgfiadi?
A) 9 B) 4 C) 6 D) 5
35.	Agar/(x) = (2x + 1)(~ - 3) bo'lsa, /(-1)
ni toping.
A) 0	8)6	C)-6	D)-3
36.	To'g'ri burchakli uchburchakning
gipotenuzasi 25 sm, katetlaridan birining
gipotenuzadagi proyeksiyasi 23,04 sm.
Ushbu uchburchakka ichki chizilgan
aylananing radiusi necha sm?
A) 2,5	B)3	01,5 D) 2
VARIANT №111
1. Muntazam to’rtburchakli piramidaning
balandligi 8 ga, asosining tomoni 12 ga teng.
Piramida yon yog'iga parallel bo'lib, asosining
markazi orqali o'tgan kesimi yuzini hisoblang.
A)72 B) 50 C)45 D) 30
2, cosg-.?.sin3g_-c.°.^.n ifodani
Sin 5a - 2COS 3a - sin a
soddalashtiring.
A)	tg3a
B)	2
01
D) ctga
3.	AgarrJ —+a = -31 bo'lsa, tga ning
14	)
qiymatini toping.
А) —	В)-—	O-— D) —
' 15	' 15	' 16	16
4.	Teng yonli uchburchakning ichki
burchakiari va uchidagi tashqi burchagi
21
yig'indisi —я- ga teng. Uchburchakning teng
16
burchakiari yig'indisini toping.
A) —я	В)— r
16	'16
o^	D)^
о	lo
24
2010 yilning testlar. 111 variant!.
Matematika
5.	<2 + 2cos2x = 0 tenglamani yeching.
A)(-l) *w—+—-,ieZ
8	2
Зя-
В) ±—+ jt.teZ
8
C)± — + лк,ке Z
8
D) (-i)‘«£+^.,fceZ
8 2
6.	Ko'rsatkichli va logarifmik funksiyaiar uchun
quyida keltirilgan xossalardan qaysilari
noto'g'ri?
1)	у = ax(a > 0,a *1) funksiyaning qiymatlar
to'plami - barcha musbat haqiqiy sonlar
to'plami;
2)	у = a*(a > 0,a 11) funksiya 0 < a < 1
bo'lganda barcha haqiqiy sonlar to'plamida
o'suvchi, a > 1 bo'lganda esa kamayuvchi
bo'ladi;
3)	logarifmik funksiyaning aniqlanish sohasi -
barcha musbat sonlar to'plami;
4)	logarifmik funksiyaning qiymatlar to'plami -
barcha musbat sonlar to'plami;
5)	agar a > 1 bo'lsa,u holda у = logax funksiya
x > 1 da manfiy qiymatlar,0 < x < 1 da
musbat qiymatlar qabul qiladi.
A)1;3;4	B)1;3;5
C)1;2; 4	D) 2; 3; 5
7.	^>/56 +2Tw • ^^56-2^0 ni hisoblang.
A) 6 B) 2 C) 4 D) 3
8.	To'rtburchakning uchta ketma-ket
tomonlarining uzunliklari 2; 3 va 4 ga, unga
ichki chizilgan aylananing radiusi 1,2 ga teng
bo'lsa, to'rtburchakning yuzini toping.
A) 7,2
B) 8,6
C)7,8
D) 6,8
.	1 + m4 m2 + 1. .	... ....
9.	(m ———--------) ni soddalashtinng.
nr-1 m-t
A)——
m+1
О m-1
B)——
71-m
D)1
x x
99 + 143
C)16	D)18
,, x x x x
10. —+—+— +—
3 15 35 63
tenglamani yeching.
A) 13 B) 26
11.1- 2sin4x < cos24x tengsizlikni yeching.
AXy^+y).kez
B)(|+2«r/q—+2rk),keZ
8	8
+ kCZ
D) (~—+2nk;— + 2itk), k£Z
4	4
12.	-1 va sonlar orasiga shunday uchta
musbat sonni joylashtirdingki, natijada
geometrik progressiya hosil bo'lsin. O'sha
qo'yilgan uchta sonning yig'indisini toping.
A) 0,5	B)^	C)0,375 D)^-
13.	2,5(ax- 5,2) = 2a - 5x - 9 tenglama a
ning qanday qiymatlarida cheksiz ko'p
yechimga ega?
A)2 B)-l 0-2	D)1
14.	rh (-1; 5; 3) van (2;-2; 4) vektorlarning
skalyar ko'paytmasini hisoblang.
A) 0 B) 12	0-24	D)-10
15.	т/э-х <2tengsizlikning yechimlari OX
o'qida joylashtirilsa, qanday uzunlikdagi
kesma hosil bo'ladi?
A) 4 B) 3,8	0 4,5	D)4,8
16.	Detai 1:5 masshtabdagi chizmada 2,1 sm
uzunlikka ega. Shu detal 1:4,5 masshtabdagi
chizmada qancha (sm) uzunlikkaega
bo'ladi?
A)£ B) 3,5	015	0)2—
5	3
17.	Maxraji 2 ga teng bo'lgan geometrik
progressiyaning dastlabki beshta hadi
yig'indisini 93 ga teng. Progressiyaning
birinchi hadini toping.
A) 4 B) 3	0 6 D) 2
25
2010 yilning testlar. 111 varianti.	Matematika
18. 1;7?;VS; va t/д sonlami o'sish tartibida joylashtiring. A)1;T2=#4;V3	B)1;V3;T2;t/4 С) Тз;Т2 = V4;1	D) 7г = 74;7з;1	26. 4.	+ 8 + 37l0 ni V 2 2V3-Vw soddalashtiring. A) 10	В)2-Зч/То
19.	arcsinx < 7/ -1 tengsizlikni yeching. A) {1} B) {-1} ОНИ) D) (0;|) 20.	x2 + y2 = 10 aylana va x + у = 2 to'g'ri chiziqning kesishishidan hosil bo'lgan vatarning uzunligini toping. A) 6	B)4V5	C)5>/2 D) 4-Тз 21.	Ildizlari Зх2 + x - 4 = 0 tenglamaning ildizlariga qarama-qarshi sonlardan iborat bo'lgan kvadrat tenglamani tuzing. A) 3x2-x + 4 = 0 B) 3x2-x-4 = 0 C)3x2-4x-1 = 0	D)3x2 + x+4 = 0 22.	Birinchi son 0,6 ga, ikkinchi son 0,15 ga teng. Birinchi son ikkinchi sondan necha foiz ortiq? A) 75 B) 25 C) 300 D) 40 23.	Tekislikka og'ma va perpendikular tushirilgan. Og'ma va tekislik orasidagi burchak arccos0,96 ga, og'maning tekislikdagi proyeksiyasi 48 ga teng. Perpendlkulaming uzunligini toping. A) 14 B) 42 O> 24.2п2 - Зап - 4n + 6a ko'phadni ko'paytuvchilarga ajrating. A) (n - 2) (2n - За) B) (5 - n) (3a + 2n) C)(2-3a)(n-5) D) (3a - n) (5 - 2n) 25. Uchburchakning a, b va c tomonlari orasida a2 = b2 + с2 - 7з be bog'lanish mavjud. Uzunligi a ga teng bo'lgan tomon qarshisidagi burchakni toping. A) 150° B)30° C) 60° D) 135°	C)-10	D)3i/w-2 27.	3— 1 2—:3,2-3 |+9,6ning qiymatini 5^3	) toping. A)l|	B)21	C)ll	D)2-l 3	0	3	10 28.	1,6'0,7 1,8 ning qiymatini toping. 4 B)5> 0115 D)f 29.	Muntazam to'rtburchakii piramida asosining tomoni 4 ga va apofemasi 6 ga teng. Piramida hajmini toping. д)32^	b)64^ 3	3 0)^	1 30.	у = 4-74л-5 funksiyaning grafigiga x0= 1 nuqtada o'tkazilgan urinma va koordinat o'qlari bilan chegaralangan uchburchakning yuzini toping. A) —	B)— O— O — ' 8	'12	Г6	6 31.	Boshlang'ich funksiyani topish uchun quyida keltirilgan formulapardan qaysilari to'g'ri? 1)	f(x) = (kx + b)p, p #-1 F(x) = kp(kx + b)”"1 + C; 2)	f(x) =1, x > 0 F(x) = Inx + C; 3)	f(x) = ela+b, к * 0 F(x) = 1 ек*+ь + C;
26
2010 yilning testlar. 112 varianti	Matematika
4) f(x) = cos(kx + b), к + 0 F(x) = ksin(kx + b) + C; 5) f (x) = e2* - cos F(x) = -1 e2x - 3sin + C. A) 2; 4; 5	B) 2; 3; 5 C)1;2;3	D) 2; 3; 4	2. Konusining o'q kesimi teng tomonli uchburchakdan, silindrniki esa kvadratdan iborat. Agar ularning to'la sirtlari tengdosh bo'lsa, hajmlarining nisbatini toping. A)	1:3 B)	2:3 C)	-ji: 7з
32. logix—+ —1—= 1 tenglama ildizlarining x log’ 4 yig'indisini toping. A) —	B)— O— D) — 16	'16	16	8	D) 1:V2 3. pi-|'-7,4^:5-j+1-|-nlhisobiang. A) 2,2	B)2-l	C)2	D) 3,2
33.	Nechta tub son 2 < x+7 < 4 2x-19 tengsizlikning yechimi bo'ladi? A) 7	B) 5	C)1	D) 3 34.	nx = nx2 -12 tenglamaning ildizlari natural son bo'ladigan n(n C N ) ning barcha qiymatlari yig'indisini toping. A) 20 B) 18 C) 22 D) 16 35.	Gipotenuzasi c ga va o'tkir burchaklari sinuslarining yig'indisi q ga teng bo'lgan to'g'ri burchakli uchburchakning yuzini toping. A)lq’(c2-1)	B)jc2(q2-1) 4	4 C)lc’(q2 + 1)	D)lg2(c2 + 1) 4	4	4. Ikki tomoni yig'indisi 1,8 ga va ular orasidagi burchagi 150° ga teng bo'lgan uchburchaklar ichida yuzasi eng katta bo'lgan uchburchakning yuzini toping. a)A ' 25 B) — ' 10 O-*L 400 d)JL ' 100 5. Muntazam DABC tetraedrda M; N; К va P nuqtalar mos ravishda DC; BC; AB va DA qirralarning o'rtalari. Agar tetraedming qirrasi
36. Ushbu 31323334...7980 sonning raqamlari yig'indisi toping. A) 460 B)453 C) 473 D) 490 VARIANT № 112 1. Quyida keltirilgan tengliklardan qaysiiari ayniyat emas? 1)	(x + a)-(x-b) = x2-(a-b)x-ab; 2)	(x - c)-(x - d) = x2 + (c - d)x + cd; 3)	(x - e) (x + d) = x2 - (e - d)x - ed; 4)	6ab + (2a3 + b3 - (3ab2 - (a3 + 2ab2 - b3))) = За3 - ab2 + 6ab; 5)	5a2 - 3b2 - ((a2 - 2ab - b2) - (5a2 - 2ab - b2)) = 9a2 + 4ab - 3b2. A)	1; 2; 4 B)	1; 3; 4 C)	1; 2; 5 D)	2; 3; 5	4 ga teng bo'lsa, MNPK+ABBC vektorlar skalyar ko'paytmasining yig'indisini hisobiang. A) 6	B)4	C) 12	D)-4 6. Teng yonli uchburchakning asosi 40 ga, unga tushirilgan balandligi 21 ga teng. Uchburchakning yon tomonini toping. A)	27 B)	29 C)19 D)31 ,	0,5-0,52	•	 7.		т	7 ning qiymatini 0,42 + 2-0,04 + 0,12	a hisobiang. A)-0,1 B) -2	C) 1	D) 10
27
2010 yilning testlar. 112 varianti.
A) 2,5
B) 0,5
C)1
D)3
9. (- )'3 + 2-4'2 + (-)"’ ni hisoblang.
3	7
A) 2	B)0	C)3-l	D)2,5
10. Agar tg|
41
— bo'lsa, ctga nihg
qiymatini toping.
А)? B)S С)-П D)'S
11.	Uchburchak ikkita burchagining qiymatlari
nisbati 5:9 kabi, uchinchi burchagi shu
burchaklaming kichigidan 10° ga kichik.
Uchburchakning eng kichik burchagini toping.
A) 30° B) 40° C) 45° D) 50°
12.	Agar 0 < q < p < к bo'lsa, Ip + ql + Ik - ql
- Ik - pl ni soddalashtiring.
A)2p + 2q-2k	B)2p
C) 2p + 2k	D) 2q
13.	/(x) = -2x2 + 18x2 + 12 funksiya o'sadigan
kesmaning uzunligini aniqlang.
A) 4 B) 5 C) 4,5 D) 6
14.	у = -6x2 + 7x - 2 kvadrat funksiyaning
nollari yig'indisini toping.
A)-1i b’1I M D)1i
ООО	О
/и
15. Isinxl tengsizlikni yeching.
A) [-—+ 2ттп; —+ 2nn], n £ Z
+—],nez
2 '
’ ' 6....6
3	2 3
С) f-- + m;- + m], n CZ
3	3
□)[-— + 2m; — + 2m], n S Z
3	3
Maternatika
2v +1
16.	у ning qanday qiymatlarida —— kasrnmg
qiymati (-1; |) oraliqqa tegishli?
A)(-|;D
B) To'g'ri javob keitirilmagan.
C)(-1;2)
О(0; 2)
17.	к ning qanday qiyrnatida lln(x +15)1 = -(x
+ к + 4)2 tenglama yechimga ega bo'ladi?
A) 15	B)-10	C)-15	D)10
18.	Muntazam oltiburchakka tashqi chizilgan
aylananing uzunligi 2n gateng. Unga ichki
chizilgan doiraning yuzini hisoblang.
A) 2tt
B)3tt
Qtt
D)|r
I 2	1	4	2
19.	ya3 -2a 3 + a 3 :a 3 ni soddalashtiring (a
z1).
A)a-2
B) a2 -1
C)a-1

20.	Trapetsiya asoslarining uzunliklari 28 va
12 ga teng. Trapetsiya diagonallari o'rtalarini
tutashtiruvchl kesrnaninq uzunligini aniqlang.
A) 8 B) 10	0 6	D)9
21.	420:(60 - 1000:x) = 12 dan x ni toping
B)8
О 36
D) 40
22.	(x - y)3 - (z - y)3 + (z - x)3 ko'phadni
ko'paytuvchilarga ajrating.
A) 3(x-y)(y-x)(x-z)
B)-3(x-y)(z-y)(x-z)
o 3(y-x)(y-z)(z-x)
D)-3(x - y)(z - y)(z - x)
23.	Tekislikka tushirilgan og'ma va
perpendikulyar orasidagi burchak
arcsin — ga teng. Og'maning uzunligi 75 ga
25
teng. Perpendikulyarning uzunligini toping.
2010 yilning testlar. 113 varianti.
A) 72	B)10-	021-	D)21
2	8
24.	Uchlari A(1; 3), B(-1; 1) va C(2; 2)
no'qtalarda joylashgan uchburchakka tashqi
chizilgan aylana markazining koordinatlarini
toping.
A) (1; 2)
B) (0,5; 1,5)
of-zl
<3 J
D) (0; 2)
25.	a ning qanday qiymatlarida 3x + 2y = 3 va
3x - 2ay = 5 to'g'ri chiziqlarning kesishish
nuqtasi musbat ordinataga ega?
A)a = 2 B)a<2 C)a<-1 D) a > 2
26.	Ikki sonning ayirmasi 5 ga teng. Agar shu
sonlardan kattasining 20% i
kichigining -7- qismiga teng bo'lsa, shu
oU
sonlarni toping.
A) 36 va 41	B) 30 va 35
C) 63 va 68	D) 45 va 50
27.	26-25 -25-24 + 24-23 -23 22- 19-5 ning
qiymatini toping.
A) 54	B)0 ОЮ6 D)8
оя c 4	, ,1® 7 .2 ... ..
28-5I?-37+1W:^-13r"hlSOblang'
A)	33-
3
B)	23-
3
О 22-
3
0 241
29. cosxcos2x = cos3x tenglama [0; 2tt]
oraliqda nechta ildizga ega?
A)3 B) 1	0 5	0 2
soddalashtiring.
A) 4	B)m-2 03 Om + 3
Maternatika
31. г!-^m-3^-l|.^|m-6^ni
soddalashtiring.
A) 4 B) m - 2 0 3 D) m + 3
32, Tekislikka og'ma va perpendikulyar
tushirilgan. Og'ma va tekislik orasidagi
burchak arccos 11 ga, og'maning tekislikdagi
proyeksiyasi 14 ga teng. Perpendikularning
uzunligini toping.
A) 14 B) 48	0 28 D) 36
33.	To'g'ri burchakli uchburchak katetlarining
gipotenuzadagi proyeksiyalari 9 va 16 ga
teng.
Uchburchakka ichki chizilgan aylananing
radiusi qancha?
A) 6 B) 6,5 C) 5 D) 5,5
34.	Ikki mototsiklchi oraliq masofasi 432 km
bo'lgan ikki shahardan bir-biriga qarab bir
vaqtda yo'lga chiqdi. Agar ulardan birining
tezligi 80 km/soat, ikkinchisiniki birinchisi
tezligining 80% ini tashkil atsa, uiar necha
soatdan keyin uchrashadi?
A) 1,5 B) 2	0 2,5	0 3
-3
35.	у=— funksiyaning boshlang'ich
funksiyasini toping.
A) 3lnx + С	В) — + C
ex
C)57’C	D>5’’"c
36.	Iog5tg36° + Iog5tg54° ni hisoblang.
A)0	B)1	С)-7э	0V2
VARIANT №113
1.	Teng yonli uchburchakning balandligi 7 ga,
asosi 48 ga teng. Uning yon tomonini toping.
A) 31 B) 45 О 55	+0) 25
2.	x2 + 5x + 7x2 +5x-5 = 17 tenglamaning
ildizlari yig'indisini toping.
A) 6
B)3
О -5-
0-3
29
28
2010 yilning testlar. 113 variant!.
Matematika
3.	ABC uchburchakda AB = AC, BM1 AC,
BM = 18 va MA = 24. ABC uchburchakning
yuzini toping.
A) 258 B) 254	-C) 270 D) 262
4.	8 + 6: (—2) - 2-(-11) ni hisoblang.
A)	99
B)	15
C)	33
.0)27
5. Uchburchakning ikki tomoni va ular
orasidagi bissektrisasi uzunligi mos ravishda
60; 40 va 24 ga teng. Uchburchak yuzini
toping.
А)400Тз	В)900-Уз
С)600%/з	D) 300^3
( 1	1 'i m m+1 .
—-------------- . — 4----nl
-m m-1; m + 2 m+2
soddalashtiring.
A)-^-
m-2
2m-2
m2-4
D)
2
m2-4
7. **	+ .-y.±l + x ni soddalashtiring.
x2 +1
A)	x
B)	x- 1
C)x + 1
D) 2x + 1
8. Muntazam to'rtburchakli piramidaning
balandligi 24 sm, apofemasi esa 26 sm.
Piramida asosining perimetrlni toping.
A)	48
B)	40
C)	80
D)	96
9.100 va 125 so'mlik daftarlardan hammasi
bo'lib 1750 so'mlik xarid qilindi. Quyida
keltirilgan sonlardan qaysi biri 100 so'mlik
daftariarning soniga teng bolishi mumkin?
A) 15 B) 14	C)17	D)16
10.4 va 64 sonlarining o'rta arifmetigi ularning
o'rta geometrigidan necha marta katta?
A) 2—	B)2— C) 2,2	D)21
4	4	8
11.	cos6x + 4cos2x > 0 tengsizlikni yeching.
A) f-y+ Z
B)f-+M-;— +Oc\keZ
И 4	)
C)\--+nk-,-+xk\keZ
Ч 4	4 J
12.	x ning qanday qiymatlarida lx2 - 811 = 81
- x2 tenglik o'rinll bo'ladi?
A) -9 s x s 9 В) X S 9
C) x > 9	D) x > -9
1	5
13.	- — ;-;... arifmetik progressiyaning
4	24
nechta hadi manfiy?
A) 2 B) 1 C) 4 D) 3
14.	a = 21+ jvab=-2j+2fcvektorlarda
yasalgan
parallelogrammning diagonallari orasidagi
burchakni toping.
1	3
A) arccos -==	B) arccos -=
V17	V21
C)arcocs- D) —
15.	Uchburchakning 24 ga teng balandligi
uning asosi uzunligini 1:8 nisbatda bo'ladi.
Shu balandlikka parallel va uchburchakning
yuzini teng ikkiga bo'ladigan to'g'ri chiziq
kesmasining uzunligini toping.
A) 12,5 B) 17 C) 21	D)18
16.	—— < x - 4 tengsizlikni yeching.
x+4
A) (-4; 4)	B)(-~;-4)
C) 0	D) (0; 4)
17.	у = 51gfunksiyaga teskari funksiya-ni
aniqlang.
A)y = 3’102
C)y = 5-10’
В) у = 3.10**
D)y = 5-10K
30
2010 yilning testlar. 113 variant!.
Matematika
18.

2
> — tengsizlikning barcha butun
sonlardagi yechimlari yig'indisini toping.
A) 53 B) 33 C) 48 D) 47
19.	a ning qanday qiymatlarida ax - 2x + 3
tenglama yechimga ega bo'lmaydi?
A) a * 1 B)a = 2 C)a*2 D)a*-2
20.	Agar rgl у + a j = 31 bo’lsa, ctga ning
qiymatini toping.
А)-—	В)-—	С)— D) —
15	'16	'15	'16
21.	^2,O°"1S ' ni hisoblang.
A) 4 B) 9 C) 5 D) 3
22.	- 2cos2x = 0 tenglamani yeching.
A)(-l) —+—-*eZ B)(-l)‘-+—,keZ
12 2	6	2
С)±^+Л,ке2	D)(-l)‘—+nk,keZ
6	12
23.	Uchburchakning b va c ga teng tomonlari
orasidagi burchagi 30° ga teng.
Uchburchakning uchinchi tomoni 16 ga teng
bo'lsa hamda uning tomonlari c2 = b2 + 16b +
256 shartni qanoatlantirsa, c ning qiymati
qanchaga teng bo'ladi?
А)1бТз В) 12^2 С) 12^3 D) 16>/2
24.	R radiusli aylanaga ichki chizilgan
muntazam 12 burchakning tomonini toping.
A)r72-V3	B)R^2-V2
C)R	D) R —
2
25.	ABC uchburchakda A va В burchakiari
bissektrisalari kesishidan hosil bo'lgan kichik
burchak 40° ga teng. Uchburchakning C
burchagini toping.
•A) 100°	B) 90°	C) 80°	D) 120°
26.3,8(2,01 - 3,81) ifodani hisoblang.
A) 6,84	B) 5,82	C) -6,84 D) -5,82
27. Uchburchakli piramidaning asosi tomonlari
1 va 2 bo'lgan teng yonli uchburchakdan
iborat. Uning barcha yon yoqlari asos tekisligi
bilan bir xil a burchak tashkil qiladi.
Piramidaning hajmini toping.
A) — В) C) D) —
4	'8	10	6
28, Agar a = -2 va b = 3 bo'lsa, rasmda la -
29	.279 ni 16 ga bo'lganda qoldiq 7 bo'ladi.
Bo'linma nechaga teng?
A) 12 B) 13	C)11 D) 17
30.	Agar у = F(x) funksiya у = f(x)
funksiyaning boshlang'ich funksiyasi bo’lsa, у
= f(~) fucnksiyaning boshlang'ich
funksiyasini toping.
A)y = 2F(-|)	B)y = lF(x)
C)y=-2F(.-£)	D)y=lF(A)
31.	Agar А, В, C va D sonlaming nisbati
2:3:4:2^ kabl bo'lsa, д ning qiymatini
ani'qlang.
B) aniqlab bo'lmaydi
e>l
°>7
__ 8л-40	.	...
32.	—-— ifoda natural son bo ladigan n
ning
natural qiymatlari nechta?
A) 6 B) 4 C) 1 D) 5
31
2010 yilning testlar. 114 varianti.
Matematika
33.	Maxraji 2 ga teng bo'lgan geometrik
progressiyaning dastlabki beshta hadi
yig'indisi 186 ga teng. Progressiyaning
birinchi hadini toping.
A) 5 В) 3 C) 6 D) 4
34.	210 + 312 yig'indining oxirgi raqamini
toping.
A) 9 B) 5 C) 1 D) 4
35.2sin43°cos17° + 2sin2 3 4 * * *32° - 1 ni
hisobiang.
C) 1
D)
36.0'tmas burchagi 120° ga, asoslarining
uzunliklari 6 va 2 ga teng bo'lgan teng yonli
trapetsiyaning perimetrini toping.
A)	12
B)	16
C)	18
D)	20
VARIANT №114
(	22~\ 1
1. x+3— :7— = 3 tenglamani yeching.
25 J 3
NA)19—- B)20— C) 18— D)19 —
'	25	25	25	25
2. x ning qanday qiymatlarida 0,(16); x va
0,(25) sonlar ishoralari almashinuvchi
geometrik progressiyaning ketma-ket
keluvchi hadlari bo'ladi?
A) 0,(20)
B) ±0,(20)
C) -0,(20)
D) -0,(21)
3. Ketma-ket kelgan oltita natural sonning
yig'indisi 417 ga teng. Shu soniarning eng
kichigini toping.
A) 67 B) 59 C) 48 D) 70
4. Agar x2 + x - 4 = 0 tenglamaning ildizlari Xi
va x2 bo'lsa, xf + x} ning qiymati qanchaga
teng bo'ladi?
A)3	B) 1
C)-13	D) 2
5.0'zaro teskari sonlami aniqlang:
1) V3-1vaV3+1;2) ^va^;
3)Vi-^va^+^;4)^va^.
A) 2; 3; 4	B) hammasi
О 1;2; 1	D) 1; 3;4
, 2kx+3 к-2+х,	,	, .	.
6. —-— = —-— tenglama к ning qanday
qiymatida yechimga ega emas?
A)|	B)|	C>7	D>1
4	5	4
7. Uchburchakning ikkita tashqi burchagi
yig'indisi 240" ga teng. Uning shu
burchakiarga qo'shni bo'lmagan ichki
burchagini toping.
A)	30”
B)	45°
0 90’
D) 60’
8.279 ni 16 ga bo'lganda qoldiq 7 bo'ladi.
Bo'linma nechaga teng?
A) 12	B)13	011	017
9.	Quyida keltirilgan tasdiqlardan qaysilari
to'g'ri?
1)	arifmetik progressiyaning ayirmasi
uchun d = a"~a' (n + 1) munosabat o'rinli;
n-1
2)	sin(a + 3), sln(a - P) va sinacosp sonlar
arifmetik progressiyaning ketma-ket
keladigan hadlari bo'ladi;
3)	arifmetik progressiya dastlabki n ta
hadining yig'indisi
uchun S„ = 2.a>. Г formula o'rinli;
4)	cheksiz kamayuvchi geometrik
progressiyaning S yig'indisi S = ga teng;
1-q
5)	geometrik progressiya dastlabki n ta
hadining yig'indisi S„ = ^2-Zl) (q 1)
q-1
formula bilan hisoblanadi.
A)	1; 2; 5
B)	1; 3; 4
О 1;4;5
D) 2; 3; 5
32
2010 yilning testlar. 114 varianti.
Matematika
10. Doiraga ichki chizilgan muntazam
uchburchakning yuzi unga ichki chizilgan
kvadratning yuzidan 18,5 ga kam. Shu
doiraga ichki chizilgan muntazam
oltiburchakning yuzini toping.
A) 8-/3 + 15	B)9>/3+6V2
C) 13,5+12^3	D)24>/3+27
11. Quyidagi tasdiqlarning qaysilari to'g'ri?
1) piramidaning hajmi asosining yuzi bilan
balandligi ko'paytmasining uch baravariga
teng; 2) ikkita o'xshash jism hajmlarlning
nisbati ularning mos chiziqli o'lchovlari
kublarining nisbatiga teng; 3) silindrning
hajmi asosining yuzi bilan balandligi
ko'paytmasining uchdan biriga teng;
4) shaming hajmi — ttR3 ga teng; 5) shar
segmenting hajmi nH2(R - у) ga teng (H -
shar segmenting balandligi, R - shaming
radius)).
A) 2; 4; 5	8)1; 2; 4
C) 2; 3; 4	D) 2; 3; 5
12.	Teng yonli uchburchakning balandligi 7
ga, asosi 48 ga teng. Uning yon tomonini
toping.
A) 31	8) 45 C) 55 D) 25
13.	n ning qanday qiymatida a (n; -2; 4)
va b (n; 3n; 1,25) vektorlar perpendikulyar
bo'ladi?
A) 6	B)3 C) 2 D) 1; 5
14.	a - 2b; 4; a + 3b; 24 sonlar proporsiyaning
3 a2 - b2
ketma-ket hadlari bo'lsa, —--— ifodaning
qiymatini toping.
A)3 B)I C)|	D)2
15.	To'g'ri burchakli uchburchakning
burchaklaridan biri 60° ga, gipotenuzaga
tushirilgan medianasi 15 ga teng. Kichik
katetning uzunligini toping.
A) 7,5 B) 10,5 C) 15 D) 12
16.	To'g'ri burchakli uchburchakning
gipotenuzasi 25 sm, katetlaridan birining
gipotenuzadagi proyeksiyasi 23,04 sm.
Ushbu uchburchakka ichki chizilgan
aylananing radiusi necha sm?
A) 2,5 B) 3	C)1,5 D) 2
17.	2n2 - Зап - 4n + 6a ko'phadni
ko'paytuvchilarga ajrating.
A) (n - 2) (2n - 3a) B) (5 - n) (3a + 2n)
C) (2 - 3a) (n - 5)	D) (3a - n). (5 - 2n)
18.	(a - 3b)2 - (3a + b)2 ni soddalashtiring.
A)	-8a2 + 12ab - 8b2
B)	8a2 + 12ab - 8b2
C)	-8a2 - 12ab + 8b2
D)	8a2 - 12ab + 8b2
19.	tg(a + P) = 5, tg(a - P) = 3 bo'lsa, tg2p ni
hisobiang.
A)-l B) 2 C) 15 D) 1
20.	Tekislikka og'ma va perpendikular
tushirilgan. Og'maning tekislikdagi
proyeksiyasi 11 ga, perpendikularning
uzunligi 60 ga teng. Og'ma va perpendikular
orasidagi burchakni toping.
..	22
A)	arccos —
61
B)	arsin —
1	61
C)	arcctgll
D)	arcsin —
21,	6-^24 ni hisobiang.
V5-V24
A)-3	B)-1	C)-8	D)-7
22.	Abssissasi x0 = 2>/з bo'lgan nuqtadan
f (x) = -/з Inx funksiyaga o'tkazilgan urinma
OY o'qi bilan qanday burchak tashkil etadi?
A) 60°
BJarctg^
C) arctg2
D) 30°
33
2010 yilning testlar. 114 varianti.
Maternatika
23, V2 + 2sin2x = 0 tenglamani yeching.
- 1
A) (-1) -+M,keZ
8
B)(-l)wl+^,keZ
о 2
C)(-l)w—+—,fceZ
8	2
D)(-l)‘My+fl*.JteZ
24.1,25 songa teskari sonn! toping.
A) 8	B)-0,8 C) 0,8	D)--2-
25. ai, a2,.... an(d * 0) arifmetik progressiya
berilgan. Quyidagi sonlardan qaysilari
arifmetik progressiya tashkil etmaydi?
1)	1,1,1....J_;
a3 ^5	^20-1
2)	ag, a4, a6,.... a2n;
3)	.A+аз A+a4 Aл-2 + ^2n-1 >
4)	ai + аз, аз + as, as + a?,а2п-з + a2n-i;
5)	А+азА + а<,А>-г+аг»-, •
A)1;2;4	B) 1; 3; 5
C)1; 4; 5	D) 2; 3; 4
26.	Agarm>0, n>0vam + n = 12V2 bo'lsa,
mn ning eng katta qiymatini toping.
A) 64 B) 66 C) 62. D) 72
27.	Boshlang'ich funksiyani topish uchun
quyida kelti rilgan formulalardan qaysilari
to'g'ri?
1)f(x) = xp, p#-1 F(x)= — + C;
p+1
2)f(x) -	,k^0,kx+b>0 F(x) = kln(kx
+ b) + C;
3)	f(x) = etoHb, к + 0 F(x) = -L ekxtb+ C;
4)	f(x) = sin(kx + b), к 10 F(x) = --L cos(kx +
b) + C;
5)	f(x) = e’ + sin3x F(x) = -1 e ’ + 3cos3x + C.
A)1;4;5	B) 1; 2; 3
C) 13; 5	D) 1; 3; 4
28.	Teng yonli ABC uchburchakning (AB = )
AC) A uchidan uchburchak tekisligiga
uzunligi 32 ga teng bo'lgan AD
perpendikulyar o'tkazildi. D nuqtadan BC
tomongacha bo'lgan rnasofa 40 ga teng.
ABC uchburchakning BC tomoniga
o'tkazilgan balandligi qanchaga teng?
A) 12 B) 24 C) 20 D) 14
29.	2 0 tengsizlikning
x=-7x+12	a a
butun sonlardan iborat yechimlari nechta?
A) 1 B) 4 C) 3 D) 2
30.	Agar bo'luvchi x - 7 ga, bo'linma x - 4 ga
va qoldiq -2 ga teng bo'lsa, bo'linuvchini
toping.
A)x2-11x-26	B)x2-11x + 26
C)x2+11x-26	D)x2+11x + 26
31.	^ + / + xy = 72
|x+y = 3,
A)	1	B)3 C) 4 D) 2
32, To'g'ri burchakli uchburchakning to'g'ri
burchagidan tushirilgan balandlik va
mediananing nisbati 15:17 kabi. Shu
uchburchak kichik katetining katta katetiga
nisbatini toping.
A)1	B)|	C)|	D)|
33.
f Ту-A +	*	1. Ax+yjy nj
(^y-Ay + x xjx + y-Jy J У
soddalashtiring.
A)Vx->/y	B)/x+A
C)A	D)1
34 5^+6_x._x_ + 1 ifodan|
№-4 №-4 x-2
soddalashtiring.
A)-1
B)1
X-2
D)ll
x + 2
34
2010 yilning testlar. 115 varianti.	z Maternatika
35. cos2	+sin2 tengsizlikni yeching. A) — + ттп < x < — + ттп, n £ Z 8	8 B)	+ 2ттп < x < — + 2nn, n £ Z 8	8 С)	+ 2ттп < x < ^ + 2nn, rp G Z D)	-—+ 4 rm < x <— + 4ттп, n 6 Z 2	2	- 0,22 - 2  0,06 + 0,32 . 5,	_	ning qiymatini 0,05 0,9 -0,05 hisoblang. A) -0,2 B) -1	C) 0,2	□) 0,25 6. Vi 1 + 6>/2 - Ji 1 - 6>/2 ni hisoblang. A)	22 B)	6 C)3^2 D)V8
36, Korxonada mahsulot ishlab chiqarish birinchi yili 20% ga, ikkinchi yili 10% ga ortdi. Mahsulot ishlab chiqarish ikki yil mobaynida necha foizga ortgan? A) 50 B) 28 C) 30 D) 32 VARIANT №115 1. a ning b ga nisbati 4:5, b ning c ga nisbati esa 7:9— kabi c ning necha foizini a tashkil qiladi? A) 70 B) 50 C) 60 D) 80 2. R radiusli aylanaga tashqi chizilgan muntazam 12 burchakning tomonini toping. V3 b)2^-r V2 + V2 C) 1,2R D)2(2-^3 )R	7.	Uchlari A(2; 3; 0), B(3; 2; 1) va C(3; 4; 1) nuqtalarda bo'lgan teng yonli uchburchakning asosidagi burcnagini toping. A) arccos-^	B)-| C) arccos —	D) — 3	6 8.	Aylananing tenglamasi x2 + y2 - 2x - 2y = 0. Uning uzunligini hisoblang. A) 2tt	B) 4tt C)8n	D)2ttV2 _ к 9.	sinTr — sinx + 1 £ 0 tengsizlik x(x£ [0; 2tt]) ning qanday qiymatlarida o'rinli? A)[tt;2tt]	B)[0;£}U[^;tt] 6	6 C)[0;£]	D)[^] О	DO 10.	Arifmetik progressiyaning birinchi va to'rtinchi hadi yig'indisi 26 ga teng, ikkinchi
3. Iog23 = a va log25 = b bo'lsa, log15135 ni a va b orqali ifodalang. А)-*±£ B)*±3£ c.b+3a	b+2a b + 2a b+a	b+2a b+3a 4. Cheksiz kamayuvchi geometrik progressiyaning hadiari yig'indisi 1,6 ga, ikkinchi hadi -0,5 ga teng. Shu progressiyaning uchinchi hadini toping А>1	B4 C)4	D)i	hadi esa beshinchi hadidan 6 ga ko'p. Shu progressiyaning to'rtinchi va sakkizinchi hadi yig'indisini toping. A) 10 B) 20	C)12	D)22 11. Tekislikka tushirilgan og'maning uzunligi 25 ga, uning tekislikdagi proyeksiyasi esa 7 ga teng. Og'ma va tekislik orasidagi burchakni toping. A) arcsin	B) arctg 24	7 C) arcsin—	D) arcsin— 25	'24
35
2010 yilning testlar. 115 varianti.
Matematika
12.f(x) =^5 + \r4 + x + ^5 + -j4^x funksiya
uchun quyidagilardan qaysi biri o'rinli bo'ladi?
A) toq ham, juft ham emas
B)	toq funksiya
C)	o'suvchi funksiya
D)	juft funksiya
13.	Muntazam to'rtburchakli piramidaning
balandligi 24 ga, asosining tomoni 14 ga
teng. Uning apofemasini toping.
A)	25
B)	28
C)	18
D)	32
14.	To'g'ri burchakii uchburchakning
gipotenuzasi 13 ga, katetlaridan biri V52 ga
teng. Gipotenuzaga tushirilgan balandlikning
uzunligini toping.
A) 5 B) 6 C) 7 D) 4
15.	Natural sonlar qatori har biri natural
sonning kvadrati bilan to'gaydigan
quyidagicha qismlarga ajratilgan: {1}, {2, 3,
4}, {5, 6, 7, 8, 9}, {10,11, 12,13, 14, 15, 16},
... 10 - qismdagi sonlar yig'indisini toping.
A) 1626 B) 1913 C) 1758 D) 1729
16_ sin^is^=0 m 0;4
cosy
oraliqqa nechta ildizga ega?
A) 7 B) 6 C) 5 D) 2
17.	Detal 1:5 masshtabdagi chizmada 2,1 sm
uzunlika ega. Shu detal 1:3 masshtabdagi
chizmada qancha (sm) uzunlikka ega
bo'ladi?
A) 15
B)21
О
°)|
D) 3,5
18.	f (x) = logs-jx2 - 2x + 5) funksiyaning
qiymatlar sohasini toping.
A)(5;«)
B)	[log25;
C)	(2; ~)
D)	[2;«)
19.	у = ^1 + Iog,,2cosx funksiya x (xe [0; 2 я- ])
ning qanday qiymatlarida aniqlangan?
A)f0;7lUf-T:2,rl
4J |_ 4 J
B) [o;4
20.	(x2 + 6x + 4)(x2 + 6x + 6) = 120
tenglamaning haqiqiy ildizlari yig'indisini
toping.
A) 5	B)-12	C)-5 D)-6
21.	Quyida keltirilgan parallelogrammlarning
qaysilari barcha yon yoqlari asos teklsligi
bilan bir xil burchak tashkil qiladigan
piramidaning asosi bo'iishi mumkin?
A)	rornb yoki kvadrat
B)	kvadrat yoki to'g'ri to'rtburchak
C)	Ixtiyoriy parallelogramm
D)	faqat to'g'ri to'rtburchak
22.	—4,8: lai = -0,5 tenglikni qanoatlantiruvchi
a ning barcha kiymatlarini toping.
A) 9,6 va -9,6 B) 0
О 2,4	D) 9,6
23.	y = Vsin25x.y*(^-) = ?
A)31
3
aVa • Va
C)2
D) 0
24.	(x2 - x - 1 Дх2 - x - 7) £ -5 tengsizlikning
eng katta butun va eng kichik butun ildizlari
ayirmasini toping.
A) 4 B) 6	0 2 D) 5
25.	у = e2"3* funksiyaning boshlang'ich
funksiyasini ko'rsating.
A)e2"3x + C	B)|e2-3x + C
O-le2-3l+C	D)-3e2"3x+C
3
36
2010 yilning testlar. 116 varianti.
Matematika
26.	(bn) (n e N) geometric progressiyada q =
2 va S4 = 3. b2 ni toping.
2	1
A) 0,8 B) 0,4	C)^	' D)M
27	.7 ga bo'lganda, qoldig'i 3 ga teng
bo'ladigan barcha ikki xonali sonlaming
yig'indisini toping.
A) 776 B) 656 C) 676 4,0)666
28.	Teng yonli uchburchakning asosi a ga,
uchidagi burchagi a ga teng. Uchburchakning
yon tomoniga tushirilgan balandligini toping.
A) a sinB)acos^-
29.	(bn) geometrik progressiyada b4 - b2 = 24
va b2 + Ьз = 6 bo'lsa, bi ning qiymatini toping.
A) 0,4	B)1	C)4 D) 2,2
5
30.	4X2 - 16x S -7 tengsizlikning butun
sonlardan iborat yechimlari yig'indisini toping.
A) 4	B)3	C)6 D) 5
31.	ax2 + bx + c kvadrat uchhad x = 8 da
nolga aylanishi hamda x = 6 da -12 ga teng
eng kichik qiymatni qabul qilishi
rna’lum. Va + b+c ni toping.
А)з/бЗ B)V65	C)8	D)y^0
32.	Agar a = 729
дЗ _Qo3 /	\
bo'lsa, —;---5----: (ya - 2) ning qiymatini
a3 +2a3 +4
toping.
A) 9 B) 6 C) 12	D)15
33.	Uchburchakning asosiga parallel to'g'ri
chiziq uning yon tomonini uchidan boshlab
hisoblaganda 5:3 kabi nisbatda,yuzini esa
yuzlarining ayirmasi 56 ga teng bo'lgan ikki
qismga ajratadi. Berilgan uchburchakning
yuzini toping.
A)	204
B)	272
C)	144
D)	256
34 0,215-1,6.0215 nih|sob|ang
3,45-3g
A) 4,3 B) 0,45 C) 43,43 D)-4,2
35.	Ko'rsatkichli va logarifmik funksiyalar
uchun quyida keltirilgan xossalardan qaysilari
noto'g'ri?
1)	у = ax(a > 0,a t1) funksiyaning aniqlanish
sohasi-barcha haqiqiy sonlar to'plami;
2)	logarifmik funksiyaning aniqlanish sohasi-
barcha musbat sonlar to'plami;
3)	logarifmik funksiyaning qiymatlar to'plami-
barcha rnusbat sonlar to'plami;
4)	у = logax logarifmik funksiya x > 0 oraliqda
agar a > 1 bo'lsa, kamayuvchi, agar 0 < a < 1
bo'lsa, o'suvchidir;
5)	agar a > 1 bo'lsa, u holda у = logax
funksiya x > 1 da manfiy qiymatlar, 0 < x < 1
da musbat qiymatlar qabul qiladi.
A) 1; 2; 4	B) 3; 4; 5	,
C)1;2;5	D)1;3;5
36.	Uchburchakning asosi 22 ga, yon
tomonlari 13 va 19 ga teng. Asosiga
tushirilgan medianasini toping
A) 18 B) 12	0)16 D) 13
VARIANT №116
1. Teng yonli ABC uchburchakda AC - asos,
CD - C burchakning bissektrisasi va z ADC
= 150" bo'lsa, Z В ning kattaligini toping.
A) 110°	B)60°	C)140o D) 80°
2. Geometrik progressiyada bi + b5 = 51 va b2
+ be = 102. Shu progressiyaning dastlabki
yettita hadi yig'indisini toping.
A)	765
B)	361
C)399
D) 381
3. a,, a2,..., an(d t C) arifmetik progressiya
berilgan. Quyidagi sonlardan qaysilari
arifmetik progressiya tashkil etadi?
1)	3i, аз, as.агп-Г,
2)	 --Д7;
3)	3i + Зг> З2 + йз, Эз + 34,	32n-i + Игл)
4)	ai + аз, аз + as, as + а7,...»2п-з + агп-ii
5)	Д + аз-А + .A + as......•
А) 1; 3; 4	В) 1; 2; 3
С) 2; 3; 5	D) 2; 4; 5
37
2010 yilning testlar. 117 varianti.
Matematika
32.	Muntazam to'rtburchakli piramidaning
balandligi 12 ga, asosining tomoni 10 ga
teng, Piramidaning apofemasini hisobiang.
A) 14	B)14,5 C) 15	D)13
33.	a ning qanday qiymatlarida a(3x - a) = 6x
- 4 tenglama bltta musbat yechimga ega?
A)	(-2; 2)
B)	(-2; »)
C)(-2;2)U(2;«)
D) (2; •»)
34.	cn = a'k""5(a > 0) sonlar ketma-ketliglning
umumiy hadi bo'lib, c2-ce= 16 bo'lsa, a
nimaga teng?
A) 2 B) 4 C) 5 D) 6
35.	Uchburchakli piramidaning asosidagi
barcha ikki yoqli burchaklar 30° ga teng. Agar
piramidaning balandligi 6 ga teng bo'lsa,
uning asosiga ichki chizilgan doiraning
radiusini toping.
A) 2^3	В)б7з	c>2	D>3
36.	(0,75)3 (““)*( ~)3,2-| ni hisobiang.
A)-2,75 B)-1,5	C)1,5	D)-2
VARIANT №117
1.	— va 4— sonlariga teskari sonlar
25	11
ko paytmasi nechaga teng?
•A)l 8)1	C)| D) 2
2.	Raqamlarining yig'indisiga bo'lganda,
bo'linmasi 4 ga va qoldig'i nolga teng
bo'ladigan ikki xonali sonlar nechta?
A) 2
B)3’
C) 4
D) 5
3. m ning qanday qiymatida
6x-m 7mx+1 .	,	.... .
—-— = —-— tenglamaning ildizi nolga
teng bo'ladi?
A)--	В)-— *C)-- D) —
2	3	3	2
,	_	б*,	•	. . . . . i
4. x + 6 = — tenglamaning nechta haqiqiy
ildizi bor?
A) 2’
B)1
C) ildizi yo'q
D) 3
65(x-8) t , .	.
5.	8 05 funksiyaning aniqlanish
sohasini toping.
A) (-»; 64) U (64; »)»
B)(-»;8)U(8; ->)
C) [0; 8)U(8;»)
D) [0; 64) U (64, «)
. 2kx+3 к-2 + х. ,	, .	.
6.	—-— = —-— tenglama к ning qanday
qiymatida yechimga ega emas?
•A)|	B)|	C)1 D) 1
7.	у = (6x - 13)ex funksiyaning hosilasini
toping.
A)	ex + x(6x-13)ex"1
B)	(6x-19)ex
C)	6ex
D)	(6x-7)ex
8.392 ni qanday songa bo'lganda bo'linma
17 va qoldiq 1 bo'ladi?
A) 23’ B) 21 C) 22 D) 19
9	.1 va 81 sonlari orasiga uchta musbat son
shunday qo'yilganki, natijada u sonlar
berilgan sonlar bilan birgalikda geometrik
progressiya hosil qilgan. Qo'yilgan soniarning
yig'indisini toping.
A)	36
B)	39»
C)	37
D)	43
10	. Trapetsiyaning o'rta chizig'i uzunligi 7 ga,
katta asosidagi burchakiari 30° va 60° ga
teng. Trapetsiyaning asoslari o'rtalarini
tutashtiruvchi kesmaning uzunligi 1 ga teng.
Trapetsiyaning kichik asosi uzunligini toping.
A) 4
B)7
C)6*
D) 5
40
2010 yilning testlar. 117 varianti.
Matematika
11.	Uchburchakli piramida asosining tomonlari
4,13 va 15 ga teng. Uning barcha yon
qirralari asos tekisligi bilan SO" burchak
tashkil qiladi. Piramidaning balandligini
toping.
'	6з£	D)g
24	' 16	8	16
12,	Tomonlarining uzunliklari-5, 6 va 9 ga teng
uchburchakning kichik balandligini toping.
A)l°£
I 20V2,
9
C) 4^2
0)2^2
13.	n ning qanday qiymatida a (n; -2; 4)
va b (n; 3n; 1,25) vektorlar perpendikuiyar
bo'ladi?
A) 6	B)3 C) 2	• D) 1; 5
14.	To'rtta sonning yig'indisi 182 ga teng
Ulardan dastlabki uchtasi 4, 5 va 10
sonlariga to'g'ri proporsional, ikkinchi va
to'rtinchi sonlar esa 7 va 5 sonlariga teskari
proporsional. Uchinchi sonni toping.
АУ80 B)60 C) 90	'D)70
w-	29
19.	Agar tg(— a) = — bo'lsa, tga ning
4	11
qiymatini toping.
A) — - B) —	Q-— *D)~—
20	9	9	' 20
20.	Tekislikka og'ma va perpendikular
tushirilgan. Og'ma va tekislik orasidagi
15
burchak arccos — ga, og'maning tekislikdagi
proyeksiyasi 30 ga teng. Perpendikulaming
uzunligini toping.
A) 16	B)30 C) 32 D) 23
21.	Vr + 2V6/	nj hisobiang
V5--У24
A) -3	* B) -1 C) -8 D) -7
22.	у = x2 - 2x - 2,75 dagi qanday nuqtada
o'tkazilgan urinma у = -4(x + 1) to'g'ri
chiziqqa parallel bo'ladi?
A)	(-1;4)
B)	(-1; 1)
C)	(1;4)
V 4 J
23. /2 + 2sin2x = 0 tenglamani yeching.
15. m ning qanday qiymatlarida у = cosx + rm
funksiya aniqlanish sohasida kamayadi?
A)(-«;-1]	B)(-«>;-1)
C)[-1;«)	D)(-1;«)
16. To'g'ri burchakli uchburchakka aylana
ichki chizilgan. Shu aylana urinish nuqtasida
uning katetlaridan birini to'g'ri burchak
uchidan boshlab hisoblaganda uzunliklan 3
va 5 bo'lgan kesmalarga ajratadi.
Uchburchakning yuzini hisobiang.
•A) 60 B) 48 C) 96 D) 120
17.2n2 - Зап - 4n + 6a ko'phadni
ko'paytuvchilarga ajrating.
•A)(n-2)(2n-3a) B) (5 - n) (3a + 2n)
C) (2 - 3a) (n - 5) D) (3a - n) (5 - 2n)
18. a = 25 + 2~* va b = 26 - 2^ bo'lsa, a2 - b2
- 2 nimaga teng?
’A) 2 В) 0	C)1	D)1
A)(-l)‘”- + ^,fceZ
8
B)(-1)‘M-+—,iteZ«
8 2
C) (-!)*•'—+—,fceZ
8	2
D) (-1)“'—+>*,*<= Z
2,6-0,21-1,8 . Г .....
24	71 70 П1П9 'Wmat'nl toping-
/,Z* /,o‘U,Zo
a>—	b)—	o—	d)-
16	12	24	'5
25.	x va z 72x - 2 7x-cos | + 1 = 0 tenglikni
qanoatlantirsa, Iz + 31х ning qiymatini toping.
A) 3 B) 27 C) 9 D) 1
41
2010 yilning testlar. 118 varianti.
Maternatika
26.	Agarm>0, n>0vam + n = 12-</2 bo'lsa,
mn ning eng katta qiymatini toping.
A) 64	B)66 C) 62	«D)72
27.	To'g'ri burchakli uchburchakning katetlari
5:6 kabi. nisbatda, gipotenuzasi esa 122 ga
teng. Gipotenuzaning balandlik kesib
ajratgan kesmalarini toping.
A)45va72	B)42va80
C) 50 va 72	D) 32 va 90
28.	Teng yonli ABC uchburchakning (AB =
AC) A uchidan uchburchak tekisligiga
uzunligi 32 ga teng bo'lgan AD
perpendikulyar o'tkazildi D nuqtadan BC
tomongacha bo'lgan masofa 40 ga teng. ABC
uchburchakning BC tomoniga o'tkazilgan
balandligi qanchaga teng?
A) 12	*B)24 C) 20 D) 14
.. (-X2 + x-'ilx2-3x+2). n .	.... .
29.	A—-л - —-----------S 0 tengsizlikmng
butun sonlardan iborat yechimlari nechta?
A) 1 B) 4	C)3	*D)2
30.	a = 4b va c + 6b = 0 (b t 0) bo'lsa, — ni
c
toping.
2,2	1	1
A)l£ ‘B)-4	0-1	D)-11
□	О	□
31.	Agar Iogo.s27 = a bo'lsa, log^ tfjs ning
qiymatini toping.
A)l+a',{	B)a2-1
C)3 + a’’	D) 1 + a-3
32.	x2 + y2 = 25 va (x - 8)2 + y2 = 25
aylanalarning umumiy vatarini o'z ichiga
olgan to'g'ri chiziq tenglamasini tuzing.
A) x = 4'
B)y = 3
С) у = x + 1
D) у = 3x - 4
__ 4+Vs^ 4 —,	,. .
33.	=-------7= ning qiymatini toping.
4-yS 4+V8
A)4^ B)Ati C)4| D)^l
4	5	8
34.	a(b + c - be) - b(c + a - ac) - c(b 4 a) ni
soddalashtiring.
A)-2bc r
B)2ac - 2bc
C) ab - ac
D) -2abc
35,1 - 2sin4x < cos24x tengsizlikni yeching.
A)f -+27tk-,-+2xk\neZ
4 2	2 J
В)^2^;1+^,пС2
C)f - + 2xk;- + 2xk\neZ
14	4 J
.. 0,28 0,23 0,9 ....
36. ——+ —-------— ifodamng qiymatini
0,84 0,03 0,05 a 4'
toping.
A)-10 B) 25	C)10	D)^
VARIANT №118
1.	(bn) (n 6 N) geometric progressiyada q = 2
va S+ = 3. b2 ni toping.
A) 0,8 B) 0,4	C)^	D)1^
2.	Doigaga ichki chizilgan muntazam
uchburchakning yuzi unda ichki chizilgan
kvadgatning yuzidan 18,5 ga kam. Shu
doiraga ichki chizilgan muntazam
oltiburchakning yuzini toping.
А)9л/з +6^2
В)	8 Уз+ 15
С)	27 + 24 7з
D)	13,5 + 12 Уз
3.	tg( — + а) = 3 bo'lsa, tga ning qiymatini
4
toping.
a4	b4 c>4 d4
42
2010 yilning testlar. 118 varianti.	Maternatika
	10.18'13-15-13+ 21'17-18-17+ 17-15-
4. tg(—- a) = — bo'lsa, tgq ning qiymatini toping. 4 b>1 C)3	r D)-—	15-14 ni hisoblang. A) 135 B) 125	0)180 D) 205 3 11. -5—songa teskari sonm toping. 4 A)-—	B)—	0)5—	D)-— 7 4	23	3	23 12. Agar a < -1 bo'lsa, quyida keltlrilgan ifodalardan qaysi birining qiymati eng katta bo'ladi?
5. To'g'ri burchakli uchburchakka kvadrat shunday ichki chizilganki, to'g'ri burchak uiar uchun umumiy. Kvadratning bir uchi gipotenuzaning o'rtasida yotadi. Agar gipotenuzaning uzunligi 24 ^2 ga teng bo'lsa, kvadratning perimetrini toping. A)	42 B)	32 C)	36 D)	48 6. a ning qanday qiymatlarida у = 9x2 - 12x - 35a parabola abssissalar o'qi bilan ikkita umumiy nugtaga ega bo'ladi? ..	4	m 18 A) a > —	B) a > — -	35	35	А) а"3 В) a’9 C) a7 D) a^ (x+3 = 0 13.	f , tenglamalar sistemasming [xy2 =12 yechimini toping. A)	(-3; -2) B)	(-3; 2) C)	(-3; -2), (-3; 2) D)	0 14.	Uchlari M(-3; 3; 1); N(3; -5; 1) va E(-4; - 1; -2) nuqtalarda bo’lgan uchburchakning MN tomoni va EF medianasi orasidagi burchakni toping. A)	60° B)	arccos 0,75 0)45° D) arccos 0,48
4	18 C)a>		D)a< — '	35	35 4	7 7. tg(arccos у arcsin —) ni hisoblang. А) — В) — C) — D) — II7	7 117	75	7 3	15. /(x) = -2sin -	+ -., f '(n) ni Vx 2 hisoblang. A)-1,5	B)^	0)2,5 D) 0,5
8.	)-(-32) + 0,5-(-8) ni hisoblang. A)	8 B)	4 C)6 D)7 9.	Uchburchakii piramida asosining tomonlari 9,12 va 15 gateng. Uning yon qirralari asos tekisligi bilan 60° burchak tashkil qiladi. Piramidaning balandligini toping. A) 1573 B)15£ C)^	D)5^ '4	' 2	4	' 2	16. (2,01 -3,81)-3,8 ifodani hisoblang. A) 5,82 B) 6,84	C)-5,82 D)-6,84 17. (x + 3)-(x - 2) < 0 tengsizlikni yeching. A)	(-«;-3) U (2;») B)	(-»; 2)u(3;») C)	(-3; 2) D)	(-»; —2)U(3;») 18. Boshlang'ich funksiyani topish uchun quyida keltiriigan formulalardan qaysilari to'g'ri? 1) f(x) = xp, p # -1 F(x) = pxp+1 + C;
43
2010 yilning testlar. 118 varianti.
Matematika
2)	f(x) =	, к # 0, kx + b > 0 F(x)
=-lln(kx + b) + C;
3)	f(x) = екиЬ, к # 0 F(x) =1 e кх*ь + C;
4)	f(x) = sin(kx + b), к # 0 F(x) = - — cos(kx +
b) + C;
5)	f(x) = e = + sin3x F(x) = -1 e * + 3cos3x + C.
A) 3; 4; 5	B) 2; 3; 5
C) 2; 3; 4	D)1;2;4
19. To'g'ri burchakli trapetsiyaning diagonal!
uni tomoni 20 ga teng bo'lgan teng tomonli
uchburchakka va to'g'ri burchakli
uchburchakka bo'ladi. Trapetsiyaning o'rta
chizig'ini toping.
A) 15 B) 18	C)10 D) 16
20. Quyidagi tasdiqiarnung qaysilari to'g'ri?
1) tomonlari a, b va c bo'lgan uchburchakka
ichki chizilgan aylananing radius! r
2S
= —-------formula bilan hisoblanadi;
a + b + c
2) radiusi R ga, markaziy burchagi a ga teng
-02
doiraviy sektorning yuzi S = a formula
bilan hisoblanadi; 3) tomonlari a va b ga, ular
orasidagi burchaklaridan biri a ga teng
bo'lgan parallelogrammning yuzi S = absina
formula bilan hisoblanadi; 4) diagonallari d,
va ds ga, ular orasidagi burchagi a ga teng
ixtiyoriy qavariq to'rtburchakning yuzi S =
did2sina formula bilan hisoblanadi;
5) o'xshash figuralar yuzlarining nisbati
ulaming mos chiziqli o'lchovlarining nisbatiga
teng.
A)1;2;3	B) 2; 3; 4
C)1; 2; 4	D)1;3;5
21.	Bir nechta natural sonming yig'indisi 85 ga
teng. Agar shu sonlaming har biridan 2 ni
ayirib, yig'indi hisoblansa, u 61 ga teng
bo'ladi. Yig'indida nechta son qatnashgan?
A) 7	B)5	C)8 D) 12
22.	(b - c)(b2 + be + c2) ifodaning b = Vs va c
= Vs bo'lgandagi qiymatini hisoblang.
A) 8	B)2	C)-8	D)-2
23.	m va n ning qanday qiymatlarida 2xm -
3ny = 12 va 3xm + 2ny = 44 to'g'ri chiziqlar
(2; 1) nuqtada kesishadi?
A) m - 8, n = 6	B) m = 6, n = 4
C)m = 12, n = 2	D)m = 4, n=10
24.	Agar /(x) = (2x -1 )(4x +1) bo'lsa, f ()
ni toping.
7	B)-4,5	C)1,5	D)4,5
A 12
25.	Agar m va n natural sonlar ^2 (n - 5) + n2
- 6mn + 17,5m = 0 tenglikni qanoatlantirsa, n
- m ni toping.
A) 6 B) 4 C) 2 D) 3
26.	Kichik diagonal! 12^3 bo'lgan muntazam
oltiburchakka tashqi chizilgan aylananing
radiusini toping.
A) 4^3 В)б7з c)12	D>14
27.	у = 3y[x-12cos(6x + 4)funksiyaning
boshlang'ich funksiyalaridan birlnl toping.
3
A)2x2 +2sin(6x + 4)
з
B)2x2 -sin(6x+4)
C)-4=-72sin(6x + 4)
2y/x
D)-^= + 72sin(6x+4)
2yx
28,1 dan 71 gacha bo'lgan toq sonlar
yig'indisi qanday raqam bilan tugaydi?
A)	4 B) 9 C) 0 D) 6
29.	x3 + 2X2 + 7 = 8x + 23 tenglamaning
ildizlari ko'paytmasini toping.
A)-4	B)16	C)-10	D)-20
30.	Agar bo'luvchi x - 8 ga, bo'linma x - 3 ga
va qoldiq -6 ga teng bo'lsa, bo'linuvchini
toping.
A^+llx + ie
B)	x2 + 11x-18
C)x2-11x+ 18
D^-Hx-W
44
2010 yilning testlar. 119 varianti.Matematika
31. Dastlabki beshta hadining yig'indisi -62
ga, dastlabki oltita hadining yig'indisi -126 ga
va maxraji 2 ga teng geometrik
progressiyaning birinchi hadini toping.
A)-T B)-3	C)-4	D)-2
32.fvx) = ^-,f(0)«?
1 — X	\ i л
A) 4 B) 2	C)3 D) 1
33.	a ning qanday qiymatlarida a(3x - a) = 6x
- 4 tenglama bitta musbat yechimga ega?
A) (-2; 2)	B) (-2; »)
C)(-2;2)U(2;«) D)(2;«)
34.	cos’ ~+sin2 tengsizlikni yeching.
A) — + ттп < x < — + тгп, n C Z
' 8	8
B) — + 2rrn < x <— + 2ттп, n 0 Z
8	8
C)—+2rm<x<—+ 2rm, nCZ
4	4
D) -— + 4 Tin < x < — + 4irn, n 0 Z
2	2
35.	у = lx2 - 4I + x2 - 2 funksiyaning qiymatlari
to'plamini toping.
A) [-2; •»)	B) [2; »)
C) [4; »)	D) (0; »)
36.	x2 + y2 - 5x - 6y + 4 = 0 aylaning abssissa
o'qidan ajratgan kesma uzunligini toping.
А)Тз B) 4	0)2^5 D) 3
VARIANT №119
2 cos2 —
1.--------2—ni soddalashtiring.
4	4
A) cosa B) -sina 0) i sina D) sina
2. x, va x2 x2 -17x+6 = 0 tenglamaning
ildizlari bo'lsa, x,x^ + xf xs ning qiymatini
toping.
A) -102
B)-32
0)102
D)77
3.	1
	* led i CM
2
> — tengsizlikning barcha butun
sonlardagi yechimlari yig'indisini toping.
'A) 53	B)33	0)48 D) 47
4.	ABC uchburchakda AB = 3, CB = 4 va
cosB = bo'lsa, AC ning qiymatini toping.
A)	6
B)	2
C)4
D) 3
5.160 dan katta bo'lmagan 7 ga karrali
barcha natural sonlaming yig'indisini toping.
A) 1617 B) 1470 0)1624 D) 1771
6.	Aylanaga yon tomoni 10 ga,
asosi ga teng bo'lgan teng yonli
uchburchak ichki chizilgan. Aylananing
radiusini toping.
A) 6,2
B) 7,2
C) 6,25
D) 6
7.	M,(1; 2), M2(3; 4), M3(-4; 3), M4(0; 5) va
Ms(5; -1) nuqtalardan qaysi birlari x2 + y2 =
25 tenglama bilan berilgan aylanada yotadi?
A) M2, M3, M4 B) Mi
C)M5	D)MbMs
8.	To'g'ri burchakli uchburchak katetlarining
gipotenuzadagi proyeksiyalari 2 va 8 ga teng.
Uchburchakning yuzini toping.
A) 40	B)16	0)10 D) 20
9.	m ning qanday
qiymatida (a2 + 2b2) tenglamaning ildizi nolga
teng bo'ladi?
A)(a2 + b2)
B)(a2-4b2)
0) a 1 b,ca = cb = ^,|a| = 3,jb| = 5
4
45
2010 yilning testlar. 119 varianti.
Matematika
10.	Tekislikka og'ma va perpendikular
tushirilgan. Og'ma va tekislik orasidagi
15
burchak arccos — ga, og'maning teklslikdagi
proyeksiyasi 30 ga teng. Perpendikularning
uzunligini toping.
A) 16	B)30 C) 32 D) 23
[(х-2)г +Ы =4
11,	Agar <	, , bo'lsa, x + у ning
yx-2|+|y| = 2
qiymatini toping.
A) 4 yokl 2 yoki 0	B) 0 yoki 3
C) 2 yoki 4	D) 0 yoki 4
12.8sin2	1 ni hisobiang.
13. Quyida keitirilgan tasdiqlardan qaysilari
noto'g'ri?
1)	arifmetik progressiyaning aylrmasi uchun d
= a" ~ 31 (n # 1) munosabat o'rinli;
n-1
2)	sin(a + p), sinacosp va sin(a - p) sonlar
arifmetik progressiyaning ketma-ket
keladigan hadlari bo'ladi;
3)	arifmetik progressiya dastlabki n ta
hadining yig'indisi
uchun S„ = 2a|~("~1)d  n formula o'rinli;
4)	cheksiz kamayuvchi geometrik
progressiyaning S yig'indisi S=-A- ga teng;
q-1
5)	geometrik progressiya dastlabki n ta
hadining yig'indisi S„ = (q # 1)
q-1
formula bilan hisoblanadi.
A)1; 3; 4
B)	1;4;5
C)	2; 4; 5
D)	2; 3; 5
0.04-2-1254 0,2'1 ... ..
14.------д~2&—:—nl hlsot)lang.
A)1 B)ll C) 0,5 D) 1,25
15.	Boshlang'ich funksiyani topish uchun
quyida keitirilgan formulalardan qaysilari
to'g'ri?
1)	f(x) = xp, p # -1 F(x) =— + C;
p+1
2)	f(x) =	, к £ 0, kx + b > 0 F(x) = kln(kx
+ b) + C;
3)	f(x) = el°ttb, к # 0 F(x) = 1 el“’b + C;
4)	f(x) = sin(kx + b), к # 0 F(x) = —1 cos(kx +
b) + C;
5)	f(x) = e ‘ + sin3x F(x) = A e “ + 3cos3x + C.
A)1;4;5	B) 1; 2; 3
C)1;3;5	D)1;3;4
16.	Muntazam uchburchakli piramida
asosining tomoni 6 ga va yon qirrasi 4 ga
teng. Piramida hajmini toping.
A>3	В)3-Л С)б7з D)9
17.22-43-98 + 16-27-38-19 yig'indining oxirgi
raqamini toping.
A) 6 B) 8 C) 2 D) 4
18. 7з - 2cos2x = 0 tenglamani yeching.
A)±—+ fflt,teZ
' 12
B)(-l)w-+—,teZ
6 2
С) ±— + як,ке Z
6
D)(-l)w^+—,keZ
12 2
19. AB(0; -3; -3) va BC(4; 9; 15) vektorlar
parallelogrammning qo'shni tomorilari. Uning
AC va BD diagonallari orasidagi burchakni
toping.
..	68	32
A) arccos—	B) arccos—
77	'77
C) arccos^	D) arccosf|
77	к ?7J
46
2010 yilning testlar. 119 varianti.	Matematika
20.	Quyidagi tasdiklarning qaysilari to'g'ri? 1)	konusning hajmi asosining yuzi bilan balandligi ko'paytmasining uchdan biriga teng; 2) ikkita o'xshash jism hajmlarining nisbati ularning mos chiziqli o'lchovlari Jkublarining nisbatiga teng; 3) silindrning hajmi asosining yu_zi bilan balandligi ko'paytmasining uchdan biriga; 4) shaming 4	Q hajmi—rr R ga teng; 5) shar sektorining hajmi it H2(R - y) ga teng (H - mos shar segmentining balandligi, R - shaming radiusi). A) 1; 4; 5	B)1,2; 4 C)1;2;3	D) 2; 3; 4 2x+1 21.	Nechta tub son 1 <—		 < 2 Эх-13 tengsizlikning yechimi bo'ladi? A) 4	B) 5	C) 1	D) 3 22.	nj soddalashtiring. 28-16V3 A)1	B)1 C)-j	D)2-V3	П2 -24 27.	ifoda natural son bo'ladigan n n ning barcha natural qiymatlari yig'indisini toping. A)54 B) 44 C)48 D) 50 .	(я I 31 . „	. 28.	Agar tg —+a =—bo Isa, tga ning (4	) 17 qiymatini toping. A) —	B)2_	c)-—	D)-— 29.	ABC uchburchakning В va C burchaklari bissektrisalari 128° burchak ostida kesishadi. A burchakning qiymatini toping. A) 104° B) 76° C) 72° D) 66° 30.	x3 - бх2 + 12 = Зх2 + 2x - 6 tenglamaning ildizlari yig'indisini toping. A) 6	B) 2	C) 9	D)-18 31.	^216-512+V32-243ni hisobiang. A) 45	B) 48	C) 49	D) 54 1	1 32.	4 - 3,3:(2 у - 1 —) ni hisobiang. A) 3,5 B) 2,5	C)-1,5	D)0,5 33./(x)=^±l,f(1) = ? Vx
23.	Detal 1:5 masshtabdagi chizmada 2,1 sm uzunlika ega. Shu detal 1:3 masshtabdagi chizmada qancha (sm) uzunlikka ega bo'ladi? A) 15	B)2^ C)i D)3,5 3	5 24.	x ning qanday qiymatlarida lx2 - 36I = 36 - x2 tenglik o'rinli bo'ladi? A) X 2 6	B) x s -6 C) x a -6	D) -6 < x s 6 25.	/-8 --2(x-2) ni Г+2Х+4	x-2 soddalashtiring. A) -2x	B) -4	C) 4	D) 0 26.	V1/3-1/9 + 1/27-1/81+... ni hisobiang. A) 0,3	B) 0,4	C) 0,5	D) 0,6	A)1	B) aniqlanmagan C)-l	D) 1 34.	-8 -6:(-2) - 2-(-11) ni hisobiang A) 17	B)-5 C) 55 D) 77 35.	(4x + 1)  (x -1) = 0 bo'lsa, 4x + 1 qanday 4	. qiymatlar qabul qilishi mumkin?	x A)faqatO	B)~lyokJ-1 C)faqat-1	D)0yoki2 4 36.	Unsakkizburchakning yuzi 4 ga, unga ichki chizilgan doiraning yuzi tt ga teng. Unsakkizburchakning perimetrini toping. A) 6	B) 9	C) 12 D) 8
47
2010 yilning testlar. 120 varianti.	Maternatika
VARIANT № 120	8. у va t 0,09 - 2 0,3 cos(2t) +1=0
2 1. ——	ni soddalashtiring. A) -2tg4a	B) cos4a C) -tg4a	D) tg4a 2. у va 10,09 - 2 0,3 -»* cos(2t) +1=0 tenglikni qanoatlantiradi. sin( )nl hisoblang. A)0	B)-2	C)|	D) 1	tenglikni qanoatlantiradi. sin(-~^ )ni hisoblang. A)0	B)-l O| 0)1 9. Quyidagi tasdiqlarning qaysilari to'g'ri?^ 1) ikkita o'xshash jism hajmlarining nisbati ularning mos chiziqli o'lchovlari kvadratlarining nisbatiga teng; 2) silindrning hajmi asosining yuzi bilan balandligi
3.8 va 18 sonlari eng kichik umumiy karralisining natural bo'luvchilarl nechta? A)	8 B)	12 C)6 D) 9 4. Tekislikka og'ma va perpendikular tushirilgan. Og'ma va tekislik orasidagi 3 burchak arccos- , og'maning tekislikdagi proyeksiyasi 24 ga teng. Perpendikuiarning uzunligini toping. A) 72	B)19|	0 32	D)16 5.412 ni 9 ga bo'lganda, qoldiq necha bo'ladi? A)	1 B)	2 C)4 D)7 6. Uchburchakli piramidaning asosi tomonlari 1 va 2 bo'lgan teng yonli uchburchakdan iborat. Uning barcha yon yoqlari asos tekisligi bilan bir xil a burchak tashkil qiladi. Piramidaning hajmini toping. A)^a	tga	.tga 4	8	10	6	ko'paytmasiga teng; 3) shaming hajmi— к R3 4 ga teng; 4) shar sektorining hajmi R2H ga teng (H - mos shar segmentining balandligi, R - shaming radiusi); 5) asosining radiusi R ga, balandligi h ga teng silindr yon sirtining yuzi 2 it Rh ga teng. A)	2; 4; 5 B)	2; 3; 4 01; 2; 4 D)1;2;5 10.	|3- x| < 4 tengsizlikning butun sonlardan iborat yechimlari nechta? A) 9	B) 4	C) 7	D) 8 11.	Uchburchakning a,b va c tomonlari orasida a2 = b2 + с2 - >/з be bog'lanish mavjud. Uzunligi a ga teng bo'lgan tomon qarshisidagi burchakni toping. A) 150°	B)30°	0 60° D) 135° 12.	Уу бекаси килоси 150 со'тдан уонд'ок сотиб олди. Уонд'окпар цобид'идан тогалангап, умумиу од'ирлигининг 60% и колди. Уу бекаси бир килограмм тогаланган усунд'ок усИун Hecha со'м сарфлаган? А) 190 В) 180 С) 220 D) 250
7. cosxcos2x = cos3x tenglama [0; 2тг] oraliqda nechta ildizga ega? A) 3 B)1 05 D) 2	13. Bir nechta natural sonning yig'indisi 75 да teng. Agar shu sonlarning har biridan 2 ni ayirib, yig'indi hisoblansa, u 63 ga teng bo’ladi. Yig'indida nechta son qatnashgan? A)	14 B)	6 05 D) 8
48
Maternatika
2010 yilning testlar. 120 varianti.
14.	Balandligi 16 ga, asosining radiusi 12 ga
teng bo'lgan konusga balandligi 10,4 gateng
bo'lgan silindr ichki chizilgan. Silindr
asosining radiusini toping.
A) 4,8 B) 5	C)4,5	D)4,2
15.	Uchburchakning tonionlari 7 va 11 ga,
uchinchi tomonining medianasi 6 ga teng.
Uchburchakning uchinchi tomonini toping.
A) 12 B) 14 C) 15 D) 16
16.	Qaysi javobda manfiy son ko'rsatilgan?
A) log, 2	B)27
5	'65
C)log,-~-	D)log21,2
7 v 45
3
17.	3- songa teskari sonni toping.
4
15	4	4	3
A) —	В)-—	C)—	D)-3-
' 4	' 15	15	4
18.	Ikki sonning ayirmasi 27 ga teng. Agar
birinchi sonni ikkinchisiga bo'lsak, bo'linma 4
ga va qoldiq, 3 ga teng chiqadi. Berilgan
sonlarning yig'indisini toping.
A) 38 B) 31 C) 43 D) 29
19.2sinx 2 i/з tengsizlikni yeching.
A)—+ 2ттп Sx <— + 2rrn, n 6 Z
4	4
В) — + 2ттп <x S — + 2ттп, n 6 Z
3	3
C) — + 2rrn < x S — + 2ттп, n G Z
’ 4	4
D)— tnnsxs — + тгп, nCZ
4	4
20.0'tmas burchagi 120° ga, asoslarining
uzunliklari 6 va 2 ga teng bo'lgan teng yonli
trapetsiyaning perimetrini toping.
A) 12	B)16 C) 18 D) 20
21.	ABCD to'rtburchak doiraga ichki
chizilgan. Z A = 120°, CB = 4 va CD = 5 BD
diagonal uzunligini toping.
A) 8	B) 20	c) ^20	D) V21
22.	(1,62 - 2,2'	):1,4 ni hisoblang.
A) 1,4	B) 1,2	C)1,5	D) 1,6
23.	a5 + a4 -2a3- 2a2 + a + 1 ni
ko'paytuvchilarga ajrating.
A)(a+1)2(a-1)3 В) (a +1)3(a-1)2
C) (a + 1)4(a-1)	D)(a+1)(a-1)4
DB = 3,6 sm
ABC uchburchakka ichki chizilgan aylananing
radiusi necha sm?
A)3 B) 2,5 C) 2 D) 2,4
25.	4J7I--8 + 3 VlO ni
V 2 2^3-710
soddalashtiring.
A) 10	B)2-3VlO
C)-10	D)3Tio-2
26.	Х1 va Xj x2 -14x+9 = 0 tenglamaning
ildizlari bo'lsa, x,xf + xf x, ning qiymatini
toping.
A) 126	B)-92	Q-126 D)-144
27.	Agara(-4; 2; 2) vab(T2 -,-4г ; 0)
vektorlar berilgan bo'lsa, 2 a va^-vektorlar
orasidagi burchakni toping.
3	2
A) — tt	B) arccos —
4	3
C)^	D) arccos I
28. a ning qanday qiymatida 9^2 tenglama
ildizga ega emas?
A) 1,8 B) 2 C) 2,2 D) 1
29. f(x) = -tg2x funksiyaning boshlang'ich
funksiyasini toping.
A)^tg3x + c
B)	tgx - x + c
C)	—x + ctgx + c
D)	x - tgx + c
49
2010 yilning testlar. 121 varianti.	Matematika
30.	(x+Qx 1) < q tgjjgsizuifHj yeching. A)(-2;1) B) (-~;-3)U[-2; 1] C)(-:-3]U(-2; 1] D) (->;-3] „ 0,22 - 2  0,06 + 0,32 . 31,		ning qiymatini 0,05 0,9-0,05 hisoblang. A)-0,2	B)-1 C) 0,2 D) 0,25 32.	к parametrning qanday .. (tor-3y = 6x qiymatlanda L	tenglamalar sistemasi yechimga ega emas? A) 2	B) 9	C) 6	D) 3 33.	Quyidagi tengliklardan qaysi biri ayniyat dpi * Iql)? 11	- Рг-<?г • o| Рг-<7г _ P2-?2 . V + Q2 q2-p2’J-,p2 + g2 PW It -- P£~P2  4\ _ P2-^ _ P2-?2 ' p2-q2 q2-ffV f-f? ff + q*' A) 3 B) Bular ichida ayniyat yo'q. C)1 D)4 34.	у = 5х - 5 funksiyaning grafigi koordinata tekisligining qaysi choraklarida yotadi? A)	I, III, IV B)	I, IV C) III, IV D) I, II	VARIANT № 121 1.	AB(-2; -1,5; -4,5) va BC(4; 7,5; 13,5) vektorlar parallelogrammning qo'shni tomonlari. Uning AC va BD diagonallari orasidagi burchakni toping. A) arccosyy	B) arccos^- ~ 76	™ 68 C) arccos—	D) arccos— 77	'77 2.	Muntazam uchburchakli piramida asosining tomoni 6 ga va yon qirrasi 4 ga teng. Piramida hajmini toping, A) 3 В)3-Уз С)б7з D)9 3.	у = 4 - ^2x + 5funksiyaninggrafigigax0 = 2 nuqtada o’tkazilgan urinma va koordinat o'qlari bilan chegaralangan uchburchakning yuzini toping. A)— 6 B) — ' 8 C)“ 4 D) — 3 4.	Agar kvadratning tomoni 5 marta qisqartirilsa, uning yuzi necha marta
35. f(x) = 0,5tg2x.	) ni hisoblang. 6 4	1 A)-	B)--	C)4	D)2	kamayadi? A) 5	B)10 C) 20 D) 25 , (9,126:0,65 + 0,46)  7,18 +1,45  28,2 . 3,452 - 0,552
36. Uchburchakning ikkita burchagi yig’indisi 70° ga teng. Shu burchaklarning bissektrisalari kesishishidan hosil bo'lgan burchaklardan kichigi necha gradusga teng? A)	50° B)	45° C)	40° D)	35°	hisoblang. A) 12,5 B) 12 C) 11,5 D) 13 6. Agar x2 + y2 = 281 va x - у = v'207 bo'lsa, xy qanchaga teng bo'ladi? A)-80	B)-160 C) 80 D) 40
50
2010 yilning testlar. 121 varianti._____
7.	(ax + 2y)(3x + Py) = yx2 + 6 ^-xy + y2
ayniyatdagi noma’lum koeffitsentlardan biri a
ni toping.
A) 4
B)~
2
C)3
D) —
2
8.	y/y'56+2^0  ^756-2V10 ni hisoblang.
A) 6 B) 2 C) 4 D) 3
9.	у = (2x - 6)lnx funksiyaning hosi Iasi ni
toping.
....	2x-3
A) 2lnx+-----
x
X
C)
X
«v-.	2x-3
D) 21n.x-----
x
10.	/(x) = x2 funksiyaning (3; 5) nuqtadan
o'tuvchl boshlang’ich funksiyasini toping.
A)y-7 B)y+7 C) 2x + 4 D)y-4
11.	Tekislikka og'ma va perpendikuiar
tushirilgan. Og'ma va tekislik orasidagi
40
burchak arccos— ga, og'maning tekislikdagi
41
proyeksiyasi 80 ga teng. Perpendikularning
uzunligini toping.
A) 36 B) 40	C)30	D)18
12.	7з + 2cos2x = 0 tenglamani yeching.
A)(-l)*4'^+—,keZ
6 2
B)±—
1 12
C) (-1)*—+—,ieZ
12 2
D)±-+®t,fceZ
6
 Matematika
13.	Quyidagi formulalardan qaysilari to'g'ri?
1)	sin(x - y) = sinx cosy - cosxsiny;
2)	tg(x - у) = ’Зх+,ЗУ xу , x-y +
1-fgx tgy	2
rm, n € Z;
. 2— 1 + cosx
3)	sin2 2 =—— I
X+ V	X —V
4)	sinx + siny = 2sin	COS 	;
5)	tgx + tgy = sin^t)/) x, у	nn, n 6
cosxcosy 2
Z.
A) 2; 4; 5	B) 1; 2; 5
C)1;3;4	D)1;3;5
14.	y= 26^~5-funksiyaning aniqlanish
5-x ’
sohasini toping.
A)	[0; 5)U(5; »)
B)	[0; 625)U (625; «)
C)(-»;5)U(5; “)
D) (-«; 625) U (625; «)
15.	^а-2а'1гЬ'1г + Ь- уг~^1г+^а ni
a - b
soddalashtiring (a > b).
A)-2b1'2	B) 2a1'2 - 2b1'2
C) 2b1'2	D) -2a1'2
16.	у = kx2 - 2kx + 5 va у = 2 - kx
funksiyalaming grafiklari к ning nechta butun
qiymatlarida kesishmaydi?
A) 2 B) 12	C)4 D) 11
17.	2x2 - 26x + 32 = 0 tenglama ildizlarining
o'rta proporsionalini toping.
A) S' B)4	C)6 D) 7
18.	Biror topshiriqni usta 20 kunda, shogird 30
kunda bajaradi. Ular birgalikda ishlasa, bu
topshiriqni necha kunda bajarishadi?
A) 10 B) 12 C) 14 D) 15
19.	Agarx2 + (~^)2= 8
4X2
bo’lsa,---ifodaning katta qiymatini toping.
x-1
A) 2	B)1	C)4	D)16
1
51
2010 yilning testlar. 121 varianti.	Matematika
20. Konusning o'q kesimi muntazam uchburchakdan, silindrniki esa kvadratdan iborat. Agar ularning hajmlari teng bo'lsa, to'la sirtlarining nisbati nimaga teng? A)V3:V2	B)42:j3 C) 1: ^3	D) 3:2 21. Uchburchakning tomonlari 4; 5 va 6 ga teng. 5 ga teng bo'lgan tomon qarshisidagi burchakning kosinusini toping. A) —	B)—	C)1	D)~ 16	'16	в	'&	28, 18n^ 162 ifoda natural son bo'ladigan n ning barcha natural qiymatlari nechta? A) 1	B) 3	C) 6	D) 2 29. Teng yonli trapetsiyaning kichik asosi 3 ga, perimetri 72 ga teng. Uning diagonali o'imas burchagini teng ikkiga bo'ladi. Trapetsiyaning o'rta chizig'ini toping. A) 8,5	B)13	C)7,5 D)T2
22.	Bir nechta natural soniarning yig'indisi 77 ga teng. Agar shu soniarning har biridan 4 ni ayirib yig'indi hisoblansa, у 53 ga teng bo'ladi. Yig'indida nechta natural son qatnashgan? A) 8	B) 24	C) 4	D) 12 23.	^2001 1997-1998-2000 +9 ni hisobiang. A)Vl3	B>2	C)V6	D)Vl7 24.	Markazi (2; 3) nuqtada joylashgan va radiusi 2 ga teng bo'lgan aylananing tenglamasini ko'rsating. A)	x2 + y2 - 4x - 6y = 0 B)	x2 + y2 - 6x - 4y + 6 = 0 C)	x2 + y2 - 4x - 6y + 9 = 0 D)	x2 + y2 - 6x - 4y + 10 = 0 1,6-0,7-1,8 .	,. 25. 14.72.03 n,n9 ^ymatmi toping. A) —	B)-L С)—	D)~ 5	' 24	'12	'3 26. a ning qanday qiymatida (a2 + 2)x = a(x - a) + 2 tenglamaning ildizlari cheksiz ko‘p bo'ladi? A)-^T2	B)T2 C)V2;-V2	D>0	a)2f b>S C)1l »>£ 31	.1 - 2cos2x > sin22x tengsizlikni yeching. A)f—+2як;—+21Л k€Z \ 3	3	J +	+	kez O^-i-nr/c^+ir/rl kez D)f—+як;—+хк\ kGZ 44	4 J 32.	Doiraga ichki chizilgan uchburchakning bir tomoni unIng diametriga teng. Doiraning yuzi 289 it ga, uchburchak tomonlaridan blrining uzunligi 30 ga teng. Shu uchburchakka ichki chizilgan doiraning yuzini toping. А) Збтг B)16tt C)20tt D) 64rr 33.	Ushbu 1234567891011 ...4950 sonning raqamlari yig'indisini toping. A) 320	B)310 C) 335 D) 330 9 34.	x2—ax+a = 0 tenglamaning ildizlardan 14 biri 2 ga teng. Uning ikkinchi ildizini toping. A) 7	B)6	C) 8	D)-7
.	f Jr	> 49, „ 27. Agar tg —+ a =— bo Isa, tga ning \4	) 31 qiymatini toping. A)—	B)-—	C)-— D) — 40	' 40	9	' 9	35. AB(0; 1; 3,5) va BC(2; 7; 12,5) vektorlar paralleiogrammning qo'shni tomonlari. Uning AC va BD diagonallari orasidagi burchakni toping. ..	46	98 A) arccos—	B) arccos— 7	99	'99 94	( 98 C) arccos—	D) arccod-—J
52
2010 yilning testlar. 122 varianti.
3d+ 2
36.-----= 2b tenglama 6 ning qanday
x-1,5
qiymatlarida manfiy yechimga ega bo'ladi?
A)	(-»; 0)
и	О
C)(-|;3)
VARIANT №122
1.	(b - c)(b2 + be + c2) ifodaning b = Vs va c
= bo'lgandagi qiymatini hisobiang.
A) 8 B) 2 C) -8 D) -2
2.	i, j va к - koordinata o'qlari bo'ylab
yo'nalgan blrlik vektorlar
va a = 5/ + ^2~j-3k bo'lsa, a vai vektorlar
orasidagi burchakning kosinusini toping.
4
B)|
c)i
3.	Tekislikka og'ma va perpendikular
tushirilgan. Og'ma va tekislik orasidagi
burchak arccos — ga, og'maning tekislikdagi
25
proyeksiyasi 14 gateng. Perpendikularning
uzunligini toping.
A) 14 B) 48 C) 28 D) 36
. .	3 . ,. 2sinor+sin2or .
4.	Agarcosa=---bo Isa,-------------ning
10 2sina-sin2or
qiymatini toping.
A) —
' 14
C) —
26
B)y
D) —
'13
_______________________Matematika
5.	x2 - x - 6 kvadrat uchhadni chiziqli
ko'paytuvchilarga ajrating.
A)(x + 3)(x-2)	B)(x-3)(x + 2)
C)(x + 3)(2-x) D)(x + 2)(3-x)
6.	4./Д--+ 8 + З-Ло ni
V 2 2V3-V10
soddalashtiring.
A) 10	B)2-3Tl0
С)-10	D)3i/io -2
7.	A + 2sin2x = 0 tenglamani yeching.
A)(-l)M^+^,*eZ
B)(-l)M^-+at,*eZ
0)(-l)w^y,^z
D)(_ir£+^,i6z
6	2
8.	/>9=’^’-’° = _L-tenglamani yeching.
A)1;9;A	B)1;9
C)1; —	D>9; —
' 81	' 81
9.	cosa =—, 0<a<— bo'lsa,
18	2
6cos—qanchaga teng bo'ladi?
A) 3 B) 5 C) 6 D) 4
10.	Isinx + 11 > 1,5 tengsizlik x ning (0; tt)
oraliqqa tegishli qanday qiymatlarida o'rinli
bo'ladi?
. ft 5x	q. t 5it
A) — <x< —	B) — < № —
' 6	6	6	6
m Tt	' -	2>r	It	2.T
C)-<x<— D) — <x< —
3	3	3	3
11.	A rap f (x) = (2x - -1 )(4x + -1) bo'lsa, f ()
ni toping.
A) 4,5	B)-1 C)-4,5 ’D)1,5
53
2010 yilning testlar. 122 varianti.	Maternatika
12.0'suvchi arifmetik progressiyaning dastlabki uchta hadining yig'indisi 24 ga teng. Shu progressiyaning ikkinchi hadini toping. A) 8	B) aniqlab bo'lmaydi C)10	D) 6 13. a = log9e112 bo'lsa, log72 ni a orqali ifodalang. A) — B)~ C) — D)~ 2a-l	a-4	2a-l	3-a	21. To'g'ri burchakli uchburchakning o'tkir burchaklari uchidan tushirilgan balandiiklari 7 va 24 ga teng. Shu uchburchakning yuzini toping. A) 84	B) 168 C) 56 D) 175 22. Agar kesmaning bir uchi A(1; -5; 4), o'rtasi C(4; -2; 3) nuqtada bo'lsa, ikkinchi uchining koordinatalari qanday bo'ladi? A) (7; -1; 2)	B) (6; 5; 3) C) (5; 4; 6)	D) (7; 1; 2)
Руц- 1 14. Nechta tub son 1 < ——- < 2 3x-13 tengsizlikning yechimi bo'ladi? A) 4	B) 5	C)1	D) 3 15. a =	, b = i/sF vac=^/sj sonlarni o'sish tartiblda joylashtiring. A)a<c<b	B) b < c < a	23. у = 4 - V4x+1 funksiyaning grafigiga x0 = 2 nuqtada o'tkazilgan urinma va koordinat o'qlari bilan chegaralangan uchburchakning yuzini toping. A) — 16 B) — ' 6
C) c < a < b	0) c < b < a 16, (ax + 2y)(3x + ₽y) = ух2 + б|- xy + y2 ayniyatdagi noma’lum koeffitsentlardan biri у ni toping. A) 7	B) 2	C) 5	D) 4 17.	Hajmi 8^3 ga teng bo'lgan muntazam tetraedrning balandligini toping. A)	4 B)	2^3 C)3 D) 4 18.	Arifmetik progressiyada a4 - a2 = 4 va a? = 14. Shu progressiyaning to'rtinchi hadini toping. A) 7	B)6	C) 12 D) 10 19.	Va = Vc - Vb bo'lsa, (a + b - c)3 ni toping. A)-27abc	B)-81abc Cj-SlaW	D)-27abc2 20.	Quyidagi ketma-ketliklardan qaysilari geometrik progressiyani tashkil etmaydi? 1) an = 2x", (x t0); 2) cn = ax", (ax # 0); 3)	-sin60' + 1. A) 3	B)1;3 C) 2	D) 1	C) — 12 D) — 8 24.	Katetlaridan biri 8-V2 ga teng bo'lgan to'g'ri burchakli uchburchak gipotenuzasining ikkinchi katetiga nisbati 5:3 ga teng. Uchburchakning yuzini toping. A) 20	B)48 C) 12 D) 24 25.	Muntazam to'rtburchakli piramidaning balandligi 8 ga, asosining tomoni 12 gateng. Piramida yon yog'iga parallel bo'lib, asosining markazi orqali o'tgan kesimi yuzini hisoblang. A) 72 B) 50 C)45 D) 30 26.	- 2,4 + 3-1 - (-2,6) ifodaning qiymatini toping. A)-10,6 B) 12,5 C)3^ D) -12,5 27.434 sonini 13 va 18 ga teskari proporsional sonlarga ajrating. A)192va242	B)224va210 C)150va284	D)252va182
54
2010 yilning testlar. 123 varianti.	Maternatika
28. Agar F'(x) = x - 4 va F(-2) = 0 bo'lsa, F(x) funksiyani aniqlang. A)	F(x) = 2x2 -4x B)	F(x)=-1x2-2x + 2 C)	F(x) = x2 -2x D) F(x)=^x2-4x-10	36.f(x) =log^ (x- 1) + V2-xfunksiyaning aniqianish sohasini toping. A)[1;2] B)(1;2) C)[1;2) D) (1; 2] VARIANT № 123 1. —-	— ni soddalashtiring. cos(2rr - (!)
29.	Teng yonli trapetsiyaning diagonal! 16 ч/з ga teng va u asosi bilan 30° li burchak tashkil etadi. Trapetsiyaning o'rta chizig'i nechaga teng? A) 12	B) 16	C) 20	D) 24 30.	Geometrik progressiyada uchinchi va yettinchi hadlarning ko'paytmasi 144 gateng. Uning beshinchi hadini toping A) 6	B)±12	D)-12 31.	m ning qanday qiymatida x(x + 4a)(x + b)(x + 4a + b) + m2 ifoda tola kvadrat bo'ladi? A) a2b2 B)±— C)+2ab D) To'g'ri javob keltirilmagan 32.	/(x) = -2x2 + 18x2 + 12 funksiya o'sadigan kesmaning uzunligini aniqlang. A) 4	B) 5	C) 4,5 D) 6 33,	a ning qanday qiymatida x2 - (a - 3)x + 18 = 0 tenglamaning ildizlarga biri 6 ga teng bo'ladi? A)-12 B) 12	C)-6 D) 6 34.	Uchburchakning tomonlari 4; 5 va 6 ga teng. 5 ga teng bo'lgan tomon qarshisidagi burchakning kosinusini toping. A) —	B)— C) —	D) — '16	46	18	'8	' cos ft	cos/? D)_^_ sin/?	sin/? 2.	Teng yonli uchburchakning asosidagi burchagi 40° ga teng. Bu uchburchakning yon tomonlari orasidagi burchakka qo'shni bo'lgan tashqi burchagining qiymatini toping. A) 90°	B)100" C) 140° D) 80° 3.	Katetlarining nisbati 2:3 kabi bo'lgan to'g'ri burchakli uchburchakning gipotenuzasii/l82 gateng. Uchburchakning yuzini toping. A)	24 B)	42 C)	36 D)	39 4.	f(x) = 1/9-x2 + lg(x -1) - 7x funksiyaning aniqianish sohasini toping. A)(0;«) B)(0;3] C) (0; 9] D)(1;3J 5.	(1 + cosx)tg у + 1 = 0 tenglamani yeching. A)-—+ 2ттк, к € Z B) tt + 2ттк, к C Z С) тгк, к £ Z D) it + тгк, к 6 Z
35. Uchburchakni ikkita burchagi yig'indisining kosinusi — ga teng. Uchinchi burchagining 4 kosinusini toping. A)_l B)1	C)|	D)-|	6. Quyidagi ketma-ketliklardan qaysilari geometrik progressiyani tashkil etmaydi? 1) a„ = | -2n; 2) a„ = 3-2'n; 3) bn = f- + 1 • A)	1; 2 B)	1; 3 C)1 D) 13
55
2010 yilning testlar. 123 varianti.
Matematika
7. Qaysi nuqtada у = x2 + 2x - 8 funksiyaning
grafigiga o'tkazilgan urinma у + 2x - 8 = 0
to'g'ri chiziqqa parallel bo'ladi?
A)(2; 8)
B)	[-2; 8)
C)(2;-8)
D) (-2;-8)
8. у = x2 + bx + 4 parabola b ning nechta
butun qiymatida abssissalar o'qiga urinadi?
A) Q .	B)1 C) 2 D) 3
.	0,13	0,02	0,7 ..
9.---------+ —:-------!— hisoblang.
0,00013 0,0005 0,0014
A)	540
B)	580
C)	620
D)1400
10	.16 - (2c - 1 )2 ni ko'paytuvchilarga
ajrating.
A) (3 - 2c) (5 - 2c)	B) (3 + 2c) (5 - 2c)
C) (2c - 3) (2c - 5)	D) (3 - 2c) (5 + 2c)
11	.15 va 35 sonlarining eng kichik umumiy
karralisi bilan eng katta umumiy
bo'luvchisining yig'indisini toping.
A) 112	B)114	C)108 D) 109
12.	ABC uchburchakda Z A = 30°, AB = 4з ,
AC = 6. A uchidan tushirilgan balandlikning
uzunligini toping.
A)|V?	B)|V7 C)^	D)£V7
13.	Agar /(x) = (3 + — )(11 + 4x) bo'lsa,
x
/(-•i) ni toping.
A)-3 B) 9	C)-5 D) 15
14.	f	- 2 ni hisoblang.
{42-J3 V2 + V3J
A) 18 B) 15 C) 12 D) 16
15.	Agarrgl— -«]=-— bo'lsa, ctga ning
<4	) li
qiymatini toping.
А)-— В) —	С)—	D)-—
’ 35	35	' 24	' 24
16.	To'rttaa sonning yig'indisi 118 ga teng.
Agar birinchi va ikkinchi sonning nisbati 2:3
kabi, ikkinchi va uchinchi sonning nisbati 3:5
kabi va uchinchi ya to'rtinchi sonning nisbati
5:6 kabi bo'lsa, birinchi va to'rtinchi sonning
yig'indisini toping.
A) 62	B)60	C)59 D) 66
17.	ДАВС da Z В = 90°, Z C = 60°. BB,
balandlik 2 ga teng. AB ni toping.
A) 4 B) 2	02^3	0)242
18.	Rasmda MN II AC. MBN uchburchakning
perimetri 42 sm. ABC uchburchakning
perimetri 84 sm. MBN uchburchakning yuzi
44 sm2. ABC uchburchakning yuzini (sm2)
toping.
A) 108 B) 99 C) 81 D) 176
19.	Muntazam to'trburchakli piramida
asosining tomoni 6 -Уз ga va apofemasi 6 ga
teng. Piramida hajmini toning.
A) 54 B) 108	C)162 D) 324
20.	Muntazam to'rtburchakli piramidaning
balandligi 8 ga, asosining tomoni 12 ga teng.
Piramida yon yog'iga parallel bo’lib, asosining
markazi orqali o'tgan kesimi yuzini hisoblang.
A) 72 B) 50 C) 45 D) 30
21.	n ning qanday qiymatida a (n; -2; 4)
va b (n; 3n; 1,25) vektorlar perpendikulyar
bo'ladi?
A) 6	B)3	C)2	D)1;5
22.	Teklslikka og'ma va perpendikulyar
tushirilgan. Og'ma va tekislik orasidagi
3
burchak arccos —ga, og’maning tekislikdagi
5
proyeksiyasi 18gateng. Perpendikulyarning
uzunligini toping.
A) 12	B)^	C)24 Ov
d	Э
56
2010 yilning testlar. 124 varianti.
23	.26-25 - 25-24 + 24 23 - 23-22 - 19-5 ning
qiymatini toping.
A) 54	B)0 C) 106 D) 8
24.	-4,8:lal = -0,5 tengiikni qanoatlantiruvchi
a ning barcha kiymatlarini tbping.
A) 9,6 va -9,6	B) 0
C) 2,4	D) 9,6
25.	(--+—+—)(y2 - ЗМ + 2) = 0 tenglamaning
6 3 2
manfiy ildizlari nechta?
A) 1 B) 2	C)3 D) 4
26.	Radius! R ga teng aylanaga ichki chizilgan
muntazam oltiburchakning tomonini toping.
A) R B)^ C)j3R D)V2f?
hisoblang.
A) 33 B) 32,97 C) 31 D) 32
28. Quyidagi ketma-ketliklardan qaysilari
geometrik progressiyani tashkil etadi?
1) a„ = 2x"; 2) Cn = ax” +1; 3) bn =
( —)n-sin60°.
5
A)1;3	B) 2; 3
C)hechbiri	D) 1; 2; 3
29. Arifmetik progressiyaning dastlabki 6 ta
hadlari 7, a2, a3, ад, a5 va 22 bo'lsa, a2 + a3 +
ад + a8 ni hisoblang.
A) 65 B) 60 C) 82 D) 58
/n
30.sinx-osx <—tengsizlikni yeching.
4
A) — + ттк < x < — + тгк, к С 2
'4	4
В)-—+ ттк <x <—+ пк, к С 2
'	8	8
С)- + ттк<хй — + пк, к€2
’ 8	8
D) —+ ттк<х< —+ тгк, кС2
8	8
31.	Kvadratning tomonini necha marta
kamaytirganda yuzi 4 marta kamayadi?
A) 5	B)2,5	C)3 D) 2
 Matematika
32.	Sinfdagi 35 ta o'quvchidan 28 tasi suzish
seksiyasiga, 14 tasi voleybol seksiyasiga
qatnashadi. Agar har bir o'quvchi, hech
bo'lmaganda, bitta seksiyaga qatnashsa,
ikkala seksiyaga qatnashadigan o'quvchilar
necha foizni tashkil etadi?
A) 20 B) 18 C)25 D)15
33.	x3(1 + (1 — x) + (1 -x)2 + (1 — x)3 + ...) =
17xz4 -1 (1 < x < 2) tenglamani yeching.
A) 0,5 B) 0,4 C) 0,25 D) 0,45
34,	f(x) = x + 1 + ctg2x funksiyaning
boshlang'ich funksiyasini toping.
B) x2 + ctgx + C
A)£--tgx + C
C)y-ctgx + C D)y + tgx + C
35.4y(5x - y) - (5x - 2)(5x + 2) + 2 ning eng
katta qiymatini topina.
A) 5 B) 6 C) 2 D) 4
36. x, у - raqamlar; xy va8y esa ikki xonali
sonlar. Agar xy6 = 8y bo'lsa, x + 1,75y ning
qiymati qanchaga teng bo'ladi?
A) 6 B) 5 C) 9 D) 8
VARIANT №124
1. a = log75l 35 bo'lsa. Iog53 ni a orqali
ifodalang.
A)	—
2zi-l
a-2
C)^
a-3
0)1^.
a-2
2.4x2 - 16x s -7 tengsizlikning butun
sonlardan iborat yechimlari yig'indisini toping.
A) 4
B)	3
C)6
D)5
3. Qadimiy masala. Meshdagi suv Anvarning
o'ziga 20 kunga, ukasiga esa 60 kunga yetadi.
Meshdagi suv ikkalaslga necha kunga yetadi?
A) 15	B)14	0)12 D) 16
57
2010 yilning testlar. 124 varianti.
Maternatika
4. X +	= 2	?
[x+y = 3,
A)1
B)3
C)4
D) 2
5,y=Vsin25x.y’(^-) = ?
D) 0
6.1 - 2cos2x = 0 tenglamani yeching.
A)(_l)‘Z.+^.ieZ B)(-l)‘f+^-,tgZ
12 2	о 2
C)+^+fflt,fceZ	D)+-+M,ieZ
12	6
7. 2--Г-т-з']-1-/-т-б'| ni
3 1.7 J 3 (.5 J
soddalashtiring.
A) 4	B)m-2 C)3 D)m + 3 * * * * * * 9 10
X2 -3xy
-9y! + №
kasrni qisqartiring.
x
x-3y
У
x + 3y
x
x+3y
D)
x
x+3y
9. f (x) = x3 funksiyaning (2; 3) nuqtadan
o'tuvchi boshlang’ich funksiyasini toping.
№	Y4	Y4	Y4
A)2L+1 B)A--1 C)±-+3 d>4--3
2	4	2	2
10. To'g'ri burchakli uchburchakning
balandligi gipotenuzani 3 va 12 ga teng
kesmalarga ajratadi. Shu balandlikni toping.
A) 12 B) 4 C) 6 D) бТз
11. Muntazam to'rtburchakli piramidaning
balandligi 24 ga, asosining tomoni 14 ga
teng. lining apofemasini toping.
A) 25 B) 28 C) 18 D) 32
12. Daryo oqimi bo'yicha motorli qayiqda 28
km va oqimga qarshi 25 km o'tildi. Bunda
butun o'tilgan yo'lga sarflangan vaqt turg'un
suvda 54 km ni o'tish uchun ketgan vaqtga
teng. Agar daryo oqimining tezligi 2 km/soat
bo'lsa, motorli qayiqning turg'un suvdagi
teziigini toping.
A) 10 B) 12	. C) 8	D)11
13.
-4—
15
4,25:0,85 + 0,5
(5,56-4,06) :3
ni
hisoblang.
A) 10,5 B) 12	C)13,5 D) 16
14.	Agar r,?|y—oj = y-bo'lsa, tga ning
qiymatini toping.
A)---	В)-—	C)— Di-
li 1 7	12	7
1	30
15.	x+------ = — tenglamaning natural
У+- 13
sonlardagi yechimida z nimaga teng?
A) 3 B) 4 C) 7 D) 2
If
16.	у = yy (k < 0) funksiyaning grafigi qaysi
choraklar orqali o'tadi?
A) il, III, IV	B) 1, II va IV
С) I valll	D) I, II valll
17.	Teng yonli trapetsiyaning kichik asosi 3
ga, perimetri 66 gateng. lining diagonali
o'tmas burchagini teng ikkiga bo'ladi.
Trapetsiyaning o'rta chizig'ini toping.
A) 12	B)10 C) 8	D)7,5
18.	--y------V- ning boshlang'ich funksiyasini
cos2| — + ll
14 )
toping.
A)4^+l]+C B)lfg^ + lj + C
C)-4t^ + lj+C D)-lfgf-J + l] + C
58
2010 yilning testlar. 124 varianti.	Maternatika
3 19. з-songa teskari sonni toping. 4 A)-3—	В)—	C)-—	D) — ’ 4	15	IS	4	28. cos + cos ~ + y- ni hisoblang. A)0	B)1	C)1	D)^-
20. T,72;V3;vaV4 sonlarni o'sish tartibida joylashtiring. A) 1;T2 = 74;Тз	B) tV3;V2;V4 C) V3 ;T2 = V4 ;1	D) 72 = V?; 7з ;1	29. Har bir ichki burchagi 150° bo'lgan qavariq ko'pburchagining nechta tomoni bor? A) 5	B)7	C) 10 D) 12 30. Koordinat tekisligida x2 + y2 < 4lyl tengsizlik bilan berilgan shaklning yuzini
21.	n(n C N) ning 8'l'5^+4n |<asr butun son bo'ladigan barcha qiymatlarini toping. A) 1;2	B) 1 C)1;2;4	D) 2 22.	a = logo,28; b = log42; c = log0,90,6; d = 1одз0,8 va I = log0,92 sonlardan qaysilari musbat? A) a, d va I	B) b va c С) a, c va d	D) c va d 23.	Teng yonli trapetsiyaning yon tomoni 41 ga, balandligi 40 ga va o'rta chizig'i 51 ga teng. Trapetsiyaning katta asosini toping. A) 55 B) 65 C) 50 D) 60 24.	Tekislikka tushirilgan og'ma va perpendikulyar orasidagi burchakarcsin— gateng. Og’maning 25 uzunligi 75 ga teng. Perpendikulyarning uzunligini toping. A) 21	B)36	C)72 D) 31— 25.413 + 413 + 413 + 413 yig'indining yarmini hisoblang. A) 224 B) 225	C)8-4’2 D)448 26.Tomonining uzunligi 30 + 15-Уз да teng muntazam uchburchakka ichki chizilgan kvadratning yuzini toping. A)1350 B) 1012 C) 506,25 D) 675 27. Vi 1 + 63/2 - ^и-бз/г ni hisobiang. A) 22	B)6	ОЗ3/2 D)Ve	toping. А) 4п В)6,5п C)12tt D)8n 31.1 - 2sin4x < cos24x tengsizlikni yeching. A)(ii;£ + ^), kOZ M 2 4 2 ' B)( —+ 2я7с;— +27rfc),.kez 8	8 C)(rrk;^+rrk),keZ D)(-- + ar/r;- + 2ffk), kGZ 4	4 32.	Arifmetik progressiyaning barcha hadiari natural sonlardan iborat. Agar a4 = 3 va 20 < a3 < 22 bo'lsa, progressiyaning ayirmasini toping. A) 8	B)10	C)7	D) 9 33.	Geometrik progressiya uchun quyidagi formulalardan qaysilari noto'g'ri? 1)b„ = blqn-1;2)b2 = bn-1-bn+2; A) 1	8)1; 3	C)3	D)2 34.	Uchburchakning tomonlari 7 va 11 ga uchinchi tomoniga tushirilgan medianasi 6 ga teng. Uchburchakning uchinchi tomonini toping. A) 12 B) 8	C)14 D) 10 35.	xi va X2 x2 + 2x - 12 = 0 tenglamaning ildizlari bo'lsa, xf + ning qiymatini toping. A)	12 B)	10 C)	28 D)	11
59
Matematika
2010 yilning testlar. 125 varianti.
36. Agar kvadratning perimetmi 10% ga
kamaytirilsa, uning yuzi necha foizga
kamayadi?
A)	10
B)	11
C)16	,
D) 19
VARIANT № 125
1.	Agar log4a - log2b = 0 va a2 - 2b2 - 8 = 0
bo’lsa, 2ab ko'paytma nechaga teng?
A) 16	B)10 C) 8 D) 12
12^-3,75-4—4,125
2.	—---------------ni hisobiang.
A) 0,5
B) 1,5
C) 0,6
D) 0,3
3.	к ning qanday
qiymatlarida ^’-k-25>x+2’5-12’5 = °'sist
[2x + y+k = 0
emsning birorta ham yechimi bo'lmaydi?
A) 3 B)-5	C)-2	D)6
4.	Uchburchak tomonlarining uzunliklari a; b
va c a2 = b2 + c2 + t/3 be tenglikni
qanotlantiradi. Uzunligi a ga teng tomon
qarshisidagi burchakni toping.
A)	125°
B)	120°
C)	135°
D)	150°
, 0,215-1,6-0215 ...
5. —--------—-y— ni hisobiang.
3,45-3—
25
A) 4,3 B) 0,45	C)-0,43 DM,2
soddalashtiring.
A)-7a -Va
B) a + Va
O-2Va
D) 0
7.	/(x) = у x3 - 5lnx funksiyaning grafigiga x0
= 2 nuqtada o'tkaziigan urinmaning burchak
koeffitsiyentini toping.
A) 3 B) 3,5	01,5 D) 2
8.	^|x-3| + 1 >2|jc—3|—1 tengsizlikni yeching.
А)(0;Я)
B)P;^]
И 4 J
О (1;1,5)
D>(H)
9.	^9 + 2-720 + ^9-2-^20 ning qiymatini
toping.
A) 3	B)1	0 4	D)2
10.	cos3x + 4cosx > 0 tengsizlikni yeching.
А) (-л + 2як;2як),к e Z
В) (2як-,л+2лк),ке2
О [у+2^k',~+2лк jfc e 2
D)^-y+2at;y+2^jteZ
11.	Ikkita kvadrat yuzlarining nisbati 25:9 kabi
Birinchi kvadratning tomoni ikkinchi
kvadratning tomonidan 10 birlik uzun. Kichik
kvadrat tomonining uzunligini toping.
A) 25 B) 15	016 D) 12
12.	Arifmetik progressiyaning birinchi va
to'rtinchi hadi yig'indisi 26 ga teng, ikkinchi
hadi esa beshinchi hadidan 6 ga ko'p. Shu
progressiyaning uchinchi va beshinchi hadi
yig'indisini toping.
A) 20 B) 21 О 22 D) 23
13.	Ja-Za^ + b—?~--v +4y[b ni
а'2-Ь7г
soddalashtiring (a > 6).
A)	-2b1'2
B)	2a1'2 - 2b1'2
02b1'2
D) -2a1'2
60
2010 yilning testlar. 125 varianti.	Matematika
14. Qirrasi 12 gateng bo'lgan kub yoqlarining markazlari tutashtirildi. Hosil bo'lgan jismning hajmini toping. A) 144 B) 288	C)216 D) 169 .. .	9	2sina+sin2r/ . 15. Agar cos a =	bo Isa,	ning 82	2 sin a -sin 2a qiymatini toping. A) —	b)—	C)— D) — 182	73	91	146	22. Quyida keitirilgan tengliklardan qaysilari ayniyat? 1)	(x + a)(x - b) = x2 - (a - b)x - ab; 2)	12X2 + jr - (8X2 -5y2 - (-1 Ox2 + (5x2 - 6y2)))=-x2+12y2; 3)	6ab + (2a3 + b3 - (3ab2 - (a3 + 2ab2 - b3))) = За3 - ab2 + 6ab; 4)	5a2 - 3b2 - ((a2 - 2ab - b2) - (5a2 - 2ab - b2)) = 9a2-3b , 5)	3a - (2c - (6a - (c - b) + c + (a + 8b) -
16.	Agar f(x) = (3 + — )(11 + 4x) bo'lsa, f (- ) ni toping. A) 15 B) 1	C) 9	D)-5 17.	Muntazam to'rtburchakli piramidaning balandligi 12 ga, asosining tomoni 10 ga teng, Piramidaning apofemasini hisobiang. A) 14	B) 14,5 C) 15 D) 13 18.	Barcha hadlari musbat bo'lgan geometrik progressiyaning birinchi had! 2 ga, beshinchi hadi 18 ga teng. Shu progressiyaning beshinchi va uchinchi hadlari ayirmasini toping. A) 10 B) 12 C) 8	D)11 19.	Teng yonli uchburchakning uchidagi burchagi 40°ga teng. Asosidagi burchakning bissektrisasi va shu burchakka qarama- qarshi tomon orasidagi burchakni toping. A)	60° B)	75° C)	85° D)	65° 20.	Agar a va b ixtiyoriy natural sonlar bo'lsa, u holda 2a + 8b ifoda quyidagi soniarning qaysi biriga qoldiqsiz bo'linadi? A) 2	B)3	C)4	D) 12 21.	Agar у = F(x) funksiya у = f(x) funksiya uchun boshlang'ich funksiya bo'lsa, у = f(-2x) funksiyaning boshlang'ich funksiyasini toping. A)y = -lF(-2x) В) у = 2F(-2x) С) у = -2F(-2x) D)y = F(-2x)	6c)) = 10a + 9b-8c. A)	1; 2; 4 B)	3; 4; 5 C)	2; 4; 5 D)	1; 2; 3 2/	\3 Д a 23.	4	sina -? ' 16	16 24. (2a- 1)(2a+ 1) + 3b(3b- 4a) ning eng kichik qiymatini toping A) —1	B)0	C)-2	D)1 x+2 1-x2	1	x_. . 1-х 1+x2 (x-1)2 1-X2 soddalashtiring. д)Л±1	C)1	D)-L 1-x	1-x	x-1 26.0'suvchi geometrik progressiyaning birinchi hadi 3 ga, yettinchi va to'rtinchi hadlarining ayirmasi 168 ga teng. Shu progressiyaning maxrajini toping. A) 3	B)|	C)^	D)2 27, AB(-1; -2; -1) va BC(3; 10; 17) vektorlar parallelogrammning qo'shni tomoniari. Uning AC va BD diagonallari orasidagi burchakni toping. Z qc>	94 A) arccos		B) arccos— \ 99j	99 _.	98	...	46 C) arccos—	D) arccos— 99	99
61
2010 yilning testlar. 126 varianti.
Matematika
28. Ushbu 1234567891011.. .4950 sonning
raqamlari yig'indisini toping.
A) 320	B)310 C) 335	D)315
29. Tekislikka tushirilgan og'ma va
perpendikulyar orasidagi burchak
5
arcsin — ga teng. Og'maning uzunligi 39 ga
teng. Perpendikulyarning uzunligini toping.
A) 72
C) 36
a
D) 27 —
’	13
30. Tomonlari 1,2, 3, 4 bo'lgan to'rtburchakka
ichki va tashqi aylana chizilgan. Uning
kichkina diagonalini toping.
31.(a + b-2)(a + b)-(a-b)2 + 1 ni
ko'paytuvchilarga ajrating.
A) (2a + 1)(2b + 1) B)(2a-1)(2b-1)
C) (a + 1)(2b-1) D)2b(a + 1)
32. Umumiy hadi an = — 2 (n C N) bo'lgan
3л+ 1
ketma ketlikning nechta hadi (1,7; 2,2)
oraliqqa kirmaydi?
A) 8	B)10 C) 4 D) 6
33.2x + 6y - 12 = 0 to'g'ri chiziq va
koordinata o'qlari bilan chegaralangan
uchburchakning yuzini toping.
A) 2 B) 1 C) 3 D) 6
34.1 + 2sin2x = 0 tenglamani yeching.
A)(-l)w—+— ,keZ
'	12 2
В)
C) (-1)“-+—,keZ
3 2
D) (-1)‘+1—+як,ке Z
3
35./(x) = sin2x + 2cosx
funksiyaning^;^ kesmadagi eng kichik
qiymatini toping.
A) 0
B)-2
С)-1,5л/з
D)-3
36. (x + 6)(x + 4)(x + 2)x ko'paytmaning eng
kichik qiymatini toping.
A) 9	B)-25	C)-16	D)-9
VARIANT № 126
ЛАВ(-2; -1,5; -4,5) vaBC(4; 7,5; 13,5)
vektorlar parallelogrammning qo'shni
tomonlari. Uning AC va BD diagonallari
orasidagi burchakni toping.
32	f 7/Л
A) arccos—	B) arccos -—
77	\ 77 J
76	68
C) arccos—	D) arccos—
77	77
2.	Agar 0 < q < p < к bo'lsa, Ip + ql + Ik - ql -
Ik - pl ni soddalashtiring.
A) 2p + 2q - 2k	B) 2p
C) 2p + 2k	D) 2q
3.	Tomonlarining uzunliklari 6, 7 va 11 ga
teng uchburchakning kichik burchagini
toping.
A) arccos - — I	B) arccos—
67	67
C) arccos—	D) arccos—
'	154	'	77
4.	(y2 - 1 )2 - (y2 -1 )(y4 + y2 +1) + у ni
soddalashtirgandan keyin nechta haddan
iborat bo'ladi?
A) 5 B) 4 C) 3 D) 6
5.	Qaysi javobda sin(-790)°,cos600° va
tg475° laming ishoralari, yozilish tartiblda
berilgan?
A)-,-,+
B) +, +
О -
D)-,-,-
62
2010 yilning testlar. 126 varianti.	Matematika
6.	To'g'ri burchakli uchburchakning kateti 7 ga, uning gipotenuzaga proyeksiyasi 1,96 ga teng. Ikkinchi katetning uzunligini toping. A) 12	B)16 C) 24	D)15 , fx2+y!-xy = 1, -	„ 7.	1 J 1	= ? [x+y = -2. A)-1 B)1 C)-3 D)2 8.	Muntazam to'rtburchakli piramidaning yon qirrasi 6 ^2 ga, yon qirra va asos tekisligi orasidagi burchak 45° ga teng. Piramidaning hajmini toping. A) 144 B) 96^2 C) 192 D) 72 9.2sin43°cosl 7° + 2sin232° - 1 ni hisoblang. 4 C)1. D) 10. ABC uchburchakning A burchagi 45° ga, BC tomoni 3 v'2 ga teng. Shu uchburchakka tashqi chizilgan aylananing radiusini toping. A)	2 B)	1 C)	6 0)3	13.	/(x) = 1 - 3cos2x - kcos2x funksiya к ning qanday qiymatida o'zgarmas bo'ladi? A)-2	B)-3	CJ-1.5 D)-1 14.	Uchburchakda medianalar kvadratlarining yig'indisini tomonlari kvadratlari yig'indisiga nisbati nechaga teng? A)(-°°;0) B)(-;3) C)1	D)| 15.	sin6x - 4sin2x < 0 tengsizlikni yeching. A)f--+at,—+A],keZ V 4	4 J В) I|,fce Z A 2	) C)f-+<— + лк \,keZ 14	4	) D) [xk^+xk^keZ 16.	Ikkinchi hadi 6 ga teng, birinchi uchta hadining yig'indisi 26 ga teng o'suvchi geometrik progressiyaning uchinchi va birinchi hadlari ayirmasini toping. A) 15	B)16 C) 14	D)13 17.	Iog,<2log2x2 = log4x2 tenglamaning yechimlari ko'paytmasini aniqlang. A>1	C)’i D|5 18.	у = Inx funksiyaning grafigiga abssissasi Xo = 1 bo'lgan nuqtada urinma o'tkazilgan. Urinmaning abssissasi 14 ga teng nuqtasi ordinatasini toping. A) 13 B) 12 C) 15 D) 14
...	f л 1	41 , „	. 11. Agar tg —+a = bo’lsa, ctga ning \ 4 J 19 qiymatini toping. A) — B) —	C)-— Ob- it	30	11	30	19. Agar bo'luvchi x - 2 ga, bo'linma x -1 ga, qoldiq 4 ga teng bo'lsa, bo'linuvchi nimaga teng? A))? + x-1	B)x2-6 C) x2 - 3x + 6	D) x2 - 5 20. Ikki sonning ayirmasi 5 ga teng. Agar shu
12. Konusining o'q kesimi teng tomonli uchburchakdan, silindrniki esa kvadratdan iborat. Agar ulaming tola sirtlari tengdosh bo'lsa, hajmlarining nisbatini toping. A) 1:3	B) 2:3 С)72:7з	D)1:T2	sonlardan kattasining 20% i kichigining -A qismiga teng bo'lsa, shu sonlami toping. A) 36 va 41	B) 30 va 35 C) 63 va 68	D) 45 va 50
63
2010 yilning testlar. 126 varianti.	Matematika
21. Agar 2*+1 = 4y va x + у = -4 bo'lsa,6y - x ni toping. A) 2	B)-1,5	C)4	D)-3 22. JL- kasrning maxrajini irratsionallikdan qutqaring. . гТз-Зл/г+Тзо 12 гУз + з-Уг-Узо B)	12 зУ2-2Уз + у30 12 D) зУг-гУз-Узо 12	28.	x2 + y2 + 4x - 6y - 3 = 0 tenglama bilan berilgan aylananing markazini toping. A)	(-2; 3) B)	(2;-3) C)	(4;-3) D)	(-4; 6) 29.	^гУгУг ni hisobiang. А) Уз2 В) УТб С) У8 D) Уб4 30.0,8 ga teskari bo'lgan songa qarama- qarshi sonni toping. A)-0,8 B) 1,25	C)-1,25 D) -1,2 31. Muntazam yigirmaburchakning yuzi 16 ga, unga ichki chizilgan doiraning yuzi 4tt ga teng. Yigirmaburchakning perimetrini toping.
23.	Quyidagi ketma-ketlikiardan qaysilari geometrik progressiyani tashkil etmaydi? 1)	an=|-2"; 2) a„ = 3'24’; 3) bn= -j + 1. A)1;2	B)1,3	C)1	D) 13 24.	a =	, b = V®3 va с = (Уз)г sonlarni o'sish tartibida joylashtiring. A)	a < b < c В)	a < c < b С) c < b < a D) c < a < b	A) 12 B) 16 C) 18 D) 20 32.	(x2 — x — 1 jfx2 — x — 7) S-5 tengsizlikning eng katta butun va eng kichik butun ildizlari ayirmasini toping. A) 4	B) 6	C) 2	D) 5 33.	у = 4x2 + 4x + 1 va у = 2x + 1 funxsiyalar grafikiari kesishish nuxtalarining koordinatalarining yig'indisini toping. A)-0,5 B) 1	C)0,5	D)1,5 fj-f’+flf’ 34.	343 y	.— nj hisobiang. V187l44
A —^B ( 0 J C	A) —	B)-	• С)-	D)- '16	2	7	3 35. tg1°-tg20-. ..tg88°-tg89’ ni hisobiang
25.	' OA = AB, Z ABC -? A) 120° B) 150° C)140° D) 135° — 4y — 5 26.	4—r-2— ni qisqartiring. У -i А)2г5	C)-^	D)2±l y+1	y-1	y-1	' y-1	A) 0 B)- 2 C)1 D) hisoblab bo'lmaydi 36. у = (2x - 4)tgx funksiyaning hosilasini toping. • \0	2.Г-4	„	2x—4 A) 2tgx +	—	B) 2tgx -	— sm x	sm x
27. a = У2,b = Уз va с = Уэ sonlarni o'sish tartibida joylashtiring. A) a < b < с	В) c < b < a С) a < c < b	D) b < a < c	C)2tgx+^-	D)2tgx-^- COS X	COS X
64
Matematika
2010 yilning testlar. 127 varianti.
VARIANT № 127	„ C0Sa-2sin3a-C0S5a ., .	. 8. 	ifodani
1.	(x - 2)x(x - 3)(x + 1) = 40 tenglama haqiqiy ildizlarining yig'indisini toping. A) 2	B) 5	C)-4	D)-1 2.	[1; 3] oraliqdagi maxraji 3 ga teng bo'lgan barcha qisqarmaydigan kasrlarning yig'indisini toping. B) 8 C)8i D) 9 3.	Muntazam yigirmaburchakning yuzi 16 ga, unga ichki chizilgan doiraning yuzi 4tt ga teng. Yigirmaburchakning perimetrini toping. A) 12 B) 16 C) 18 D) 20 4.	210 + 312 yig'indining oxirgi raqamini toping. A) 9 B)5 C)1 D) 4 5.1 - 2cos2x > sin22x tengsizlikni yeching. A)(-+iTk; — + nk), kGZ 4	4 B)(-- + 2nk;| + 2TTk),keZ C) (i+TTkin + nk), kGZ D) + ттк; —+ nk), kCZ 2	2	sin5a-2cos3a-sina soddalashtiring. A) tg3a B) 2	C) 1	D) ctga 9.	Nolga teng bo'lmagan x, y, z sonlar ko'rsatilgan tartibda ishorasi o'zgaruvchi geometrik progressiyani, x + у; у + z; z + x sonlar esa arifmetik progressiyani tashkil etadl. Geometrik progressiyaning maxrajini toping. A)-2 B)-1 Q-3 D)-4 10.	x + у = ^2+7з7 ;ху=1.х5у + х/-? A) 51	В) 18 С) 47 D) 29 11.	Bir son ikkinchi sondan 6 ta ortiq. Ularning o'rta arifmetigi 23 ga teng. Shu sonlardan kattasini toping. A) 27	B)23 C) 26 D) 33 12.	ДАВС da Z В = 90°, Z C = 60°. BB, balandlik 3 ga teng. AB ni toping. A) 12	B)6	С)бТ2 О)б7з 13.	Agar bo'luvchi x - 2 ga, bo'linma x-1 ga, qoldiq 4 ga teng bo'lsa, bo'linuvchi nimaga teng? A)x2 + x-1	B)x2-6 C)x2-3x + 6	D)x2-5 14.	ABCD trapetsiyaning o'rta chizig'i uni o'rta chiziqlari 13 va 17 bo'lgan ikkita trapetsiyaga ajratadl. ABCD trapetsiyaning katta asosini
6. Ildizlari 4 +77 va 4 -77 bo'lgan, kvadrat tenglama tuzing. A) x2 + 8x + 9 = 0 B) x2 + 9x - 8 = 0 C)x2-8x + 9 = 0 D)x2 + 8x-9 = 0 7.4cos22x - 2,5 = cos4x.tenglamani yeching. A)±^+T’nez B)|+^,nez cjj+^.nez 71	71П	-> d -+—,nez ' 6 2	toping. A) 19 B) 21	C) 18 D) 30 15. Teng yonli uchburchakning yon tomoniga tushirilgan balandligi bilan ikkinchi yon tomoni orasidagi burchak 20 ga teng. Teng yonli uchburchakning asosidagi burchagini toping. A) 50° B) 48° C) 55° D) 58° 16. Agar rd — - a I=—bo’lsa, tga ning к 4 J 11 qiymatini toping. A)-—	B)-—	C)— D) — 1 24	1 35	' 35	' 24
65
2010 yilning testlar. 127 varianti.	Maternatika
1 + m4 m2 + 1.	.. . .... 17.	(m —-	) ni soddalashtinng. ПГ -1 /77—1 A)	—	B) — m + 1	1-/77 C) m -1	D) 1 18.	Agar geometrik progressiyaning dastlabki 4 ta hadiga mos ravishda 1; 1; 4 va 13 sonlarini qo'shsak, uiar arifmetik progressiyani tashkil etadi. Geometrik progressiyaning maxrajini toping. A) 3	B) 4	C) 2	D) -3 19.	Bir nechta natural sonlarning yig'indisi 60 ga teng. Agar shu sonlarning har biriga 2 ni qo'shib yig'indi hisoblansa, u 78 ga teng bo'ladi. Yig'indida nechta son qatnashgan? A) 9	B) 18 C) 5	D) 16 20.	/(x) = x - — funksiyaning (6; 2) nuqtadan o'tuvchi boshlang'ich funksiyasini toping. у2	у3	Y2	Y3 A) — -— + 20	B)—+ —-56 2	6	2	6 y2	y.3	y2	j.3 C)2L-2L+18	D) — - — -18 2	6	'26	24.	/(x) =-2L_ x2 + 1 funksiyaning grafigiga Xo = -— nuqtada o'tkaziigan urinmaning OX o'qi 3 bilan tashkil qilgan burchagini toping. A) 60°	B)30°	0)150° D) 120° 25.	Uchburchakli piramida asosining tomonlari 11,13 va 20 ga teng. Lining barcha yon qirralari asos tekisligi bilan 60° burchak tashkil qiladi. Piramidaning balandligini toping. A)“A B)^	0^ D)^ 6	12	18	'12 26.	Agar x < у < z bo'lsa, lx - yl - Iz - yl - Iz - xl ni soddalashtiring. A) 2z - 2y	B) 2y - 2z C) 2x	D) 2y 27.	m ning qanday qiymatida x(x + a)(x + 4b)(x + a + 4b) + 100m2 ifoda tola kvadrat bo'ladi? A) — 100 B) Bunday qiymat mavjud emas. 0 To'g'ri javob keltirilmagan.
„ [4(x-3)-3<8x+1 21. j	, tengsizhklar |2+x(x+3)<(x+2)2+5 sistemasini yeching. A) (-4; «)	B) 0 C) (4; 7]	D) [-7; -4) 22. Tekislikka tushirilgan og'maning uzunligi 75 ga, uning tekislikdagi proyeksiyasi esa 72 ga teng. Og'ma va tekislik orasidagi burchakni toping. 7	24 A) arcsin—	B) arcsin— 25	25 7	12 C) arctg—	D) arccos—	D)±T 28.	Uchburchakli muntazam piramida asosining tomoni 24 ga teng. Yon yog'i asos tekisligi bilan 30° li burchak hosil qiladi. Piramidaning balandligini toping. A) 12 B) 4	C)6	D) 8 29.	Tomoning uzunligi 16 + 8>/з ga eng muntazam uchburchakka ichki chizilgan kvadratning yuzini toping. A) 384 B)192 C) 288 D) 144 30.	x2 + у2 - 4x - 6y - 3 = 0 tenglama bilan berilgan aylananing radiusini toping.
23. a ning qanday qiymatida faqat bitta (x; y)  xx... [x + y = a,	,	... juftlik |	tenglamalar sistemasini qanoatlantiradi? A)|i“ B)-1;1 C)-3; 3 D)-3	A) 3	B) 5	C)6	D) 4,2 31. Son o'qida 4,2 sondan masofasi 17 dan oshmaydigan songacha bo'lgan oraliqda nechta butun son mavjud? A) 21	B) 35 C) 32 D) 34
66
2010 yilning testlar. 128 varianti.	Maternatika
32. |x -14| log2(x - 4) = 3(14 - x) tenglama ildizlarining yig'indisini toping. A) 26	B)42 C) 24	D)30-l 8	2) f(x) =	— ,k#0, kx + b>0 F(x) = kln(kx + b) + C; 3) f(x) = екх+ь, к * 0 F(x) = 1 ekx+b + C;
33. Agar/(x) = (2x + 3)(^-3) bo'lsa, /(-1) ni toping. A) 6	В) 0	C) -3 D) -6 34 V^24+V8T + Vi92+3V-375 nj V- 375 hisoblang. A)--®1 ' 125 B) 2 C)-1 D)-“ ' 125 35.	+	г оtengslzlikning №-7x+12 butun sonlardan iborat yechimlari nechta? A) 1	B) 4	C) 3	D) 2 36, Olti haddan iborat geometrik progressiyaning dastlabki uchta hadining yig'indisi 168 ga, keyingi uchtasiniki esa 21 _ ga teng. Shu progressiyaning birinchi hadini toping. A)	96 B)	86 C) 126 D) — ' 2	4) f(x) = sin(kx + b), k# 0 F(x) = —1 cos(kx + b) + C; 5) f(x) = e2* - cos — F(x) =—e2x - 3sin -jj- + C. 3	2	3 A)	1; 3; 5 B)	3; 4; 5 C)	1; 3; 4 D)	2; 3; 4 3.	< x - 4 tengsizlikni yeching. x+4 A) (-4; 4)	B)(—;-4) C) 0	D) (0; 4) 4.	Ushbu 31323334...7980 sonning raqamlari yig'indisini toping. A) 460 B) 453 C) 473 D) 480 5.	(x2 + x+1/r>+3x+4)<otengslzlikning x2 + 5x+6 butun sonlardan iborat yechimlari nechta? A)	4 B)	5 C)	2 D)	3 6. Berilgan to'rtta sonning har biriga 3 ni qo'shib, so'ngra ularning har birini 2 ga ko'paytirib chikach, hosil bo'lgan sonlar yig'indisi 62 ga teng bo'ldi. Berilgan sonlar yig'indisi nechaga teng?
VARIANT № 128	A) 23 B) 20 C) 18 D) 21
1. Paroxod daryo oqimi bo'ylab 48 km va oqimga qarshi shuncha masofani 5 soatda bosib o'tdi. Agar daryo oqimining tezligi soatiga 4 km bo'lsa, paroxodning turg'un suvdagi tezligini toping. A) 12 ' B) 16 C) 20 D) 24 2. Boshlang'ich funksiyani topish uchun quyida keltirilgan formulalardan qaysilari to'g'ri? l)f(x) = x₽, p^-1 F(x) = pxp+1 + C;	7. Agar kamayuvchini 26 ta va ayriluvchini 12 ta orttirilsa, ayirma qanday o'zgaradi? A)	14taortadi B)	4 ta kamayadi C)	4 ta ortadi D)	28 ta kamayadi 8. (0,2-0,05 - 0,05);0,125 + 0,96 ni hisoblang. A) -2,45 B) 0,64 C) 0,43 D) 3,95
67
2010 yilning testlar. 128 varianti.
Matematika
9.	1 - 2cos2x > sin22x tengsizlikni yeching.
A)f-+2rr/r,—+2жЛ kCZ
лз 3 J
B)^+’rk;ir+ irkj, kCZ
C)|--+^;-+'»lrl kCZ
4 2	2 J
D)f- + ^;—+ xk\ kCZ
4 4	4 J
X	X	X	X	X x	-
10.	1--H----+----F —— H-—’ = 6
3	15	35	63	99	143
tenglamani yeching.
A) 13 B) 26	C)16 D) 18
12	1
11.--;=+-=—f=---------=-4ning
2+V3 75-73 2 + 75
qiymatini toping.
А)75-7з
В) 2
С) 4
d) Vs + Vs"
12.	Qaysi nuqtada у = x2 + 2x - 8
funksiyaning grafigiga o'tkazilgan urinrna у +
2x - 8 = 0 to'g'ri chiziqqa parallel bo'ladi?
A) (2; 8)	B) [-2; 8)
C) (2; -8)	D) (-2; -8)
13.	Yig'indisi 15 ga teng bo'lgan uchta son
arifmetik progressiyaning dastlabki uchta
hadidir. Agar shu sonlarga mos ravishda 1; 3
va 9 sonlari qo'shilsa,hosil bo'lgan sonlar
o'suvchi geometrik progressiyaning ketma-
ket hadlari bo'ladi. Geometrik
progressiyaning dastlabki 6 ta hadi
yig'indisini toping.
A)248 B)250 C)252 D) 254
It.	и
AB = 6 sm,
AD = 4 sm,
DC = 3 sm,
BC-?
A) 4 B) 4,5	t)5 D) 5,5
15. к ning qanday qiymatida yi =-x va у г
5
21
= kx--funksiyalarning grafiklari o'zaro
5
parallel bo'ladi?
A) —	B) —
5	21
C)D)—-
'	' 41
16,(0,75)3^-|V|^ -41 ni hisoblang.
A)-1,75 В) 1,5	C)-2	D)-2,75
17. Ilog3xl - log3x - 3 < 0 tengsizlikni yeching.
A) (1; «)
BH^M)
C)(0;1)
18. (3z - x)3 + (x - 2y)3 - (3z - 2y)3 ko'phadni
ko'paytuvchilarga ajrating.
A)	3(3z - x)(x - 2y)(3z - 2y)
B)	To'g'ri javob keltirilmagan.
C)-3(3z-2y)(3z-x)(x-2y)
D) Ko'paytuvchilarga ajralmaydi.
.jg 3sina + 2
3
---------r —--------ifodaning eng katta
5 +cosy? tgy + ctg1?
qiymatini toping.
A) 4,75 B) 6,25 C) 2,75 D) 3,45
20, Quyidagi tenglamalardan qaysi biri ildizga
ega emas?
A)	10x2-12x + 4 = 0
B)	6x2-11x + 3 = 0
C)	18x2 + 24x + 8 = 0
D)x2 + x- 6 = 0
21. Tekislikka tushirilgan Og'ma va
12
perpendikular orasidagi burchak arcsin — ga
teng. Og'maning Io uzunligi 26 ga teng.
Perpendikularning uzunligini toping.
A)10— B) 12 C) 10 D) 20
6
68
2010 yilning testlar. 128 varianti.	Matematika
22. ^3 + 2^2 ^17-1272 ni hisoblang. A) 2 B)1 D)2^	4) diagonaliari d, va d2 ga, ular orasidagi burchagi a ga teng ixtiyoriy qavariq to'rtburchakning yuzi S = did2sina formula bilan hisoblanadi; 5) o'xshash figuralar yuzlarining nisbati ularning mos chiziqli o'lchovlari kvadratlarining nisbatiga teng. A)1;3;4	B) 3; 4; 5 C)1;3;5	D)1;2;5 27. Tomonining uzunligi ga teng muntazam
(jr A	29 23. Agar tg —+a = — bo'lsa, ctga ning 1^4	)	11 qiymatini toping. A)±	B)_^ C)_± D)2£ '20	' 9	20	9	uchburchakka ichki chizilgan kvadratning yuzini toping. A) 294	B) 147 C)220,5	D) 110,25 28. Quyidagi mulohazalaming qaysi biri natural sonlarga nisbatan noto'g'ri?
24. m ning qanday ., [x-y=m-1 .	,	. qiymatlanda-l у 3/n 4tenglamalar sistemasining yechimi koordinat tekisligining I choragiga tegishli bo'ladi? A)	(2; «о) B)	») C)(|;2)	A)	Oxirgi raqami 0 yoki 4 bo'lgan son 4 ga. bo'linadi. B)	Faqat o'ziga va birga bo'lingan son tub son bo'ladi. C) Berilgan sonlarga bo'linadigan sonlaming eng kichigi bu sonlaming eng kichik karralisi bo'ladi. D) Oxirgi raqami 0 yoki 5 bo'lgan son 5 ga bo'linadi. 29,0^'^.0.2-1nlhisoblang. 4-25°	a
25. у ning qanday qiymatlarida —j-- kasrning qiymati (-1; —) oraliqqa tegishli? A)(-bl) B) To'g'ri javob keltirilmagan. C)(-1; 2) D)(0; 2) 26. Quyidagi tasdlqlarning 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, rnarkaziy burchagi a ga teng doiraviy sektoming yuzi S _p2 =	a formula bilan hisoblanadi; 3) tomoni 180 a ga, burchaklaridan biri a ga teng rombning yuzi S = a2sina formula bilan hisoblanadi;	A)i	B)ll C) 0,5	D) 1,25 30. To'rtburchakii muntazam piramida asosining tomoni 2 marta kattalashtirildl, balandligi esa 2 marta kichiklashtirildi. Hosil bo'lgan piramida hajmining dastlabki piramida hajmiga nisbatini toping. A) 4:1 B) 1:2	C)1:1	D)2:1 31. V2 + 2cos2x = 0 tenglamani yeching. k) (“D —+—,AeZ 8 2 B) ±—+ nk,kz Z 8 C) ±—+лк,ке Z 8 D)(-l)‘** —+—.keZ 8	2
69
2010 yilning testlar. 129 varianti.	Maternatika
32.	A(-4; 1; 1), B(1; 4; 0), C(1; -2; 2) va D(-5; -5; 3) nuqtalar berilgan. AC va BD vektorlar orasidagi burchakni toping. A) 60° B) 90° C) 45° D) 30° 33.	Ikki xonali son o'zmmg raqamlari yig'indisidan 4 marta katta. Raqamlari kvadratlarining yig'indisi 80 ga teng. Shu ikki xonali sonning kvadratini hisoblang. A) 196 B) 7056 C)169 D) 2304 34.	ABC uchburchakda Z A = 30°, AB = 7з , AC = 4. A uchidan tushirilgan balandlik uzunligini toping. A)yV21 B)|V21 OyVJT D)yV21	3. a > 0; b < 0; lai # Ibl. Quyidagi ifodalardan qaysi birining qiymati musbat bo'lmasligi mumkin? A)a-b B) la + bl C) a3b2 D)lai - Ibl 4. Agar a C N bo'lsa, quyidagi ifodalardan qaysi birining qiymati har doim butun son bo'ladi? A)^ B)^l О-Ц^
X2 35. /(x) = -x + — funksiyaning (6; 2) nuqtadan o'tuvchi boshlang'ich funksiyasini toping. A)-£+—-18	B)-—+—-16 2	6	2	6 №	Y^	Y& C)-f + f + 18	D)-^ + ^- + 16 Z	0	d	О	5 p) fa"+a/a + 2) 6 5. -—- ]L. ni soddalashtiring. aVa-Va А) 2a"2 B) 2a 1 C) a’’ D) a'3
1	1 36. Agar P =—X-—y-(x + 2u) vaQ =-1х+-1у-(х + 5и) bo'lsa, PQ ni toping. A) 4y	B)2y	C)^y D)-4y	6./(x)=^L,f'(2)-? A)-1 B)-2 C) 2 0)1 7. (a + b)(a + b + 1)- (a-b)(a-b-1) ni ko'paytuvchilarga ajrating.
VARIANT №129 1. Tekislikka og'ma va perpendikular tushirilgan. Og'maning tekislikdagi proyeksiyasi 12 ga, perpendikulaming uzunligi 35 ga teng. Og'ma va perpendikular orasidagi burchakni toping. ..	 12	24 A) arcsin —	B) arccos — 37	37 C) arctg y|	D) arcsin Ц-	A)	4a(b +1) B)	2(a + b)(6 + 1) C)2a(2b+ 1) D) 2a(b- 1) 8. A(12; 20) aylanadagi nuqta, C(5; -4) nuqta aylananing markazi bo'lsa, aylananing radiusini toping. A) 15 B) 16 C) 17 D) 25 9.12 va 312 sonlarning umumiy bo'Iuvchilari nechta? A) 4
2. Agar tga = --bo'lsa, 2cosig~sln2? n| 2	2sin2ct-sin2a	B) 2 C)6
hisoblang. A)1	B)2	C)-4 D)-l	D) 3
70
2010 yilning testlar. 129 varianti,
Maternatika
10.	Muntazam to'rtburchakli piramidaning
balandligi 24 sm, apofdmasi esa 26 sm.
Piramida asosining perimetrini loping.
A) 48 B) 40 C) 80 D) 96
№
11.	/(x) = -x+— funksiyaning (6; 2)
nuqtadan o'tuvchi boshiang'ich funksiyasini
toping.
A)- —+-—18
2	6
C)--+—+18
2	6
-—16
6
B)-2
D)“V+T+16
2	6
12.	Agartgl—+al = ~— bolsa, ctga ning
qiymatini toping.
A)-^	B)-£ C)3i D)35
24	35	35	24
13.	Agar a (1; -1; 3) vab(4; 3; 0) bo'lsa, a
ning qanday
qiymatida 4a + ab vektor b- a vektorga
perpendikular bo'ladi?
A)2,1	B)1	C)|	D)-±
14.	7 + 5^2 + ^-7~TS’n' soddalashtiring.
A) 2	B) -1
C) 2^2+1	D)-2
+
15.	Цт^п! qisqartiring.
y^-x2'’
A)x^+y^ B)^A
16.	Katetlaridan biri 4 ^2 ga teng bo'lgan
to'g'ri burchakli uchburchak gipotenuzasining
ikkinchi katetiga nisbati 5:3 gateng.
Uchburchakning yuzini toping.
A) 20 B) 48 C) 12 D) 24
17.	Trapetsiya asoslarining uzunliklari 28 va
12 ga teng. Trapetsiya diagonallari o'rtalarini
tutashtiruvchl kesmaning uzunligini aniqlang.
A) 8	B)10	C)6	D)9
18.	Nolga teng bo'lmagan x, y, z sonlar
ko'rsatilgan tartibda ishorasi o'zgaruvchi
geometrik progressiyani, x + у; у + z; z + x
sonlar esa arifmetik progressiyani tashkil
etadi. Geometrik progressiyaning maxrajini
toping.
A)-2
B)-1
C)-3
DM
19.	Uchburchakning tomonlari 11 va 23 ga,
uchinchi tomoniga tushirilgan medianasi 10
ga teng. Uchburchakning uchinchi tomonini
toping.
A) 30 B) 15 О 25 D) 28
20.0,0000087 sonini standart ko'rinishda
yozing.
A) 8,7-1 O'6	B) 8,7-107
О 8,7-1 O'6	D) 8,7-1 O'7
21. 7з - 2sin2x = 0 tenglamani yeching.
A)(-l)‘y+M,iteZ
В)(-1)‘-^-+ЛЛе2
C)(-l) —+—,*eZ
o 2
D)(-l)‘—+-fc,*eZ
12 2
22. Muntazam to'rtburchakii piramidaning
hajmi 19200 ga, balandligi esa 9 ga teng.
Piramida apofemasi uzunligini toping.
A) 27 B) 39 C) 41 D) 36
23.17-11 -14 11 + 27-23 - 24-23 + 21-19-
18-19 ni hisoblang.
A) 159 B) 165	0 203 D) 143
24. у = x2 + px + q parabola x = 5 nuqtada Ox
o'qiga urinadi. — ni toping.
P
A) 1 B)-2	0 2,5	D)-2,5
71
2010 yilning testlar. 130 varianti.	Matematika
25. a ning qanday qiymatlarida ax + 2y = 3 va Зх - у = -1 tor'g'ri chiziqlar kesishadi? A) a/2 B)a = 0 C)aM D)aCR	1	'2	1 34.	=• + -=—==-	==• - 4 ning 2 + Тз V5-V3 2 + 75 qiymatini toping.
26.	у = Jlxl-3 +	funksiyaning *	<10-X aniqlanish sohaslni toping. A) (3; 10) U {-3}	B) (-»;-3]U [3; 10) C)[-3;10]	D)(-10; 3] 27.	Agar x va, z orasida x2 + z2 + x + 2z + 1-^=0 munosabat o'rinli bo'lsa, x-z ning qiymati qancha bo'ladi? A) 0,5	B)-0,8 C) 0,25 D) 1 28.	/(x) = 7з -sinx + cos—. /'f—1 = ? J	3 2»	^6^ A) 0,5	B)^	C)0	£ ' 2 29.	3x2 < 16x - 5 tengsizlikning butun yechimlari ko'paytmasini toping. A) 120	B)12 C) 24 D) 30 30.	Perimetri 28 bo'lgan uchburchakning bissektrisasi uni perimetrlari 16 va 24 bo'lgan uchburchakiarga ajratadi. Berilgan uchburchakning bissektrisasini toping. A) 8	B) 5	C) 7	D) 6 31.	Aylanaga tashqi chizilgan to'rtburchakning uchta ketma-ket tomonlari nisbati 1:2:3 kabi. Agar to'rtburchakning perimetri 24 ga teng bo'lsa, uning eng kichik tomonini toping. A) 3,6 B) 4	C) 3	D) 4,5 32.	Agar hadlari haqiqiy sondan iborat bo'lgan o'suvchi geometrik progressiyaning birinchi uchta hadi yig'indisi 7,ko'paytmasi 8 ga teng bo'lsa, shu progressiyaning beshinchi hadini toping. A) 12 B) 20	C)6	D) 16 33.	к ning qanday qiymatida lln(x + 15)1 = -(x + к + 4)2 tenglama yechimga ega bo'ladi? A) 15 B)-10 C)-15 D)10	А)75-7з	B)2 0 4	D)7s+73 35. /(-2) = 5 va /(2) = 3 shartni qanoatlantiruvchi chiziqli funksiyani aniqlang. A)/(x)=2x-1	B)f(x)=-lx + 4 O/(x)=-|x + 4	D)/(x) = 2x + 1 36.^8-372-^4 + 55/2 + 1/5-472 ni hisobiang. A) 2+72	B)2-T2 OT2-1	D)3-T2 VARIANT № 130 1.1,25 songa teskari sonni toping. A) 8	B)-0,8 0 0.8	D)-| 2.	xi va x2 x2 -13x + 12 = 0 tenglamaning ildizlari bo'lsa, x,xf + xf хг ning qiymatini toping. A) 156 B) 94 0 -156 D) -152 3.	Mahsulotning narxi birinchi marta 25% ga, ikkinchi marta yangi bahosi yana 20% ga oshirildi. Mahsulotning oxirgi bahosi necha foizga kamaytirilsa, uning narxi dastlabki narxiga teng bo'ladi? A) 45 B) 48	0 50	D)33^ 4.	a va b ning qanday ., .. [6x-15y = b,l ,	, qiymatlarida J ay-12 ten9'arnaar sistemasi yechimga ega emas? A) a = 10, b = 18 B)a^-10, b = 18 Oa#10, b = 18 D)a#10, b*18
72
2010 yilning testlar. 130 varianti.
Matematika
5.	Balandligi 12 ga, Asosining radiusi 6 ga
teng bo'lgan konusga yasovchisi 4 ga teng
bo'lgan silindr ichki chizilgan. Silindr
asosining radiusini toping.
A) 4 В) 3 C) 2 D) 2,6
6.
.	38 47	. ,,	3	4	. ,	,
Agar— + — = a bo'lsa, — + — quyidagilard
11 51	41 51 a
an qaysi biriga teng?
A) 4 - a
B)3-a
C)3-|
D)2-a
7.	у = e“ -sin5x funksiyaning boshlang'ich
funksiyalaridan birini toping.
A) 8c”'+5cos5x B)8e”'-5cos5x
C)—c8'-—cos5a	D)	+ — cos5x
8	5	'8	5
8.	^x-^ = ^sin30’ + sin~ tenglamani
yeching.
A) 2-'	B)0 C) 2	D)|
9.	To'g’ri burchakli uchburchakka kvadrat
shunday ichki chizilganki, to'g'ri burchak ular
uchun umumiy. Kvadratning bir uchi
gipotenuzaning o'rtasida yotadi. Agar
gipotenuzaning uzunligi 24 ^2 ga teng bo'lsa,
kvadratning perimetrini toping.
A)	42
B)	32
C)	36
D)	48
10. ^в+з-Уг-^ё-з-Уг-Тб+ТУг ni
hisobiang.
A)2-i/2 B)3-j2 C)1+j2 D)2 + i/2
11. ABC uchburchakda Z A = 30°, AB = Уз ,
AC = 6. A uchidan tushirilgan balandlikning
uzunligini toping.
A)|V7	В)|У7 C)^- O7V7
111	Э	3 a2-b2	IJ —;	Г+Э2Ь2 - a2 - b2	1	44-»^ ™ a2 + b2
soddalashtiring (b > a > 0).
A) 27a	B) 2v/b
C)2(Vb-^)	D)2(Va-Vb)
13	1	1 x-2xs - у’ + у _.
( x-y	x-i.y2	1	nl )	4уг
soddalashtiring.	
2^ + Vy)	m 'Ix + Jy
С)У?+Уу	°4
14.	Tekislikka og'ma va perpendikulyar
tushirilgan. Og'maning tekislikdagi
proyeksiyasi 7 ga, perpendikulyarning
uzunligi 24 ga teng, Og'ma va perpendikulyar
orasidagi burchakni toping.
12	24
A) arcsin — B) arctg —
25	7
C) arcsin ~ D) arcsin —
15.	(a + b)(a - b + 1) + (a - b)(a + b - 1) - 26
ni soddalashtiring.
A) 2a-2b	B) 2b
C)2a2-ab2	D)2a
16.	AB(1; -1; -2) va BC(3; 7; 14) vektorlar
parallelogrammning qo'shni tomonlari. lining
AC va BD diagonallari orasidagi burchakni
toping.
A)	62 arccos— 63	B)	( 62> arccos 	 V 63 J
C)	34 arccos— 63	D)	58 arccos— 63
17.	Agar uchburchakning A, В va C
burchaklari 1; 2 va 3 sonlarga proporsional
bo'lsa, В burchakni toping.
A)	30°
B)	60°
C)	90°
D)	45“
73
2010 yilning testlar. 130 varianti.
18.	y =---funksiyaning grafigiga Xo =1
6 л-4
nuqtada o’tkazilgan urinma va koordinat
o'qlari bilan chegaralangan uchburchakning
yuzini toping.
A)^-	В)-	С)-	D)-
8	'2	'4	2
19.	Agar x-y = 5vaxy=14 bo'lsa, x3y + xy3
ning qiymati qancha bo'ladi?
A) 354 B) 273 C) 742 D) 216
20.	To'g'ri burchakli uchburchakka kvadrat
shunday ichki chizilganki, to'g'ri burchak ular
uchun umumiy. Kvadratning bir uchi
gipotenuzaning o'rtasida yotadi. Agar
gipotenuzaning uzunligi 24 VF ga teng bo'lsa,
kvadratning perimetrini toping.
A) 36 B) 48 C) 42 D) 28
, a + b . a°,5 + b0,s 2ewsbw!. .
a-2a05b0'5 + b'(a0S-b0'5 a-b '
soddalashtiring.
.. 2-fab	Ja-Jb
A)' r—"r	°) г— rr
Ja+Jb	ia+^Jb
C)4a+Jb	D) 1
22.	(2x - 1 )-(x - 1,5) = 0 bo'lsa, 2x - 1 qanday
qiymatlar qabul qiladi?
A) faqat	B)2yoki0
C)0 yoki 1,5	D)0yoki-1
23.	Muntazam to'trburchakii piramida
asosining tomoni 6 ^3 ga va apofemasi 6 ga
teng. Piramida hajmini toning.
A) 54	B)108 C) 162 D) 324
24.	Quyidagi tasdiqlaming qaysilari to'g'ri?
1)	ikkita o'xshash jism hajmlarining nisbati
ularning mos chiziqli o'lchovlari
kvadratlarining nisbatiga teng; 2) silindrning
hajmi asosining yuzi bilan balandligi
ko'paytmasiga teng; 3) shaming hajmi — ж r3
4
ga teng; 4) shar sektorining hajmi |-^ R2H ga
teng (H - mos shar segmentining balandligi,
R - shaming radiusi); 5) asosining radiusi R
Matematika
ga, balandiigi h ga teng silindr yon sirtining
yuzi 2rrRh ga teng.
A) 2; 4; 5	B) 2; 3; 4
C)1;2;4	D)1;2; 5
n3 _. 2n2 — 12
25.	----------(n e N) kasrning natural
n
sonlardan iborat barcha qiymatlari yig'indisini
toping.
A) 105 B) 102 C) 124 D) 146
26.	Agar 2sin6x(cos43x - sin43x) = sinkx
tenglik hammna vaqt o'rinli bo'lsa, к ni toping.
A) 24 B) 12 C) 18 D) 6
27.	Kichik diagonal! 12-^3 bo'lgan muntazam
oltiburchakka tashqi chizilgan aylananing
radiusini toping.
А)4^3 В)б7з C) 12	D)14
28.	2 - 3lx - 5I = -4 tenglamaning ildizlari
yig'indisini toping.
A) 8 B) 7 C) 9 D) 10
29.	279 ni 16 ga bo'lganda qoldiq 7 bo'ladi.
Bo'linma nechaga teng?
A) 12 B) 13 C) 17 D) 11
30.	cos3x + 4cosx < 0 tengsizlikni yeching.
А)	|-+2л*;—+2flt|,iteZ
Д2 2 J
В)	I-- + 2л*;- + 2Л UeZ
Ч 2	2	)
С) (2л^;лч-2Л),4е Z
D) (-Д’ + 2л£;2л&), к е Z
31.	к ning qanday qiimatlarida у
=—1 funksiyaning grafigi C(-2; -3)
nuqtadan o'tadi?
A)-1 B) 4	C)1	D)1
32.5 va 405 sonlari orasiga uchta musbat son
shunday qo'yilganki, natijada u sonlar
berilgan sonlar bilan birgalikda geometrik
progressiya hosil qilgan. Qo'yilgan sonlaming
yig'indisini toping.
A) 199	B)195 C) 180 D) 192
74
2010 yilning testlar 130 varianti.
Matematika
7
33.	Agar arj = bo'lsa, tga ning
qiymatini toping
A) —
12
B)-H
5
C)-—
12
D) —
5
7r —IQ
34.	Nechta tub son 3 < —-— < 5
3 л -17
tengsizlikning yechimi bo'ladi?
A) 5	B) 2	C) 7	D) 3
35.	0.21 :(0,05 +	) - 2,5-1,4 ni hisoblang.
A) -2,45	B) -2,55 C) -2	D) -3,35
36.1 + 2cos2x = 0 tenglamani yeching.
A)(-l),+‘—+—.keZ
'	12	2
B) ± —+^fc,ire Z
' 12
C).(-l)My+-y-,£eZ
D) ±—+ лк,ке Z
3
75