Matematikadan 30 talik testlar to‘plami - 50-ta variant

Matematika(8000008) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Ifodani soddalashtiring: 7. y = 3x2 − 6x + 7 kvadrat funksiyaning abssissa
5 (a − b) a2 − b2 o‘qiga nisbatan simmetrik funksiyasini
 2  :
3 a + b2 (a + b)2 − 2ab aniqlang.
5 5 5 A) y = 3x2 + 6x + 7 B) y = 3x2 − 6x + 7
A) − B) C) C) y = −3x2 + 6x − 7 D) y = −3x2 − 6x − 7
3 (a + b) 3 (a − b) 3 (a + b)
5
D) − √
3 (a − b) 8. Uzunligi 128 ga teng bo‘lgan AB kesmaning
uchlari radiusi 5 ga, balandligi 8 ga teng
2. Rasmda A va B nuqtalar son o‘qida silindrning pastki va yuqori asoslaridagi
tasvirlangan. 2A + B ning son qiymatini aylanalarda yotadi. Silindr markaziy o‘qidan
toping. AB kesmagacha bo‘lgan eng qisqa masofani
9, 5 birlik 7 birlik toping.
√ √
A) 3 B) 4 C) 19 D) 17
B -3 0 2,5 A
9. 15 · 221 · 517 ko‘paytma nechta nol bilan
A) 12,5 B) 9,5 C) 8 D) 6,5 tugaydi?
−−→ A) 18 B) 21 C) 19 D) 22
3. ABCD parallelogramm uchun AB (3; 5; −7) va
−−→ 10. Markazlari har xil nuqtalarda bo‘lgan 3 ta
AD (−11; 7; 3). Parallelogramm aylana ko‘pi bilan nechta nuqtada kesishadi?
diagonallarining keshishgan nuqtasi O bo‘lsa,
−→ A) 6 B) 7 C) 4 D) 3
OA vektorning koordinatalari yig‘indisini
toping. 11. To‘g‘ri burchakli parallelepipedning qirralari
nisbati 2:1:3 kabi. Agar parallelepipedning to‘la
A) 1 B) 0 C) −1 D) 2
sirti 198 dm2 ga teng bo‘lsa, uning hajmini
  (dm3 ) toping.
π
4. sin x + 2 cos x + = 0 tenglamaning barcha A) 162 B) 192 C) 154 D) 148
6
ildizlarini toping. 12. ABCD teng yonli trapetsiyaga radiusi 2 ga
teng bo‘lgan aylana ichki chizilgan. Agar
π trapetsiya asoslarining nisbati 4:9 kabi bo‘lsa,
A) x = + 2πk, k ∈ Z
6 kichik asos uzunligini toping.
π 8 8 3 5
B) x = + πk, k ∈ Z A) B) C) D)
2 5 3 8 8
π 13. y = −x + 1 va y = x2 − 5x + 6 funksiyalarning
C) x = + 2πk, k ∈ Z
3 grafiklari orasidagi eng qisqa masofani toping.
√ √
π 2 1 3
D) x = − + πk, k ∈ Z A) B) C) 0 D)
3 2 2 2
14. Agar ABC uchburchakning burchaklari
3 ∠A : ∠B : ∠C = 2 : 3 : 4 shartlarni
5. Agar m = 4, n = bo‘lsa,
7 qanoatlantirsa, uchburchakning qaysi tomoni
m − 6n + 3m − 2mn m2 + 6n − 3m − 2mn
2
eng katta bo‘ladi?
:
m2 − 6n − 3m + 2mn m2 + 6n + 3m + 2mn A) AC B) BC C) aniqlab bo‘lmaydi
ifodaning qiymatini toping.
D) AB
9
A) 1 B) 49 C) D) 14 15. Quyidagi jumlalardan qaysilari noto‘g‘ri?
49
1) agar natural son 6 ga bo‘linsa, u holda 12 ga
ham bo‘linadi; 2) agar natural son 12 ga
6. m ning qanday qiymatida 4x2 − 5x + m = 0
1 bo‘linsa, u holda 6 ga ham bo‘linadi; 3) agar
tenglamaning x1 va x2 ildizlari 4x1 + 3x2 = 3 natural son 12 ga bo‘linmasa, u holda 6 ga ham
2
tenglikni qanoatlantiradi? bo‘linmaydi; 4) agar natural son 6 ga
bo‘linmasa, u holda 12 ga ham bo‘linmaydi.
A) −6 B) 6 C) −1,5 D) 1,5
A) 1, 3 B) 1, 2 C) 3, 4 D) 2, 3


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T-108 Matematika(8000008) - Sotish taqiqlanadi!
√
16. A aralashmaning bir kilogrammi 12000 so‘m, B 23. 4x − x2 ≤ x − 5 tengsizlik nechta butun
aralashmaning bir kilogrammi 18000 so‘m. A yechimga ega?
va B aralashmalardan mos ravishda 4:1 A) 4 B) 6 C) yechimga ega emas D) 2
nisbatda tayyorlangan 1 kg aralashmaning
narxini (so‘m) aniqlang. 24. n ning qanday qiymatida 2n + 3 ning 60%i
45 ga teng bo‘ladi?
A) 14800 B) 13200 C) 14200 D) 12800
√ A) 32 B) 24 C) 36 D) 42
17. Asosi 4 2 ga teng va unga yopishgan
burchaklari 30◦ va 45◦ bo‘lgan uchburchakning 25. f (x) = x2 funksiyaning (0;0) va (1;1)
yuzasini toping. nuqtalaridan o‘tuvchi to‘g‘ri chiziqqa parallel
√ √  √
A) 4 3 + 2 B) 8 3 − 1 C) 8 3+1 bo‘lgan urinma tenglamasini tuzing.
√  A) y = x − 0, 125 B) y = x − 0, 2
D) 16 3 − 1
C) y = x − 0, 25 D) y = x − 0, 225
18. Agar tg α + ctg α = 3 bo‘lsa,
tg 2 α − 2 tg α + ctg α ifodaning qiymatini toping. 4, (2) + 4, (4) + 4, (6)
26. Hisoblang: .
A) 2 B) 1 C) 3 D) 4 4, (3) + 4, (5) + 4, (7)
  40 38 42 39
1 1 √ √  A) B) C) D)
19. Hisoblang: √ − √ · 12 − 75 41 39 43 40
2− 3 2+ 3
A) −18 B) −15 C) −12 D) −9 4x
27. f (x) = funksiyaning aniqlanish sohasini
x+2
20. log2 (x + 1) + log2 (8 − x) > 3 tengsizlikni toping.
yeching.
A) (−∞; −2) ∪ (−2; ∞) B) (−∞; 0]
A) (0; 7) B) (−1; 8) C) (−1; 0) ∪ (7; 8) C) (−∞; −2) ∪ [0; ∞) D) (−∞; −2]
D) (7; 8)
28. Arifmetik progressiyaning ikkinchi va oltinchi
21. f (x) = x2 − x + 1 funksiyaning (0; 2) nuqtadan
hadlarining yig‘indisi 72 ga teng. Arifmetik
o‘tuvchi boshlang‘ich funksiyasini toping.
progressiyaning ikkinchi hadining beshinchi
1 1 7
A) F (x) = x − x2 + x3 − 1 hadiga nisbati
10
ga teng bo‘lsa, uning oltinchi
2 3
hadini toping.
1 1
B) F (x) = x − x2 + x3 + 1 A) 48 B) 44 C) 42 D) 40
2 3
1 1 29. A = {1; 2; 3; 4}, B = {x| x = 2n − 1, n ∈ A}
C) F (x) = x − x2 + x3 + 2 bo‘lsa, A ∩ B to‘plamni aniqlang.
2 3
1 1 A) {1; 2; 4} B) {1; 3} C) {1; 3; 4}
D) F (x) = x − x2 + x3 − 2 D) {1; 2; 3}
2 3
 √  √ √ 3x+1 + 3x+2 + 3x+3
22. 2 4 x · 7 + 4 3 · 2 x − 3x = x tenglama 30. f (x) = funksiya berilgan
5x+2 + 14 · 5x
ildizlarining o‘rta arifmetik qiymatini toping. bo‘lsa, 9 · f (−2) ni hisoblang.
A) 1 B) 0 C) 4 D) 2
A) 25 B) 1,44 C) 0,36 D) 9




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Matematika(8000032) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. 0, 1, 2, 3, 4, 5 raqamlardan jami nechta 11. Soddalashtiring:
3 xonali sonlar tuzish mumkin? sin(2α + β) + sin(2α − β) tg β − tg 2α
− .
A) 180 B) 125 C) 210 D) 216 sin(2α − β) − sin(2α + β) tg β
A) 1 B) 0 C) 2 D) −1
2. y = 6x2 − 24x − 21 kvadrat funksiyaning 12. Oltita musbat son geometrik progressiyani
simmetriya o‘qi bo‘lgan chiziqni aniqlang. tashkil qiladi. Geometrik progressiyaning
A) x = 0 B) x = 2 C) x = 4 D) x = 1 9
dastlabki ikkita hadining ko‘paytmasi ga,
8
3. Uchburchakning ikki tomoni va ular orasidagi
oxirgi ikkita hadining ko‘paytmasi esa 288 ga
mediana uzunliklari mos ravishda 15; 13; 7
teng. Shu progressiyaning oxirgi ikkita
bo‘lsa, shu uchburchakning yuzini toping.
hadining yig‘indisini toping.
A) 84 B) 70 C) 78 D) 72 A) 48 B) 34 C) 36 D) 18
4. Rasmda berilgan ABC uchburchakda AD 3
bissektrisa. Agar ∠ADC = 113◦ bo‘lsa, B 13. 6 12 + 612 + 612
+ ... + 612 + 612 yig‘indining
4
burchak C burchakdan necha gradusga katta? 32 ta
qismi quyidagilardan qaysi biriga teng?
B
A) 214 · 312 B) 2 · 613 C) 215 · 313
D) 4 · 612
D
 x2 −(2x+1)2
2
14. √ ≤ 1 tengsizlikni yeching.
3 3−1
A C 1 1
A) (−∞; −1] ∪ − ; ∞ B) −1; −
3 3
A) 23◦ B) 46◦ C) 47◦ D) 67◦
2 2
C) (−∞; −1] ∪ − ; ∞ D) −1; −
64 − x2 3 3
5. ≤ 0 tengsizlikning [5; 11) oraliqqa
x−1 − 8x−2 15. f (x) = e−3x+2 · sin 3x funksiyaning hosilasini
tegishli barcha natural yechimlarining o‘rta toping.
arifmetigini toping.
1 2 1 3 A) 3e−3x+2 · (cos 3x − sin 3x)
A) 6 B) 7 C) 7 D) 6
6 5 2 5 B) −3e−3x+2 · (cos 3x − sin 3x)
√
6. (3x − 8) −4x2 + 3x + 10 = 0 tenglama nechta C) −3e−3x+2 · (cos 3x + sin 3x)
haqiqiy ildizga ega. D) 3e−3x+2 · (cos 3x + sin 3x)
A) 2 B) 1 C) 3 D) 0 16. 43 · 47 · 28 · 32 − 18 · 63 · 27 ayirma qanday
lg 3+lg 5 raqam bilan tugaydi?
7. Hisoblang: 5 lg 25−lg 5
A) 6 B) 8 C) 4 D) 2
A) 5 B) 1 C) 15 D) 10 17. α tekislik va uni kesib o‘tmaydigan AB kesma
8. n ning qanday qiymatida 2n + 3 ning 60%i berilgan. Kesmaning uchlaridan α tekislikkacha
45 ga teng bo‘ladi? bo‘lgan masofalar AA1 =18 cm, BB1 =13 cm
A) 36 B) 32 C) 24 D) 42 bo‘lsa, AB kesmani A uchidan boshlab
hisoblaganda 3:2 nisbatda bo‘luvchi C
9. y = (x − 4) · (x − 1)2 funksiyaning ekstremum nuqtadan α tekislikkacha bo‘lgan masofani
nuqtalaridan o‘tuvchi to‘g‘ri chiziq tenglamasini (cm) toping.
tuzing. A) 14 B) 15 C) 15,5 D) 16
A) y = 2 − 2x B) y = 2x + 2 √
18. Agar a = 3 3 − 2 bo‘lsa,
C) y = 2x − 2 D) y = −2x − 2 a4 + 5a3 + 15a − 9
+ 9a−4 :
 √ 1 a6 + 3a4
10. Hisoblang: 28 − 10 3 −  −1
√ a5 + 2a4
7+4 3 : − 4 ning qiymatini toping.
√ √ a+3
A) 7 B) 3 − 2 3 C) 7 − 2 3 D) 3 √ √
A) 3 3 B) 23 C) 12 3 D) 5


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T-108 Matematika(8000032) - Sotish taqiqlanadi!

19. Ko‘paytuvchilarga ajrating: 24. f (x) = x2 + bx + c funksiyaning nollari 2 va 3
2bx − 3ay − 6by + ax bo‘lsa, c ni toping.
A) (2b − a) · (x + 3y) B) (a − 2b) · (x + 3y) A) −5 B) 6 C) 5 D) −6
C) (a + 2b) · (x − 3y) D) (a + 2b) · (3y − x)
25. Agar rombning bir diagonalini 50% ga
2 2 2 2
20. · · · ... · : 128 sonni kamaytirib, ikkinchi diagonalini 2 marta
10 100 1000 1 00 
. . . 0
uzaytirilsa, rombning yuzi qanday o‘zgaradi?
10 ta
standart shaklga keltiring. A) 50% ga kamayadi B) aniqlab bo‘lmaydi
A) 8 · 10−55 B) 8 · 10−45 C) 8 · 10−54 C) 50% ga ortadi D) o‘zgarmaydi
D) 8 · 10−44
26. Uchlari A(0; 0), B(3; −1), C(6; 2) va D(1; 2)
21. Rasmda A va B to‘plamlar va U universial nuqtalarda bo‘lgan to‘rtburchakning qaysi
to‘plam tasvirlangan. Quyidagi to‘plamlardan tomoni eng katta?
qaysi biri bo‘yalgan sohaga mos to‘plamni
A) BC B) CD C) AB D) AD
tasvirlaydi? (A = U \A; B  = U \B)

B
cos 68◦ · cos 8◦ − cos 82◦ · cos 22◦
27. Hisoblang: .
A cos 53◦ · cos 23◦ − cos 67◦ · cos 37◦
1 3
A) 0 B) C) D) 1
2 4

U
28. Uchlari Oxy tekisligining (0; 0), (0; 2), (4; 2) va
(1; 0) nuqtalarida bo‘lgan to‘rtburchakni Ox
o‘qi atrofida aylantirishdan hosil bo‘lgan
A) (A ∩ B) ∩ (A ∪ B)
jismning hajmini toping.
B) (A ∩ B  ) ∪ (A ∩ B) A) 8π B) 9π C) 6π D) 12π
C) (A ∩ B  ) ∪ (A ∩ B)
29. Matematikadan yozma ish topshirgan
D) (A ∩ B  ) ∪ (A ∩ B) 1 7
π o‘quvchilarning qismi "5" baho, qismi "4"
8 8 12
22. Integralni hisoblang: sin 6x · sin 2xdx. baho olgan. "3" baho olganlar esa "5" baho
π

√ √
16
√ olganlar sonidan 6 taga ko‘p. Agar 2 ta
3− 2 2− 2 2 2−1 o‘quvchi "2" baho olgan bo‘lsa, nechta o‘quvchi
A) B) C)
√16 8 8 "4" baho olgan?
2 2−1 A) 14 B) 35 C) 28 D) 12
D)
16
 2 √ 30. x = 3, 61(91), y = 3, 62, z = 3, 6(191) va
23. x + 8x + 15 4x − 9 = 0 tenglamaning
t = 3, 619(1) sonlarini kamaytirish tartibida
haqiqiy ildizlar yig‘indisini (agar yagona bo‘lsa, yozing.
ildizini) toping.
A) x > z > y > t B) y > t > z > x
A) 2,25 B) −0,75 C) −2,75 D) −5,75
C) y > x > t > z D) y > x > z > t




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Matematika(8000056) - Sotish taqiqlanadi! T-108

MATEMATIKA
5 4
1. Hisoblang: b− 3 + 2b− 3 + b−1
9. + 8b ifodaning
139 · 163 − 160 · 139 + 141 · 175 − 172 · 141 4 1
b− 3 +
A) 870 B) 864 C) 852 D) 840 b
1
  b = bo‘lgandagi qiymatini toping.
16 8
(27 + 79) · 2 + · 45−1 1 1
45 A) 2 B) 12 C) 3 D) 4
2. Hisoblang:  2 · 0, (5) 2 8
1
0, (55) +
0, (555) log3 12 + log4 12 1
4 10. Hisoblang: + · log2 4
A) 9 B) 1 C) 0, (5) D) 1 log3 12 · log4 12 2
5 A) 1 B) 3 C) 2 D) 0

3. Bitta daftar 600 so‘m va u bitta qalamning 11. Agar f (x) 13-darajali ko‘phad bo‘lsa,
narxidan 400 so‘mga qimmat. O‘quvchi y = x14 · f (x) funksiyaning hosilasi nechanchi
3600 so‘mga daftarlar va qalamlar sotib oldi. darajali ko‘phad bo‘ladi?
Quyida keltirilgan sonlardan qaysi biri xarid A) 27 B) 26 C) 25 D) 52
qilingan qalamlarning soni bo‘la oladi?
π π π π
A) 4 B) 5 C) 1 D) 3 12. Hisoblang: sin · cos3 − cos · sin3 .
12 12 12 12
√ √ √
7 3 3 3 1
−1 A) B) C) D)
8 8 1 4 8 6 8
4. Hisoblang: + +
7 7 2 13. 52314 sonning raqamalari joylarini almashtirib,
8 1 bilan tugaydigan nechta har xil son hosil
1 8 2 3 qilish mumkin?
A) B) C) D)
7 7 3 2 A) 25 B) 20 C) 24 D) 30

5. 6, 3; 4, 4; −3, 8; x va 7, 6 sonlarning o‘rta 14. Qirralari 2 dm, 3 dm va 4 dm bo‘lgan to‘g‘ri
arifmetigi 3,3 ga teng. x ning qiymatini toping. burchakli parallelepiped shaklidagi quti ichiga
A) 1,8 B) 2,6 C) 2 D) 2,3 eng ko‘pi bilan qirrasi 7 cm bo‘lgan kublardan
nechtasini joylashtirish mumkin?
6. Grafigi A (−2; 11) nuqtadan o‘tuvchi A) 40 B) 45 C) 69 D) 42
y = kx + 5 funksiya abssissalar o‘qini qaysi 15. 24; 36; 48; ... arifmetik progressiyada an = 180
nuqtada kesib o‘tadi?
      2n + 5
2 2 1 bo‘lsa, ning qiymatini toping.
A) −1 ; 0 B) 1 ; 0 C) 0; 1 n−3
 3 3 2 1 4
1 A) 1, 5 B) 3 C) 3 D) 3
D) 1 ; 0 10 7
2
16. (x0 ; y0 ) nuqta y = 3x2 − bx + 12 parabola
7. Agar (x − 1)3 · (2x − 1)7 = uchining koordinatalari bo‘lsa, y0 + 3x20 ning
= a + a1 x1 + a2 x2 + ... + a9 x9 + a10 x10 bo‘lsa, qiymatini toping.
a + a1 ni toping. A) 15 B) 12 C) 18 D) 9
A) −10 B) −14 C) −16 D) −17
17. α tekislik va uni kesib o‘tmaydigan AB=13 cm
kesma berilgan. AB kesmaning uchlaridan α
8. Tenglamani yeching: tekislikkacha bo‘lgan masofalar AA1 =4 cm,
x
= 0.
(sin (x + 1, 5π) − 1) · tg BB1 =9 cm. AB kesma yotuvchi to‘g‘ri chiziq
2 bilan α tekislik hosil qilgan burchakning
A) 2πk, k ∈ Z B) πk, k ∈ Z kosinusini toping.
π
C) π + 2πk, k ∈ Z D) + πk, k ∈ Z 5 9 4 12
2 A) B) C) D)
13 13 13 13


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T-108 Matematika(8000056) - Sotish taqiqlanadi!

18. f (x) = x2 − x + 1 funksiyaning (0; 2) nuqtadan 24. ABC uchburchakning AC tomonidan D nuqta
o‘tuvchi boshlang‘ich funksiyasini toping. shunday olinganki, bunda BD = DC (rasm).
Agar ∠BAC = 33◦ va ∠BDC = 42◦ bo‘lsa,
1 1 ∠ABC ni toping.
A) F (x) = x − x2 + x3 + 2
2 3 B
1 1
B) F (x) = x − x2 + x3 + 1
2 3
1 1
C) F (x) = x − x2 + x3 − 1
2 3 A D C
1 1
D) F (x) = x − x2 + x3 − 2 A) 75◦ B) 78◦ C) 79◦
D) 80◦
2 3 
3 3

a2 + b2 a−b a−b √
25. Ushbu − 1 1 · √ − a
19. Tekislikda A(1; 1), B(3; 4), C(x; y) nuqtalar a−b a2 + b2 ab
−−→ −→ x y √
berilgan. Agar AB = AC bo‘lsa, + ni ifodaning a = 2, b = 8 dagi qiymatini toping.
y x √ √
A) − 2 B) 2 2 C) 2 D) 0
toping.
1 1 1 1 3|x| − 27
A) 2 B) 2 C) 2 D) 2 26. ≥ 0 tengsizlikni yeching.
12 6 4 3 x−3

A) [−3; 3) ∪ (3; +∞)
x3 9x
20. ≤ tengsizlikning butun yechimlari B) [−3; +∞)
x−2 x−2
sonini toping. C) (−∞; 3) ∪ (3; +∞)
A) 6 B) 4 C) 5 D) 7 D) [0; 3) ∪ (3; +∞)
27. Ko‘paytuvchilarga ajrating:
21. Agar rombning bir diagonalini 50% ga
(3a + 2b)2 − (2a + 3b)2
kamaytirib, ikkinchi diagonalini 2 marta
uzaytirilsa, rombning yuzi qanday o‘zgaradi? A) −5 (a + b) · (a − b) B) (5a + b) · (a − b)
C) 5 (a + b) · (a − b) D) (a + 5b) · (a − b)
A) o‘zgarmaydi B) 50% ga kamayadi ⎧
C) 50% ga ortadi D) aniqlab bo‘lmaydi ⎪
⎪ 3 7 1
⎨ + =1
x+2 6+y 4
28. (x; y) sonlar juftligi 10 14 1
22. ABCD parallelogramda C o‘tkir burchak. ⎪
⎪
⎩ − =−
E nuqta AB tomonda yotadi. Agar x+2 y+6 2
tenglamalar sistemasini qanoatlantiradi.
AE:EB nisbat 2:3 kabi bo‘lsa,
(x − y)y ning qiymatini toping.
AECD to‘rtburchak yuzining
BCE uchburchak yuziga nisbatini toping. A) 125 B) 1 C) 36 D) 16
7 5 3 4 29. A = {(x, y) | x2 + y 2 = 4, x, y ∈ R},
A) B) C) D)
3 3 2 3 B = {(x, y) | x − y = 2, x, y ∈ R} bo‘lsa, A ∩ B
to‘plamni aniqlang.
23. x2 + ax = 1 tenglamaning x1 va x2 ildizlari A) {(2; 0) ; (0; −2)} B) {(−2; 0) ; (0; −2)}
x1 x2 C) {(2; 0) ; (0; 2)} D) {(−2; 0) ; (0; 2)}
+ = −18 tenglikni qanoatlantirsa,
x2 x1
a2 − 2 ning qiymatini toping. 3 5
30. Hisoblang: 17 − 1−
A) 34 B) 14 C) 2 D) 7 2 9
A) 4 B) 2 C) 3,8 D) 3




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Matematika(8000080) - Sotish taqiqlanadi! T-108

MATEMATIKA

213 + 193 13. log22 (8x) = 3 log2 x + 27 tenglamaning ildizlari
1. Hisoblang: − 21 · 19
72 − 32 ko‘paytmasini toping.
A) 4 B) 3 C) 16 D) 9 1 1
A) 4 B) C) 2 D)
8 4
2. f (x) = x2 + bx + 3 funksiyaning nollaridan biri
1 bo‘lsa, b ni toping.
A) −3 B) −4 C) 3 D) 4 14. Agar f (x) funksiya uchun
c + x · f (x) = (x − 1) · (2x − 1)11 munosabat
3. Hisoblang: 0, 84 · 109 : 7000000. o‘rinli bo‘lsa, f  (1) ni toping(c−o‘zgarmas son).
A) 12 B) 1200 C) 120 D) 240 A) 1 B) −1 C) 2 D) 0
4. Karim ota 71 yoshda. Uning nabiralarining
o‘rtacha yoshi 21 da. Nabiralari bilan Karim
15. Rasmda ABCD to‘rtburchak va unga tashqi
otaning yoshlari o‘rta arifmetigi 26 ga teng.
chizilgan aylana tasvirlangan. Agar AB=5,
Karim otaning nechta nabirasi bor?
BC=4, CD=3 va AD=2 bo‘lsa, ∠ABC ning
A) 9 B) 12 C) 10 D) 8 kosinusini toping.
 2 B
x + 4y = 21
5. tenglamalar sistemasi nechta
y 2 − 4x = 21
haqiqiy yechimga ega?
A) 3 B) 2 C) 1 D) 4
C
6. (a − 3) (a − 4) − 3 (a − 2) ifodaga qanday eng A
kichik butun son qo‘shilganda, ifodaning
qiymati ixtiyoriy a ∈ R uchun musbat bo‘ladi? D
A) 7 B) 6
C) 8 D) 9 7 6 5 8
 3 A) B) C) D)
512 · 24  −3 −5 13 13 13 13
7. Hisoblang:  2 · 2−4 ·4
27 · 128
1 16. 7 soat 12 minut 40 sekundni sekundlarda
A) 4 B) C) 8 D) 1 ifodalang.
2
A) 25920 B) 25960 C) 25880 D) 25860
√  x2 −10x+16
8. 5−2 x−2
≥ 1 tengsizlikni yeching.
A) (−∞; 8] B) [8; ∞) C) (2; 8) ∪ (8; ∞) 17. Piramida asosining diagonallari soni
D) (−∞; 2) ∪ (2; 8] piramidaning qirralar soniga teng.
Piramidaning yoqlari soni bilan uchlari soni
9. y = −x4 + 8x2 − 9 funksiyaning eng katta
yig‘indisini toping.
qiymati a bo‘lsa, a + 5 quyidagi sonlardan qaysi
biriga qoldiqsiz bo‘linadi? A) 12 B) 16 C) 8 D) 14
A) 6 B) 8 C) 5 D) 9
18. 34974 sonning raqamalari joylarini almashtirib
10. m ning qanday qiymatida 4x2 − 5x + m = 0
1 jami nechta har xil 5 xonali son hosil qilish
tenglamaning x1 va x2 ildizlari 4x1 + 3x2 = 3 mumkin?
2
tenglikni qanoatlantiradi? A) 20 B) 120 C) 60 D) 30
A) 6 B) 1,5 C) −6 D) −1,5
11. Agar sin α · cos α = −0, 25 va 1, 6 < α < 3, 1 19. Agar geometrik progressiyaning umumiy hadi
bo’lsa, cos α − sin α ning qiymatini toping. 1 1 1
√ √ √ √ bn = 3 · 2n bo‘lsa, + + ... + yig‘indini
A) 2 B) − 1, 5 C) 1, 5 D) − 2 b1 b2 b10
hisoblang.
12. Agar 3a + 3−a = 3 bo‘lsa, 32a − 2 · 3a + 3−a 341 341 681 681
A) B) C) D)
ifodaning qiymatini toping. 512 1024 1024 512
A) 2 B) 3 C) 1 D) 4


1
T-108 Matematika(8000080) - Sotish taqiqlanadi!
√
20. Rasmda shtrixlangan soha yuzini toping. 26. Hisoblang: 2017 · 2021 + 4
(A − nuqta parabolaning uchi) A) 2019 B) 2009 C) 2011 D) 2021
y 27. Agar f (x) chiziqli funksiya uchun
A(1;4) f (1) + f (x − 3) = 7x − 2 bo‘lsa, f (x) ni toping.
A) f (x) = 7x + 6 B) f (x) = 7x + 4
(0;3) C) f (x) = 7x − 2 D) f (x) = 7x + 2
f (x) = ax2 + bx + c
28. A = {a; b; c; d; e; f } to‘plamning nechta qism
to‘plamlarida, b elementi bo‘lib, c elementi
qatnashmaydi?
x A) 16 B) 28 C) 8 D) 32
0 1 3
29. Katetlari uzunliklari 6 cm va 7 cm ga teng
1 1 2 bo‘lgan to‘g‘ri burchakli uchburchakning
A) 8 B) 9 C) 5 D) 6
3 3 3 gipotenuzasi atrofida to‘liq aylantirishdan hosil
21. Soatning minut mili 15 minutda necha bo‘lgan jismning hajmini (cm3 ) toping.
√ √ √
gradusga buriladi? 882π 85 588π 85 441 85
A) B) C)
A) 60◦ B) 75◦ C) 105◦ D) 90◦ 85√ 85 85
441π 85
22. Agar tg α + ctg α = 3 bo‘lsa, D)
tg 2 α − 2 tg α + ctg α ifodaning qiymatini toping. 85
A) 1 B) 2 C) 3 D) 4 30. Rasmdan tasvirlangan DEF G kvadratning
yuzasi 12 ga, DEC burchak 30◦ ga teng bo‘lsa,
23. Uchlari A(0; 0), B(3; −1), C(6; 2) va D(1; 2) ABC to‘g‘ri burchakli uchburchakning
nuqtalarda bo‘lgan to‘rtburchakning qaysi perimetrini toping.
tomoni eng katta?
B
A) CD B) AD C) AB D) BC
24. Ko‘paytuvchilarga ajrating:
(3a + 2b)2 − (2a + 3b)2 G
A) (a + 5b) · (a − b) B) 5 (a + b) · (a − b)
C) −5 (a + b) · (a − b) D) (5a + b) · (a − b) F
D
25. Agar a va b natural sonlar yig‘indisi 7 ga
qoldiqsiz bo‘linsa, 37a + 9b ni 7 ga bo‘lgandagi A
E
C
qoldiqni toping.  √  √ √
A) 5 3 + 3 B) 15 + 7 3 C) 15 + 8 3
A) 2 B) 1 C) 0 D) 6 √
D) 12 + 7 3




2


Matematika(8000104) - Sotish taqiqlanadi! T-108

MATEMATIKA
√
2 1 3
1. (3 − a) (a + 4) − a (−a − 6) ifodaning a = 2 10. + = 4 tenglamaning eng kichik
5 cos x sin x
bo‘lgandagi qiymatini toping. musbat yechimini toping.
2 3 π π 2π 2π
A) 24 B) 10 C) 21 D) 8 A) B) C) D)
5 5 6 3 9 3
√
5
2. 8 · 28x+5 = 16x+100 tenglamani yeching.
x − 25 x2 − 6
A) 9 B) 10 C) 11 D) 12 11. √ +√ ifodaning x = 6 dagi
5+ x 6−x
3. Quyidagi jumlalardan qaysilari noto‘g‘ri? qiymatini toping.
1) agar natural son 6 ga bo‘linsa, u holda 12 ga √
A) 1 B) −2 6 C) −11 D) −1
ham bo‘linadi; 2) agar natural son 12 ga
bo‘linsa, u holda 6 ga ham bo‘linadi; 3) agar
natural son 12 ga bo‘linmasa, u holda 6 ga ham 12. y = 4 cos3 2x + sin2 2x funksiyaning qiymatlari
sohasini toping.
bo‘linmaydi; 4) agar natural son 6 ga  √ 
bo‘linmasa, u holda 12 ga ham bo‘linmaydi. A) [0; 4] B) 0; 17 C) [−4; 4]
 √ 
A) 1, 3 B) 1, 2 C) 3, 4 D) 2, 3 D) 1; 17

4. Birinchi son ikkinchi sondan 12 ga ortiq.
13. y = 3x2 − 6x + 7 kvadrat funksiyaning abssissa
Ularning o‘rta arifmetigi 49 ga teng. Ikkinchi
o‘qiga nisbatan simmetrik funksiyasini
sonni toping.
aniqlang.
A) 43 B) 46 C) 39 D) 45
A) y = 3x2 + 6x + 7 B) y = −3x2 + 6x − 7
5. (x + 1) · (|x| − 1) ≥ 2 tengsizlikni yeching. C) y = −3x2 − 6x − 7 D) y = 3x2 − 6x + 7
√   √  √ 
A) 3; + ∞ B) −∞; − 3 ∪ 3; + ∞
√   √ 
C) (−∞; 0] ∪ 3; + ∞ D) −∞; − 3 14. |2x − 3| = 3x + 1 tenglama nechta haqiqiy
yechimga ega?
6. Rasmda berilgan ma’lumotlarga ko‘ra x necha
gradus? A) 0 B) 1 C) 2 D) cheksiz ko‘p

15. log23 (x − 1) − 2log3 (x − 1) > 3 tengsizlikning
78◦
barcha haqiqiy yechimlari to‘plamini toping.

4
A) 1;
α + 26◦ 3
α x B) (28; +∞)
4
C) −∞; ∪ (28; +∞)
3
A) aniqlab bo‘lmaydi B) 97◦ C) 102◦
D) 93◦ 4
D) 1; ∪ (28; +∞)
3
7. Hisoblang:
2, 2 + 2, 2 + ... + 2, 2 + 1, 1 + 1, 1 + ... + 1, 1
    x + 2, x ≤ −1
8 ta 16 ta 16. Agar f (x) = bo‘lsa,
x2 , x > −1
A) 35,2 B) 17,6 C) 70,4 D) 52,8
0
8. f (x) = 3x + b funksiya b ning qanday 6x3 · f (x)dx integralni hisoblang.
−2
qiymat(lar)ida toq funksiya bo‘ladi?
A) −4,8 B) −7,8 C) −8,4 D) −8,8
A) b > 0 B) b = 2n − 1, n ∈ N C) b < 0
D) b = 0
17. f (x) = 3x2 − 7x + 2 funksiyaga (3; f (3))
1 1 nuqtadan o‘tkazilgan urinma tenglamasini
9. 1 ; 1 ; 1; ... sonlar arifmetik progressiyaning
6 12 toping.
hadlari bo‘lsa, eng kichik musbat hadini toping.
A) y = 11x + 3 B) y = 11x − 25
1 1 1 1
A) B) C) D) C) y = −11x − 3 D) y = 11x − 21
24 3 12 4


1
T-108 Matematika(8000104) - Sotish taqiqlanadi!

18. ABC uchburchakning AB va BC tomonlaridan b
24. a va b natural sonlar uchun a + = 10 bo‘lsa, u
mos ravishda E va F nuqtalar shunday tanlab 3
olinganki B uchidan boshlab hisoblaganda (AB holda ab ifodaning eng katta qiymatini toping.
va BC tomonlarini) 2:3 nisbatda bo‘ladi. Agar A) 75 B) 54 C) 63 D) 72
ABC uchburchakning yuzi 75 ga teng bo‘lsa,
AEF uchburchakning yuzini toping.
25. Agar y = ln (5x + 1)2 − ln (2x + 1)5 + 4
A) 16 B) 15 C) 20 D) 18 funksiyaning grafigiga (x0 ; y0 ) nuqtada
19. Rasmda A va B to‘plamlar va U universial o‘tkazilgan urinma Ox o‘qiga parallel bo‘lsa,

to‘plam tasvirlangan. Quyidagi to‘plamlardan x20 + y02 ni toping.
qaysi biri bo‘yalgan sohaga mos to‘plamni A) 4 B) 5 C) 3 D) 6
tasvirlaydi? (A = U \A; B  = U \B)

B
 2    2
A 26. x2 + 1 + 5 x4 − 1 − 6 x2 − 1 = 0
tenglama nechta haqiqiy ildizga ega?
A) 1 B) 3 C) 2 D) 0


U 27. Muntazam to‘rtburchakli kesik piramida
asoslarining tomonlari 9 cm va 15 cm. Kesik
A) (A ∩ B  ) ∪ (A ∩ B) piramidaning diagonali 18 cm bo‘lsa, uning
balandligini (cm) toping.
B) (A ∩ B  ) ∪ (A ∩ B)
A) 6 B) 9 C) 7 D) 8
C) (A ∩ B  ) ∪ (A ∩ B)
D) (A ∩ B) ∩ (A ∪ B) 28. Mahsulotning narxi ketma-ket ikki marta
20. Tekislikda joylashgan AB kesmaning uzunligi oshirilgach yangi narxi dastlabkisidan
12 cm va BC kesmaning uzunligi esa 3 cm ga 124 foizga oshdi. Narx 1-marta 60 foizga
teng. AC kesmaning uzunligi (cm) oshirilgan bo‘lsa, 2-marta necha foizga
quyidagilarning qaysi biriga teng bo‘la olmaydi? oshirilgan?
A) 8 B) 9 C) 11 D) 10 A) 64 B) 30 C) 40 D) 32
21. Agar √ x = 17 bo‘lsa,√
x x − 64 4 x 8
+√ : √ −1 −4 29. α tekislik va uni kesib o‘tmaydigan AB=13 cm
x − 16 x+4 4− x
kesma berilgan. AB kesmaning uchlaridan α
ifodaning qiymatini toping.
√ √ tekislikkacha bo‘lgan masofalar AA1 =4 cm,
A) 4 B) −4 C) 17 D) − 17 BB1 =9 cm. AB kesma yotuvchi to‘g‘ri chiziq
22. ā (12; −5) vektor bilan Ox o‘qi orasidagi bilan α tekislik hosil qilgan burchakning
burchak kosinusini toping. kosinusini toping.
5 5 12 12 5 4 9 12
A) − B) − C) D) − A) B) C) D)
12 13 13 5 13 13 13 13
23. Agar
 b > a > c > 0 bo‘lsa,
(a − b)2 · (a − c)2 · (b − c)2 ifoda 30. Tekislikda o‘zaro kesishmaydigan a va b to‘g‘ri
quyidagilardan qaysi biriga teng? chiziqlar berilgan. a to‘g‘ri chiziqda 2 ta, b
A) (c − b)(c − a)(a − b) to‘g‘ri chiziqda 4 ta nuqta berilgan. Uchlari bu
B) (b − a)(a − c)(c − b) nuqtalarda bo‘lgan jami nechta to‘rtburchak
C) (c − a)(a − b)(b − c) mavjud?
D) (a − b)(a − c)(b − c)
A) 6 B) 5 C) 12 D) 8




2


Matematika(8000128) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. (7; −12) nuqtaning ordinatalar o‘qiga nisbatan π
11. sin 3x = cos(x − ) tenglamaning [0; π]
simmetrik bo‘lgan nuqtasini toping. 6
kesmadagi barcha yechimlari yig‘indisini toping.
A) (−7; 12) B) (7; 12) C) (12; −7)
2π 5π π π
D) (−7; −12) A) B) C) D)
3 6 6 3
2. Ifodani soddalashtirting:
sin 4α cos 2α sin 2α 12. Аylаnаgа ichki chizilgаn to‘g‘ri
· − + 1.
1 + cos 4α 1 + cos 2α 1 + cos 2α to‘rtburchаkning tоmоnlаri 32 vа 24 gа tеng.
A) 1 B) tg α + 1 C) cos α + 1 Аylаnаning uzunligini tоping.
D) sin α + 1 A) 80π B) 20π C) 40π D) 48π
3. Uzunligi 12π bo‘lgan aylanaga muntazam  
2 2 1
oltiburchak va ABC uchburchak ichki 13. (2x − 3) − 4 (2 − x) − 3 x − 1 ifodaning
3
chizilgan. ABC uchburchakning o‘tkir burchagi 2
60◦ bo‘lib, uning AB tomoni aylananing x = dagi qiymatini toping.
3
markazidan o‘tadi. Muntazam oltiburchakning 1 1
yuzi ABC uchburchakning yuzidan qanchaga A) −1 B) −2 C) −3 D) 2
3 3
katta?
√ √ √ √
A) 36 3 B) 18 3 C) 48 3 D) 32 3 14. A = {x| x ≥ 2, x ∈ Z} to‘plamning Z
to‘plamgacha to‘ldiruvchi A to‘plamini toping.
4. Agar a ∈ (−0, 4; 0, 4) bo‘lsa, x4 + 0, 32 = 2a2 (A = Z\A)
tenglamalar nechtadan haqiqiy ildizlarga ega?
A) 2 B) 0 C) 0 yoki 2 D) 4 A) A = {x| x ≤ 1, x ∈ Z}
5. (−2a + 3b)2 algebraik ifoda quyidagilardan B) A = {x| x ∈ Z}
qaysi biriga aynan teng? C) A = {x| x ≤ 2, x ∈ Z}
A) 4a2 − 12ab + 9b2 B) 4a2 − 6ab + 9b2 D) A = {x| x < 1, x ∈ Z}
C) 4a2 + 6ab + 9b2 D) 4a2 + 12ab + 9b2
15. Piramidaning asosi to‘g‘ri burchakli
49 · 812 + 15 · 643 · 93
6. Hisoblang: · (0, (4))−1 uchburchakdan iborat bo‘lib, uning
129 + 45 · 68 gipotenuzasi 2 dm. Piramidaning har bir yon
√
A) 0,(1) B) 1,5 C) 0,5 D) 4 qirrasi 5 dm bo‘lib, ular asos tekisligi bilan α
7. Rasmda A va B nuqtalar son o‘qida burchak tashkil qiladi. tg α ni toping.
√
tasvirlangan. 2A + B ning son qiymatini 1 5
A) 1 B) C) D) 2
toping. 2 2
9, 5 birlik 7 birlik
3
16. Agar charxpalak 5 minutda 23 marta aylansa,
B -3 0 2,5 A 4
u 12 minutda necha marta aylanadi?
A) 6,5 B) 8 C) 12,5 D) 9,5 1
A) 57 B) 53 C) 54 D) 61
8. Arifmetik progressiyaning yettinchi hadi 2
birinchi hadining 25%iga teng. Agar
17. f (x) = ax2 + bx + c funksiyaning grafigi
a2 + a4 + a6 = 90 bo‘lsa, birinchi va beshinchi
A(−2; 5), B(3; 10) va C(−1; −2) nuqtalardan
hadi yig‘indisini toping.
o‘tadi. f  (3) − 2f (2) ning qiymatini toping.
A) 82 B) 76 C) 78 D) 72
A) 4 B) 6 C) −3 D) 9
9. Agar piramidaning qirralari soni bilan uchlari   √   √ √
soni yig‘indisi 34 bo‘lsa, uning yoqlari sonini 18. 2 x · 7 + 4 3 · 2 x − 3x = x tenglama
4

toping. ildizlarining o‘rta arifmetik qiymatini toping.
A) 10 B) 13 C) 12 D) 11 A) 4 B) 2 C) 0 D) 1
10. x2 · |x + 2| + x2 + 4x + 4 ≤ 0 tengsizlik nechta  3  3  2 
butun yechimga ega? 19. Hisoblang: 27 · 3−1 + 3−2 − 3−3 +3
A) cheksiz ko‘p B) 0 C) 3 D) 1 A) 6 B) 5 C) 4 D) 3


1
T-108 Matematika(8000128) - Sotish taqiqlanadi!

20. Tekislikda o‘zaro kesishmaydigan a va b to‘g‘ri 25. Ifodani
 7 soddalashtiring:
 1  (b > 0; b = 81)
1
chiziqlar berilgan. a to‘g‘ri chiziqda 2 ta, b b 12 − 3b 3 4b 4 + 12
to‘g‘ri chiziqda 4 ta nuqta berilgan. Uchlari bu 5 1
nuqtalarda bo‘lgan jami nechta to‘rtburchak b 6 − 9b 3
1 1
mavjud? A) −4 B) 4b 3 C) 4b 12 D) 4
A) 5 B) 12 C) 8 D) 6
2x−2 √ 26. Ikkita natural sonning yig‘indisi 15 ga teng
21. 8 x = 4x−1 tenglamaning ildizlari x1 va x2 bo‘lsa, ularning ko‘paytmasi quyidagi sonlardan
bo‘lsa, |x1 − x2 | ni toping. qaysi biriga teng bo‘lishi mumkin?
A) 4 B) 5 C) 1 D) 6 A) 34 B) 37 C) 35 D) 36
x2 + 6x + 7
22. Integralni hisoblang: dx 31+log4 5 · 4log5 3 · 5log3 4
x2 + 6x + 10 27. Hisoblang:
3log5 4 · 4log3 5 · 5log4 3
A) x + 3arctg (x + 3) + C A) 2 B) 4 C) 3 D) 1
B) x + 3 arcsin (x + 6) + C
28. f (x) = x2 − 2x + c funksiyaning nollaridan biri
C) x − 3arctg (x + 3) + C
3 bo‘lsa, ikkinchisini toping.
D) x − 3 arcsin (x + 1) + C A) 0 B) −1 C) 1 D) −5
23. Birinchi moddiy nuqta
S1 (t) = t3 − 3t2 + 6t + 2 [m], ikkinchisi 29. Agar ikkita to‘g‘ri chiziq kesishganidan hosil
1 bo‘lgan burchaklarning ikkitasini gradus
S2 (t) = t3 + t2 − 3t + 1 [m] qonuniyat bo‘yicha
3 o‘lchovlari 8:7 nisbatda bo‘lsa, bu
harakatlanmoqda. Ularning tezlanishlari teng burchaklarning farqini toping.
bo‘lgan vaqtdagi birinchisining tezligini (m/s) A) 12◦ B) 7◦ C) 9◦ D) 8◦
toping. (t − vaqt, s)
A) 9,5 B) 4 C) 6 D) 8 30. Ikki sonning yig‘indisi 78 ga teng. Agar shu
1
24. y = −3x + 7 chiziqli funksiyaning (0; 0) sonlardan birining 40%i ikkinchisining
4
nuqtaga nisbatan simmetrigini toping. qismiga teng bo‘lsa, berilgan sonlardan
A) y = −3x + 7 B) y = 3x − 7 kattasini toping.
C) y = −3x − 7 D) y = 3x + 7
A) 44 B) 56 C) 48 D) 40




2


Matematika(8000152) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Tenglamani yeching: 8. To‘g‘ri burchakli parallelepipedning uchta turli
x−2 x−2 x−2 x−2 1 yoqlarining diagonallari 7; 8 va 9 dm bo‘lsa,
+ + + =1
3·5 5·7 7·9 9 · 11 11 parallelepipedning diagonali uzunligini (dm)
A) 14 B) 4 C) 11 D) 8 hisoblang.
√ √ √ √
A) 94 B) 4 6 C) 97 D) 6 3
2. (4x − 1)2 − (3 + 4x) (x − 2) − x (10x − 1) ≤
≤ 25 − 2x tengsizlikning eng katta va eng 9. Ketma-ket kelgan uchta tub sonlar yig‘indisi
kichik butun yechimlari yig‘indisini toping. quyidagi sonlardan qaysi biriga teng bo‘lishi
mumkin?
A) 4 B) 0 C) 3 D) 1
A) 21 B) 9 C) 15 D) 6
3. 2m + 3; 3m + 5; 4m + 7; ... hadlari berilgan
3 1
arifmetik progressiyaning dastlabki to‘qqizta 10. a ning 18% i 60 ning qismiga teng. a ning
5 5
hadi yig‘indisi 153 ga teng. m ning qiymatini qismi 15 sonidan qanchaga ko‘p?
toping.
A) 25 B) 10 C) 15 D) 20
A) 2 B) 1 C) −1 D) 3
11. Agar prizmaning qirralari soni bilan yoqlari
4. Rasmda y = f (x) funksiya grafigi va unga soni yig‘indisi 38 bo‘lsa, uning uchlari sonini
(3; 2) nuqtadan o‘tkazilgan urinmasi toping.
tasvirlangan. Agar g (x) = (x − 2) · f (x) A) 20 B) 10 C) 18 D) 9
bo‘lsa, g  (3) ni toping.
y 12. Qutida 4 ta qora va 5 oq shar bor. Qutidan
tavakkaliga olingan ikkita sharning ikkalasi
4
ham oq shar bo‘lishi ehtimolligini toping.
2 5 1 1
A) B) C) D)
9 18 3 6
2
f (x) 13. Agar tg α + ctg α = 3 bo‘lsa,
1 tg 2 α − 2 tg α + ctg α ifodaning qiymatini toping.
x A) 4 B) 2 C) 1 D) 3
0 3

14. 15 · 221 · 517 ko‘paytma nechta nol bilan
2 1 1 2 tugaydi?
A) 1 B) 1 C) 2 D) 2 A) 22 B) 18 C) 19 D) 21
3 3 3 3
15. f (x) = kx + 2 funksiya k ning qanday
5. y = x2 − 2x + 2 kvadrat funksiyaning y=2 qiymatlarida kamayuvchi bo‘ladi?
chiziqqa nisbatan simmetrik funksiyasini
A) k > 0 B) k < 0 C) k ∈ R
aniqlang.
D) k = 2n − 1, n ∈ N
A) y = −x2 + 2x + 1 B) y = −x2 + 2x + 2
C) y = −x2 + 2x D) y = −x2 + 2x − 2 16. A, B, C, D, E va F nuqtalar tartib bo‘yicha
muntazam oltiburchakning uchlari bo‘lsa,
2x+2 − 24 quyidagi vektorlardan qaysi biri AD vektorga
6. ≥ 1 tengsizlikni yeching.
2x+1 − 8 teng?
   
 
1 A) 2 DC + DE  B) −2  DC + DE 
A) (0; 2) B) ; +∞ C) (2; +∞) C) −2 DC − DE D) 2 DC − DE
2
D) (−∞; 2) ∪ [3; +∞)
17. Hisoblang:
7. Agar ikkita to‘g‘ri chiziq kesishganidan hosil −2019 + 2019 − 2019
 + ... + 2019 − 2019
bo‘lgan burchaklarning ikkitasini gradus 2019 ta

o‘lchovlari 8:7 nisbatda bo‘lsa, bu A) 2019 B) 0 C) −2019 D) 2018
burchaklarning farqini toping. 18. Hisoblang: (tg 435◦ − tg 375◦ ) : sin 120◦ .
A) 7◦ B) 9◦ C) 12◦ D) 8◦ A) 3 B) 2 C) 1 D) 4


1
T-108 Matematika(8000152) - Sotish taqiqlanadi!

1
24. Rasmdan foydalanib, ((A ∩ B) ∪ C) ∩ D
19. x · cos x2 dx integralni hisoblang.
0 to‘plamning elementlari sonini toping.
cos 1 sin 1 sin 1 D
A) B) − C) 0 D) A B C
2 2 2 d
√ a m
20. Agar x = 13 bo‘lsa, b
c l n
x−4 √ e
√ − x − 3 − 3 ni hisoblang. k, p, q
x−3−1
A) −4 B) −2 C) 2 D) 4 A) 1 B) 3 C) 4 D) 0
21. Rasmda ABC uchburchak va uning o‘zaro 25. Hisoblang:
perpendikulyar AD va CE medianalari (log2 3 + 4 log3 2 − 4) · log2 3 + log2 12.
tasvirlangan. Agar AB=8 va BC=10 bo‘lsa, A) 2 B) 8 C) 4 D) log2 9
AC ni toping.
B 26. Ikki shahar orasidagi masofa 126 km. Bu
masofa 1:6000000 masshtabli xaritada necha
millimetrga teng bo‘ladi?
D
A) 0,21 B) 2,1 C) 210 D) 21
E √
O 2 − 15 √
27. √ − 2 + 1 ni hisoblang.
2+1−4
A C A) 4 B) −2 C) 0 D) 2

√ |x − 1|
43 41 42 28. x2 − x · − 6 = 0 tenglamaning haqiqiy
A) 2 B) 4 2 C) 2 D) 2 x−1
5 5 5 ildizlari ko‘paytmasini toping.
3n2 + 2n − 18 A) −4 B) 36 C) −9 D) −6
22. Ushbu kasrning qiymati natural
n 2
son bo‘ladigan n (n ∈ N ) ning barcha 29. (3 − a) (a + 4) − a (−a − 6) ifodaning a = 2
5
qiymatlari yig‘indisini toping. bo‘lgandagi qiymatini toping.
A) 39 B) 38 C) 33 D) 36 2 3
A) 21 B) 10 C) 24 D) 8
23. Teng yonli uchburchakning ikki tomoni 2 va 5 5
5 ga teng. Uchburchakning eng kichik
17 75x2
medianasi uzunligini toping. 30. f (x) = + funksiyaning eng kichik
√ 3x2 17
33 √
A) 6,5 B) 13 C) D) 33 qiymatini toping.
2 A) 6 B) 12 C) 10 D) 8




2


Matematika(8000176) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Agar y = f (x) funksiya uchun 11. Ixtiyoriy uchtasi bir to‘g‘ri chiziqda yotmagan
x · f (3x − 2) = x4 + 2x − 5 shart bajarilsa, 10 ta nuqtani o‘zaro tutashtirib ko‘pi bilan
f  (1) ni toping. nechta har xil kesma hosil qilish mumkin?
8 2 A) 10 B) 45 C) 55 D) 90
A) 8 B) −2 C) D) −
3 3 12. Uchlari S(1; 1; 1), A(13; 1; 1), B(1; 13; 1) va
2. Ko‘paytuvchilarga ajrating: C(1; 1; 13) nuqtalarda bo‘lgan muntazam
x (3x − 4y) − 6x + 8y uchburchakli piramidaning hajmini toping.
A) (x − 2) · (3x − 4y) B) (x − 2) · (3x + 4y) A) 366 B) 144 C) 256 D) 288
C) (x + 2) · (3x − 4y) D) (x − 2) · (4y − 3x) 13. Hisoblang:
√ √ √ √
6 3 108 − 5 3 256 + 12 4 32 − 8 4 162
1 √ √ √
3. Integralni hisoblang: (2x + 1) cos(x2 + x)dx A) − 4 2 B) 0 C) −2 3 4 D) 2 3 4
0 14. b2 ning qanday qiymatlarida f (x) = x2 + bx + 3
A) −2 sin 2 B) sin 2 C) − sin 2 D) 2 sin 2 funksiya abssissalar o‘qini ikkita nuqtada kesib
o‘tadi?
4. f (x) = (k + 2) x + 2 funksiya k ning qanday A) b2 = 12 B) b2 > 12 C) b2 > 0
qiymatlarida o‘suvchi bo‘ladi? D) b2 < 12
A) k > −2 B) k ∈ R C) k < −2 15. Silindrning balandligi 5 ga, o‘q kesimining
D) k < 0 diagonali 13 ga teng. Silindr asosining radiusini
 3 3

a2 + b2 a−b a−b √ toping.
5. Ushbu − 1 · √ − a √ √
a−b 1 A) 6 B) 4 3 C) 6 2 D) 12
√ a2 + b2 ab
ifodaning a = 2, b = 8 dagi qiymatini toping. 16. To‘g‘ri burchakli uchburchakning tomonlari
√ √ ayirmasi 1,5 ga teng bo‘lgan arifmetik
A) − 2 B) 2 C) 0 D) 2 2
progressiyani tashkil etadi. Uchburchakning
 √ 4x+5 √  −2x
6. 4 2 = 2 3 tenglamani yeching. perimetrini toping.
17 21 9 15 A) 17 B) 16 C) 15 D) 18
A) − B) − C) − D) −
16 16 16 16 17. 24; 36; 48; ... arifmetik progressiyada an = 180
2n + 5
7. g(x) = (f (x))96 funksiya berilgan. Agar bo‘lsa,
n−3
ning qiymatini toping.
g  (1)
f  (1) = 0 va f (1) = −1 bo‘lsa,  ning 4 1
f (1) A) 3 B) 3 C) 1, 5 D) 3
qiymatini toping. 7 10
A) 97 B) 95 C) 1 D) −96 2
18. Agar sin α = bo‘lsa,
5
8. ABCD parallelogrammning BC va CD
cos6 α − 3 cos4 α + 3 cos2 α + sin6 α − 1 ning
tomonlaridan mos ravishda M va N nuqtalar
qiymatini toping.
shunday tanlab olinganki C uchidan boshlab
hisoblaganda (BC va CD tomonlarini) 1:3 A) 0 B) −2 C) 1 D) −1
nisbatda bo‘ladi. Agar parallelogrammning 19. 34974 sonning raqamalari joylarini almashtirib
yuzi 64 ga teng bo‘lsa, AM N D jami nechta har xil 5 xonali son hosil qilish
to‘rtburchakning yuzini toping. mumkin?
A) 32 B) 38 C) 36 D) 40 A) 120 B) 20 C) 30 D) 60
√ √  
x+1 x+2 7 2x − x2 − 4 (x + 3)
9. √ +√ = tenglama nechta 20. > 0 tengsizlikni yeching.
x+2 x+3 6 x2 − 9
haqiqiy ildizga ega? A) (−∞; 2) ∪ (2; 3) B) (−∞; 3) C) (2; 3)
A) 0 B) 1 C) 2 D) 4 D) (−∞; −3) ∪ (−3; 3)
10. Agar f (x) 3
 =log2 x + 1 bo‘lsa, 21.
9 − x2
=
9 − x2
1 2x + 5 x−5
tenglama nechta haqiqiy
f (2) + f = f (x) tenglamani yeching.
x ildizga ega?
√ √ √
A) 2 B) 3 4 C) 2 2 D) 4 8 A) 4 B) 0 C) 3 D) 2


1
T-108 Matematika(8000176) - Sotish taqiqlanadi!

22. Kasrning maxraji suratidan 8 ga ortiq bo‘lib, 5 2
26. 2019 − 2017 ni hisoblang.
ularning yig‘indisi 30 ga teng. Bu kasrning 26 13
suratidan 1 ni ayirib, maxrajiga 1 ni qo‘shsak, 27 24 53 51
A) B) C) D)
kasrning qiymati quyidagilardan qaysi biriga 13 13 26 26
teng bo‘ladi?
3 5 1 2 27. Ikki shahar orasidagi masofa 126 km. Bu
A) B) C) D)
7 6 2 5 masofa 1:6000000 masshtabli xaritada necha
23. Hisoblang:   millimetrga teng bo‘ladi?
5
(0, (2) + 3, 6 (1)) : 1 − 1, 91 (6) + 42, 5. A) 210 B) 2,1 C) 21 D) 0,21
6
A) −0, 5 B) 0, 5 C) −3, 5 D) 3, 5 √
3 3
24. A = {1; 2; 3; 4}, B = {x| x = 2n − 1, n ∈ A} 28. Hisoblang: √ +√ + 3
3 − 12 3
bo‘lsa, A ∩ B to‘plamni aniqlang.
A) 2 B) −3 C) 3 D) −2
A) {1; 3; 4} B) {1; 2; 3} C) {1; 3}
D) {1; 2; 4}
29. y ning qanday qiymatlarida a (−2; y; −9)
25. sin x = sin 1 tenglamaning barcha yechimlarini
vektorning uzunligi 11 ga teng bo‘ladi?
toping.
A) y = ±7 B) y = ±9 C) y = ±6
k
A) x = (−1) + πk, k ∈ Z D) y = ±2
B) x = 1 + 2πk, k ∈ Z
30. 2513 + 16127 + 27 yig‘indi qanday raqam bilan
C) x = −1 + 2πk, k ∈ Z
tugaydi?
D) x = 1 + πk, k ∈ Z
A) 5 B) 8 C) 3 D) 6




2


Matematika(8000200) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Tenglamani yeching: tg (2x + 3) = tg (3x − 2) 8. α tekislik va uni kesib o‘tmaydigan AB=13 cm
kesma berilgan. AB kesmaning uchlaridan α
A) x = 5 + πk, k ∈ Z tekislikkacha bo‘lgan masofalar AA1 =4 cm,
B) x = πk, k ∈ Z BB1 =9 cm. AB kesma yotuvchi to‘g‘ri chiziq
bilan α tekislik hosil qilgan burchakning
C) x = 1 + πk, k ∈ Z
kosinusini toping.
1 + πk 12 4 5 9
D) x = , k∈Z A) B) C) D)
5 13 13 13 13
 √  2 
2. x · cos 3xdx integralni hisoblang. 9. y = 6 − x + log(4−x) x − 4 funksiyaning
aniqlanish sohasini toping.
x 1
A) − · sin 3x − cos 3x + C
3 9 A) (2; 4)
x 1 B) (−∞; −2) ∪ (2; 4)
B) − · sin 3x + cos 3x + C
3 9 C) (−∞; −2) ∪ (2; 3) ∪ (3; 4)
x 1
C) · sin 3x + cos 3x + C D) (2; 3) ∪ (3; 4) ∪ (4; 6)
3 9
x 1 10. b2 ning qanday qiymatlarida f (x) = x2 + bx + 3
D) · sin 3x − cos 3x + C funksiyaning grafigi abssissalar o‘qidan
3 9
yuqorida joylashadi?
3. Agar qisqarmaydigan kasrning surati 3 ga A) b2 > 12 B) b2 > 0 C) b2 = 12
6 D) b2 < 12
orttirilsa, kasrning qiymati ga, maxraji 2 ga
7
3 11. Quyidagi fikrlardan qaysi biri natural sonlar
kamaytirilsa, kasrning qiymati ga teng uchun har doim to‘g‘ri?
4
7
bo‘ladi. Berilgan kasrning qismini toping. A) barcha tub sonlar toq sonlardir
27
3 1 1 2 B) ikkita tub sonlar yig‘indisi juft son bo‘ladi
A) B) C) D)
4 12 6 3 C) faqat uchta natural bo‘luvchiga ega bo‘lgan
 son biror tub sonning kvadratiga teng bo‘ladi
2
4. Hisoblang: 125 3 · 4 · 3 (0, 027)2 + 3 D) ikkita tub sonlar ko‘paytmasi toq son bo‘ladi
A) 6 B) 12 C) 3 D) 13  √
|x − 3| = 3√ y + 2
12. tenglamalar sistemasi
3x + 2 |y + 2| = 3 x − 3
5. k ning qanday qiymatlarida =k+2 nechta haqiqiy yechimga ega?
4x − 3
tenglamaning ildizi 1 dan kichik bo‘ladi? A) 3 B) 2 C) 4 D) 1
A) (−∞; −1, 25) ∪ (3; ∞) 13. Agar OA : AA1 : A1 A2 : A2 A3 = 3 : 1 : 4 : 1
B) (−∞; −3) ∪ (1, 25; ∞) C) (−3; 1, 25) bo‘lsa, AB : A1 B1 : A2 B2 : A3 B3
D) (−1, 25; 3) (AB||A1 B1 ||A2 B2 ||A3 B3 ) nisbatni aniqlang.
(rasm)
6. y = (x − 4) · (x − 1)2 funksiyaning ekstremum
nuqtalaridan o‘tuvchi to‘g‘ri chiziq tenglamasini B B1 B2 B3
O
tuzing.
A) y = 2x − 2 B) y = −2x − 2 A
C) y = 2 − 2x D) y = 2x + 2 A1
 x  x A2
1 1
7. − ≤ 12 tengsizlikning (−4; 4) A3
4 2
oralig‘idagi butun yechimlar sonini toping.
A) 3 : 1 : 4 : 1 B) 6 : 1 : 8 : 1 C) 3 : 2 : 4 : 9
A) 5 B) 2 C) 3 D) 6 D) 3 : 4 : 8 : 9


1
T-108 Matematika(8000200) - Sotish taqiqlanadi!
 
2x − x2 − 4 (x + 3) 22. (−2a + 3b)2 algebraik ifoda quyidagilardan
14. > 0 tengsizlikni yeching.
x2 − 9 qaysi biriga aynan teng?
A) (−∞; 2) ∪ (2; 3) B) (−∞; 3) C) (2; 3) A) 4a2 − 12ab + 9b2 B) 4a2 + 6ab + 9b2
D) (−∞; −3) ∪ (−3; 3) C) 4a2 − 6ab + 9b2 D) 4a2 + 12ab + 9b2
15. 6 ta to‘g‘ri chiziqlar ko‘pi bilan tekislikni
nechta qismga ajratadi? 23. 117 soni 90 sonidan necha foizga ortiq?
A) 16 B) 15 C) 21 D) 22 A) 35 B) 30 C) 25 D) 40
16. Grafigi A (−2; 11) nuqtadan o‘tuvchi
y = kx + 5 funksiya abssissalar o‘qini qaysi 25
24. Radiusi bo‘lgan sferaga balandligi 8 ga teng
nuqtada kesib o‘tadi? 4
      bo‘lgan konus ichki chizilgan. Konusning
1 1 2
A) 1 ; 0 B) 0; 1 C) −1 ; 0 hajmini toping.
 2  2 3
2 A) 96π B) 144π C) 192π D) 72π
D) 1 ; 0
3
17. A = {x| x2 ≤ 64, x ∈ R}, 25. Agar f (x) = (3x − 2)18 bo‘lsa, f  (1) ni
B = {x| x2 > 4, x ∈ N } bo‘lsa, A ∩ B hisoblang.
to‘plamni aniqlang. A) 36 B) 54 C) 27 D) 18
A) {2; 3; 4; 5; 6; 7; 8} B) {3; 4; 5; 6; 7; 8}
C) [2; 8] D) (2; 8] 26. 0, 0016 · 0, 004 · 0, 050 · 106 ko‘paytmaning
18. Tenglamani yeching: qiymati quyidagilardan qaysi biriga teng?
(3x + 1) + (3x + 3) + (3x + 5) + ... + (3x + 19) = A) 0,32 B) 0,032 C) 32 D) 3,2
= 40
A) −3 B) −2 C) −1 D) 2 27. Agar A (−2; 6; −9), B (−12; 6; −9), C (4; 6; 5)
19. Agar n va m natural sonlar uchun va D (14; −8; 15) nuqtalar berilgan bo‘lsa,
6n − 4m 1 2 AB + BC + CD vektorning koordinatalarini
= 1 tenglik bajarilsa, +
n n m toping.
ifodaning eng katta qiymatini toping. A) (16; −14; 24) B) (10; −11; 8)
7 13 6 9 C) (16; 14; −24) D) (−16; 0; −14)
A) B) C) D)
10 20 10 10
20. Hisoblang: 28. Rasmda ABC uchburchak va uning BD
√ √ √ √ √
19 + 2 · 38 + 57 − 6 − 2 medianasi tasvirlangan. Agar AC=2BD va
√ √ ∠CAB = 22◦ bo‘lsa, ACB burchakni toping.
3+ 2
B
A) 17 B) 19 C) 15 D) 18
21. Rasmda markazi K nuqtada bo‘lgan doira
tasvirlangan. Uning bo‘yalgan (shtrixlangan) A C
D
qismi yuzasini toping.
A) 58◦ B) 52◦ C) 62◦ D) 68◦
y
 −1
A(0; 5) a3 b + 2a2 b − 3ab 1 − a2
29. · + 2b
a3 + 5a2 + 6a a2 + 3a + 2
√
K(2 3; 3) 1
ifodaning a = , b = −6 dagi qiymatini toping.
3
x
O 1 1
A) −6 B) −6 C) D) 9
 √  4 (π − 3) 2 (π − 3) 3 3
A) 2 2π − 3 3 B) C)
3 3
√ 30. Agar tg α + ctg α = 3 bo‘lsa,
4 2π − 3 3
D) tg 2 α − 2 tg α + ctg α ifodaning qiymatini toping.
3 A) 3 B) 2 C) 4 D) 1




2


Matematika(8000224) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. (x − 3)log(x−3) (49−x ) ≤ 13 tengsizlikni yeching.
2
11. F (x) funksiya f (x) = x2 − x + 2 funksiyaning
A) (−7; −6] ∪ [6; 7) B) (3; 7) C) [6; 7) boshlang‘ich funksiyasi. F (x) funksiyaning
D) (3; 4) ∪ (4; 6] [0; 2] kesmadagi eng kichik qiymati 2 ga teng
bo‘lsa, uning [0; 2] kesmadagi eng katta
2. Hisoblang:
qiymatini toping.
(tg 435◦ − tg 375◦ ) · sin2 70◦ · sin2 50◦ · sin2 10◦ :
2 1 2 1
: sin 120◦ A) 5 B) 5 C) 6 D) 6
1 1 1 3 3 3 3
A) B) 1 C) D)
16 4 8 12. Grafigi A (−2; 11) nuqtadan o‘tuvchi
3. Ifodani
 soddalashtiring:  y = kx + 5 funksiya abssissalar o‘qini qaysi
1 1 1 nuqtada kesib o‘tadi?
+ + ·      
a · (a + 1) (a + 1) · (a + 2) (a + 2) · (a + 3) 2 2 1
A) 1 ; 0 B) −1 ; 0 C) 1 ; 0
a2 + 3a  3  3 2
·
9 1
D) 0; 1
1 1 2
A) a B) C) D) a + 3
3 9 13. Rasmda ABCD parallelogrammda BD
2
3n + 2n − 18 diagonal hamda BC va AD tomonlarini mos
4. Ushbu kasrning qiymati natural ravishda teng ikkiga bo‘luvchi AE va
n
son bo‘ladigan n (n ∈ N ) ning barcha CF kesmalar o‘tkazilgan. Agar
qiymatlari yig‘indisini toping. F DN uchburchakning yuzi 6 ga teng bo‘lsa,
A) 39 B) 36 C) 33 D) 38 BCD uchburchakning yuzini toping.
B E C
5. Yog‘liligi 5% bo‘lgan 12 litr sut bilan yog‘liligi
2% bo‘lgan necha litr sut aralashtirilsa, M

yog‘liligi 4,4% bo‘lgan sut hosil bo‘ladi? N
A) 4,2 B) 3 C) 2,5 D) 2
6. To‘g‘ri burchakli parallelepipedning uchta turli A F D
yoqlarining diagonallari 7; 8 va 9 dm bo‘lsa, A) 36 B) 42 C) 30 D) 54
parallelepipedning diagonali uzunligini (dm)
hisoblang. 14. Zokirning 25000 so‘m, Azizaning esa 17000 so‘m
√ √ √ √ puli bor. Zokir pulining necha foizini Azizaga
A) 97 B) 4 6 C) 94 D) 6 3
bersa, ularning pullari miqdori teng bo‘ldi?
7. Hisoblang:
 2   2 A) 18 B) 18,5 C) 14,5 D) 16
5√ 10
72 · − 15 + (−45) · −2 + 2x − y
6 3 15. Аgаr 4x = 125 vа 8y = 5 bo‘lsа, ni
y
1 √ 3 tоping.
+ · 3 −312
6 A) 6 B) −8 C) −6 D) 8
A) 23 B) 106 C) 1298 D) 98
−−
→ 16. A = {x| x ≥ 2, x ∈ Z}, B = {x| x < 8, x ∈ Q}
8. A, B, C nuqtalar uchun AB(−4; 3; − 4) va bo‘lsa, A ∩ B to‘plamning elementlari sonini
−→
AC(4; 3; − 3). ABC uchburchakning BC aniqlang.
tomonining uzunligini toping. A) 6 B) ∞ C) 8 D) 7
√ √
A) 8, 06 B) 65 C) 63 D) 8 17. Agar 43 − 2 (x − 6 (1 − 2 (2 − 3x))) = 63x
9. f (x) = cos (sin 2x − 1) funksiyaning x0 =0 tenglamaning ildizi x0 bo‘lsa, x20 − 3 ning
nuqtadagi hosilasini toping. qiymatini toping.
A) 0 B) −2sin1 C) 2cos1 D) 2sin1 A) 1 B) 6 C) −2 D) 13
√
10. Asosi 4 2 ga teng va unga yopishgan 18. Muntazam tetraedrning qirrasi 9 ga teng.
burchaklari 30◦ va 45◦ bo‘lgan uchburchakning Uning asosiga tashqi chizilgan aylananing
yuzasini toping. markazidan uning yon yoqigacha bo‘lgan eng
√ √  √
A) 8 3 + 1 B) 8 3 − 1 C) 4 3+2 qisqa masofani toping.
√ √ √ √
√ 
D) 16 3 − 1 A) 3 2 B) 6 C) 2 3 D) 2 6


1
T-108 Matematika(8000224) - Sotish taqiqlanadi!

19. Ko‘paytuvchilarga ajrating: 24. Tengsizlikni yeching:
x (3x − 4y) − 6x + 8y (3x − 12)2 · (4x − 12) ≥ (3x − 12) · (4x − 12)2
A) (x + 2) · (3x − 4y) B) (x − 2) · (3x − 4y) A) [4; +∞) B) (−∞; 0] ∪ [3; 4]
C) (x − 2) · (3x + 4y) D) (x − 2) · (4y − 3x) C) (−∞; 0] D) [0; 3] ∪ [4; +∞)
25. f (x) = x2 + bx − 1 funksiya abssissalar o‘qini
20. Quyida berilgan sonlardan eng kattasini toping. ikkita nuqtada kesib o‘tadigan b ning barcha
5 47 7 23 qiymatlarini toping.
A) B) C) D) A) b < −2 B) b < 2 C) b ∈ R D) b > 2
9 72 12 36
26. Hisoblang: 70 · 10−5 + 1, 8 · 10−4
21. Ikkita to‘g‘ri chiziqning kesishishidan hosil A) 8, 8 · 10−4 B) 88 · 10−6 C) 0, 88 · 10−1
bo‘lgan burchaklardan uchtasining yig‘indisi D) 8, 8 · 10−3
215◦ ga teng bo‘lsa, shu burchaklardan
3n
kattasining gradus o‘lchovini aniqlang. 27. Umumiy hadi xn = + 1 formula bilan
2
A) 115◦ B) 135◦ C) 145◦ D) 125◦ berilgan ketma-ketlikning dastlabki yigirmata
hadining o‘rta arifmetigini toping
22. Agar musbat a va b sonlar uchun
25 36 3 3 1 1
a + b = 14 bo‘lsa, + A) 16 B) 14 C) 14 D) 16
a b
ning eng kichik 4 4 4 4
qiymatini toping. 28. 43 · 47 · 28 · 32 − 18 · 63 · 27 ayirma qanday
61 121 123 62 raqam bilan tugaydi?
A) B) C) D)
7 14 14 7 A) 6 B) 4 C) 2 D) 8
29. Merganning nishonga tekkizish ehtimoli 0,8 ga
tg4x · tgx
23. = 0 tenglamani yeching. teng. U nishonga 3 marta o‘q uzganda barcha
tg2x o‘qlari nishonga tegishining ehtimolligini
toping.
3π
A) x = + πk, k ∈ Z A) 0,912 B) 0,8 C) 0,72 D) 0,512
4 ⎧
π ⎪
⎪ x y 2
B) x = + πk, k ∈ Z ⎨ − =2
2 y x 3
30. x va y sonlar 1
⎪
⎪
π ⎩ x−y =1
C) x = + πk, k ∈ Z 3
4 tenglamalar sistemasini qanoatlantirsa,
D) ∅ 3x + 1 ning eng katta qiymatini toping.
A) 10 B) 2 C) 3 D) 7




2


Matematika(8000248) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. 12 − 4x < x2 ≤ 9x tengsizlikni 1 1
11. 1 ; 1 ; 1; ... sonlar arifmetik progressiyaning
qanoatlantiruvchi barcha tub sonlar yig‘indisini 6 12
toping. hadlari bo‘lsa, eng kichik musbat hadini toping.
1 1 1 1
A) 17 B) 15 C) 24 D) 12 A) B) C) D)
4 24 12 3
2. Soddalashtiring: (a < 0)
√ a 12. log23 (27x) = log3 x6 tenglamaning ildizini
3 −a + √ toping.
−a
√ √ √ √ A) haqiqiy ildizga ega emas B) 3 C) 27
A) 4 a B) 2 a C) 2 −a D) 4 −a
 4  3  3 D) 9
3. −x3 · x2 : −x5 ifodaning x = −2 dagi 
qiymatini toping. 13. y = 1, 44 − x2 funksiya grafigiga o‘tkazilgan
urinma abssissa o‘qini (−2;0) nuqtada kesib
A) 0, 5 B) 8 C) −4 D) −8
o‘tsa, uning tenglamasini toping.
4. Uchburchakning asosiga tushirilgan balandligi 2 4 3 3
20 cm bo‘lib, asosidan 2 cm ga katta. Agar shu A) y = x + B) y = x +
3 3 4 2
balandlik 10% ga kamaytirilib, asosi esa 3 6 4 8
4 cm ga uzaytirilsa, uchburchakning yuzi C) y = x + D) y = x +
5 5 5 5
qanday o‘zgaradi?
A) 18 cm2 ga kamayadi B) 18 cm2 ga ortadi 14. f (x) = x2 − 5x − 6 funksiyaning nollari
C) 12 cm2 ga ortadi D) o‘zgarmaydi ko‘paytmasini toping.
A) −6 B) 6 C) 5 D) 0
5. Agar n va m natural sonlar uchun
6n − 4m 1 2 15. Agar P = 3a2 + 4b, Q = −2a2 − 3b bo‘lsa,
= 1 tenglik bajarilsa, +
n n m P + Q + 4b ni toping.
ifodaning eng katta qiymatini toping.
A) −a2 − 5b B) a2 + 5b C) −a2 + 5b
9 6 13 7 D) a2 − 5b
A) B) C) D)
10 10 20 10 √
16. 6x − x2 · (2x − 5) > 0 tengsizlikni nechta
6. −1, 25 soniga qarama-qarshi bo‘lgan sonning
butun son qanoatlantiradi?
teskarisi 0, 1 dan qanchaga katta?
A) cheksiz ko‘p B) 4 C) 0 D) 3
A) 1,15 B) 0,3 C) 0,4 D) 0,7
17. 2 ta har xil kitobni 12 ta o‘quvchidan 2 tasiga
7. Qisqarmaydigan oddiy kasrning maxraji
bittadan berish sharti bilan necha xil usulda
suratidan 3 birlikka katta. Agar kasrning
berish mumkin?
suratiga 1, maxrajiga 2 qo‘shilsa, hosil bo‘lgan
2 A) 66 B) 156 C) 132 D) 78
kasrning qiymati ga teng bo‘ladi. Berilgan
3 18. Qirralari 2 dm, 3 dm va 4 dm bo‘lgan to‘g‘ri
kasrning maxraji quyidagi sonlardan qaysi burchakli parallelepiped shaklidagi quti ichiga
biriga qoldiqsiz bo‘linadi? eng ko‘pi bilan qirrasi 7 cm bo‘lgan kublardan
A) 3 B) 8 C) 5 D) 6 nechtasini joylashtirish mumkin?
 −2
1 + mn−1 m−1 mn−1 n A) 42 B) 69 C) 45 D) 40
8. −1 · −1 −1 : ·
(mn) m n−n m n−m m 19. Rasmda tasvirlangan to‘g‘ri prizmaning
ifodaning m = 4 va n = 2, 5 bo‘lgandagi hajmini (dm3 ) toping.
qiymatini toping. 80cm

A) 10 B) 16 C) 1,6 D) −1, 5
9. f (x) = 13x5 + 6x3 − 27 funksiya berilgan
cm




bo‘lsa, f (f (x)) funksiyaning darajasi toping.
140




A) 9 B) 25 C) 15 D) 10
10. Agar cos 34◦ = a va sin 31◦ = b bo‘lsa, 20cm
sin 22◦ + sin 28◦ ni a va b orqali ifodalang.
  50cm
A) b2− a2 B) a2 − b2 C) 2 a2 − b2
D) 2 b2 − a2 A) 156 B) 169 C) 196 D) 182


1
T-108 Matematika(8000248) - Sotish taqiqlanadi!

20.
x2 + 4y = 21
tenglamalar sistemasi nechta 25. Agar a, b vektorlar uchun 2a + b = 6i + 9j va
y 2 − 4x = 21 a + 2b = −3i + 6j o‘rinli bo‘lsa, a vektorni
haqiqiy yechimga ega? toping.
A) 1 B) 4 C) 2 D) 3 A) ā (−5; −4) B) ā (−5; 4) C) ā (5; 4)
21. 2 · 116 − 5 natural son qaysi raqam bilan D) ā (5; −4)
tugaydi? 1  
26. 1 + cos−1 2α + tg 2α 1 − cos−1 2α + tg 2α
A) 2 B) 6 C) 7 D) 5 2
22. Rasmda ABCD parallelogrammga BD ifodaning α = 15◦ dagi qiymatini toping.
diagonal hamda BC va AD tomonlarini mos 1 2 √ √
A) √ B) √ C) 3 D) 2 3
ravishda teng ikkiga bo‘luvchi AE va 3 3
CF kesmalar o‘tkazilgan. Agar
27. Rasmda bo‘yalgan sohaning yuzasini toping.
ABCD parallelogrammning yuzi 72 ga teng y
bo‘lsa, BEM uchburchakning yuzini toping. 1
E
B C y = ax2 + bx + c


M
x
0 1 1
2
N
4 5 1 2
A) B) C) D)
A D 3 6 2 3
F
28. A = {x| x ≥ 2, x ∈ Z} to‘plamning Z
A) 6 B) 9 C) 8 D) 7,2 to‘plamgacha to‘ldiruvchi A to‘plamini toping.
 2 2
23. x − 12x + 10 = (3x + 10)2 tenglamaning (A = Z\A)
barcha yechimlari yig‘indisini toping.
A) A = {x| x ≤ 1, x ∈ Z}
A) 3 B) 19 C) 24 D) 20
24. Rasmda ABCD to‘g‘ri to‘rtburchak, BAD B) A = {x| x < 1, x ∈ Z}
burchakning AP bissektrisasi tasvirlangan. C) A = {x| x ≤ 2, x ∈ Z}
Agar BP =4 va P C=5 bo‘lsa, AP CD D) A = {x| x ∈ Z}
trapetsiyaning yuzini toping.
P 29. 6, 3; 4, 4; −3, 8; x va 7, 6 sonlarning o‘rta
B C arifmetigi 3,3 ga teng. x ning qiymatini toping.
A) 2,3 B) 2,6 C) 2 D) 1,8
1 π
30. f (x) = 2 funksiyaning x0 =
A D sin (2x − π) 4
nuqtadagi hosilasini toping.
A) 28 B) 24 C) 25 D) 27
A) 1 B) −2 C) −1 D) 0




2


Matematika(8000272) - Sotish taqiqlanadi! T-108

MATEMATIKA
 √
1. 4x − x2 x2 + 2x − 15 > 0 tengsizlikni 10. Uchlari Oxy tekisligining (0; 0), (0; 2), (4; 2) va
yeching. (1; 0) nuqtalarida bo‘lgan to‘rtburchakni Ox
A) [3; 4) B) (0; 3) ∪ (3; 4) o‘qi atrofida aylantirishdan hosil bo‘lgan
C) (−∞; −5] ∪ [3; 4) D) (3; 4) jismning hajmini toping.
A) 9π B) 12π C) 8π D) 6π
x2 − 7 |x| + 12
2. = 0 tenglama nechta haqiqiy π
(x − 3)2 11. sin 3x = cos(x − ) tenglamaning [0; π]
ildizga ega? 6
kesmadagi barcha yechimlari yig‘indisini toping.
A) 4 B) 2 C) 1 D) 3
π 5π π 2π
A) B) C) D)
n2 − n + 3 6 6 3 3
3. Agar n natural son uchun kasrning
n+1 12. 25log 5 x − 5 · 2log2 x = 24 tenglamaning ildizi x0
qiymati (2; 3) oralig‘ida joylashgan bo‘lsa,
bo‘lsa, x20 − 5x0 + 7 ning qiymatini toping.
kasrning shu oraliqdagi qiymatini toping.
A) 31 B) 30 C) 32 D) 33
A) 2,25 B) 2,75 C) 2,4 D) 2,5
13. Tekislikda o‘zaro kesishmaydigan a va b to‘g‘ri
√ 8x · 4x−1
4
4. 4x+1 = √ tenglamani yeching. chiziqlar berilgan. a to‘g‘ri chiziqda 2 ta, b
2 to‘g‘ri chiziqda 4 ta nuqta berilgan. Uchlari bu
1 2 5 nuqtalarda bo‘lgan jami nechta to‘rtburchak
A) B) 54 C) D) −
3 3 6 mavjud?
A) 5 B) 8 C) 6 D) 12
5. g(x) = x3 · f (x) funksiya berilgan. Agar
g  (2) 14. Mahsulotning narxi ketma-ket ikki marta
f  (2) = f (2) = 0 bo‘lsa,  ning qiymatini oshirilgach yangi narxi dastlabkisidan
f (2)
toping. 124 foizga oshdi. Narx 1-marta 60 foizga
A) 20 B) 22 C) 18 D) 24 oshirilgan bo‘lsa, 2-marta necha foizga
  √ oshirilgan?
 
6. |a| = 3 va b = 2, a va b vektorlar orasidagi A) 32 B) 64 C) 30 D) 40
π 15. f (x) = (x − 3)2 + 1 parabola uchining
burchak ga teng. 2a − b va 3a + 4b
4 koordinatalari ko‘paytmasini toping.
vektorlarning skalyar ko‘paytmasini toping.
√ √ A) 4 B) −2 C) −3 D) 3
A) 42 B) 46 + 5 2 C) 46 + 15 2 D) 61
16. Hisoblang: 70 · 10−5 + 1, 8 · 10−4
a2 + bc − ac − ab b A) 0, 88 · 10−1 B) 88 · 10−6 C) 8, 8 · 10−4
7. Agar 2 + c + b = 2 tenglikda D) 8, 8 · 10−3
ab − bc + ac − c
a = 18, b = −2 bo‘lsa, c ning qiymatini toping. 17. Sportchi seshanba kuni yugurish mashg‘ulotini
A) −19 B) 20 C) 9 D) 11 boshlab, 1350 metr masofaga yugurdi. Keyingi
har bir kunda esa oldingisidan 180 metr
8. Ko‘paytuvchilarga ajrating: (a + b)2 − c2 masofaga ortiq yugurdi. Sportchi 4410 metr
A) (a + b − c) · (a − b + c) masofaga yugurgan kuni mashg‘ulotini tugatdi.
B) (a − b − c) · (a + b + c) Sportchi haftaning qaysi kuni mashg‘ulotini
C) (a + b − c) · (a − b − c) tugatgan?
D) (a + b − c) · (a + b + c) A) chorshanba B) payshanba C) juma
D) shanba
9. Parallelogrammning tomonlari 10 va 14, o‘tmas
burchagi 150◦ ga teng. Barcha burchaklarining 18. a va b raqamlar yig‘indisi 13 ga qoldiqsiz
bissektrisalari o‘zaro kesishib, to‘g‘ri bo‘linadi. Agar aba ko‘rinishdagi uch xonali
to‘rtburchak hosil bo‘lgan. Shu to‘g‘ri sonlarni 13 ga bo‘lganda bir xil qoldiq qolsa,
to‘rtburchakning yuzini toping. shu qoldiqni toping.
A) 4 B) 12 C) 6 D) 8 A) 4 B) 6 C) 2 D) 0


1
T-108 Matematika(8000272) - Sotish taqiqlanadi!

19. A va B to‘plamlarning elementlari mos 25. ABC uchburchakning burchaklari 2:3:1
ravishda 24 va 36 sonlarining natural nisbatda. Agar eng kichik tomoni 5 cm bo‘lsa,
bo‘luvchilaridan iborat bo‘lsa, A ∩ B eng katta tomoni uzunligini (cm) toping.
√ √
to‘plamning elementlari sonini aniqlang. A) 5 2 B) 8 C) 10 D) 5 3
A) 6 B) 4 C) 8 D) 12
 √ √ √ 
20. Agar f (x) funksiya uchun 26. Hisoblang: 10 27 − 4 75 + 11 48 :
c + x · f (x) = (x − 1) · (2x − 1)11 munosabat  2
 √  1√4
o‘rinli bo‘lsa, f  (1) ni toping(c−o‘zgarmas son). : 2 3 − − 81
3
A) 1 B) 0 C) 2 D) −1 1
 A) 16 B) 8 C) 26 D) 24
21. 4x · ln 3xdx integralni hisoblang. 3

A) 4x2 ln 3x − 2x2 + C  2
27. x3 + 35x = 144x4 tenglamaning natural
B) 2x2 ln 3x − x2 + C
yechimlari yig‘indisini toping.
C) 2x2 ln 3x − 2x2 + C A) 35 B) 12 C) 7 D) 5
D) x2 ln 3x − 2x2 + C
22. Hisoblang: 28. α tekislik va uni kesib o‘tmaydigan AB kesma
(−9)3 : (−9)2 + (−10)3 : (−10) − (−2)8 : (−2)7 berilgan. Kesmaning uchlaridan α tekislikkacha
A) 93 B) −89 C) −197 D) 89 bo‘lgan masofalar AA1 =18 cm, BB1 =13 cm
23. Agar sin β + cos β = 1, 35 bo‘lsa, β burchakka bo‘lsa, AB kesmani A uchidan boshlab
mos keluvchi nuqta qaysi chorakda joylashgan? hisoblaganda 3:2 nisbatda bo‘luvchi C
nuqtadan α tekislikkacha bo‘lgan masofani
A) I B) III C) II D) IV
(cm) toping.
24. Rasmda markazi K nuqtada bo‘lgan aylana
tasvirlangan. Quyidagilardan qaysi biri A) 16 B) 15 C) 15,5 D) 14
berilgan aylananing tenglamasi bo‘ladi?
y 29. Agar f (x) funksiya (−∞; +∞) da qat’iy
o‘suvchi funksiya bo‘lsa, y = 3f (x) − 8 funksiya
A(0; 6) uchun quyidagi mulohazalardan qaysi biri doim
to‘g‘ri bo‘ladi?
K(2; 4)
A) qat’iy o‘suvchi
B) dastlab kamayadi, keyin o‘sadi
C) qat’iy kamayuvchi
x
O D) dastlab o‘sadi, keyin kamayadi

A) x2 + y 2 + 4x + 8y + 12 = 0 30. Uzunligi 80 metr bo‘lgan sim uzunliklari
B) x2 + y 2 − 4x − 8y + 24 = 0 5:7:13 nisbatda bo‘lingan. Hosil bo‘lgan
simlardan eng yengilining uzunligini (m)
C) x2 + y 2 − 4x − 8y + 12 = 0
toping.
D) x2 + y 2 − 4x − 8y + 16 = 0
A) 17 B) 16,6 C) 16,4 D) 16




2


Matematika(8000296) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Ifodani
 soddalashtiring:
 11. Hisoblang:
n2 1 1 sin 112◦
2 + n+m : + − cos 7◦ · cos 14◦ · cos 28◦ · cos 56◦ .
3 2 16 sin 7◦
m − mn 
m−n m 1 3
: − A) B) 1 C) 0 D)
m2 + mn n2 + mn 2 4
n m m
A) B) C) 12. y = 3x2 − 6x + 7 kvadrat funksiyaning
n−m m+n n−m
n ordinatalar o‘qiga nisbatan simmetrik
D)
m−n funksiyasini aniqlang.
3 1 A) y = −3x2 + 6x − 7 B) y = 3x2 + 6x + 7
2. a ning 18% i 60 ning qismiga teng. a ning C) y = 3x2 − 6x + 7 D) y = −3x2 − 6x − 7
5 5
qismi 15 sonidan qanchaga ko‘p?
A) 15 B) 25 C) 20 D) 10 13. a = 14, 88 · 1014 ; b = 28, 42 · 108 va
c = 34, 317 · 1011 sonlardan qaysilari 12 ga
3. f (x) = (x − 3)2 + 1 parabola uchining qoldiqsiz bo‘linadi?
koordinatalari ko‘paytmasini toping.
A) faqat b B) barchasi C) a va c
A) 4 B) 3 C) −3 D) −2 D) faqat c
 
4. Agar a (x − 2)2 + b (x − 2c) = 2 x2 − x + 16
tenglik ayniyat bo‘lsa, a + b + c ning qiymatini n2 − 6
14. n− natural soni uchun =3
toping. 335 + 18 · 316 + 1
A) 2 B) 6 C) −2 D) 8 n−3
tenglik o‘rinli bo‘lsa, ning qiymatini
5. Oltiburchakli prizmada nechta turli diagonal 814
toping.
o‘tkazish mumkin?
1 1
A) 12 B) 24 C) 18 D) 9 A) B) 27 C) 9 D)
3 9
6. Ifodani soddalashtiring:
5 (a − b) a2 − b2 15. a sonining 24%i 108 ning 18%iga teng bo‘lsa,
 2  :
3 a + b2 (a + b)2 − 2ab a ni toping.
5 5 5 A) 76 B) 72 C) 81 D) 88
A) − B) C)
3 (a − b) 3 (a + b) 3 (a − b)
5 16. f (x) = log2 x funksiyaning (1;0) va (2;1)
D) −
3 (a + b) nuqtalaridan o‘tuvchi to‘g‘ri chiziqqa parallel
7. Uchburchakning ikki tomoni va ular orasidagi bo‘lgan urinma tenglamasining burchak
mediana uzunliklari mos ravishda 15; 13; 7 koeffitsiyentini toping.
bo‘lsa, shu uchburchakning yuzini toping. 1 1 2
A) B) C) 1 D)
A) 70 B) 84 C) 72 D) 78 3 2 3
8. Kovak shar devorining hajmi 156π ga,
17. A = {a; b; c; d; e; f } to‘plamning nechta qism
devorning qalinligi 3 ga teng. Tashqi sharning
to‘plamiga, a element tegishli bo‘ladi?
radiusini toping.
A) 8 B) 64 C) 16 D) 32
A) 7 B) 6 C) 5 D) 4
1 2 2 1
9. a = 0, 6 3 · 1, 3− 5 , b = 0, 7− 3 · 0, 3− 5 va 18. 6 kishidan 4 ta kishini va bu 4 kishidan 2
1 2
c = 1, 8 3 · 0, 3− 5 sonlardan qaysilari 1 dan kishini necha xil usulda tanlab olish mumkin?
katta? A) 144 B) 120 C) 90 D) 60
A) a va c B) b va c C) faqat b D) a va b
√
4 x+1 8x · 4x−1
10. a ning qanday qiymatlarida uzunliklari mos 19. 4 = √ tenglamani yeching.
2
ravishda a + 2; 4 va 2a − 1 bo‘lgan kesmalardan 1 2 5
uchburchak yasash mumkin? A) B) C) − D) 54
3 3 6
A) (1; 7) B) (0; 7) C) (1; 8) D) (0; 5)


1
T-108 Matematika(8000296) - Sotish taqiqlanadi!

20. Rasmda berilgan ABC uchburchakda AD 26. f (x) = (sin x + cos x)2 funksiyaning
bissektrisa. Agar ∠ADC = 113◦ bo‘lsa, B boshlang‘ich funksiyasini toping.
burchak C burchakdan necha gradusga katta?
B 1
A) F (x) = −x − cos 2x + C
2
D 1
B) F (x) = −x + cos 2x + C
2
1
C) F (x) = x + cos 2x + C
2
A C
1
A) 67◦ B) 23◦ C) 46◦ D) 47◦ D) F (x) = x − cos 2x + C
2
 17 
 b − 1 (b + 1)
x2 + 4y = 21 27. Agar b = −3 bo‘lsa, 16
21. tenglamalar sistemasi nechta b + b15 + b14 + ... + b + 1
y 2 − 4x = 21 ifodaning qiymatini toping.
haqiqiy yechimga ega?
A) 8 B) 16 C) 15 D) 4
A) 2 B) 1 C) 4 D) 3
2
28. Agar sin α = bo‘lsa,
5
22. log23 (27x) = log3 x6 tenglamaning ildizini
cos6 α − 3 cos4 α + 3 cos2 α + sin6 α − 1 ning
toping.
qiymatini toping.
A) 3 B) 27 C) 9
A) 0 B) 1 C) −1 D) −2
D) haqiqiy ildizga ega emas
29. y = 17xto‘g‘ri chiziqqa parallel
 bo‘lgan
 3  3  2  11 · 36x x+1 1
f (x) = +6 · funksiyaning
23. Hisoblang: 27 · 3−1 + 3−2 − 3−3 +3 2 ln 6
urinma tenglamasini tuzing.
A) 6 B) 4 C) 5 D) 3
27 17
A) y = 17x + B) y = 17x +
√ ln 36 ln 36
24. 5 − 11x − 3x2 ≥ 1 tengsizlikning butun 23 13
yechimlari sonini toping. C) y = 17x + D) y = 17x +
ln 36 ln 36
A) 2 B) 4 C) 3 D) 5 30. Ixtiyoriy uchtasi bitta to‘g‘ri chiziqda
yotmaydigan A, B, C va D nuqtalar berilgan.
25. Hisoblang: −16, 28 + 8, 192 − 2, 131 + 9, 42. −−
→ −−→
Agar AB = 0, 8DC bo‘lsa, ABCD to‘rtburchak
A) −0, 668 B) −0, 648 C) −0, 789 turini aniqlang.
D) −0, 799 A) kvadrat B) parallelogramm
C) to‘g‘ri to‘rtburchak D) trapetsiya




2


Matematika(8000320) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Rasmda y = f (x) funksiyaning grafigi 7. Uchlari A(3; 6), B(5; 12) va C(9; 4) nuqtalarda
tasvirlangan. f  (x) · f (x) ≥ 0 tengsizlikning bo‘lgan uchburchakning BD medianasi
(0; 6) oraliqdagi yechimlarini toping. bo‘yicha yo‘nalgan birlik vektorni toping.
y    
1 7 3 4
4 A) √ ;− √ B) ;−
5 2 5 2 5 5
 



y=
3  
3 4 1 7



f(
C) − ; D) √ ; √


x)
5 5 5 2 5 2
8. Teng yonli uchburchakning perimetri 32 cm ga
x
−3 −2 −1 1 2 3 4 5 6 teng. Agar teng tomonlarining o‘rtalarini
−1 tutashtiruvchi kesma uzunligi 6 cm bo‘lsa,
uchburchakning yuzini (cm2 ) toping.
A) (0; 3] B) (0; 6) C) [3; 6) D) ∅ A) 56 B) 48 C) 54 D) 42
9. Oltiburchakli prizmada nechta turli diagonal
2. Kitobning narxi 12500 so‘m edi. Dastlab uning
o‘tkazish mumkin?
narxi 16% ga arzonlashdi, so‘ng 1850 so‘mga
qimmatlashdi. Kitobning oxirgi narxi necha A) 12 B) 24 C) 9 D) 18
so‘m bo‘ldi? 10. Ifodani soddalashtiring:
   
A) 12450 B) 12260 C) 12350 D) 12220 14π 8π
sin α + sin α − + sin α +
3 3
3. Rasmda ABCD parallelogramm tasvirlangan. A) cos α B) 0 C) 1 D) sin α
G nuqta BE va DF kesmalarning kesishish  √ √ −1
nuqtasi. Agar BF = F C va CE = ED bo‘lsa, a2 − 12 6 + 6a − 2a 6 36 − a2
11. · √
SABCD
ni toping. (a − 6)9 + a2 + (6 − a)9 − 24 a + 24
SABGD √
ifodaning a = 6 + 5 dagi qiymatini toping.
F √ √
B C A) 5 B) − 5 C) −1 D) 31
G
E 12. √
Agar a = 7 bo‘lsa,
√
a2 − 6a + 9 + a2 − 12a + 36 ifodani
A D qiymatini toping.
5 3 A) 4 B) 5 C) 7 D) 6
A) B) 2 C) D) 1 √ √
3 2 mn · 4 m m2 + 4
13. √
4
− 2 ifodaning m = 6
(m + 2) ·√ m−1 n2 m − 4
3|x| − 27
4. ≥ 0 tengsizlikni yeching. va n = 4 3 bo‘lgandagi qiymatini toping.
x−3 √ √
A) −2 3 B) 2 C) −0, 5 D) 3
A) [0; 3) ∪ (3; +∞) 14. Mis va ruxdan iborat qotishmaning massasi
B) [−3; 3) ∪ (3; +∞) 18 kg. Qotishmaning 60%ini rux tashkil qiladi.
Qotishmaning 50%ini mis tashkil qilishi uchun
C) [−3; +∞)
unga necha kilogramm mis qo‘shish kerak?
D) (−∞; 3) ∪ (3; +∞)
A) 3,4 B) 1,8 C) 4,2 D) 3,6
5. y = 3x2 − 12x + 15 kvadrat funksiyaning 15. Agar 0 < a < 1 bo‘lsa, quyidagilardan qaysi
qiymatlari to‘plamini aniqlang. biri ma’noga ega?
A) [2; +∞) B) [7; +∞) C) [−1; +∞) A) log2 loga (a + 1) B) log2 loga log2 3
D) [3; +∞) π
C) loga loga D) lg lg lg a
4
6. 0; 1; 2; 3; 4; 5 raqamlardan jami nechta
16. sin 4x = sin 3x tenglamaning eng kichik musbat
raqamlari takrorlanmaydigan 3 xonali sonlar
yechimini toping.
tuzish mumkin?
4π π 2π 6π
A) 180 B) 100 C) 216 D) 125 A) B) C) D)
7 7 7 7


1
T-108 Matematika(8000320) - Sotish taqiqlanadi!

17. Oltita musbat son geometrik progressiyani 24. To‘g‘ri chiziqda bir biri bilan ustma-ust
tashkil qiladi. Geometrik progressiyaning tushmaydigan 5 ta nuqta tanlangan. To‘g‘ri
9 chiziqda jami nechta kesma hosil bo‘ladi?
dastlabki ikkita hadining ko‘paytmasi ga,
8 A) 7 B) 10 C) 9 D) 4
oxirgi ikkita hadining ko‘paytmasi esa 288 ga
 dx
teng. Shu progressiyaning oxirgi ikkita 25. integralni hisoblang.
hadining yig‘indisini toping. sin (x − 1) · cos2 (x − 1)
2

A) 18 B) 36 C) 48 D) 34 A) 2ctg (2x − 2) + C B) 2tg (2x − 2) + C
C) −2ctg (2x − 2) + C D) −2tg (2x − 2) + C
18. Hisoblang:
3, 6 · 4, 8 + 5, 4 · 3, 6 + 4, 8 · 9, 2 − 4, 8 · 5, 6. 26. f (x) = ln xx−1 funksiyaning hosilasini toping.
A) 48 B) 54 C) 43,2 D) 72
1
A) f  (x) = ln x + +1
19. f (x) = −x + b funksiya b ning qanday x
qiymatlarida o‘suvchi bo‘ladi? 1
B) f  (x) = ln x − +1
A) b = 2n − 1, n ∈ N B) b < 0 C) b > 0 x
D) b ning hech qanday qiymatida C) f  (x) = ln x + 1
2
20. a va b natural sonlar uchun a +
b
= 10 bo‘lsa, u D) f  (x) = ln x − + 1
3 x
holda ab ifodaning eng katta qiymatini toping. x3 9x
27. ≤ tengsizlikning butun yechimlari
A) 54 B) 63 C) 75 D) 72 x−2 x−2
sonini toping.
21. Uchta tengdosh prizma balandliklari A) 7 B) 6 C) 4 D) 5
h1 : h2 : h3 =1:9:4 nisbatda bo‘lsa, prizmalar
1 2 3
asoslarining yuzlari qanday nisbatda bo‘ladi? 28. Amallarni bajaring: 3 − 2 −
6x 3x y 4y 2
A) S1 : S2 : S3 = 16 : 81 : 1
B) S1 : S2 : S3 = 4 : 9 : 1 2y 2 − 8xy − 9x2 2y 2 − 8xy − 9x3
A) B)
C) S1 : S2 : S3 = 36 : 4 : 9 12x3 y 2 12x3 y 2
2 2 3
D) S1 : S2 : S3 = 2 : 3 : 1 2y − 8x y − 9x 2y − 8xy 2 − 9x3
2
C) D)
  12x3 y 2 12x3 y 2
22. x2 + 9x = x2 + 9x − 20 tenglamaning haqiqiy √ √
ildizlari yig‘indisini toping. 29. Agar x2 − 3−2 x− 4+2 3 = 0
tenglamaning ildizlari x1 va x2 bo‘lsa, u holda
A) 9 B) yechimga ega emas C) −10 |x1 − x2 | ni toping.
D) −9 √ √ √ √
A) 3 B) 7 C) 11 D) 2
23. Agar A = {a, b, c, d, e} bo‘lsa, B ⊂ A (B = A, 30. a va b raqamlar yig‘indisi 7 ga qoldiqsiz
B = ∅) shartlarni qanoatlantiruvchi necha har bo‘linadi. Agar aba ko‘rinishidagi uch xonali
xil B to‘plam mavjud? sonlarni 7 ga bo‘lganda bir xil qoldiq qolsa, shu
A) 32 B) 14 C) 16 D) 30 qoldiqni toping.
A) 6 B) 2 C) 0 D) 4




2


Matematika(8000344) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. α tekislik va uni kesib o‘tadigan AB kesma 12. ABCD parallelogramda C o‘tkir burchak.
berilgan. Kesmaning uchlaridan α tekislikkacha E nuqta AB tomonda yotadi. Agar
bo‘lgan masofalar AA1 =12 cm, BB1 =13 cm AE:EB nisbat 2:3 kabi bo‘lsa,
bo‘lsa, AB kesmani A uchidan boshlab AECD to‘rtburchak yuzining
hisoblaganda 3:2 nisbatda bo‘luvchi C BCE uchburchak yuziga nisbatini toping.
nuqtadan α tekislikkacha bo‘lgan masofani 4 3 5 7
A) B) C) D)
(cm) toping. 3 2 3 3
A) 3,6 B) 3,2 C) 3 D) 4  
 9 

13.   > 2 4 tengsizlikning barcha butun
2. 43 · 47 · 28 · 32 − 18 · 63 · 27 ayirma qanday x − 3 7
raqam bilan tugaydi? yechimlari yig‘indisini toping.
A) 4 B) 6 C) 2 D) 8 A) 12 B) 18 C) 21 D) 15
1 2 1
3.  + = tenglama 14. A = {x| x ≥ 2, x ∈ Z} to‘plamning Z
x3 + 2 + 3 x3 + 2 + 7 2 to‘plamgacha to‘ldiruvchi A to‘plamini toping.
nechta haqiqiy ildizga ega? (A = Z\A)
A) 4 B) 2 C) 0 D) 1
A) A = {x| x < 1, x ∈ Z}
4. Agar ā (x; 2) va b (5; y) o‘zaro kollinear
vektorlar bo‘lsa, 2xy − 3 ning qiymatini toping. B) A = {x| x ≤ 1, x ∈ Z}
A) 7 B) 13 C) 17 D) 3 C) A = {x| x ∈ Z}
5. b2 ning qanday qiymatlarida f (x) = x2 + bx + 3 D) A = {x| x ≤ 2, x ∈ Z}
funksiya abssissalar o‘qini ikkita nuqtada kesib
15. y = cos2 2x − tg 2x · ctg 2x funksiyaning
o‘tadi?
qiymatlari sohasini toping.
A) b2 > 12 B) b2 = 12 C) b2 > 0
A) [0; 1] B) (−2; −1) ∪ (−1; 0) C) [−1; 0]
D) b2 < 12
√ D) (−1; 0)
 sin x
6. √ dx integralni hisoblang. 16. 
f (x) = 24tgx − 24x + 6π + 11 funksiyaning
x
π π
1 √ 1 √ − ; kesmadagi eng katta qiymatini toping.
A) − cos x + C B) cos x + C 4 4
2 √ 2 √ √ √
C) −2 cos x + C D) 2 cos x + C A) 14 3 + 11 B) 12 3 + 13 C) 24
D) 35
7. Aylanada 5 ta har xil nuqta berilgan. Uchlari
bu nuqtalarda bo‘lgan jami nechta turli vatar 3 1
17. a ning 18% i 60 ning qismiga teng. a ning
mavjud? 5 5
A) 12 B) 10 C) 15 D) 6 qismi 15 sonidan qanchaga ko‘p?
8. 6, 3; 4, 4; −3, 8; x va 7, 6 sonlarning o‘rta A) 10 B) 15 C) 20 D) 25
arifmetigi 3,3 ga teng. x ning qiymatini toping. tg4x · tgx
A) 2,6 B) 1,8 C) 2 D) 2,3 18. = 0 tenglamani yeching.
tg2x
 3 4  2 3  5 3
9. −x · x : −x ifodaning x = −2 dagi π
qiymatini toping. A) x = + πk, k ∈ Z
2
A) −4 B) −8 C) 8 D) 0, 5
B) ∅
10. y = log33 x − 12 funksiyaning qiymatlar 3π
to‘plamini toping. C) x = + πk, k ∈ Z
4
A) (−∞; 12) B) (12; ∞) C) (−∞; ∞) π
D) (0; ∞) D) x = + πk, k ∈ Z
4
11. y = −x4 + 8x2 − 9 funksiyaning eng katta
qiymati a bo‘lsa, a + 5 quyidagi sonlardan qaysi 19. f (x) = x2 − 5x − 6 funksiyaning nollari
biriga qoldiqsiz bo‘linadi? ko‘paytmasini toping.
A) 5 B) 9 C) 6 D) 8 A) 5 B) 6 C) 0 D) −6


1
T-108 Matematika(8000344) - Sotish taqiqlanadi!

20. Tenglamani yeching:    3|x| − 27
26. ≥ 0 tengsizlikni yeching.
1, 4 · (2 + 0, 6) · 4 + 0, 62 · 16 + 0, 64 · x = x−3
0, 68 − 256
A) 16 − 0, 64 B) −1 C) 0, 64 − 16 D) 1 A) [−3; 3) ∪ (3; +∞)
7 B) [0; 3) ∪ (3; +∞)
−1
8 8 1 C) [−3; +∞)
21. Hisoblang: + +
7 7 2 D) (−∞; 3) ∪ (3; +∞)
8
3 1 8 2
A) B) C) D)
2 7 7 3
27. Uchburchakli prizmaning yon qirralari orasidagi
n2 − n + 3
22. Agar n natural son uchun kasrning masofalar 37 cm, 15 cm va 26 cm ga teng. Agar
n+1 prizmaning yon qirrasi uzunligi 5 cm bo‘lsa,
qiymati (2; 3) oralig‘ida joylashgan bo‘lsa,
uning hajmini (cm3 ) toping.
kasrning shu oraliqdagi qiymatini toping.
A) 760 B) 790 C) 780 D) 770
A) 2,4 B) 2,75 C) 2,25 D) 2,5
23. 12 ta qatordan iborat bo‘lgan musiqa zalining
birinchi qatorida 28 ta o‘rindiq bor. Keyingi
har bir qatordagi o‘rindiqlar soni oldingi 28. Kasrning
√ maxrajini irratsionallikdan qutqaring:
qatordagidan 4 taga ko‘p. Musiqa zalida jami 3
√ √
nechta o‘rindiq bor? 2 3 − 13 − 1
√ √ √ √
A) 600 B) 612 C) 576 D) 504 1 − 2 3 − 13 1 − 2 3 + 13
A) B)
4xy 4
24. x+y− : √ √ √4 √
y+x 1 − 2 3 − 13 1 − 2 3 + 13
x y 2xy C) D)
: − − + 2y ifodaning 2 2
y + x y − x x2 − y 2
1
x = 2 va y = 2 bo‘lgandagi qiymatini toping.
3
 2  
1 1 29. −1, 5a2 b3 · −100a3 b4 ifodani
A) 7 B) C) 2 D) 4
3 3 soddalashtiring.
25. Rasmda ABC uchburchak va uning A) 225a7 b9 B) 225a7 b10 C) −225a7 b9
BD bissektrisasi tasvirlangan. Agar AB=5 va D) −225a7 b10
BC=7 bo‘lsa, DC : AC nisbatni toping.
B

30. O‘tmas burchagi α ga teng rombga ichki
chizilgan aylananing uzunligi L ga teng bo‘lsa,
rombning yuzasini toping.
L2 L2 L2
A D C A) B) C) · sin α
2πsin2 α π 2 sin α π2
5 5 7 7 2L2
A) B) C) D) D) 2 · cos α
12 7 5 12 π




2


Matematika(8000368) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. ⎧
Tengsizliklar sistemasini yeching: 11. To‘rtburchakli muntazam prizma asosining
⎨ x−4 x+4 diagonalini uning yon yoqi diagonaliga nisbati
≥
x+4 x−4 2:3 kabidir. Agar bu prizma asosining yuzi
⎩
(2 − x) (x + 6) > 0 14 dm2 bo‘lsa, uning hajmini (dm3 ) hisoblang.
√ √
A) (−6; −4) ∪ [0; 2) ∪ (2; 4) B) [0; 2) A) 196 B) 7 147 C) 7 161 D) 98
C) (−6; 0] D) (−6; −4) ∪ [0; 2)
12. Uchta sonning o‘rta arifmetigi 24, 3 ga teng.
3m+1 + 31−m Agar ulardan ikkitasi 34,8 va 18,9 bo‘lsa,
2. Kasrni qisqartiring: m  
(9 + 1) 32−m + 31−m uchinchi sonni toping.
1 1 1 A) 21,1 B) 19,8 C) 19,2 D) 18,6
A) B) m C) 31−m D)
4 4·3 8
13. Agar 2m + 3n = 72 (m, n ∈ N ) bo‘lsa, n ning
3. f (x) = kx + 3 funksiya k ning qanday eng katta qiymatini toping.
qiymatlarida toq funksiya bo‘ladi?
A) 22 B) 24 C) 20 D) 18
A) k ning hech bir qiymatida B) k < 0
C) k > 0 D) k ∈ R 3 1
14. a ning 18% i 60 ning qismiga teng. a ning
   5 5
4. m2 − n−1 m + n−2 m−1 + n − m (mn)−2 qismi 15 sonidan qanchaga ko‘p?
3
ifodaning m = , n = 0, (4) dagi qiymatini A) 25 B) 10 C) 20 D) 15
4
toping. 15. Hisoblang: −16, 28 + 8, 192 − 2, 131 + 9, 42.
3 A) −0, 668 B) −0, 789 C) −0, 799
A) 0,25 B) 1 C) 1 D) 4
4 D) −0, 648
5. A = {a; b; c; d; e; f } to‘plamning nechta qism
3 2
to‘plamlarida, b elementi bo‘lib, c elementi 16. 
3
+
3
= 2 tenglama
qatnashmaydi? 9x2 − 1 + 3 9x2 − 1 + 2
nechta haqiqiy ildizga ega?
A) 16 B) 28 C) 8 D) 32
A) 1 B) 0 C) 4 D) 2
16 − 0, 362
6. Hisoblang: . 17. Tenglamani yeching:
1, 4 · 4, 12 − 1, 52 · 1, 4
3 · 2x−2 − 5 · 2x−4 = 18 − 2x−3
A) 2,6 B) 3,64 C) 2,36 D) 4,36
  A) 5 B) −2 C) 3 D) 4
1
3 9
√
7. Hisoblang: 7 log64 49 − log3 log2 2 + 1.
18. Silindrning asosida 2 dm uzunlikdagi vatar 60◦
A) 12 B) 6 C) 11 D) 9 kattalikdagi yoyga tiralgan. Silindrning o‘q
8. Agar x=3, y=4 bo‘lsa, xy 2 x2 y − 13xyxy kesimi kvadratdan iborat bo‘lsa, uning hajmini
(dm3 ) toping.
ifodaning qiymatini toping. √ √
A) 144 B) −144 C) 72 D) −72 A) 8 3π B) 16π C) 4 3π D) 32π

1 1 1 1 5 19. Rasmda y = f (x) funksiyaning grafigi
9. 1− 1− ... 1 − 1− ·x = 1 tasvirlangan. f  (x) · f (x) ≥ 0 tengsizlikning
3 4 8 9 9
1 (0; 6) oraliqdagi yechimlarini toping.
tenglama ildizining qismini toping. y
14
A) 0, 5 B) 2 C) 1 D) 3, 5 4
y=




10. ABCD parallelogrammning BC va CD 3
f(
x)




tomonlaridan mos ravishda M va N nuqtalar
shunday tanlab olinganki C uchidan boshlab
hisoblaganda (BC va CD tomonlarini) 2:1 x
nisbatda bo‘ladi. Agar parallelogrammning −3 −2 −1 1 2 3 4 5 6
yuzi 54 ga teng bo‘lsa, AM N uchburchakning −1
yuzini toping.
A) 36 B) 12 C) 18 D) 24 A) [3; 6) B) (0; 3] C) (0; 6) D) ∅


1
T-108 Matematika(8000368) - Sotish taqiqlanadi!

20. Agar OA : AA1 : A1 A2 : A2 A3 = 3 : 1 : 4 : 1 π
24. sin 3x = cos(x − ) tenglamaning [0; π]
bo‘lsa, AB : A1 B1 : A2 B2 : A3 B3 6
(AB||A1 B1 ||A2 B2 ||A3 B3 ) nisbatni aniqlang. kesmadagi barcha yechimlari yig‘indisini toping.
(rasm) π π 2π 5π
A) B) C) D)
3 6 3 6
B B1 B2 B3
O 25. Arifmetik progressiyaning ikkinchi va oltinchi
hadlarining yig‘indisi 72 ga teng. Arifmetik
A progressiyaning ikkinchi hadining beshinchi
A1 7
hadiga nisbati ga teng bo‘lsa, uning oltinchi
A2 10
hadini toping.
A3 A) 42 B) 44 C) 40 D) 48
 √ √
A) 3 : 2 : 4 : 9 B) 6 : 1 : 8 : 1 C) 3 : 1 : 4 : 1 26. Hisoblang: 8 − 2 7 − 7 − 2
D) 3 : 4 : 8 : 9 A) −2 B) −1 C) 0 D) −3
  27. Bitta tashqi burchagi 15◦ ga teng bo‘lgan
21. A(6; 7) nuqtadan y = 2 x2 − 4x + 6 parabola muntazam ko‘pburchakning nechta tomoni bor?
uchigacha bo‘lgan masofani toping.
√ √ A) 32 B) 26 C) 30 D) 24
A) 3 2 B) 4 2 C) 4 D) 5 28. 3 ta turli lavozimga nomzodlari ko‘rsatilgan 5
kishidan 3 kishini necha xil usul bilan saylash
√ 4 sin4 α mumkin?
22. Agar tg α = 7 bo‘lsa,
5 sin2 α + 15 cos2 α A) 56 B) 60 C) 70 D) 64
ifodaning qiymatini toping.
29. a (1; 2); b (2; 1) va c (x; 2) vektorlar uchun
A) 0, 48 B) 0, 49 C) 0, 47 D) 0, 5 a · c + b · c + a · b = 13 bo‘lsa, x ni toping.
  A) 2 B) 1 C) −1 D) −2
23. f (x) = x2 − x + 2 · (x − 1) funksiyaning 1
x0 = 1 nuqtadagi hosilasini toping. 30. Integralni hisoblang: (2x + 1) cos(x2 + x)dx
0
A) −2 B) 0 C) 2 D) 1
A) − sin 2 B) −2 sin 2 C) 2 sin 2 D) sin 2




2


Matematika(8000392) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. f (x) = x2 + bx + c funksiyaning nollari 2 va 3 9. y = −3x + 7 chiziqli funksiyaning x=1 to‘g‘ri
bo‘lsa, c ni toping. chiziqqa nisbatan simmetrigini toping.
A) −5 B) 5 C) −6 D) 6 A) y = −3x − 1 B) y = −3x + 9
C) y = 3x − 9 D) y = 3x + 1
2. 1 gektar maydonga o‘rtacha 0,6 sentner zig‘ir
urug‘i ekiladi. 1:10000 masshtabli xaritada 10. (7; −12) nuqtaning ordinatalar o‘qiga nisbatan
bo‘yi 20 cm va eni 12 cm bo‘lgan to‘g‘ri simmetrik bo‘lgan nuqtasini toping.
to‘rtburchak shaklidagi yer maydoniga zig‘ir A) (−7; 12) B) (−7; −12) C) (7; 12)
urug‘i ekish uchun o‘rtacha necha sentner kerak D) (12; −7)
bo‘ladi? 11. Beshburchakli prizmada nechta turli diagonal
A) 40 B) 144 C) 400 D) 14,4 kesim mavjud?
3. A = {x| x = 4n + 3, n ∈ N }, A) 2 B) 10 C) 3 D) 5
B = {x| x = 6n + 5, n ∈ N } bo‘lsa, A ∩ B 12. α, β va γ − uchburchakning ichki burchaklari.
to‘plamni aniqlang. 2
Agar ctg β = − bo‘lsa, tg (α + γ) ning
3
A) {x| x = 12n + 11, n ∈ N } qiymatini toping.
B) {x| x = 24n − 13, n ∈ N } 2 2 1 1
A) − B) C) −1 D) 1
3 3 2 2
C) {x| x = 24n − 1, n ∈ N }
13. 34974 sonning raqamalari joylarini almashtirib
D) {x| x = 12n − 1, n ∈ N } jami nechta har xil 5 xonali son hosil qilish
   
4. x2 − 5x − 4 · x2 − 5x + 3 − 8 = 0 mumkin?
tenglamaning haqiqiy ildizlari yig‘indisini A) 20 B) 60 C) 30 D) 120
toping. 14. 117 soni 90 sonidan necha foizga ortiq?
A) 5 B) 1 C) 10 D) 4 A) 35 B) 30 C) 25 D) 40
√ √
5. Yoyiq burchakning A nuqtasidan chiquvchi 5 7+7 5 √
ikkita nur uni 2:4:3 nisbatdagi burchaklarga 15. Hisoblang: √ − 5
35
ajratadi. Eng katta burchakni toping. √ √ √ √ √ √
A) 7 − 5 B) 5 C) 7 + 5 D) 7

β x3 9x
γ 16. ≤ tengsizlikning butun yechimlari
α x−2 x−2
A sonini toping.
A) 80◦ B) 90◦ C) 40◦ D) 60◦ A) 7 B) 5 C) 4 D) 6
     3n
6. a2 − b2 a2 + b2 a4 + b4 a8 + b8 ifodaning 17. Umumiy hadi xn = + 1 formula bilan
√ √ 2
a = 8 6, b = 4 2 bo‘lgandagi qiymatini toping. berilgan ketma-ketlikning dastlabki yigirmata
A) 20 B) 4 C) −10 D) 2 hadining o‘rta arifmetigini toping
7. ABCD parallelogrammning BC va CD 1 3 1 3
A) 16 B) 16 C) 14 D) 14
tomonlaridan mos ravishda M va N nuqtalar 4 4 4 4
shunday tanlab olinganki C uchidan boshlab 18. Ifodani soddalashtiring (x > 0):
hisoblaganda (BC va CD tomonlarini) 1:3 2 2 2
+ +
nisbatda bo‘ladi. Agar parallelogrammning x (x + 2) (x + 2) (x + 4) (x + 4) (x + 6)
yuzi 64 ga teng bo‘lsa, AM N D 2x + 12 24 12
to‘rtburchakning yuzini toping. A) 2 B) 2 C) 2
x + 6x x + 6x x + 6x
A) 40 B) 32 C) 36 D) 38 6
D) 2
8. Ikki natural sonning EKUKi 168 ga teng va x + 6x
ularning nisbati 3:4 kabi bo‘lsa, kichik sonni 31+log4 5 · 4log5 3 · 5log3 4
19. Hisoblang:
toping. 3log5 4 · 4log3 5 · 5log4 3
A) 48 B) 36 C) 56 D) 42 A) 1 B) 4 C) 2 D) 3


1
T-108 Matematika(8000392) - Sotish taqiqlanadi!

20. Hisoblang: cos6 11◦ − 3 cos4 11◦ + 2 cos2 11◦ + 25. 
Agar m = 8 bo‘lsa, 
+ sin6 11◦ − sin2 11◦ √ 2 √ √ 2 √
( m + 3) − 12 m − ( m − 2) + 8 m
A) 0 B) 1 C) 2 D) −1 ifodaning qiymatini toping.
√ √
21. Uchburchakli piramida asosining tomonlari A) 1√ − 4 2 B) −4 2 − 1 C) −5
9 dm, 10 dm va 17 dm ga teng. Piramidaning D) 4 2 − 1
barcha yon yoqlari asos tekisligi bilan 45◦ li 26. 83, 4 · 0, 625 − 3, 34 · 2, 5 − 8, 34 · 3, 75 ni
burchak tashkil etsa, uning hajmini (dm3 ) hisoblang.
toping. A) 12,5 B) 1,25 C) 1,275 D) 12,75
A) 22 B) 24 C) 26 D) 28 27. 0, 0016 · 0, 004 · 0, 050 · 106 ko‘paytmaning
qiymati quyidagilardan qaysi biriga teng?
22. ABCD parallelogrammda, AD katta
tomonidagi A va D burchaklarining A) 3,2 B) 0,032 C) 0,32 D) 32
 √  √
bissektrisalari parallelogrammning ichki 28. 2x2 + 6 − 3 x = 3 3 tenglamaning eng
sohasida kesishgan bo‘lsa, tomonlari orasida katta ildizini toping.
√ √ √
qaysi munosabat to‘g‘ri bo‘ladi? A) 3 B) 2 3 C) 3 D) 0, 5 3
A) 2AB < AD B) 2DC < AD 
29. Integralni hisoblang: sin4 2xdx
C) 2AB > AD D) 2AB = AD
1
23. Agar y = f (x) funksiya uchun A) x − 2 sin 4x + sin 8x + C
2
x · f (3x − 2) = x4 + 2x − 5 shart bajarilsa,
f  (1) ni toping. 3 1 1
B) x + sin 4x − sin 8x + C
2 8 8 8 64
A) −2 B) − C) 8 D)
3 3 3
C) x + 2 sin 4x − sin 8x + C
8
24. f (x) = 3x2 − 7x + 2 funksiyaga (3; f (3))
3 1 1
nuqtadan o‘tkazilgan urinma tenglamasini D) x − sin 4x + sin 8x + C
8 8 64
toping.
A) y = 11x − 21 B) y = 11x + 3 30. Agar 3x + 33−x = 12 tenglamaning ildizlari x1
C) y = 11x − 25 D) y = −11x − 3 va x2 bo‘lsa, x1 + x2 + x1 · x2 ni hisoblang.
A) 7 B) 6 C) 5 D) 4




2


Matematika(8000416) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Soddalashtiring:
 9. Merganning nishonga tekkizish ehtimoli 0,8 ga
√ 2  4
 √ 4 teng. U nishonga 2 marta o‘q uzganda
2 1 − 10 − 2 10 − 4 .
√ √ o‘qlaridan biri nishonga tegishining
A) −4 10 B) 2 C) 4 10 D) 6 ehtimolligini toping.
    A) 0,8 B) 0,32 C) 0,16 D) 0,5
1 2 3 1 3 4
2. 2 a b · −3 a b ifodani
4 3 10. To‘rtburchakli muntazam prizma asosining
soddalashtiring.
diagonalini uning yon yoqi diagonaliga nisbati
1 1 1
A) −7 a5 b7 B) −7 a5 b7 C) −7 a5 b7 2:3 kabidir. Agar bu prizma asosining yuzi
12 3 4
14 dm2 bo‘lsa, uning hajmini (dm3 ) hisoblang.
1 5 7 √ √
D) −7 a b A) 98 B) 196 C) 7 147 D) 7 161
2

3. Rasmda grafigi keltirilgan f (x) funksiya uchun 11. Agar 43 − 2 (x − 6 (1 − 2 (2 − 3x))) = 63x
quyidagi tengliklardan qaysi biri to‘g‘ri? tenglamaning ildizi x0 bo‘lsa, x20 − 3 ning
y qiymatini toping.
4 A) 13 B) 1 C) −2 D) 6
y=




3 12. Funksiya grafigidan foydalanib, (−3; 6) oraliqda
f(
x)




f (x) · f  (x) ≤ 0 tengsizlikning eng katta manfiy
butun yechimini toping.
x
−3 −2 −1 0 1 2 3 4 5 6 y
−1
3




x)
f(
=
A) f  (−2) + f (−1) = 0




y
B) f  (−1) + f (−1) = 0 1
C) f  (−1) + f (−2) = 0 4
x
D) f  (−2) + f (−2) = 0 −3 −2 −1 0 1 2 3 5 6
−1
log3 12 + log4 12 1
4. Hisoblang: + · log2 4 A) −3 B) −1
log3 12 · log4 12 2
A) 0 B) 3 C) 2 D) 1 C) manfiy yechimga ega emas D) −2

5. Ketma-ket kelgan uchta tub sonlar yig‘indisi 3n
13. Umumiy hadi xn = + 1 formula bilan
quyidagi sonlardan qaysi biriga teng bo‘lishi 2
mumkin? berilgan ketma-ketlikning dastlabki yigirmata
hadining o‘rta arifmetigini toping
A) 21 B) 6 C) 9 D) 15
1 3 1 3
A) 14 B) 14 C) 16 D) 16
 1 4 4 4 4
6. 2 dx integralni hisoblang.
sin (2x − 3)  
2 2 1
ctg (3 − 2x) ctg (3 − 2x) 14. (2x − 3) − 4 (2 − x) − 3 x − 1 ifodaning
A) + C B) − +C 3
2 3
2
ctg (3 − 2x) ctg (3 − 2x) x = dagi qiymatini toping.
C) + C D) − +C 3
3 2
1 1
A) −2 B) −3 C) 2 D) −1
x 1 3 3
7. Tengsizlikni yeching: − ≤0
x−2 x
A) (2; +∞) B) (−∞; 0) C) (0; 2) 15. y = 3x2 − 6x + 7 kvadrat funksiyaning (0; 0)
D) (0; 3) nuqtaga nisbatan simmetrik funksiyasini
aniqlang.
8. Hisoblang: sin6 1 − 3 sin4 1 + 3 sin2 1 + cos6 1 + 1 A) y = 3x2 + 6x + 7 B) y = −3x2 + 6x − 7
A) −2 B) −1 C) 0 D) 2 C) y = 3x2 − 6x + 7 D) y = −3x2 − 6x − 7



1
T-108 Matematika(8000416) - Sotish taqiqlanadi!

16. Agar to‘g‘ri burchakli
√ uchburchakning √ 24. 0, 0016 · 0, 004 · 0, 050 · 106 ko‘paytmaning
katetlaridan biri 2 2 ga, gipotenuzasi 4 5 ga qiymati quyidagilardan qaysi biriga teng?
teng bo‘lsa, gipotenuzaga tushurilgan A) 0,032 B) 3,2 C) 32 D) 0,32
bissektrisa uzunligini toping.  6
√ a4 · a3
A) 4 B) 2 3 C) 3 D) 6 25.  3 ifodaning daraja ko‘rsatkichini
 √ a5
2 aniqlang.
17. Hisoblang: tg π − arccos .
2 A) 8 B) 7 C) 6 D) 5
√ √ 26. 7 soat 12 minut 40 sekundni sekundlarda
3 3
A) − B) 1 C) D) −1 ifodalang.
3 3
A) 25920 B) 25960 C) 25880 D) 25860
0, 4 (2) − 0, 2 (8) 27. ABCD qavariq to‘rtburchakka aylana ichki
18. Hisoblang:
0, (8) + 0, (7) chizilgan. Agar AB = 8 va BC = 12 bo‘lsa,
A) 0,8 B) 0,36 C) 0,4 D) 0,08 CD − AD ayirmani toping.
3 1 A) 4 B) 3 C) 2 D) aniqlab bo‘lmaydi
19. a ning 18% i 60 ning qismiga teng. a ning 28. Rasmda markazi K nuqtada bo‘lgan doira
5 5
qismi 15 sonidan qanchaga ko‘p? tasvirlangan. Uning bo‘yalgan (shtrixlangan)
A) 20 B) 25 C) 15 D) 10 qismi yuzasini toping.
y
20. f (x) = −x + b funksiya b ning qanday
qiymatlarida o‘suvchi bo‘ladi? A(0; 5)
A) b > 0 B) b = 2n − 1, n ∈ N
√
C) b ning hech qanday qiymatida D) b < 0 K(2 3; 3)

21. f (x) = 3|x| − 2 funksiyaning qiymatlar sohasini O
x
toping. √
A) (0; +∞) B) (−2; +∞) C) (−1; +∞) 2 (π − 3) 4 2π − 3 3
D) [−1; +∞) A) B)
3 3
4 (π − 3)  √ 
22. Muntazam to‘rtburchakli kesik piramida C) D) 2 2π − 3 3
3
asoslarining tomonlari 9 cm va 15 cm. Kesik
−−→
piramidaning diagonali 18 cm bo‘lsa, uning 29. A, B, C nuqtalar uchun CB(−3; 5; − 4) va
−→
balandligini (cm) toping. CA(4; 3; − 5). ABC uchburchakning C
A) 9 B) 7 C) 6 D) 8 uchidan AB tomoniga tushirilgan balandlik
uzunligini toping.
23. B = ∅ va B ⊂ A. A va B to‘plamlarning √ √
A) 36, 5 B) 6, 04 C) 37 D) 6
elementlari soni mos ravishda m va n ga teng. √ √
Agar n + 3m=18 bo‘lsa, A to‘plamning x+1 x+2 7
30. √ +√ = tenglama nechta
elementlari sonini toping. x+2 x+3 6
A) 5 B) 2 C) 4 D) 3 haqiqiy ildizga ega?
A) 2 B) 1 C) 4 D) 0




2


Matematika(8000440) - Sotish taqiqlanadi! T-108

MATEMATIKA
√
1. (a − 3) (a − 4) − 3 (a − 2) ifodaga qanday eng 12. f (x) = (x2 + x) · x2 + 1 funksiyaning x0 = 0
kichik butun son qo‘shilganda, ifodaning nuqtadagi hosilasini toping.
qiymati ixtiyoriy a ∈ R uchun musbat bo‘ladi? A) 1 B) −1 C) 2 D) 0
A) 8 B) 7 C) 6 D) 9 √
13. Hisoblang: 20192 − 2017 · 2021
2. To‘rtburchakli muntazam prizma asosining
A) 18 B) 12 C) 8 D) 2
diagonalini uning yon yoqi diagonaliga nisbati
2:3 kabidir. Agar bu prizma asosining yuzi 14. Sakkizta haddan iborat arifmetik
14 dm2 bo‘lsa, uning hajmini (dm3 ) hisoblang. progressiyaning toq o‘rindagi hadlari yig‘indisi
√ √ 168 ga, juft o‘rindagi hadlari yig‘indisi 200 ga
A) 7 161 B) 7 147 C) 98 D) 196
teng. Shu progressiyaning oltinchi hadini
3. Hisoblang:
toping.
− (−3, 8) + (−6, 2) − (− (+2, 8) + (−8, 4)).
A) 58 B) 42 C) 50 D) 66
A) −13,6 B) 13,6 C) −1,2 D) 8,8
4. Asosining tomonlari 13 dm; 14 dm va 15 dm 15. ABCD parallelogrammning BC va CD
bo‘lgan uchburchakli to‘g‘ri prizmaning yon tomonlaridan mos ravishda M va N nuqtalar
qirrasi asosining kichik balandligiga teng. shunday tanlab olinganki C uchidan boshlab
Prizmaning to‘la sirtini (dm2 ) toping. hisoblaganda (BC va CD tomonlarini) 1:3
10 nisbatda bo‘ladi. Agar parallelogrammning
A) 672 B) 710 C) 638, 4 D) 470, 4 yuzi 64 ga teng bo‘lsa, AM N D
13
to‘rtburchakning yuzini toping.
5. f (x) = |3 − 2x| − 4 funksiyaning eng kichik
A) 36 B) 32 C) 38 D) 40
qiymatini toping.
A) −4 B) −3,5 C) 1,5 D) 0 16. Agar 3a + 3−a = 3 bo‘lsa, 32a − 2 · 3a + 3−a
ifodaning qiymatini toping.
6. Hisoblang:  
5 A) 3 B) 2 C) 1 D) 4
(0, (2) + 3, 6 (1)) : 1 − 1, 91 (6) + 42, 5.
6 17. Rasmda tasvirlangan ABCD kvadratning
A) −0, 5 B) 3, 5 C) −3, 5 D) 0, 5 perimetri p ga teng. Agar
  √   √ √ CF : F G : GD = 1 : 2 : 3 bo‘lsa, EF G
7. 2 4 x · 7 + 4 3 · 2 x − 3x = x tenglama
uchburchakning yuzasini toping.
ildizlarining o‘rta arifmetik qiymatini toping.
B C
A) 1 B) 2 C) 4 D) 0
F
8. Agar cos 34◦ = a va sin 31◦ = b bo‘lsa,
sin 22◦ + sin 28◦ ni a va b orqali ifodalang. E
  G
A) 2 b2 − a2  B) a2 − b2 C) b2 − a2
D) 2 a2 − b2
9. Quyidagi fikrlardan qaysi biri natural sonlar A D
uchun har doim to‘g‘ri?
p2 p2 p2 p2
A) B) C) D)
A) barcha tub sonlar toq sonlardir 96 72 48 192

B) ikkita tub sonlar ko‘paytmasi toq son bo‘ladi 18. y = 6x2 − 24x − 21 kvadrat funksiyaning
simmetriya o‘qi bo‘lgan chiziqni aniqlang.
C) faqat uchta natural bo‘luvchiga ega bo‘lgan
son biror tub sonning kvadratiga teng bo‘ladi A) x = 0 B) x = 1 C) x = 4 D) x = 2

D) ikkita tub sonlar yig‘indisi juft son bo‘ladi 19. 25log 5 x − 5 · 2log2 x = 24 tenglamaning ildizi x0
10. 6 ta to‘g‘ri chiziqlar ko‘pi bilan nechta nuqtada bo‘lsa, x20 − 5x0 + 7 ning qiymatini toping.
kesishadi? A) 32 B) 30 C) 31 D) 33
A) 15 B) 28 C) 21 D) 12 20. 20% li va 40% li eritmalar aralashtirilib, 34% li
11. Agar ABC uchburchak√uchun 500 gramm eritma hosil qilindi. Har bir
AC 2 = BC 2 + AB 2 + 2AB · BC bo‘lsa, u eritmadan necha grammdan aralashtirilgan?
holda ∠ABC ni toping. A) 250 va 250 B) 200 va 300 C) 150 va 350
A) 30◦ B) 60◦ C) 135◦ D) 45◦ D) 100 va 400


1
T-108 Matematika(8000440) - Sotish taqiqlanadi!

21. 7 soat 12 minut 40 sekundni sekundlarda (x + 3)2 − 4
26. · (x − 1) = 24 tenglamaning
ifodalang. x+5
A) 25880 B) 25920 C) 25960 D) 25860 ildiziga nisbatan quyidagilardan qaysi biri
to‘g‘ri?
22. Uchlari A(3; 0), B(0; 2) va C(0; 0) nuqtalarda
bo‘lgan uchburchakning CM bissektrisasi A) tub son
bo‘lsa, M nuqtaning koordinatalarini toping.
      B) manfiy son
3 3 5 5 6 6
A) ; B) ; C) ; C) 3 ga karrali son
4 4 6 6 5 5
4 4 D) 2 ga karrali son
D) ;  x  x
3 3 1 1
27. − ≤ 12 tengsizlikning (−4; 4)
 4 2
(x − 2)dx
23. 2 integralni hisoblang. oralig‘idagi butun yechimlar sonini toping.
x − 4x + 17
 2 A) 2 B) 3 C) 5 D) 6
A) ln  x2 − 4x + 17 + C 1 2 3
B) ln x2 − 4x + 17 + C 28. Amallarni bajaring: 3 − 2 −
 −2 6x 3x y 4y 2
C) ln x2 − 4x + 17 +C
√
2
2y 2 − 8xy − 9x2 2y 2 − 8xy 2 − 9x3
D) ln x − 4x + 17 + C A) B)
12x3 y 2 12x3 y 2
2 3
24. 
f (x) = 24tgx − 24x + 6π + 11 funksiyaning 2y − 8xy − 9x 2y − 8x2 y − 9x3
2
C) D)
π π
− ; kesmadagi eng katta qiymatini toping. 12x3 y 2 12x3 y 2
4 4 29. Agar A to‘plamga 1 ta element qo‘shilgandagi
√
A) 14√3 + 11 B) 24 C) 35 qism to‘plamlari soni A to‘plamdan 1 ta
D) 12 3 + 13 element chiqarilib tashlangandagi qism
to‘plamlari sonidan 24 taga ko‘p bo‘lsa,
25. Quyida  berilgan
 sonlardan qaysi biri
√ 3πx A to‘plamning qism to‘plamlari sonini toping.
3 tg − 1 = 0 tenglamaning ildizi bo‘la A) 32 B) 16 C) 8 D) 4
2

olmaydi? 3 √ √
2 1 1 7 30. 2 2 : 2 ni hisoblang va natijani ratsional
A) B) C) 2 D) ko‘rsatkichli daraja shaklida tasvirlang.
3 9 9 9 5 7 1 3
A) 2− 12 B) 2− 12 C) 2− 12 D) 2− 4




2


Matematika(8000464) - Sotish taqiqlanadi! T-108

MATEMATIKA
 1 9. 0; 1; 2; 3; 4; 5 raqamlardan jami nechta
1. 2 dx integralni hisoblang.
sin (2x − 3) raqamlari takrorlanmaydigan 3 xonali sonlar
ctg (3 − 2x) ctg (3 − 2x) tuzish mumkin?
A) + C B) − +C
3 3 A) 180 B) 100 C) 216 D) 125
ctg (3 − 2x) ctg (3 − 2x)
C) − + C D) +C
2 2 √ √ −2x
4x+5
⎧ 10. 4
2 = 2 3 tenglamani yeching.
⎪ ab = 1 1
⎪
⎪ 21 17 15 9
⎪
⎪ a+b 3 A) − B) − C) − D) −
⎪
⎨ ac 16 16 16 16
1
2. a, b, c sonlar = −1 sistemani
⎪
⎪ a+c 3
⎪
⎪
⎪
⎪ bc 1
⎩ = −2 11. Sayyoh belgilangan yo‘lning
b+c 6
qismini bosib
qanoatlantiradi. a − b + c ning qiymatini o‘tgach, yo‘l yarmigacha yana 16 km qolgan
toping. bo‘lsa, belgilangan yo‘l uzunligini (km) toping.
A) −2 B) −3 C) 1 D) 5 A) 42 B) 36 C) 48 D) 54

3. y = 1, 44 − x2 funksiya grafigiga o‘tkazilgan
urinma abssissa o‘qini (−2;0) nuqtada kesib 3
12. 612 + 612 + 612 + 12 12
 ... + 6 + 6  yig‘indining
o‘tsa, uning tenglamasini toping. 4
32 ta
3 6 4 8
A) y = x + B) y = x + qismi quyidagilardan qaysi biriga teng?
5 5 5 5
3 3 2 4 A) 214 · 312 B) 4 · 612 C) 2 · 613
C) y = x + D) y = x + D) 215 · 313
4 2 3 3
4. Hisoblang:

2 4 13. 2513 + 16127 + 27 yig‘indi qanday raqam bilan
1, 08 − : − 0, 25 : 0, (33) + 0, (8) tugaydi?
25 7
2 8 8 2 A) 6 B) 3 C) 8 D) 5
A) 1 B) 3 C) 1 D)
9 9 9 3
14. To‘g‘ri burchakli parallelepipedning uchta turli
5. A = {x| x = 4n + 3, n ∈ N },
yoqlarining diagonallari 7; 8 va 9 dm bo‘lsa,
B = {x| x = 6n + 5, n ∈ N } bo‘lsa, A ∩ B
parallelepipedning diagonali uzunligini (dm)
to‘plamni aniqlang.
hisoblang.
√ √ √ √
A) {x| x = 12n − 1, n ∈ N } A) 94 B) 6 3 C) 97 D) 4 6
B) {x| x = 12n + 11, n ∈ N }
C) {x| x = 24n − 1, n ∈ N } 15. f (x) = x2 − x + 2 · (x − 1) funksiyaning
x0 = 1 nuqtadagi hosilasini toping.
D) {x| x = 24n − 13, n ∈ N }
A) −2 B) 1 C) 2 D) 0
6. Arifmetik progressiyaning dastlabki o‘n ikkita
hadining yig‘indisi 168 bo‘lsa, a5 + a8 ni toping.  
 9 
A) 13 B) 28 C) 56 D) 14 
16.   > 2 4 tengsizlikning barcha butun
x − 3 7
7. −3; 6; 8 va x sonlarining o‘rta arifmetigi y ning yechimlari yig‘indisini toping.
1 A) 18 B) 12 C) 15 D) 21
qismiga teng. Agar 3x − 2y = 15 bo‘lsa,
3
y ning qiymatini toping.
A) 24 B) 32 C) 28 D) 18 17. a (−12; 13; −15) vektorning Oxy tekisligidagi
proyeksiyasi bo‘lgan vektorni toping.
8. Hisoblang: A) p (0; 13; −15) B) p (−12; 0; −15)
3, 6 · 4, 8 + 5, 4 · 3, 6 + 4, 8 · 9, 2 − 4, 8 · 5, 6. C) p (−12; 13; 0) D) p (0; 0; −15)
A) 43,2 B) 54 C) 72 D) 48


1
T-108 Matematika(8000464) - Sotish taqiqlanadi!

18. Rasmda ABC uchburchakka aylana ichki 22. Tenglamani yeching: tg (4x + π) · tg (3x) = 1
chizilgan. Agar AB=14, BC=13 va AC=15
bo‘lsa, aylana markazi O nuqtadan π πk
A) x = + , k∈Z
A nuqtagacha bo‘lgan masofani toping. 7 7
B π πk
B) x = + , k∈Z
14 7
π πk
C) x = + , k∈Z
3 7
O
π πk
D) x = + , k∈Z
A C 4 7
√ √ √ √ n2 − 6
A) 65 B) 52 C) 80 D) 84 23. n− natural soni uchun =3
335 + 18 · 316 + 1
n−3
tenglik o‘rinli bo‘lsa, ning qiymatini
814
19. Rasmda markazi K nuqtada bo‘lgan aylana toping.
tasvirlangan. Quyidagilardan qaysi biri 1 1
berilgan aylananing tenglamasi bo‘ladi? A) 9 B) 27 C) D)
3 9
y
24. y = 3x2 − 6x + 7 kvadrat funksiyaning
A(0; 6) ordinatalar o‘qiga nisbatan simmetrik
funksiyasini aniqlang.
A) y = 3x2 − 6x + 7 B) y = −3x2 − 6x − 7
K(2; 4)
C) y = −3x2 + 6x − 7 D) y = 3x2 + 6x + 7
2
25. Agar a = bo‘lsa,
3

x a+4 a2 − 10a + 25 1
O · − 2 ifodaning
2 2 2
a − 5a a + 8a + 16
qiymatini toping.
A) x2 + y 2 − 4x − 8y + 24 = 0
1 1
B) x2 + y 2 + 4x + 8y + 12 = 0 A) −4 B) −1 C) −1 D) −2
2 2
C) x2 + y 2 − 4x − 8y + 16 = 0 26. Hisoblang: sin6 1 − 3 sin4 1 + 3 sin2 1 + cos6 1 + 1
D) x2 + y 2 − 4x − 8y + 12 = 0 A) 2 B) −2 C) −1 D) 0
27. f (x) = kx + 3 funksiya k ning qanday
qiymatlarida toq funksiya bo‘ladi?
20. Agar ABC uchburchakning burchaklari A) k ning hech bir qiymatida B) k < 0
∠A : ∠B : ∠C = 2 : 3 : 4 shartlarni C) k ∈ R D) k > 0
qanoatlantirsa, uchburchakning qaysi tomoni
m2 − 9
eng katta bo‘ladi? 28. m ning qanday qiymatlarida va
m2 − 1
A) AC B) aniqlab bo‘lmaydi C) AB 2m + 6
D) BC ifodalar bir-biriga teng bo‘ladi?
m−1
A) −5; 6 B) −5; 3 C) −3; 5 D) −5; −3
 
1 2 3 1
21. Bitta nuqtadan tekislikka og‘ma va 29. 2 a b · −3 a3 b4 ifodani
4 3
perpendikulyar o‘tkazilgan bo‘lib, ular orasidagi soddalashtiring.
burchak 15◦ ga√teng. Agar perpendikulyarning 1 1 1
uzunligi 12 + 6 3 cm bo‘lsa, og‘maning A) −7 a5 b7 B) −7 a5 b7 C) −7 a5 b7
2 4 3
tekislikdagi proyeksiyasi uzunligini (cm) toping. 1 5 7
√ √ D) −7 a b
A) 6 · 7 + 4 3 B) 12 C) 6 · 7 − 4 3 12
D) 6 30. Agar f (x + 2) = log3 x2 − 6x + 27 + 6 bo‘lsa,
f (2) ning qiymatini toping.
A) 6 + log3 7 B) 9 C) 8 D) 6 + log3 19

2


Matematika(8000488) - Sotish taqiqlanadi! T-108

MATEMATIKA
   
1. Hisoblang: (3−2 )−1 + (2−2 )−2 + 1 11. m2 − n−1 m + n−2 m−1 + n − m (mn)−2
3
A) 5 B) 6 C) 8 D) 4 ifodaning m = , n = 0, (4) dagi qiymatini
4
2. To‘g‘ri burchakli uchburchakning eng kichik toping.
tomoni uzunligi 5 ga teng va qolgan tomonlari 3
A) 1 B) 0,25 C) 1 D) 4
uzunliklari natural son bo‘lsa, uchburchakning 4
yuzini toping. 12. Tekislikda ixtiyoriy uchtasi bitta to‘g‘ri
A) 35 B) 6 C) aniqlab bo‘lmaydi D) 30 chiziqda yotmaydigan 11 ta nuqta berilgan.
Uchlari berilgan nuqtalarda bo‘lgan jami
3. Hisoblang: nechta turli kesma mavjud?
(−9)3 : (−9)2 + (−10)3 : (−10) − (−2)8 : (−2)7 A) 55 B) 54 C) 52 D) 50
A) −89 B) −197 C) 89 D) 93 13. A murakkab sonlar to‘plami va B juft sonlar
to‘plami bo‘lsa, A ∩ B to‘plamni aniqlang.
4. f (x) = e2x · (sin x + cos x) funksiya berilgan.
A) {x|x = 2n + 2, n ∈ N }
f  (x) − f (x) ni toping.
B) {x|x = 2n, n ∈ N } C) ∅
A) −2e2x sin x B) 2e2x sin x C) 2e2x cos x D) {x|x = 2n − 2, n ∈ N }
D) −2e2x cos x
4
5. y = (x − 4) · (x − 1)2 funksiyaning ekstremum 14. f (x) = − 2 funksiyaning qiymatlar sohasini
x
nuqtalaridan o‘tuvchi to‘g‘ri chiziq tenglamasini toping.
tuzing. A) [−2; ∞) B) (−∞; −2) ∪ (−2; ∞)
A) y = −2x − 2 B) y = 2 − 2x C) (−∞; 0) ∪ (0; ∞) D) (−∞; 0]
C) y = 2x + 2 D) y = 2x − 2  
2x − 1 6x + 5
15. Agar f = bo‘lsa,
6. Ikkidan katta bo‘lgan barcha tub sonlarni 4 ga 3 3
bo‘lganda qanday qoldiqlar qoladi? f (1) − f (−2) ni hisoblang.
A) 2, 3 B) 0, 1, 2, 3 C) 1, 2, 3 D) 1, 3 A) 9 B) −3 C) 3 D) −12

√ 4 sin4 α 16. Ko‘phadlarni ko‘paytiring:
7. Agar tg α = 7 bo‘lsa, (a + 3) · (a + 1) · (a − 3)
5 sin2 α + 15 cos2 α
ifodaning qiymatini toping. A) a3 − a2 + 9a − 9 B) a3 + a2 − 9a − 9
A) 0, 48 B) 0, 49 C) 0, 47 D) 0, 5 C) a3 + a2 + 9a − 9 D) a3 − a2 − 9a − 9
17. Arifmetik progressiyaning yettinchi hadi
8. Piramida asosining diagonallari soni
birinchi hadining 25%iga teng. Agar
piramidaning qirralar soniga teng.
a2 + a4 + a6 = 90 bo‘lsa, birinchi va beshinchi
Piramidaning yoqlari soni bilan uchlari soni
hadi yig‘indisini toping.
yig‘indisini toping.
A) 72 B) 76 C) 78 D) 82
A) 8 B) 16 C) 14 D) 12
18. Tenglamani yeching:   
9. Silindrning asosida 2 dm uzunlikdagi vatar 60◦ 1, 4 · (2 + 0, 6) · 4 + 0, 62 · 16 + 0, 64 · x =
kattalikdagi yoyga tiralgan. Silindrning o‘q 0, 68 − 256
kesimi kvadratdan iborat bo‘lsa, uning hajmini
A) −1 B) 16 − 0, 64 C) 0, 64 − 16 D) 1
(dm3 ) toping.
√ √  2
A) 16π B) 8 3π C) 4 3π D) 32π 19. x2 − 2x − 4 (x − 1)2 + 7 = 0 tenglamaning
barcha haqiqiy ildizlari ko‘paytmasini toping.
10. Agar A (−2; 6; −9), B (−12; 6; −9), C (4; 6; 5)
va D (14; −8; 15) nuqtalar berilgan bo‘lsa, A) 3 B) −3 C) 1 D) −1
AB + BC + CD vektorning koordinatalarini 20. Integralni hisoblang:
toping. 2 2
(x − x + 1)3 · (2x − 1)dx
A) (16; −14; 24) B) (10; −11; 8) 1
C) (−16; 0; −14) D) (16; 14; −24) A) 20 B) 6,5 C) 13 D) 10


1
T-108 Matematika(8000488) - Sotish taqiqlanadi!

5, 342 + 10, 68 · 3, 66 + 3, 662 25. Qisqarmaydigan oddiy kasrning maxraji
21. Hisoblang: .
9 · 12, 72 + 5, 28 · (4, 73 + 4, 27) suratidan 3 birlikka katta. Agar kasrning
1 1 suratiga 1, maxrajiga 2 qo‘shilsa, hosil bo‘lgan
A) 2 B) 3 C) D) 2
2 3 kasrning qiymati ga teng bo‘ladi. Berilgan
√ 3
10 − 3x kasrning maxraji quyidagi sonlardan qaysi
22. < 0 tengsizlikni yeching.
log2 |x − 3| biriga qoldiqsiz bo‘linadi?
     
1 1 1 A) 5 B) 3 C) 8 D) 6
A) 3; 3 ∪ 3 ;4 B) 2; 3
 3 3  3 26. Hisoblang:
1 1 π π π π π
C) 3; 3 D) (2; 3) ∪ 3; 3 sin6 − 3 sin4 + 2 sin2 + cos6 − cos2
3 3 7 7 7 7 7
√ √ A) 0 B) 2 C) 1 D) −1
mn · 4 m m2 + 4
23. √ − ifodaning m = 6
4
(m + 2) ·√ m−1 n2 m − 4
2 27. Ikki shahar orasidagi masofa 240 km.
va n = 4 3 bo‘lgandagi qiymatini toping. 1:6000000 masshtabli xaritada bu masofa necha
√ √ santimetrga teng bo‘ladi?
A) −2 3 B) −0, 5 C) 2 D) 3
A) 4 B) 40 C) 1,2 D) 0,4
24. Rasmdan foydalanib x ning qiymatini toping.
28. Uchlari A(1; −1), B(1; 3), C(5; 3) va D(6; −1)
nuqtalarda bo‘lgan ABCD to‘rtburchakning
yuzasini toping.
8 A) 20 B) 18 C) 14 D) 12
50◦ ( √  x2 −10x+16
x 29. 5−2 x−2
≥ 1 tengsizlikni yeching.
4 A) (−∞; 2) ∪ (2; 8] B) [8; ∞) C) (−∞; 8]
50◦ (
D) (2; 8) ∪ (8; ∞)
12  
 9 

30.   > 2 4 tengsizlikning barcha butun
x − 3 7
A) 8 B) berilgan ma’lumotlar yetarli emas yechimlari yig‘indisini toping.
C) 9 D) 6,5
A) 12 B) 18 C) 21 D) 15




2


Matematika(8000512) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. f (x) = e2x · (sin x + cos x) funksiya berilgan. 9. Tekislikda o‘zaro kesishmaydigan a va b to‘g‘ri
f  (x) − f (x) ni toping. chiziqlar berilgan. a to‘g‘ri chiziqda 2 ta, b
A) −2e2x cos x B) 2e2x sin x C) 2e2x cos x to‘g‘ri chiziqda 4 ta nuqta berilgan. Uchlari bu
D) −2e2x sin x nuqtalarda bo‘lgan jami nechta to‘rtburchak
mavjud?
⎧
⎪
⎪ ab 1 A) 6 B) 8 C) 5 D) 12
⎪
⎪ =1
⎪
⎪ a+b 3
⎨ ac 1 10. Qisqarmaydigan oddiy kasrning maxraji
2. a, b, c sonlar = −1 sistemani suratidan 3 birlikka katta. Agar kasrning
⎪
⎪ a + c 3
⎪
⎪ bc suratiga 1, maxrajiga 2 qo‘shilsa, hosil bo‘lgan
⎪
⎪
⎩ = −2 2
b+c kasrning qiymati ga teng bo‘ladi. Berilgan
qanoatlantiradi. a − b + c ning qiymatini 3
toping. kasrning maxraji quyidagi sonlardan qaysi
biriga qoldiqsiz bo‘linadi?
A) −2 B) 5 C) 1 D) −3
A) 8 B) 6 C) 5 D) 3
3. Yon tomonining uzunligi 5 dm bo‘lgan teng
11. A(2; 3), B(3; −4), C(−6; 5) va D(−5; 4)
yonli trapetsiyaga doira ichki chizilgan. Agar
nuqtalardan qaysi biri koordinatalar boshidan
trapetsiyaning yuzi 20 dm2 bo‘lsa, doiraning
eng uzoqda joylashgan?
yuzini (cm2 ) toping.
A) D nuqta B) C nuqta C) A nuqta
A) 400π B) 40π C) 16π D) 20π
D) B nuqta
4. Uchlari Oxy tekisligining (0; 0), (3; 0), (2; 3) va  √ √ −1
(0; 3) nuqtalarida bo‘lgan trapetsiyani Oy o‘qi a2 − 12 6 + 6a − 2a 6 36 − a2
12. · √
atrofida aylantirishdan hosil bo‘lgan jismning (a − 6)9 + a2 + (6 − a)9 − 24 a + 24
√
hajmini toping. ifodaning a = 6 + 5 dagi qiymatini toping.
√ √
A) 19π B) 12π C) 18π D) 7π A) 31 B) − 5 C) 5 D) −1

5. Agar P = 3a2 + 4b, Q = −2a2 − 3b bo‘lsa, 13. Rasmda ABC uchburchak va uning
P + Q + 4b ni toping. BD bissektrisasi tasvirlangan. Agar AB=5 va
BC=7 bo‘lsa, DC : AC nisbatni toping.
A) −a2 + 5b B) −a2 − 5b C) a2 − 5b
B
D) a2 + 5b

6. log23 (27x) = log3 x6 tenglamaning ildizini
toping.
A) haqiqiy ildizga ega emas B) 3 C) 9
D) 27 A D C
5 7 7 5
7. Hisoblang: A) B) C) D)
  12 5 12 7
2 4
1, 08 − : − 0, 25 : 0, (33) + 0, (8)
25 7 14. (bn ) geometrik progressiyada b6 − b3 = 84 va
2 2 8 8 b5 − b2 = 42 bo‘lsa, b2 + b4 ni toping.
A) 1 B) C) 3 D) 1
9 3 9 9 A) 36 B) 30 C) 51 D) 27

8. Kasrning 15. α tekislik va uni kesib o‘tmaydigan AB kesma
√ maxrajini irratsionallikdan qutqaring:
3 berilgan. Kesmaning uchlaridan α tekislikkacha
√ √ bo‘lgan masofalar AA1 =18 cm, BB1 =13 cm
2 3 − 13 − 1
√ √ √ √ bo‘lsa, AB kesmani A uchidan boshlab
1 − 2 3 − 13 1 − 2 3 + 13 hisoblaganda 3:2 nisbatda bo‘luvchi C
A) B)
√4 √ √4 √ nuqtadan α tekislikkacha bo‘lgan masofani
1 − 2 3 − 13 1 − 2 3 + 13 (cm) toping.
C) D)
2 2 A) 16 B) 15 C) 14 D) 15,5


1
T-108 Matematika(8000512) - Sotish taqiqlanadi!

16. Rasmda shtrixlangan soha yuzini toping. 111 222 333
22. Hisoblang: + +
(A − nuqta parabolaning uchi) 333 666 999
y A) 1,6 B) 2 C) 1 D) 1,5
A(1;4) 23. y = x2 − 8x + 17 kvadrat funksiyaning x=2
chiziqqa nisbatan simmetrik funksiyasini
(0;3) aniqlang.
f (x) = ax2 + bx + c
A) y = x2 + 6x + 10 B) y = x2 − 2x + 2
C) y = x2 + 1 D) y = x2 − 4x + 5
24. Ketma-ket kelgan ikkita toq natural sonlarning
x kvadratlari farqi 72 ga teng bo‘lsa, shu
0 1 3
sonlarning kichigini toping.
2 1 1 A) 19 B) 15 C) 13 D) 17
A) 6 B) 8 C) 5 D) 9
3 3 3
1
17. Funksiya grafigidan foydalanib, (−3; 6) oraliqda 25. 1 + cos−1 2α + tg 2α 1 − cos−1 2α + tg 2α
2
f (x) · f  (x) ≤ 0 tengsizlikning eng katta manfiy ifodaning α = 15◦ dagi qiymatini toping.
butun yechimini toping. 2 √ √ 1
A) √ B) 2 3 C) 3 D) √
3 3
y
3 26. 15 · 221 · 517 ko‘paytma nechta nol bilan
x)
f(




tugaydi?
=
y




A) 21 B) 19 C) 22 D) 18
1
4 27. ABCD parallelogrammning BC va CD
x tomonlaridan mos ravishda M va N nuqtalar
−3 −2 −1 0 1 2 3 5 6
−1 shunday tanlab olinganki C uchidan boshlab
hisoblaganda (BC va CD tomonlarini) 2:1
A) −2 B) −3 C) −1 nisbatda bo‘ladi. Agar parallelogrammning
D) manfiy yechimga ega emas yuzi 54 ga teng bo‘lsa, AM N uchburchakning
18. Agar k < 0, b > 0 bo‘lsa, y = kx + b chiziqli yuzini toping.
funksiyaning grafigi qaysi choraklarda yotadi? A) 12 B) 36
C) 24 D) 18
 
A) I, II va III B) I, II va IV C) I, III va IV √ √ π π
D) II, III va IV 28. A = − 3; 3 , B = − ; va
 2 2
3 2 √ 
19. Tenglamani yeching: = . √ 7
3 3 C = − 5; bo‘lsa, (A ∪ B) ∩ C to‘plamni
4− 2
2 (1 − 2x) aniqlang.
x−3  
√ √ π π
1 1 A) − 5; 3 B) − ;
A) 8 B) 4 C) − D)  2 2√ 
8 4 √ √ √ 7
2x+2 − 24 C) − 3; 3 D) − 3;
20. ≥ 1 tengsizlikni yeching. 2
2x+1 − 8
  29. (4x − 1)2 − (3 + 4x) (x − 2) − x (10x − 1) ≤
1
A) ; +∞ B) (−∞; 2) ∪ [3; +∞) ≤ 25 − 2x tengsizlikning eng katta va eng
2
C) (2; +∞) D) (0; 2) kichik butun yechimlari yig‘indisini toping.
21. Hisoblang: A) 4 B) 3 C) 0 D) 1
(tg 435◦ − tg 375◦ ) · sin2 70◦ · sin2 50◦ · sin2 10◦ : 30. Magazinda birinchi kuni 76% tarvuz sotildi.
: sin 120◦ Ikkinchi kuni esa qolgan 54 ta tarvuz sotildi.
1 1 1 Birinchi kuni nechta tarvuz sotilgan?
A) 1 B) C) D)
16 8 4
A) 168 B) 171 C) 176 D) 163




2


Matematika(8000536) - Sotish taqiqlanadi! T-108

MATEMATIKA

3 10. Tenglamani yeching: tg (4x + π) · tg (3x) = 1
1. Integralni hisoblang: |x − 2|dx
−3
π πk
A) 6 B) 9,5 C) 13 D) 16,5 A) x = + , k∈Z
4 7
2. Uchburchakning asosiga tushirilgan balandligi π πk
B) x = + , k∈Z
20 cm bo‘lib, asosidan 2 cm ga katta. Agar shu 7 7
balandlik 10% ga kamaytirilib, asosi esa π πk
4 cm ga uzaytirilsa, uchburchakning yuzi C) x = + , k∈Z
3 7
qanday o‘zgaradi?
π πk
A) 18 cm2 ga ortadi B) 12 cm2 ga ortadi D) x = + , k∈Z
14 7
C) 18 cm2 ga kamayadi D) o‘zgarmaydi
√ √
3. f (x) = x2 funksiyaning (0;0) va (1;1) 5 7+7 5 √
11. Hisoblang: √ − 5
nuqtalaridan o‘tuvchi to‘g‘ri chiziqqa parallel 35
√ √ √ √ √ √
bo‘lgan urinma tenglamasini tuzing. A) 7 + 5 B) 7 C) 7 − 5 D) 5
A) y = x − 0, 125 B) y = x − 0, 225
C) y = x − 0, 25 D) y = x − 0, 2
12. f (x) = x2 − 5x − 6 funksiyaning nollari
4. y = x2 − 2x + 2 kvadrat funksiyaning y=2 ko‘paytmasini toping.
chiziqqa nisbatan simmetrik funksiyasini A) 5 B) 0 C) −6 D) 6
aniqlang.
A) y = −x2 + 2x B) y = −x2 + 2x + 1 243x 5 · 27x
C) y = −x2 + 2x + 2 D) y = −x2 + 2x − 2 13. Agar 3x = 2 bo‘lsa, + − 81x ning
32 8
qiymatini toping.
5. (5a − 3b) − (−4b + 7a) ifodani soddalashtiring.
A) −9 B) −2 C) −10 D) −5
A) −2a + b B) 2a + b C) −2a − b
D) 2a − b
14. Merganning nishonga tekkizish ehtimoli 0,8 ga
6. 4680 sonini tub ko‘paytuvchilarga ajrating. teng. U nishonga 3 marta o‘q uzganda barcha
o‘qlari nishonga tegishining ehtimolligini
A) 23 · 3 · 52 · 13 B) 23 · 32 · 5 · 11
toping.
C) 23 · 32 · 53 D) 23 · 32 · 5 · 13
A) 0,912 B) 0,72 C) 0,8 D) 0,512
7. 0, 372 + 3, 649 + 4, 8463 yig‘indining qiymatini
yuzdan birlar xonasigacha yaxlitlang. 15. 12 ta qatordan iborat bo‘lgan musiqa zalining
A) 7,87 B) 8,87 C) 7,84 D) 8,84 birinchi qatorida 28 ta o‘rindiq bor. Keyingi
har bir qatordagi o‘rindiqlar soni oldingi
⎧ qatordagidan 4 taga ko‘p. Musiqa zalida jami
⎪
⎪ ab 1
⎪
⎪ =1 nechta o‘rindiq bor?
⎪
⎪ a+b 3
⎨ ac 1 A) 576 B) 612 C) 600 D) 504
8. a, b, c sonlar = −1 sistemani
⎪
⎪ a+c 3
⎪ bc
⎪
⎪
⎪ 16. Masofa 5% ga orttirilib, tezlik 30% ga
⎩ = −2
b+c kamaytirilsa, harakatlanish vaqti necha foizga
qanoatlantiradi. a − b + c ning qiymatini
ortadi?
toping.
A) 45 B) 35 C) 25 D) 50
A) −2 B) −3 C) 5 D) 1

9. To‘la sirtining yuzi 54π ga teng silindrning 17. Uchta sonning o‘rta arifmetigi 24, 3 ga teng.
hajmi eng ko‘pi bilan qanchaga teng bo‘lishi Agar ulardan ikkitasi 34,8 va 18,9 bo‘lsa,
mumkin? uchinchi sonni toping.
A) 54π B) 56π C) 58π D) 52π A) 19,8 B) 21,1 C) 18,6 D) 19,2



1
T-108 Matematika(8000536) - Sotish taqiqlanadi!

18. Oy o‘qiga perpendikulyar va 1 3 3 3 3 5 1
23. Hisoblang: 1 · 3 + 2 · 3 − 3 · 3 − 1
y = (x − 4)2 · ex + 2 funksiya grafigiga urinma 2 5 4 5 5 6 2
bo‘lgan to‘g‘ri chiziq tenglamalarini aniqlang. A) −0, 5 B) −1, 5 C) 0,5 D) 0

A) y = 4 · e2 + 2; y = 4 24. Tenglamani yeching:
x−2 x−2 x−2 x−2 1
B) y = 2 · e2 + 4; y = 4 + + + =1
3·5 5·7 7·9 9 · 11 11
C) y = 4 · e2 + 2; y = 2 A) 14 B) 4 C) 11 D) 8
D) y = 2 · e2 + 4; y = 2
19. Ikki to‘g‘ri chiziqning kesishishidan hosil 25. Rasmda ABC uchburchakka aylana ichki
4 chizilgan. Agar AB=14, BC=13 va AC=15
bo‘lgan o‘tmas burchak sinusi ga teng bo‘lsa, bo‘lsa, aylana markazi O nuqtadan
5
o‘tkir burchak tangensini toping. A nuqtagacha bo‘lgan masofani toping.
B
3 3 4 3
A) B) C) D) −
4 5 3 5

2
20. y = − 3 − 1 funksiya grafigi
lg (x − 2) O
abssissalar o‘qini qaysi nuqtada kesib o‘tadi?
kesib o‘tmaydi B) (102; 0)
A) √ A C
√ √ √ √
C) 10 + 2; 0 D) (0; 102) A) 80 B) 65 C) 52 D) 84
21. To‘g‘ri burchakli parallelepipedning A uchidan
chiquvchi 8; 9 va 12 dm qirralaridan mos 26. f (x) = 3|x| − 2 funksiyaning qiymatlar sohasini
ravishda A nuqtadan boshlab hisoblaganda toping.
qirralari 3; 5 va 6 dm bo‘lgan piramida qirqib A) (−1; +∞) B) (−2; +∞) C) (0; +∞)
olingan. (rasm) Qolgan qismining hajmini D) [−1; +∞)
(dm3 ) hisoblang.
C1 D1 3a7 + 2a6 − 3a − 2
27.  ifodaning qiymati 8 ga
B1 A1 (3a + 2) · a4 + a2 + 1
teng bo‘ladigan a ning barcha qiymat(lar)ini
toping.
L √
A) ±2 B) ± 7 C) 2 D) ±3
C D
M  √
B K A 28. x2 − 2x − 24 10x − x2 < 0 tengsizlikning
eng katta butun yechimini toping.
A) 819 B) 849 C) 774 D) 834
A) 5 B) 7 C) 9 D) 6
22. Rasmda A va B to‘plamlar va U universial
to‘plam tasvirlangan. (A ∩ B  ) ∪ (A ∩ B) π √
to‘plamning elementlarini aniqlang(A =U \A, 29. 2 cos(2πx − ) + 2 = 0 tenglamaning eng
3
B  =U \B). kichik musbat yechimini toping.
11 21 13 13
B A) B) C) D)
A 12 24 12 24
f
c
d
a g √
e b 30. |a| = 3 va b = 2, a va b vektorlar orasidagi
h
π
j burchak ga teng. 2a − b va 3a + 4b
U i k 4
vektorlarning skalyar ko‘paytmasini toping.
A) {c, d, e} B) {f, g, h} C) {c, d, e, f, g, h} √ √
D) {a, b, i, j, k} A) 61 B) 46 + 15 2 C) 46 + 5 2 D) 42




2


Matematika(8000560) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. ABCD parallelogrammning BC, CD 11. 2 · 7 · 11 · 19 · 23 son quyidagi sonlardan qaysi
tomonlarida mos ravishda yotuvchi M , biriga ko‘paytirilsa, uning natural bo‘luvchilari
N nuqtalar BC : M C = 5 : 3 va soni ikki marta ortadi?
DC : N C = 3 : 1 shartlarni qanoatlantiradi. A) 2 B) 3 C) 11 D) 7
Agar parallelogrammning yuzi 35 ga teng
12. To‘g‘ri to‘rtburchak shaklidagi yer maydonning
bo‘lsa, BM N D to‘rtburchakning yuzini toping.
to‘rtta tomoni 360 m uzunlikdagi devor bilan
A) 12 B) 14 C) 16 D) 15 o‘ralgan. Bu yer maydonining eng katta yuzasi
2. f (x) = |3 − 2x| − 4 funksiyaning eng kichik necha m2 bo‘ladi?
qiymatini toping. A) 32400 B) 3240 C) 81000 D) 8100
A) 1,5 B) −4 C) −3,5 D) 0 13. Hisoblang:  
3. Rasmda A va B nuqtalar son o‘qida 5
(0, (2) + 3, 6 (1)) : 1 − 1, 91 (6) + 42, 5.
tasvirlangan. 2A + B ning son qiymatini 6
toping. A) −3, 5 B) −0, 5 C) 3, 5 D) 0, 5
9, 5 birlik 7 birlik 14. Tengsizlikni
 2 yeching:

x + 2x + 1 (x − 3) (x + 4)
B -3 0 2,5 A < 0.
x2 − 4x + 4
A) 6,5 B) 12,5 C) 9,5 D) 8
A) (−∞; −4) ∪ (3; ∞)
4. Piramidaning asosi to‘g‘ri burchakli
uchburchakdan iborat bo‘lib, uning B) (−∞; −4) ∪ (−1; 2) ∪ (3; ∞)
gipotenuzasi
√ 2 dm. Piramidaning har bir yon C) (−4; −1) ∪ (−1; 2) ∪ (2; 3)
qirrasi 5 dm bo‘lib, ular asos tekisligi bilan α
D) (−4; −1) ∪ (2; 3)
burchak tashkil qiladi. tg α ni toping.
√
1 5 31+log4 5 · 4log5 3 · 5log3 4
A) 2 B) C) 1 D) 15. Hisoblang:
2 2 3log5 4 · 4log3 5 · 5log4 3
5. Agar geometrik progressiyaning umumiy hadi A) 2 B) 1 C) 3 D) 4
bn = 3 · 2n bo‘lsa, b21 + b22 + b23 + ... + b28 16. Agar to‘g‘ri burchakli
√ uchburchakning √
yig‘indini hisoblang. katetlaridan biri 2 2 ga, gipotenuzasi 4 5 ga
   
A) 12 · 214 − 1 B) 3 · 216 − 1 teng bo‘lsa, gipotenuzaga tushurilgan
C) 12 · 216 − 1 D) 3 · 214 − 1 bissektrisa uzunligini toping.
√
6. Biri ikkinchisidan 3 marta katta bo‘lgan ikki A) 2 3 B) 3 C) 4 D) 6
sonning yig‘indisi 9,64 ga teng. Shu sonlarning 17. A = {x| x2 ≤ 64, x ∈ R},
kichigini toping. B = {x| x2 > 4, x ∈ N } bo‘lsa, A ∩ B
A) 2,41 B) 2,21 C) 2,31 D) 2,16 to‘plamni aniqlang.
7. x3 + mx2 − 4x + n = 0 tenglamaning ildizlari A) {3; 4; 5; 6; 7; 8} B) [2; 8]
x1 = 3 va x2 = −2 bo‘lsa, 3m + n ning C) {2; 3; 4; 5; 6; 7; 8} D) (2; 8]
qiymatini toping. 3x+1 + 3x+2 + 3x+3
18. f (x) = funksiya berilgan
A) 8 B) −12 C) 3 D) 6 5x+2 + 14 · 5x
8. y = −3x + 7 chiziqli funksiyaning x=1 to‘g‘ri bo‘lsa, 9 · f (−2) ni hisoblang.
chiziqqa nisbatan simmetrigini toping. A) 0,36 B) 1,44 C) 9 D) 25
A) y = −3x + 9 B) y = 3x + 1 19. Agar qisqarmaydigan kasrning surati 3 ga
C) y = 3x − 9 D) y = −3x − 1 6
orttirilsa, kasrning qiymati ga, maxraji 2 ga
7
9. 6x − 9 = x2 (|x − 3| + 1) tenglama nechta
3
haqiqiy ildizga ega? kamaytirilsa, kasrning qiymati ga teng
4
A) 1 B) 4 C) 3 D) 2 7
bo‘ladi. Berilgan kasrning qismini toping.
sin 12 − sin 10◦
◦
tg 1◦ 3 27
10. Hisoblang: ◦ ◦ − ◦ + .
sin 10 + sin 12 tg 11 2 1 3 2 1
A) B) C) D)
A) −1 B) 1 C) 1, 5 D) 2 12 4 3 6


1
T-108 Matematika(8000560) - Sotish taqiqlanadi!

20. Quyidagi to‘g‘ri chiziq tenglamalaridan qaysi 25. Tashkilot 10 ta xodimidan 3 tasini Buxoroga,
biri y = 4x to‘g‘ri chiziqqa parallel va qolganlarini Samarqandga xizmat safariga
y = x3 − 3x2 − 5x funksiya grafigiga urinma yuboradigan bo‘ldi. Tashkilot bu guruhlarni
bo‘ladi? necha xil usulda tuzishi mumkin?
A) y = 4x − 28 B) y = 4x − 26 A) 240 B) 60 C) 120 D) 180
C) y = 4x − 25 D) y = 4x − 27 26. Ifodani soddalashtiring:
1 4x + 5 7 1
21. Integralni hisoblang: dx a− 2 − 2
2 a 1
0 x + 3x + 2 5 + a2 − − 1.
27 2 4 27 a− 2 − a−1 a
A) ln B) ln C) ln D) ln
4 27 27 2 A) a + 1 B) a2 − 1 C) a − 1 D) 1 − a2
22. (3; 4) nuqtani koordinatalar boshiga nisbatan 27. Ifodani soddalashtiring:
soat mili harakati yo‘nalishida 90◦ ga burish 5 (a − b) a2 − b2
 2  :
natijasida hosil bo‘lgan nuqtaning 3 a + b2 (a + b)2 − 2ab
koordinatalarini aniqlang. 5 5 5
A) − B) C) −
A) (3; −4) B) (−4; 3) C) (−3; 4) 3 (a + b) 3 (a − b) 3 (a − b)
D) (4; −3) 5
D)
23. To‘g‘ri burchakli parallelepipedning A uchidan 3 (a + b)
 3 3

chiquvchi 8; 9 va 12 dm qirralaridan mos a2 + b2 a−b a−b √
ravishda A nuqtadan boshlab hisoblaganda 28. Ushbu − 1 1 · √ − a
a−b a2 + b2 ab
qirralari 3; 5 va 6 dm bo‘lgan piramida qirqib √
ifodaning a = 2, b = 8 dagi qiymatini toping.
olingan. (rasm) Qolgan qismining hajmini √ √
(dm3 ) hisoblang. A) 0 B) 2 C) 2 2 D) − 2
√
C1 D1 1 3
29. + = 4 tenglamaning eng kichik
B1 A1 cos x sin x
musbat yechimini toping.
π 2π π 2π
L A) B) C) D)
6 9 3 3
C D 30. Yoyiq burchakning A nuqtasidan chiquvchi
M ikkita nur uni 2:4:3 nisbatdagi burchaklarga
B K A
ajratadi. Eng katta burchakni toping.
A) 849 B) 819 C) 774 D) 834
√ √ √
32 + 50 − 72 β
24. Hisoblang: √
18 γ α
√
5 A
A) 1 B) C) 2 D) 3
3
A) 60◦ B) 80◦ C) 40◦ D) 90◦




2


Matematika(8000584) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Uchta sonning o‘rta arifmetigi 24, 3 ga teng. 12. Agar a√va b ratsional sonlar uchun
Agar ulardan ikkitasi 34,8 va 18,9 bo‘lsa, 3
a+b· = 3 bo‘lsa, u holda a2 + b2 ifodaning
uchinchi sonni toping. 3
A) 18,6 B) 21,1 C) 19,8 D) 19,2 qiymatini toping.
A) 9 B) 13 C) 7 D) 27
2. ABC uchburchakning burchaklari 2:3:1
nisbatda. Agar eng kichik tomoni 5 cm bo‘lsa, 13. Rasmda ABCD parallelogrammga BD
eng katta tomoni uzunligini (cm) toping. diagonal hamda BC va AD tomonlarini mos
√ √ ravishda teng ikkiga bo‘luvchi AE va
A) 8 B) 10 C) 5 3 D) 5 2
CF kesmalar o‘tkazilgan. Agar
3. a = 14, 88 · 1014 ; b = 28, 42 · 108 va ABCD parallelogrammning yuzi 72 ga teng
c = 34, 317 · 1011 sonlardan qaysilari 12 ga bo‘lsa, BEM uchburchakning yuzini toping.
qoldiqsiz bo‘linadi? E
B C
A) barchasi B) faqat c C) faqat b
D) a va c M

4. (x0 ; y0 ) nuqta y = 3x2 − bx + 12 parabola
N
uchining koordinatalari bo‘lsa, y0 + 3x20 ning
qiymatini toping.
A D
A) 18 B) 9 C) 15 D) 12 F

5. Hisoblang: 0, 84 · 109 : 7000000. A) 8 B) 9 C) 7,2 D) 6
A) 12 B) 240 C) 120 D) 1200 14. Agar log2 a = 2, (3) va log2 b = 3, (6) bo‘lsa,
 a · b + 1 ning qiymatini toping.
6. y = 1, 44 − x2 funksiya grafigiga o‘tkazilgan A) 21,3 + 1 B) 33 C) 25,9 + 1 D) 65
urinma abssissa o‘qini (−2;0) nuqtada kesib
o‘tsa, uning tenglamasini toping. 15. f (x) = 3x + b funksiya b ning qanday
2 4 3 3 qiymat(lar)ida toq funksiya bo‘ladi?
A) y = x + B) y = x + A) b > 0 B) b = 0 C) b = 2n − 1, n ∈ N
3 3 4 2
4 8 3 6 D) b < 0
C) y = x + D) y = x +
5 5 5 5 16. Qirralari 4 dm, 5 dm va 8 dm bo‘lgan to‘g‘ri
burchakli parallelepipedni tashqi tomonidan
7. f (2x + 1) = x4 + 4x2 funksiya berilgan.
qirrasi 1 dm bo‘lgan kublarning nechtasini
f  (3) ni toping.
terib, qirralari 6 dm, 7 dm va 10 dm bo‘lgan
A) 12 B) 6 C) 8 D) 0 to‘g‘ri burchakli parallelepiped yasash mumkin?
 √  √
8. x − x2 + 8 − x + x2 + 8 = 4 tenglama A) 260 B) 252 C) 192 D) 184
 √ √ √ 
nechta haqiqiy ildizga ega? 17. Hisoblang: 10 27 − 4 75 + 11 48 :
 2
A) 1 B) 2 C) 4 D) 0  √  1√4
: 2 3 − − 81
9. (5a − 3b) − (−4b + 7a) ifodani soddalashtiring. 3
1
A) −2a − b B) 2a + b C) −2a + b A) 8 B) 16 C) 26 D) 24
3
D) 2a − b
π 1
10. [1; 200] sonlar to‘plamida nechta natural son 18. Agar 0 < α, β < lar uchun tgα = va
2 2
6 ga (qoldiqsiz) bo‘linib, 9 ga (qoldiqsiz) 15 β
bo‘linmaydi? sin β = bo‘lsa, sin 2α + tg ni hisoblang.
17 2
A) 33 B) 11 C) 22 D) 44 2 5 5 7
√ √ A) B) C) D)
11. 5x + 4 ≤ 4x + 5 tengsizlikning eng katta va 5 2 7 5
eng kichik yechimlari yig‘indisini toping. 19. Tenglamani yeching:
3 4 2 1 3 · 2x−2 − 5 · 2x−4 = 18 − 2x−3
A) − B) − C) D)
5 5 5 5 A) 4 B) 5 C) −2 D) 3


1
T-108 Matematika(8000584) - Sotish taqiqlanadi!

20. 6 ta to‘g‘ri chiziqlar ko‘pi bilan nechta nuqtada 27. Muntazam tetraedrning qirrasi 9 ga teng.
kesishadi? Uning asosiga tashqi chizilgan aylananing
A) 21 B) 12 C) 15 D) 28 markazidan uning yon yoqigacha bo‘lgan eng
qisqa masofani toping.
21. (24; 204] oraliqda 3 ga karrali bo‘lgan barcha √ √ √ √
natural sonlar yig‘indisi qanday raqam bilan A) 3 2 B) 6 C) 2 3 D) 2 6
tugaydi? 28. Markazi
 √ (0; 0) nuqtada bo‘lgan aylanadagi
A) 6 B) 2 C) 0 D) 5 3 1
√ √ √ √ A ; nuqtani soat mili harakatiga
10 · 12 · 18 · 20 2 2
22. kasrning qiymati natural
a qarama-qarshi yo‘nalishida aylana bo‘ylab
son bo‘lishi uchun a quyidagi sonlardan qaysi 120◦ ga burish natijasida hosil bo‘lgan
biriga teng bo‘lishi kerak? nuqtaning koordinatalari yig‘indisini toping.
√ √ √ √ √ √
A) 6 B) 2 C) 5 D) 3 3−1 − 3+1
23. Mis va ruxdan iborat qotishmaning massasi A) 1 B) −1 C) D)
2 2
18 kg. Qotishmaning 60%ini rux tashkil qiladi.
Qotishmaning 50%ini mis tashkil qilishi uchun 29. Agar x2 − 7x + 12 = 0 tenglamaning ildizlari
unga necha kilogramm mis qo‘shish kerak? tgα va tgβ bo‘lsa, tg (α + β) ifodaning
qiymatini toping.
A) 1,8 B) 3,4 C) 4,2 D) 3,6
7 7 7 7
2
a + bc − ac − ab b A) − B) C) D) −
24. Agar 2 + c + b = 2 tenglikda
6 6 11 11
ab − bc + ac − c
a = 18, b = −2 bo‘lsa, c ning qiymatini toping. 30. f (x) = (sin x + cos x)2 funksiyaning
A) −19 B) 9 C) 20 D) 11 boshlang‘ich funksiyasini toping.
25. Uchlari A(10; 11), B(10; 3) va C(2; 3)
1
nuqtalarda bo‘lgan uchburchakning B uchidan A) F (x) = −x + cos 2x + C
2
AC tomonga BD balandlik tushirilgan. D
nuqtaning koordinatalari yig‘indisini toping. 1
√ √ B) F (x) = −x − cos 2x + C
A) 13 B) 8 2 C) 9 D) 10 2 2
  √ 1
26. (x + 4) + 4 3 (x − 3)2 + 5 3 x2 + x − 12 = 0
3 2 C) F (x) = x + cos 2x + C
2
tenglama nechta haqiqiy ildizga ega?
1
A) 2 B) 3 C) 0 D) 1 D) F (x) = x − cos 2x + C
2




2


Matematika(8000608) - Sotish taqiqlanadi! T-108

MATEMATIKA

x2 + 1, x ≤ 1 1 1 1 1 5
1. Agar f (x) = bo‘lsa, 9. 1− 1− ... 1 − 1− ·x = 1
x, x>1 3 4 8 9 9
2 1
x · f (x)dx integralni hisoblang. tenglama ildizining
14
qismini toping.
−1
7 4 5 8 A) 3, 5 B) 0, 5 C) 1 D) 2
A) B) C) D)
3 3 3 3

2. (x2 − 121)2 · (32 − 14x − x2 ) =
  √ 10. Matematikadan yozma ish topshirgan
= 121 − x2 · 32 − 14x − x2 tenglikni nechta 1 7
butun son qanoatlantiradi? o‘quvchilarning qismi "5" baho, qismi "4"
8 12
A) 15 B) 16 C) 18 D) 14 baho olgan. "3" baho olganlar esa "5" baho
olganlar sonidan 6 taga ko‘p. Agar 2 ta
3 o‘quvchi "2" baho olgan bo‘lsa, nechta o‘quvchi
3. 6 12 + 612 + 612+ ... + 612 + 612 yig‘indining
4 "4" baho olgan?
32 ta
qismi quyidagilardan qaysi biriga teng? A) 28 B) 14 C) 12 D) 35
A) 215 · 313 B) 214 · 312 C) 4 · 612
D) 2 · 613

4. ABC uchburchakning AC tomonidan D nuqta 11. a soni quyidagilardan qaysi biriga teng
shunday olinganki, bunda BD = DC (rasm). bo‘lganda a; a + 6 va a + 14 sonlar tub sonlar
Agar ∠BAC = 33◦ va ∠BDC = 42◦ bo‘lsa, bo‘ladi?
∠ABC ni toping.
A) 13 B) 19 C) 17 D) 11
B




12. Agar a − b = 8 va a · b = 9 bo‘lsa, a + b ni
A D C
toping.
√
A) 75◦ B) 79◦ C) 78◦ D) 80◦ A) 11 B) 9 C) 10 D) 108
5π 3π π
5. Hisoblang: + tg
tg · cos − 1.
16 16 8
A) 1 B) −1 C) 2 D) 0
13. Rasmda ABC uchburchak va uning o‘zaro
6. 34974 sonning raqamalari joylarini almashtirib perpendikulyar AD va CE medianalari
jami nechta har xil 5 xonali son hosil qilish tasvirlangan. Agar AB=8 va BC=10 bo‘lsa,
mumkin? AC ni toping.
B
A) 60 B) 20 C) 30 D) 120
 √ √ √ 
7. Hisoblang: 10 27 − 4 75 + 11 48 :
2
 √  1√4 E
D
: 2 3 − − 81
3 O
1
A) 8 B) 16 C) 24 D) 26
3
A C
  
8. To‘g‘ri burchakli parallelepipedning barcha √ 42 43 41
qirralari uzunliklari yig‘indisi 48 dm. Agar
√ A) 4 2 B) 2 C) 2 D) 2
5 5 5
parallelepipedning diagonali uzunligi 5 2 dm
bo‘lsa, uning to‘la sirti yuzini (dm2 ) toping.
A) 82 B) 104 C) 94 D) 108



1
T-108 Matematika(8000608) - Sotish taqiqlanadi!

14. Rasmda f (x) = ax2 + bx + c funksiyaning 20. Algebraik ifodaning qiymatini toping.
grafigi va unga o‘tkazilgan urinma tasvirlangan 0, 25ab − 0, 3b2 , bunda a=4 va b=3.
bo‘lsa, a ni toping. A) −0,3 B) 3 C) −3 D) 0,3
y
π π
21. tg( − x) · ctg(x − ) = 0 tenglamaning eng
4 6
6 katta manfiy yechimini toping.
π 3π π π
A) − B) − C) − D) −
3 4 6 4
√5
22. 8 · 28x+5 = 16 x+100 tenglamani yeching.
2 A) 12 B) 10 C) 11 D) 9
23. Radiusi 3 va 4 ga teng bo‘lgan ikki shar
markazlari orasidagi masofa 5 ga teng. Shar
x sirtlari kesishishidan hosil bo‘lgan aylananing
0 3 6
f (x) uzunligini toping.
A) 2, 4π B) 5π C) 4π D) 4, 8π
5 4 2 1
A) − B) − C) − D) − 24. k ning qanday qiymatida y = kx2 − 3
9 9 3 3
funksiyaning grafigi A (−2; 9) nuqtadan o‘tadi?
15. Ifodani soddalashtiring: A) −6 B) 6 C) −3 D) 3
√ √ −1 √
4
m−4 4
m+4 44m 111 222 333
√ −√ · √ 25. Hisoblang: + +
4
m+4 4
m−4 4
m−4 333 666 999
√ √
4
m+4 √ 4
m+4 A) 1,5 B) 1,6 C) 1 D) 2
A) − B) − m − 4 C)
4

√4 4
x3 9x
D) −4 ( 4 m + 4) 26. ≤ tengsizlikning butun yechimlari
x−2 x−2
16. y = −x4 + 8x2 − 9 funksiyaning eng katta sonini toping.
qiymati a bo‘lsa, a + 5 quyidagi sonlardan qaysi A) 6 B) 7 C) 4 D) 5
biriga qoldiqsiz bo‘linadi? 1
27. Sayyoh belgilangan yo‘lning qismini bosib
A) 8 B) 9 C) 5 D) 6 6
o‘tgach, yo‘l yarmigacha yana 16 km qolgan
49 · 812 + 15 · 643 · 93
17. Hisoblang: · (0, (4))−1 bo‘lsa, belgilangan yo‘l uzunligini (km) toping.
129 + 45 · 68 A) 42 B) 54 C) 36 D) 48
A) 0,5 B) 4 C) 1,5 D) 0,(1) 28. Аylаnаgа ichki chizilgаn to‘g‘ri
18. y = kx + b chiziqli funksiyaning grafigi I, II va to‘rtburchаkning tоmоnlаri 32 vа 24 gа tеng.
IV choraklarda yotsa, k va b larni nol bilan Аylаnаning uzunligini tоping.
taqqoslang. A) 48π B) 80π C) 40π D) 20π
A) k > 0, b < 0 B) k > 0, b > 0 29. Agar log2 a = 2, (3) va log2 b = 3, (6) bo‘lsa,
C) k < 0, b < 0 D) k < 0, b > 0 a · b + 1 ning qiymatini toping.
 17  A) 33 B) 65 C) 25,9 + 1 D) 21,3 + 1
b − 1 (b + 1)
19. Agar b = −3 bo‘lsa, 16 30. Agar A = {a, b, c, d, e} bo‘lsa, B ⊂ A (B = A,
b + b15 + b14 + ... + b + 1
ifodaning qiymatini toping. B = ∅) shartlarni qanoatlantiruvchi necha har
xil B to‘plam mavjud?
A) 8 B) 15 C) 4 D) 16
A) 32 B) 16 C) 30 D) 14




2


Matematika(8000632) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. x = 0, 495 · 1015 ; y = 0, 537 · 108 va 2
8. x ning qanday qiymatida y = x − 3
z = 0, 4953 · 1014 sonlardan qaysilari 15 ga 3
qoldiqsiz bo‘linadi? 5
funksiyaning qiymati ga teng bo‘ladi?
A) faqat x va z B) faqat y C) barchasi 9
D) faqat x va y 1 1 2 1
A) 5 B) −1 C) 4 D) 2
3 3 3 3
2. A = {x| x ≥ 2, x ∈ Z}, B = {x| x < 8, x ∈ Q}
bo‘lsa, A ∩ B to‘plamning elementlari sonini 9. Soatning minut mili 156◦ burilganda soat mili
aniqlang. necha gradus burchakka buriladi?
A) 6 B) 7 C) 8 D) ∞ A) 13◦ B) 6,5◦ C) 5,2◦ D) 2,6◦
3. Agar x2 y > 0 bo‘lsa, quyidagilarning qaysi biri 10. Hisoblang: 0, 84 · 109 : 7000000.
x va y ning barcha haqiqiy qiymatlarida to‘g‘ri A) 1200 B) 12 C) 240 D) 120
bo‘ladi?
x+y 11. 9, 142 + 2, 76 · 0, 86 − 9, 14 · 6, 38 ni hisoblang.
A) > 0 B) x2 + y > 0
xy A) 91,4 B) 8,6 C) 27,6 D) 2,76
C) x3 + y 3 > 0 D) (x + y)2 > 0
12. f (x) = x2 + bx − 1 funksiya abssissalar o‘qini
4. Ixtiyoriy uchtasi bitta to‘g‘ri chiziqda ikkita nuqtada kesib o‘tadigan b ning barcha
yotmaydigan A, B, C va D nuqtalar berilgan. qiymatlarini toping.
−−
→ −−→
Agar AB = 0, 8DC bo‘lsa, ABCD to‘rtburchak A) b > 2 B) b < −2 C) b < 2 D) b ∈ R
turini aniqlang.  
13. Agar f (x + 2) = log3 x2 − 6x + 27 + 6 bo‘lsa,
A) trapetsiya B) parallelogramm
f (2) ning qiymatini toping.
C) to‘g‘ri to‘rtburchak D) kvadrat
A) 6 + log3 19 B) 6 + log3 7 C) 8 D) 9
5. Funksiya grafigidan foydalanib, (−2; 6) oraliqda
f (x) · f  (x) ≥ 0 tengsizlikning eng kichik 14. Hisoblang:
natural yechimini toping. (tg 435◦ − tg 375◦ ) · sin2 70◦ · sin2 50◦ · sin2 10◦ :
: sin 120◦
1 1 1
y A) B) C) 1 D)
3 4 8 16
x)




15. Ketma-ketlikning istalgan 2 ta ketma-ket
f(
=
y




hadining yig‘indisi 10 ga teng. Agar uchinchi
1 hadi 7 ga teng bo‘lsa, ketma-ketlikning
4
x dastlabki to‘qqizta hadi yig‘indisini toping.
−3 −2 −1 0 1 2 3 5 6
A) 43 B) 47 C) 45 D) 37
−1
16. Rasmda ABC uchburchakka aylana ichki
A) 2 B) 3 C) 1 D) 4 chizilgan. Agar AB=14, BC=13 va AC=15
 2 2 bo‘lsa, aylana markazi O nuqtadan
6. x + 5x + 1 + 2x2 + 10x = 1 tenglama
nechta haqiqiy ildizga ega? A nuqtagacha bo‘lgan masofani toping.
B
A) 2 B) 3 C) 1 D) 4
7. Rasmda doira teng bo‘laklarga (sektorlarga)
bo‘lingan. Doiraning necha foizi bo‘yalgan?
O


A C
√ √ √ √
A) 84 B) 52 C) 80 D) 65
17. Tenglamani yeching:   
1, 4 · (2 + 0, 6) · 4 + 0, 62 · 16 + 0, 64 · x =
0, 68 − 256
A) 62,5 B) 60,5 C) 65 D) 55 A) 16 − 0, 64 B) 1 C) 0, 64 − 16 D) −1


1
T-108 Matematika(8000632) - Sotish taqiqlanadi!

18. Koordinatalar o‘qlari va f (x) = 2x + 7 ning 23. Agar f (x) 13-darajali ko‘phad bo‘lsa,
grafigi bilan chegaralangan yuzani (rasm) y = x14 · f (x) funksiyaning hosilasi nechanchi
toping. darajali ko‘phad bo‘ladi?
y
A) 52 B) 26 C) 25 D) 27
π π π π
24. Hisoblang: sin · cos3 − cos · sin3 .
12 12 12 12
√ √ √
)




3 1 3 3
f (x




A) B) C) D)
8 8 6 4
y=




3 3 √
25. Hisoblang: √ +√ + 3
3 − 12 3
x
0 A) 2 B) −3 C) 3 D) −2
7 49 49 26. f (x) = 3|x| − 2 funksiyaning qiymatlar sohasini
A) 7 B) C) D)
2 4 2 toping.
 3 3

a2 + b2 a−b a−b √ A) (−2; +∞) B) (−1; +∞) C) (0; +∞)
19. Ushbu − 1 · √ − a
a−b 1
a2 + b2 ab D) [−1; +∞)
√
ifodaning a = 2, b = 8 dagi qiymatini toping. 27. Agar
 b > a > c > 0 bo‘lsa,
√ √
A) − 2 B) 2 2 C) 0 D) 2 (a − b)2 · (a − c)2 · (b − c)2 ifoda
20. Rasmda tasvirlangan to‘g‘ri prizmaning quyidagilardan qaysi biriga teng?
hajmini (dm3 ) toping. A) (a − b)(a − c)(b − c)
80cm B) (b − a)(a − c)(c − b)
C) (c − b)(c − a)(a − b)
D) (c − a)(a − b)(b − c)
28. To‘g‘ri burchakli parallelepipedning uchta turli
cm
140




yoqlarining diagonallari 7; 8 va 9 dm bo‘lsa,
parallelepipedning diagonali uzunligini (dm)
20cm hisoblang.
√ √ √ √
A) 94 B) 6 3 C) 4 6 D) 97
50cm
a−3 a+5 a−8
A) 169 B) 156 C) 182 D) 196 29. Ifodani soddalashtiring: − −
36 12 6
21. 2 ta har xil kitobni 12 ta o‘quvchidan 2 tasiga
15 − 4a −2a − 9 2a − 9
bittadan berish sharti bilan necha xil usulda A) B) C)
berish mumkin? 18 9 9
4a − 15
A) 66 B) 132 C) 156 D) 78 D)
18
22. −3; 6; 8 va x sonlarining o‘rta arifmetigi y ning
1 1 (4x − 1)dx
qismiga teng. Agar 3x − 2y = 15 bo‘lsa, 30. Integralni hisoblang: 
3 0 2x2 − x + 4
y ning qiymatini toping. √ √ √
A) 2√− 5 B) 2 5 − 4 C) 4 − 5
A) 24 B) 28 C) 32 D) 18
D) 5 − 2




2


Matematika(8000656) - Sotish taqiqlanadi! T-108

MATEMATIKA
 
2x − 1 6x + 5 9. Rasmda ABC teng yonli (AB = BC)
1. Agar f = bo‘lsa,
3 3 uchburchak tasvirlangan. Bunda BD⊥AC,
f (1) − f (−2) ni hisoblang. DE⊥BC va EF ||AC. Agar AB=11 va CD=5
A) −3 B) −12 C) 9 D) 3 bo‘lsa, EF ni toping.
B

2. 
Agar x = 1 va y = 2 bo‘lsa,

x 6
− :
x−y+6 x+y+6
x2 + y 2 + 2xy − 36 y G
: 2 2 + ni hisoblang. F E
x − y + 12x + 36 x + y + 6
A) 1 B) 2 C) 3 D) 0 A D C
810 1000 840 960
  A) B) C) D)
 x+1 5  11 121 121 121 121

3. 2 3 −  < tengsizlikni yeching.
2 2
  10. 2 ta har xil kitobni 12 ta o‘quvchidan 2 tasiga
1
A) (8; +∞) B) −∞; C) (−∞; 8) bittadan berish sharti bilan necha xil usulda
8 berish mumkin?
D) (0; 8)
A) 78 B) 156 C) 132 D) 66
4. Rasmda tasvirlangan trapetsiyaning yuzasini x2 − 3x + 4
(cm2 ) hisoblang. Har bir katak tomoni 1 cm li 11.  2  ≤ 0 tengsizlikning natural
x − 10 · (x − 1)
kvadrat. yechimlari yig‘indisini toping.
A) 3 B) 4 C) 5 D) 6

12. 2 (5a − 3) − 3 (4a − 5) + 4 (a − 5) ifodani
soddalashtiring.
A) 2a + 11 B) −2a − 11 C) −2a + 11
D) 2a − 11

1 6
13. = 2 tenglamaning ildizlari
|x| x + 2x
A) 68 B) 56 C) 72 D) 64 ko‘paytmasini toping.
A) 4 B) −32 C) 0 D) −8
5. Magazinda birinchi kuni 76% tarvuz sotildi. 14. To‘g‘ri burchakli uchburchakning tomonlari
Ikkinchi kuni esa qolgan 54 ta tarvuz sotildi. ayirmasi 1,5 ga teng bo‘lgan arifmetik
Birinchi kuni nechta tarvuz sotilgan? progressiyani tashkil etadi. Uchburchakning
A) 168 B) 176 C) 163 D) 171 perimetrini toping.
A) 17 B) 18 C) 16 D) 15
√
6. Hisoblang: 2017 · 2021 + 4  2
A) 2019 B) 2009 C) 2011 D) 2021 15. x2 − 2x − 4 (x − 1)2 + 7 = 0 tenglamaning
barcha haqiqiy ildizlari ko‘paytmasini toping.
7. Quyidagi sonlardan nechtasi butun son? A) 1 B) −3 C) 3 D) −1
 √ 2, 48
1) 2 + 144; 2) 7, 12; 3) π − 1, 14; 4) − 16. Hisoblang:
1, 24 (tg 435◦ − tg 375◦ ) · sin2 70◦ · sin2 50◦ · sin2 10◦ :
A) 3 B) 4 C) 2 D) 1 : sin 120◦
1 1 1
A) 1 B) C) D)
8. f (x) = |3 − 2x| − 4 funksiyaning eng kichik 8 4 16
qiymatini toping.
17. 5 · 195 ni 6 ga bo‘lgandagi qoldiqni toping.
A) −3,5 B) 1,5 C) −4 D) 0
A) 2 B) 4 C) 3 D) 5


1
T-108 Matematika(8000656) - Sotish taqiqlanadi!

18. y = 1, 44 − x2 funksiya grafigiga o‘tkazilgan 25. Kesik konusga shar ichki chizilgan. Agar kesik
urinma abssissa o‘qini (−2;0) nuqtada kesib konus asoslarining radiuslari 2 va 4 bo‘lsa, shu
o‘tsa, uning tenglamasini toping. konus yon sirtining yuzini toping.
2 4 3 3 A) 48π B) 72π C) 36π D) 24π
A) y = x + B) y = x +
3 3 4 2
26. Rasmda y = f (x) funksiyaning grafigi
4 8 3 6
C) y = x + D) y = x + tasvirlangan. Quyidagi tengsizliklardan qaysi
5 5 5 5
biri to‘g‘ri?
1 y
19. Integralni hisoblang: (2x + 1) cos(x2 + x)dx
0 4




y=
A) − sin 2 B) −2 sin 2 C) sin 2 D) 2 sin 2 3




f(
x)
3 5
20. Hisoblang: 17 − 1−
2 9 x
−3 −2 −1 1 2 3 4 5 6
A) 4 B) 3 C) 3,8 D) 2 −1
21. To‘g‘ri burchakli parallelepipedning barcha
qirralari uzunliklari yig‘indisi 44 dm. Agar A) f  (5) · f (2) > 0 B) f  (4) · f (3) > 0
parallelepipedning to‘la sirtining yuzi 72 dm2 C) f  (1) · f (3) > 0 D) f  (4) · f (5) > 0
bo‘lsa, uning diagonali uzunligini (dm) toping.
√ √ 27. a (−12; 13; −15) vektorning Oxy tekisligidagi
A) 5 2 B) 7 C) 8 D) 61 proyeksiyasi bo‘lgan vektorni toping.
22. Tenglamani yeching: tg (4x + π) · tg (3x) = 1 A) p (−12; 13; 0) B) p (0; 13; −15)
C) p (−12; 0; −15) D) p (0; 0; −15)
π πk
A) x = + , k∈Z 28. Tengsizlikni yeching:
14 7
log 1 (log2 (2 − x)) + 1 ≥ 0.
π πk 3
B) x = + , k∈Z A) [−6; 2) ∪ (2; ∞) B) [−6; 2) C) [−6; 1)
4 7
D) (1; 2)
π πk
C) x = + , k∈Z 29. A = {(x, y) | x2 + y 2 = 4, x, y ∈ R},
7 7
π πk B = {(x, y) | x − y = 2, x, y ∈ R} bo‘lsa, A ∩ B
D) x = + , k∈Z to‘plamni aniqlang.
3 7
A) {(−2; 0) ; (0; 2)} B) {(2; 0) ; (0; −2)}
23. (bn ) geometrik progressiyada b6 − b3 = 84 va
C) {(2; 0) ; (0; 2)} D) {(−2; 0) ; (0; −2)}
b5 − b2 = 42 bo‘lsa, b2 + b4 ni toping.
30. Karim ota 71 yoshda. Uning nabiralarining
A) 27 B) 36 C) 30 D) 51
o‘rtacha yoshi 21 da. Nabiralari bilan Karim
1 3 3 3 3 5 1
24. Hisoblang: 1 · 3 + 2 · 3 − 3 · 3 − 1 otaning yoshlari o‘rta arifmetigi 26 ga teng.
2 5 4 5 5 6 2 Karim otaning nechta nabirasi bor?
A) 0,5 B) −0, 5 C) −1, 5 D) 0
A) 9 B) 8 C) 12 D) 10




2


Matematika(8000680) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. 2x = 2 − x tenglama nechta haqiqiy ildizga ega? 11. Rasmda tasvirlangan yopiq siniq chiziq bilan
A) aniqlab bo‘lmaydi B) 1 C) 2 chegaralangan soha yuzasini (cm2 ) toping. (har
D) yechimga ega emas bir katakning tomonlari 1 cm dan)

x2 − 7 |x| + 12
2. = 0 tenglama nechta haqiqiy
(x − 3)2
ildizga ega?
A) 4 B) 2 C) 3 D) 1

3. Hasan, Husan va ularning 3 nafar o‘rtoqlari
orasidan ixtiyoriy tanlangan 3 kishining orasida
Hasan va Husan bo‘lishi ehtimolligini toping.
A) 0,25 B) 0,4 C) 0,2 D) 0,3

4. Suv solingan idishdan 80 foiz suv olindi,
so‘ngra yana qolgan suvning 25 foizi olindi. A) 132 B) 140 C) 194 D) 135
Idishda necha foiz suv qolgan? 12. Agar k < 0, b = 0 bo‘lsa, y = kx + b chiziqli
A) 30 B) 15 C) 20 D) 18 funksiyaning grafigi qaysi choraklarda yotadi?
A) III va IV B) II va IV C) I va II
5. Hisoblang: (tg 435◦ − tg 375◦ ) : sin 120◦ .
D) I va III
A) 3 B) 2 C) 1 D) 4    
1 1
13. Hisoblang: 2018 − : 1−
6. Sakkizta haddan iborat arifmetik 2018 2018
progressiyaning toq o‘rindagi hadlari yig‘indisi 1
A) 2018 B) 2019 C) 2017 D) 2018
168 ga, juft o‘rindagi hadlari yig‘indisi 200 ga 2018
teng. Shu progressiyaning oltinchi hadini
toping. 14. A = {x| x2 ≤ 64, x ∈ R},
B = {x| x2 > 4, x ∈ N } bo‘lsa, A ∩ B
A) 66 B) 50 C) 58 D) 42
to‘plamni aniqlang.
7. Hisoblang: A) (2; 8] B) {2; 3; 4; 5; 6; 7; 8}
 3 
sin 1 − cos3 1 sin2 1 + cos2 1 C) {3; 4; 5; 6; 7; 8} D) [2; 8]
2· − +1
sin 1 − cos 1 tg 1 + ctg 1 15. Agar
 √ x = 17 bo‘lsa, √   
A) 3 B) 1, 5 C) 1, 25 D) 2 x x − 64 4 x 8
+√ : √ −1 −4
√ x − 16 x+4 4− x
8. Uzunligi 128 ga teng bo‘lgan AB kesmaning ifodaning qiymatini toping.
√ √
uchlari radiusi 5 ga, balandligi 8 ga teng A) 17 B) 4 C) − 17 D) −4
silindrning pastki va yuqori asoslaridagi 16. Integralni hisoblang:
aylanalarda yotadi. Silindr markaziy o‘qidan 2 2
AB kesmagacha bo‘lgan eng qisqa masofani (x − x + 1)3 · (2x − 1)dx
1
toping.
√ √ A) 6,5 B) 20 C) 13 D) 10
A) 3 B) 19 C) 4 D) 17
17. f (2x + 1) = x4 + 4x2 funksiya berilgan.
9. Ikki shahar orasidagi masofa 126 km. Bu f  (3) ni toping.
masofa 1:6000000 masshtabli xaritada necha A) 0 B) 8 C) 12 D) 6
millimetrga teng bo‘ladi?  
17 7 2 3 1
18. Hisoblang: 7 − 9 : − ·4 +3
A) 21 B) 210 C) 2,1 D) 0,21 36 12 9 26 3
A) −6 B) 13 C) −7 D) 1
10. y = 3x2 − 12x + 15 kvadrat funksiyaning
19. Agar piramida asosining diagonallari soni 44 ta
qiymatlari to‘plamini aniqlang.
bo‘lsa, bu piramidaning qirralar soni yoqlari
A) [3; +∞) B) [−1; +∞) C) [7; +∞) sonidan qanchaga ko‘p?
D) [2; +∞)
A) 9 B) 10 C) 11 D) 12


1
T-108 Matematika(8000680) - Sotish taqiqlanadi!

20. Ko‘paytuvchilarga ajrating: 24. x = 35 · 47, y = 63 · 28, z = 95 · 39, t = 48 · 35.
x (3x − 4y) − 6x + 8y Berilgan sonlardan qaysilari 15 ga qoldiqsiz
A) (x + 2) · (3x − 4y) B) (x − 2) · (3x + 4y) bo‘linadi?
C) (x − 2) · (3x − 4y) D) (x − 2) · (4y − 3x) A) faqat z B) x, y va t C) x va y
D) z va t
25. Rasmda ABC uchburchak va uning BD
21. Tengsizlikni
 yeching:  medianasi tasvirlangan. Agar AC=2BD va
|x − 6| · log 1 (x − 2) + 1 < 0. ∠CAB = 22◦ bo‘lsa, ACB burchakni toping.
3
B
A) (5; ∞) B) (2; 6) ∪ (6; ∞) C) (2; 5)
D) (5; 6) ∪ (6; ∞)
A C
D
22. Funksiya grafigidan foydalanib, (−3; 6) oraliqda
f (x) · f  (x) ≤ 0 tengsizlikning eng katta manfiy A) 68◦ B) 58◦ C) 62◦ D) 52◦
√
butun yechimini toping. 26. Hisoblang: 2017 · 2021 + 4
A) 2011 B) 2019 C) 2021 D) 2009
y 27. Agar x2 y > 0 bo‘lsa, quyidagilarning qaysi biri
3
x va y ning barcha haqiqiy qiymatlarida to‘g‘ri
x)
f(




bo‘ladi?
=
y




1 A) x2 + y > 0 B) x3 + y 3 > 0
x+y
4
x C) (x + y)2 > 0 D) >0
−3 −2 −1 0 1 2 3 5 6
xy
 2 
−1 x − 9 : (3 + x) − 2
28.  2  = (x − 1) : (x + 1)
x − 16 : (x − 4) + 2
A) −3 B) −1
tenglamaning ildizini toping.
C) manfiy yechimga ega emas D) −2
1 4
A) 3, 5 B) x ∈ ∅ C) D)
9 5
23. (3; 4) nuqtani koordinatalar boshiga nisbatan
soat mili harakati yo‘nalishida 90◦ ga burish 29. Hisoblang: (3−2 )−1 + (2−2 )−2 + 1
natijasida hosil bo‘lgan nuqtaning A) 8 B) 6 C) 5 D) 4
koordinatalarini aniqlang.
30. Uchburchakning ikki tomoni va ular orasidagi
A) (4; −3) B) (−4; 3) C) (3; −4) mediana uzunliklari mos ravishda 15; 13; 7
D) (−3; 4) bo‘lsa, shu uchburchakning yuzini toping.
A) 84 B) 72 C) 70 D) 78




2


Matematika(8000704) - Sotish taqiqlanadi! T-108

MATEMATIKA

1 9. 1 dan 1000 gacha bo‘lgan natural sonlarning
1. x · cos x2 dx integralni hisoblang.
0 nechtasi 17 ga qoldiqsiz bo‘linadi?
sin 1 cos 1 sin 1 A) 58 B) 57 C) 59 D) 56
A) B) 0 C) D) −
2 2 2 10. Kasrning
√ maxrajini irratsionallikdan qutqaring:
2. Radiusi 3 va 4 ga teng bo‘lgan ikki shar 3
√ √
markazlari orasidagi masofa 5 ga teng. Shar 2 3 − 13 − 1
sirtlari kesishishidan hosil bo‘lgan aylananing √ √ √ √
1 − 2 3 − 13 1 − 2 3 + 13
uzunligini toping. A) B)
√ 4 √ √2 √
A) 2, 4π B) 5π C) 4, 8π D) 4π
1 − 2 3 + 13 1 − 2 3 − 13
3. Rasmda ABCD parallelogrammda BD C) D)
4 2
diagonal hamda BC va AD tomonlarini mos
ravishda teng ikkiga bo‘luvchi AE va 11. Hisoblang:
CF kesmalar o‘tkazilgan. Agar 139 · 163 − 160 · 139 + 141 · 175 − 172 · 141
F DN uchburchakning yuzi 6 ga teng bo‘lsa, A) 840 B) 864 C) 852 D) 870
BCD uchburchakning yuzini toping. 12. a1 ; a2 ; a3 ; ...; an+1 ; an+2 arifmetik
B E C
progressiyaning yig‘indisi 390 ga teng. Agar
M n+3
a3 + an = 30 bo‘lsa, ning qiymatini
9
N
toping.
1 2
A F D A) 2 B) 3 C) 3 D) 2
3 3
A) 42 B) 30 C) 54 D) 36 13. f (x) = ln(2x + 5) funksiyaning x0 =2 nuqtadagi
4. Beshta bir xil qog‘ozchaning har biriga quyidagi hosilasini toping.
harflardan biri takrorlanmasdan yozilgan: A, 2 4 2
T, N, S, O. Qog‘ozchalar qutiga solingan va A) − B) 0 C) D)
9 9 9
yaxshilab aralashtirilgan. Qutiga qaramasdan
14. Hisoblang:
bittalab olingan va olingan tartibda o‘qilganda
SON so‘zi hosil bo‘lish ehtimolligini toping. −2019 + 2019 − 2019
 + ... + 2019 − 2019
2019 ta
1 1 1 1
A) B) C) D) A) −2019 B) 2018 C) 2019 D) 0
60 30 40 120
5. Yog‘liligi 5% bo‘lgan 12 litr sut bilan yog‘liligi 15. Agar 3a + 3−a = 3 bo‘lsa, 32a − 2 · 3a + 3−a
2% bo‘lgan necha litr sut aralashtirilsa, ifodaning qiymatini toping.
yog‘liligi 4,4% bo‘lgan sut hosil bo‘ladi? A) 2 B) 1 C) 4 D) 3
A) 4,2 B) 3 C) 2,5 D) 2 16. 2 cos2 x − cos x − 1 = 0 tenglamaning eng kichik
 
|x| + x 2 6x musbat yechimini toping.
6. − + 2 = 0 tenglama nechta 2π 3π π π
x−2 x−2 A) B) C) D)
haqiqiy ildizga ega? 3 4 4 6
A) 2 B) 0 C) 3 D) 1 17. Agar x=3, y=4 bo‘lsa, xy 2 x2 y − 13xyxy
7. (tg α − ctg α) · (tg α + ctg α) ifodaning ifodaning qiymatini toping.
α = 75◦ bo‘lgandagi qiymatini toping. A) −144 B) 144 C) −72 D) 72
√ √ √
A) 8 3 B) 8 C) −8 3 D) 4 2
16 − 0, 362
8. Tenglamani yeching. 18. Hisoblang: .
1, 4 · 4, 12 − 1, 52 · 1, 4
x+2 x−6 x 1
−3 +2 +4 A) 4,36 B) 2,36 C) 2,6 D) 3,64
2 3 6 3
− = −1 19. y = −x + 1 va y = x2 − 5x + 6 funksiyalarning
1 1 (1, 2)
2+ 4−2 grafiklari orasidagi eng qisqa masofani toping.
2 3 √ √
1 1 1 2 3
A) 30 B) C) − D) −30 A) B) 0 C) D)
15 15 2 2 2


1
T-108 Matematika(8000704) - Sotish taqiqlanadi!

20. (x + 1) · (|x| − 1) ≥ 2 tengsizlikni yeching. 26. f (x) = −x + b funksiya b ning qanday
√ √
A) (−∞; 0] ∪ 3; + ∞ B) 3; + ∞ qiymatlarida o‘suvchi bo‘ladi?
√ √
C) −∞; − 3 ∪ 3; + ∞ A) b = 2n − 1, n ∈ N B) b < 0 C) b > 0
√
D) −∞; − 3 D) b ning hech qanday qiymatida
27. Rasmda berilgan ma’lumotlardan foydalanib,
21. A(6; 7) nuqtadan y = 2 x2 − 4x + 6 parabola α − β ni aniqlang.
uchigacha bo‘lgan masofani toping. α
√ √
A) 4 2 B) 5 C) 3 2 D) 4
87◦
22. ABCD parallelogrammda, AD katta
β
tomonidagi A va D burchaklarining
bissektrisalari parallelogrammning ichki
sohasida kesishgan bo‘lsa, tomonlari orasida 79◦
qaysi munosabat to‘g‘ri bo‘ladi?
A) 2DC < AD B) 2AB = AD A) 12◦ B) 6◦ C) 8◦
C) 2AB > AD D) 2AB < AD D) aniqlab bo‘lmaydi
28. A(a; −1), B(1 − a; 2a + 1) va C(a + 1; −3)
2 nuqtalar bitta to‘g‘ri chiziqda yotsa, shu to‘g‘ri
23. y = − 3 − 1 funksiya grafigi chiziq tenglamasini tuzing.
lg (x − 2)
abssissalar o‘qini qaysi nuqtada kesib o‘tadi? A) y = −2x + 3 B) y = 2x + 3
√ C) y = 3x + 2 D) y = −3x + 2
A) kesib o‘tmaydi B) 10 + 2; 0
C) (102; 0) D) (0; 102) 29. To‘g‘ri burchakli parallelepipedning bir uchidan
chiquvchi qirralari a; b va c bo‘lib,
x − 25 x2 − 6 1 1 1 1
24. √ +√ ifodaning x = 6 dagi + + = tenglikni qanoatlantiradi. Agar
5+ x 6−x a b c 2
qiymatini toping. parallelepiped to‘la sirtining yuzi 288 bo‘lsa,
√ uning hajmini toping.
A) 1 B) −11 C) −1 D) −2 6
A) 432 B) 144 C) 576 D) 288
2x − y 30. A, B va C sonli to‘plamlarning elementlari soni
25. Аgаr 4x = 125 vа 8y = 5 bo‘lsа, ni
y mos ravishda 10; 12 va 15 ta. A ∪ B ∪ C
tоping. to‘plamning elementlari soni eng kamida necha
A) −6 B) 6 C) −8 D) 8 bo‘la oladi?
A) 12 B) 15 C) 22 D) 27




2


Matematika(8000728) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Bir nechta natural sonlarning yig‘indisi 47 ga 2
7. Agar a = bo‘lsa,
teng. Agar shu sonlarning har biri 2 ga ortirilib 3

yig‘indisi hisoblansa, u 63 ga teng bo‘ladi. a+4 a2 − 10a + 25 1
Yig‘indida nechta son qatnashgan? 2 · 2 − 2 ifodaning
a − 5a a + 8a + 16 2
A) 8 B) 7 C) 6 D) 9 qiymatini toping.
1 1
A) −4 B) −1 C) −2 D) −1
2. 1 gektar maydonga o‘rtacha 0,6 sentner zig‘ir 2 2
urug‘i ekiladi. 1:10000 masshtabli xaritada
bo‘yi 20 cm va eni 12 cm bo‘lgan to‘g‘ri 8. Muntazam tetraedrning qirrasi 9 ga teng.
to‘rtburchak shaklidagi yer maydoniga zig‘ir Uning asosiga tashqi chizilgan aylananing
urug‘i ekish uchun o‘rtacha necha sentner kerak markazidan uning yon yoqigacha bo‘lgan eng
bo‘ladi? qisqa masofani toping.
√ √ √ √
A) 400 B) 144 C) 14,4 D) 40 A) 2 6 B) 6 C) 2 3 D) 3 2

9. 4680 sonini tub ko‘paytuvchilarga ajrating.
3. Hisoblang: sin 14◦ + cos 14◦ · tg 38◦ − 1.
A) 23 · 3 · 52 · 13 B) 23 · 32 · 5 · 11
A) 2 B) 0 C) 1 D) −1
C) 23 · 32 · 53 D) 23 · 32 · 5 · 13
  
4. (3x − 2) + (3x − 2) + 4 (3x − 2)4 ≥ 4
2 3 3
10. log22 (8x) = 3 log2 x + 27 tenglamaning ildizlari
tengsizlikning eng katta manfiy butun yechimi ko‘paytmasini toping.
bilan eng kichik musbat butun yechimi 1 1
A) 4 B) 2 C) D)
yig‘indisini toping. 8 4
A) tengsizlik yechimga ega emas B) 3 C) 1
D) 4 11. To‘g‘ri burchakli parallelepipedning bir uchidan
chiquvchi qirralari a; b va c bo‘lib,
1 1 1 1
5. ABCD parallelogramda D o‘tmas burchak. + + = tenglikni qanoatlantiradi. Agar
a b c 2
E nuqta AB tomonda yotadi. Agar parallelepiped to‘la sirtining yuzi 288 bo‘lsa,
AE:EB nisbat 2:3 kabi bo‘lsa, uning hajmini toping.
BCDE to‘rtburchak yuzini DAE uchburchak
A) 576 B) 288 C) 432 D) 144
yuziga nisbatni toping.
11 11 12. Integralni hisoblang:
A) 3 B) C) 4 D)
3 4 2 2
(x − x + 1)3 · (2x − 1)dx
1
6. Rasmda y = f (x) funksiya grafigi va unga A) 13 B) 10 C) 20 D) 6,5
(2; 2) nuqtadan o‘tkazilgan urinmasi

tasvirlangan. Agar g (x) = x2 − 2 · f (x) 13. Rasmdan foydalanib, agar AC : A1 C1 = 5 : 3
bo‘lsa, g (2) ni toping. va BD : B1 D1 = 7 : 4 bo‘lsa, u holda
y SA1 B1 C1 D1 : SABCD ni toping.
B C
C1
B1
O
2

A1 D1
A D
x
0 2 5 24 12 15 20
A) B) C) D)
35 35 24 21
f(
x)
14. f (x) = x2 + bx + c funksiyaning nollari 2 va 3
1 2 2 1 bo‘lsa, c ni toping.
A) 9 B) 6 C) 9 D) 6
3 3 3 3 A) 5 B) 6 C) −6 D) −5



1
T-108 Matematika(8000728) - Sotish taqiqlanadi!

7 23. 0; 1; 2; 3; 4; 5 raqamlardan jami nechta
−1
8 8 1 raqamlari takrorlanmaydigan 3 xonali sonlar
15. Hisoblang: + +
7 7 2 tuzish mumkin?
8 A) 180 B) 216 C) 100 D) 125
1 8 2 3
A) B) C) D)
7 7 3 2 24. Ikkita to‘g‘ri chiziq kesishganidan hosil bo‘lgan
16. Hisoblang: burchaklardan biri ikkinchisidan 36◦ ga katta
⎛ √ √

√ √ ⎞2 bo‘lsa, ularning nisbatini toping.
1009 + 12 7 1009 − 12 7
⎝  ⎠
√ √ + √ √ A) 4:3 B) 6:5 C) 5:4 D) 3:2
1009 − 12 7 1009 + 12 7
A) 4036 B) 4038 C) 2018 D) 2019 1 4
25. −1 a4 b3 c2 : − a2 b2 c2 bo‘lishni
17. B = ∅ va B ⊂ A. A va B to‘plamlarning 2 3
elementlari soni mos ravishda m va n ga teng. bajaring.
Agar n + 3m=18 bo‘lsa, A to‘plamning 1 1
A) 1 a2 b B) 2a2 b C) −1 a2 b D) −2a2 b
elementlari sonini toping. 8 8
A) 4 B) 3 C) 5 D) 2
18. Sportchi seshanba kuni yugurish mashg‘ulotini 26. Agar f (x) chiziqli funksiya uchun
boshlab, 1350 metr masofaga yugurdi. Keyingi f (1) + f (x − 3) = 7x − 2 bo‘lsa, f (x) ni toping.
har bir kunda esa oldingisidan 180 metr A) f (x) = 7x + 4 B) f (x) = 7x − 2
masofaga ortiq yugurdi. Sportchi 4410 metr C) f (x) = 7x + 6 D) f (x) = 7x + 2
masofaga yugurgan kuni mashg‘ulotini tugatdi.
Sportchi haftaning qaysi kuni mashg‘ulotini 27. a, b, c sonlar uchun 7a = 2b = 3c va
tugatgan? 3 5 2 2
− + = 3 tengliklar o‘rinli bo‘lsa,
A) juma B) shanba C) chorshanba a b c 5
D) payshanba b
− a ning qiymatini toping.
19. f (2x + 1) = x4 + 4x2 funksiya berilgan. c
f  (3) ni toping. 3 1 11 5
A) − B) 1 C) D) −
A) 8 B) 0 C) 6 D) 12 14 14 14 7

20. 2ā + b va 2ā − b perpendikulyar vektorlar    
berilgan. Agar |a| = 5 bo‘lsa, b ni toping. 28. x2 − 5x − 4 · x2 − 5x + 3 − 8 = 0
tenglamaning haqiqiy ildizlari yig‘indisini
A) 12 B) 10 C) 8 D) 9
 6 toping.
a4 · a3 A) 10 B) 4 C) 5 D) 1
21.  3 ifodaning daraja ko‘rsatkichini
a5
√
aniqlang. 29. Agar sin α + cos α = 2 bo‘lsa,
A) 6 B) 7 C) 8 D) 5 tg 3 α + ctg3 α ning qiymatini toping.
22. Tenglamani yeching. A) 4 B) 2 C) 3 D) 1
x+2 x−6 x 1
−3 +2 +4
2 3 6 3
− = 2x+2 − 24
1 1 (1, 2)−1 30. ≥ 1 tengsizlikni yeching.
2+ 4−2 2x+1 − 8
2 3
1
1 1 A) (0; 2) B) ; +∞ C) (2; +∞)
A) 30 B) C) − D) −30 2
15 15
D) (−∞; 2) ∪ [3; +∞)




2


Matematika(8000752) - Sotish taqiqlanadi! T-108

MATEMATIKA

2 10. y = 17xto‘g‘ri chiziqqa parallel bo‘lgan
1. y = − 3 − 1 funksiya grafigi 11 · 36x 1
lg (x − 2) f (x) = + 6x+1 · funksiyaning
abssissalar o‘qini qaysi nuqtada kesib o‘tadi? 2 ln 6
urinma tenglamasini tuzing.
(0; 102) B)
A) √  kesib o‘tmaydi 13 23
C) 10 + 2; 0 D) (102; 0) A) y = 17x + B) y = 17x +
ln 36 ln 36
 2 17 27
2. x2 − 12x + 10 = (3x + 10)2 tenglamaning C) y = 17x + D) y = 17x +
barcha yechimlari yig‘indisini toping. ln 36 ln 36
A) 19 B) 24 C) 20 D) 3
11. Agar m = 8 bo‘lsa,
3. Integralni hisoblang: √ 2 √ √ 2 √
( m + 3) − 12 m − ( m − 2) + 8 m
2 2
(x − x + 1)3 · (2x − 1)dx ifodaning qiymatini toping.
√ √
1 A) 4 2 −
A) 6,5 B) 13 C) 10
D) 20 √1 B) −5 C) −4 2 − 1
D) 1 − 4 2
−−→
4. ABCD parallelogramm uchun AB (3; 5; −7) va
−−→ 12. f (x) = x2 − 2x + c funksiyaning nollaridan biri
AD (−11; 7; 3). Parallelogramm
diagonallarining keshishgan nuqtasi O bo‘lsa, 3 bo‘lsa, c ni toping.
−→ A) −3 B) −5 C) 1 D) 0
OA vektorning koordinatalari yig‘indisini
toping. √ √
A) −1 B) 2 C) 1 D) 0 x+1 x+2 7
13. √ +√ = tenglama nechta
 3  3  2  x+2 x+3 6
5. Hisoblang: 27 · 3−1 + 3−2 − 3−3 +3 haqiqiy ildizga ega?
A) 4 B) 3 C) 5 D) 6 A) 4 B) 0 C) 1 D) 2

6. Hisoblang:
3|x| − 27
− (−3, 8) + (−6, 2) − (− (+2, 8) + (−8, 4)). 14. ≥ 0 tengsizlikni yeching.
x−3
A) 13,6 B) −13,6 C) −1,2 D) 8,8
7. Hisoblang: A) [−3; 3) ∪ (3; +∞)
π π π B) (−∞; 3) ∪ (3; +∞)
log0,25 tg + log0,25 cos + log0,25 ctg .
4 4 4
C) [−3; +∞)
1 1
A) B) 1 C) 0 D) − D) [0; 3) ∪ (3; +∞)
4 2
8. Rasmda ABCD to‘g‘ri to‘rtburchak, BAD 15. AB kesmani A uchidan boshlab hisoblaganda
burchakning AP bissektrisasi tasvirlangan. C nuqta 3:4 nisbatda, D nuqta esa AC kesmani
Agar BP =4 va P C=5 bo‘lsa, AP CD 4:3 nisbatda bo‘ladi. Agar AB kesmaning
trapetsiyaning yuzini toping. uzunligi 49 cm bo‘lsa, u holda AD kesmaning
P uzunligini (cm) toping.
B C
A) 21 B) 12 C) 9 D) 16

1 3 3 3 3 5 1
16. Hisoblang: 1 · 3 + 2 · 3 − 3 · 3 − 1
A D 2 5 4 5 5 6 2
A) 27 B) 24 C) 28 D) 25 A) 0,5 B) 0 C) −1, 5 D) −0, 5

9. x va y lar uchun  
1 4 3 2 4
y 2 + 2x (x + y) + 3 (2x + 3) = 0 tenglik o‘rinli 17. −1 a b c : − a2 b2 c2 bo‘lishni
2 3
x2 + y 2 bajaring.
bo‘lsa, ifodaning qiymatini toping.
6 1 1
4 A) 1 a2 b B) 2a2 b C) −1 a2 b D) −2a2 b
A) 2 B) 1 C) 3 D) 8 8
3


1
T-108 Matematika(8000752) - Sotish taqiqlanadi!

18. Rasmdan foydalanib, ((A ∩ B) ∪ C) ∩ D 24. Agar geometrik progressiyaning umumiy hadi
to‘plamning elementlari sonini toping. bn = 3 · 2n bo‘lsa, b21 + b22 + b23 + ... + b28
D yig‘indini hisoblang.
A B C    
A) 3 · 214 − 1 B) 12 · 216 − 1
d
a
c l
m C) 3 · 216 − 1 D) 12 · 214 − 1
b e n
25. 59 + 1 natural son uchun quyidagi fikrlardan
k, p, q
qaysi biri to‘g‘ri?
A) 1 B) 3 C) 4 D) 0 A) juft va murakkab son
B) toq va murakkab son C) toq va tub son
19. Biri ikkinchisidan 3 marta katta bo‘lgan ikki D) juft va tub son
sonning yig‘indisi 9,64 ga teng. Shu sonlarning 26. ABCD trapetsiyaning AB katta asosida
kichigini toping. E nuqta olingan. CE kesma AD yon tomoniga
A) 2,31 B) 2,16 C) 2,21 D) 2,41 parallel. Agar AE:EB=3:5 bo‘lsa,
AECD to‘rtburchak yuzini BCE uchburchak
20. 3 dm×4 dm×8 dm o‘lchamli to‘g‘ri burchakli yuziga nisbatini toping.
parallelepipedlardan nechtasini terib eng kichik 3 6 3 5
A) B) C) D)
hajmli kub hosil qilish mumkin? 2 5 5 6
A) 216 B) 72 C) 180 D) 144 27. f (x) = x · cos x2 funksiyaning x0 =0 nuqtadagi
hosilasini toping.
21. −3; 6; 8 va x sonlarining o‘rta arifmetigi y ning
A) 1 B) −1 C) 0 D) 2
1
qismiga teng. Agar 3x − 2y = 15 bo‘lsa, 28. To‘rtburchakli muntazam prizma asosining
3
y ning qiymatini toping. diagonalini uning yon yoqi diagonaliga nisbati
A) 32 B) 24 C) 28 D) 18 2:3 kabidir. Agar bu prizma asosining yuzi
14 dm2 bo‘lsa, uning hajmini (dm3 ) hisoblang.
√ √
22. Hisoblang: A) 196 B) 7 147 C) 98 D) 7 161
π 5π 3π 9π 29. y = kx + b chiziqli funksiyaning grafigi I, II va
cos4 + cos4 + cos4 + cos4 +1
8 8 8 8 IV choraklarda yotsa, k va b larni nol bilan
3 3 1 5 taqqoslang.
A) B) C) D)
2 4 2 2 A) k > 0, b > 0 B) k < 0, b < 0
C) k < 0, b > 0 D) k > 0, b < 0
23. 6 ta to‘g‘ri chiziqlar ko‘pi bilan tekislikni 9 4
nechta qismga ajratadi? 30. > 2 tengsizlikning barcha butun
x−3 7
A) 16 B) 22 C) 15 D) 21 yechimlari yig‘indisini toping.
A) 15 B) 21 C) 18 D) 12




2


Matematika(8000776) - Sotish taqiqlanadi! T-108

MATEMATIKA

3 2 11. x3 + mx2 − 4x + n = 0 tenglamaning ildizlari
1.  + = 2 tenglama
3
9x2 − 1 + 3
3
9x2 − 1 + 2 x1 = 3 va x2 = −2 bo‘lsa, 3m + n ning
nechta haqiqiy ildizga ega? qiymatini toping.
A) 1 B) 2 C) 0 D) 4 A) 6 B) 3 C) −12 D) 8
2. ABCD trapetsiyaning AB katta asosida
E nuqta olingan. DE kesma BC yon tomoniga  
parallel. Agar BCDE to‘rtburchak yuzining 2x − x2 − 4 (x + 3)
12. > 0 tengsizlikni yeching.
AED uchburchak yuziga nisbati 6:5 kabi x2 − 9
bo‘lsa, AE:EB nisbatni toping. A) (−∞; 2) ∪ (2; 3) B) (−∞; −3) ∪ (−3; 3)
5 3 5 3 C) (2; 3) D) (−∞; 3)
A) B) C) D)
6 2 3 5
3. f (x) = 13x5 + 6x3 − 27 funksiya berilgan
13. x = 3, 61(91), y = 3, 62, z = 3, 6(191) va
bo‘lsa, f (f (x)) funksiyaning darajasi toping.
t = 3, 619(1) sonlarini kamaytirish tartibida
A) 10 B) 9 C) 15 D) 25 yozing.
√ √
11 − 4 11 − 12 A) y > t > z > x B) x > z > y > t
4. √ − √ ni hisoblang.
C) y > x > t > z D) y > x > z > t
11 − 3 + 1 11 − 3 − 3
A) −2 B) 2 C) −4 D) 4
 2     14. Ikki shahar orasidagi masofa 126 km. Bu
5. a − b2 a2 + b2 a4 + b4 a8 + b8 ifodaning
√ √ masofa 1:6000000 masshtabli xaritada necha
a = 8 6, b = 4 2 bo‘lgandagi qiymatini toping.
millimetrga teng bo‘ladi?
A) 2 B) −10 C) 20 D) 4
A) 210 B) 0,21 C) 2,1 D) 21
6. Faqat 3 ta natural bo‘luvchiga ega bo‘lgan ikki
xonali natural sonlarning eng kattasini toping.
A) 51 B) 46 C) 81 D) 49 15. Rasmda shtrixlangan soha yuzini toping.
√ (A − nuqta parabolaning uchi)
7. a b vektorlar uchun |a|  = 4,
 = 3, |b|
 va 
a∧b = 30◦ ga teng. λ ning qanday qiymatida y
    A(1;4)
2a − λb va a − b vektorlar perpendikulyar
bo‘ladi? (0;3)
A) 1,2 B) 0,3 C) 0,6 D) −0,3 f (x) = ax2 + bx + c

8. ⎛
Soddalashtiring, (a = 0): ⎞
⎝(−2a)3 · (−2a)3 · ... · (−2a)3 ⎠ : x
0 1 3
⎛ 14 marta ⎞
1 2 1
: ⎝(−2a)4 · (−2a)4 · ... · (−2a)4 ⎠ A) 5 B) 9 C) 6 D) 8
3 3 3
10 marta
A) −8a3 B) −2a C) 1 D) 4a2
9. To‘g‘ri burchakli uchburchakning tomonlari 16. f (x) = x2 + bx + c funksiyaning nollari 2 va 3
ayirmasi 1,5 ga teng bo‘lgan arifmetik bo‘lsa, b ni toping.
progressiyani tashkil etadi. Uchburchakning A) −6 B) −5 C) 6 D) 5
perimetrini toping.
A) 16 B) 17 C) 18 D) 15
17. y = 3x−3 + 12 funksiyaning qiymatlar sohasini
10. To‘g‘ri burchakli parallelepipedning qirralari
toping.
nisbati 2:1:3 kabi. Agar parallelepipedning to‘la
sirti 198 dm2 ga teng bo‘lsa, uning hajmini A) (−∞; ∞) B) (15; ∞) C) (12; ∞)
(dm3 ) toping. D) [12; ∞)
A) 192 B) 154 C) 162 D) 148


1
T-108 Matematika(8000776) - Sotish taqiqlanadi!

18. Rasmda A va B to‘plamlar va U universial 24. Ixtiyoriy uchtasi bir to‘g‘ri chiziqda yotmagan
to‘plam tasvirlangan. (A ∩ B  ) ∪ (A ∩ B) 10 ta nuqtani o‘zaro tutashtirib ko‘pi bilan
to‘plamning elementlarini aniqlang(A =U \A, nechta har xil kesma hosil qilish mumkin?
B  =U \B). A) 90 B) 10 C) 55 D) 45

A
B 25. Katetlari uzunliklari 6 cm va 7 cm ga teng
f bo‘lgan to‘g‘ri burchakli uchburchakning
c
a
d g gipotenuzasi atrofida to‘liq aylantirishdan hosil
b
e
h bo‘lgan jismning hajmini (cm3 ) toping.
√ √ √
i j k 882π 85 588π 85 441 85
U A) B) C)
85√ 85 85
A) {a, b, i, j, k} B) {c, d, e} 441π 85
C) {c, d, e, f, g, h} D) {f, g, h} D)
85
19. Masofa 5% ga orttirilib, tezlik 30% ga
kamaytirilsa, harakatlanish vaqti necha foizga (2a − 3b + 3)2 − 4 (a − 2b − 1)2
26. + 2a + b
ortadi? 7b − 4a − 1 √
A) 45 B) 35 C) 25 D) 50 ifodaning a = 8 va b = 8 − 3 bo‘lgandagi
20. Oltita musbat son geometrik progressiyani qiymatini toping.
√ √
tashkil qiladi. Geometrik progressiyaning A) 21 B) − 3 C) 3 D) 11
9
dastlabki ikkita hadining ko‘paytmasi ga,
8 27. Aylanada 6 ta har xil nuqta belgilangan.
oxirgi ikkita hadining ko‘paytmasi esa 288 ga Uchlari bu nuqtalarda bo‘lgan jami nechta har
teng. Shu progressiyaning oxirgi ikkita xil uchburchak chizish mumkin?
hadining yig‘indisini toping. A) 20 B) 15 C) 18 D) 10
A) 36 B) 18 C) 34 D) 48
21. Tengsizlikni yeching: 28. 
f (x) = 24tgx − 24x + 6π + 11 funksiyaning
log 1 (log2 (2 − x)) + 1 ≥ 0. π π
− ; kesmadagi eng katta qiymatini toping.
3
4 4
A) [−6; 2) B) (1; 2) C) [−6; 2) ∪ (2; ∞) √
A) 14√3 + 11 B) 35 C) 24
D) [−6; 1)
D) 12 3 + 13
22. f (x) = log2 x funksiyaning (1;0) va (2;1)
nuqtalaridan o‘tuvchi to‘g‘ri chiziqqa parallel  
16
bo‘lgan urinma tenglamasining burchak (27 + 79) · 2 + · 45−1
45
koeffitsiyentini toping. 29. Hisoblang:  2 · 0, (5)
1
1 2 1 0, (55) +
A) 1 B) C) D) 0, (555)
2 3 3
4
23. Hisoblang: A) 0, (5) B) 1 C) 1 D) 9
1 sin 112◦ 5
+ − cos 7◦ · cos 14◦ · cos 28◦ · cos 56◦ .
2 16 sin 7◦ 30. Agar tg α + ctg α = 3 bo‘lsa,
1 3 tg 2 α − 2 tg α + ctg α ifodaning qiymatini toping.
A) B) 0 C) 1 D)
2 4 A) 1 B) 4 C) 3 D) 2




2


Matematika(8000800) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Ko‘paytuvchilarga ajrating: 11. y = (x − 4) · (x − 1)2 funksiyaning ekstremum
(3a + 2b)2 − (2a + 3b)2 nuqtalaridan o‘tuvchi to‘g‘ri chiziq tenglamasini
A) 5 (a + b) · (a − b) B) (5a + b) · (a − b) tuzing.
C) (a + 5b) · (a − b) D) −5 (a + b) · (a − b) A) y = 2x − 2 B) y = −2x − 2
C) y = 2x + 2 D) y = 2 − 2x
2. 1 gektar maydonga o‘rtacha 0,6 sentner zig‘ir
urug‘i ekiladi. 1:10000 masshtabli xaritada 12. Agar sin4 x − cos4 x = m bo‘lsa, cos2 x ni m
bo‘yi 20 cm va eni 12 cm bo‘lgan to‘g‘ri orqali ifodalang.
to‘rtburchak shaklidagi yer maydoniga zig‘ir 1−m m+1 1+m
urug‘i ekish uchun o‘rtacha necha sentner kerak A) B) − C)
2 2 2
bo‘ladi? m−1
D)
A) 144 B) 14,4 C) 40 D) 400 2
3. 73 + 11 · 7 ni 6 ga bo‘lgandagi qoldiqni toping. 13. (24; 204] oraliqda 3 ga karrali bo‘lgan barcha
A) 3 B) 1 C) 2 D) 0 natural sonlar yig‘indisi qanday raqam bilan
tugaydi?
4. Rаdiusi 6 gа tеng bo‘lgan aylanaga ichki
chizilgаn muntаzаm uchburchаk yuzini tоping. A) 6 B) 0 C) 5 D) 2
√ √ √
A) 27 3 B) 108 3 C) 27 D) 18 3 14. Kesik konusga shar ichki chizilgan. Agar kesik
konus asoslarining radiuslari 2 va 4 bo‘lsa, shu
5. Tanga 7 marta tashlanganda 5 marta gerb va
konus yon sirtining yuzini toping.
2 marta raqam tomoni tushishining
ehtimolligini toping. A) 36π B) 48π C) 24π D) 72π
21 10 1 1 15. Yoyiq burchakning A nuqtasidan chiquvchi
A) B) C) D)
128 49 128 32 ikkita nur uni 2:4:3 nisbatdagi burchaklarga
√ ajratadi. Eng katta burchakni toping.
Agar a = 3 3 − 2 bo‘lsa, 
6. 
a4 + 5a3 + 15a − 9
+ 9a−4 :
a6 + 3a4 β
 5 −1
a + 2a4 γ α
: − 4 ning qiymatini toping.
a+3 A
√ √
A) 12 3 B) 5 C) 3 3 D) 23 A) 80◦ B) 40◦ C) 90◦ D) 60◦
7. ā (12; −5) vektor bilan Ox o‘qi orasidagi 16. x3 + mx2 − 4x + n = 0 tenglamaning ildizlari
burchak kosinusini toping. x1 = 3 va x2 = −2 bo‘lsa, 3m + n ning
5 12 12 5
A) − B) − C) D) − qiymatini toping.
12 5 13 13
A) −12 B) 8 C) 6 D) 3
8. f (x) = x2 − 2x + c funksiyaning nollaridan biri
17. Hisoblang: 0, 04 · 10−8 · 2, 3 · 1012 .
3 bo‘lsa, c ni toping.
A) 9200 B) 92 C) 920 D) 9,2
A) 0 B) 1 C) −3 D) −5
9. Toza suvga tuz aralashtirilgandan so‘ng massasi 18. O‘zaro teskari sonlarni
√ aniqlang.
√
10 1 8 3 3  √ 
850 gramm bo‘ldi. Agar tuzning massasi toza 1) √ va √ ; 2) va ; 3) 2 3 − 3
3 24
suvning massasidan 75% ga kam bo‘lsa, toza  5 √2  5  √   √ 
suvning massasi necha gramm bo‘lgan? va 3 + 2 3 ; 4) 2 2 − 3 va 3 + 2 2 .
A) 620 B) 660 C) 640 D) 680 A) 1, 2 va 4 B) 1 va 3 C) hammasi
D) faqat 1
1 1
10. b = −a va c = bo‘lsa, a ni c orqali 19. Agar a va b haqiqiy 0<b
10 10−b √
3 3
sonlar
√ uchun
3 3
√ a<√
ifodalang. bo‘lsa, u holda − a + b + a − b2 ni
2

A) a = lg c B) a = lg lg c C) a = c soddalashtiring.
D) a = 101−c A) 2b − 2a B) 0 C) −2a D) 2b


1
T-108 Matematika(8000800) - Sotish taqiqlanadi!

x2 − 3x + 4 26. Soddalashtiring:
20.  2  ≤ 0 tengsizlikning natural sin(log2 3 + log3 2) + sin(log2 3 − log3 2)
x − 10 · (x − 1) −
yechimlari yig‘indisini toping. sin(log2 3 − log3 2) − sin(log2 3 + log3 2)
2 tg log3 2 − tg log2 3
A) 3 B) 6 C) 5 D) 4 − .
tg log3 2
21. Silindrning asosida 2 dm uzunlikdagi vatar 60◦ A) 0 B) −2 C) 1 D) −1
kattalikdagi yoyga tiralgan. Silindrning o‘q
27. A = {x| x ≥ 2, x ∈ Z}, B = {x| x < 8, x ∈ Q}
kesimi kvadratdan iborat bo‘lsa, uning hajmini
bo‘lsa, A ∩ B to‘plamning elementlari sonini
(dm3 ) toping.
√ √ aniqlang.
A) 8 3π B) 16π C) 4 3π D) 32π
A) 6 B) ∞ C) 8 D) 7
 
17 7 2 3 1 28. O‘tkir burchakli uchburchakning ikki
22. Hisoblang: 7 − 9 : − ·4 +3
36 12 9 26 3 tomonining uzunliklari ayirmasi 2 cm ga teng,
A) −7 B) 1 C) −6 D) 13 bu tomonlarining uchinchi tomonga
proyeksiyalari 9 cm va 5 cm bo‘lsa,
23. Agar f (x) 9-darajali ko‘phad bo‘lsa, uchburchakka tashqi chizilgan aylana radiusini
y = (x − 1)2 · f (x) + x funksiyaning x0 =1 toping.
nuqtadagi hosilasini toping. 5 3 1 2
A) 0 B) 2 C) 1 D) −1 A) 5 B) 6 C) 8 D) 7
12 10 8 7
 2    2 log3 12 + log4 12 1
24. x2 + 1 + 5 x4 − 1 − 6 x2 − 1 = 0 29. Hisoblang: + · log2 4
tenglama nechta haqiqiy ildizga ega? log3 12 · log4 12 2
A) 1 B) 0 C) 3 D) 2 A) 0 B) 2 C) 1 D) 3
 (x − 2)dx
25. y = x2 − 2x + 2 kvadrat funksiyaning y=2 30. integralni hisoblang.
x2 − 4x + 17
chiziqqa nisbatan simmetrik funksiyasini  
A) ln x2 − 4x + 17 + C
aniqlang. √
B) ln x2 − 4x + 17 + C
A) y = −x2 + 2x − 2 B) y = −x2 + 2x  −2
C) ln x2 − 4x + 17 +C
C) y = −x2 + 2x + 1 D) y = −x2 + 2x + 2  2 2
D) ln x − 4x + 17 + C




2


Matematika(8000824) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Merganning nishonga tekkizish ehtimoli 0,8 ga 11. ABC uchburchakning burchaklari 2:3:1
teng. U nishonga 3 marta o‘q uzganda barcha nisbatda. Agar eng kichik tomoni 5 cm bo‘lsa,
o‘qlari nishonga tegishining ehtimolligini eng katta tomoni uzunligini (cm) toping.
√ √
toping. A) 5 2 B) 10 C) 8 D) 5 3
A) 0,8 B) 0,72 C) 0,512 D) 0,912
√ √ √ 12. 2 (5a − 3) − 3 (4a − 5) + 4 (a − 5) ifodani
2. x = 3 4, y = 2 va z = 12 105 sonlarni
soddalashtiring.
kamayish tartibida joylashtiring.
A) 2a − 11 B) −2a − 11 C) 2a + 11
A) x > z > y B) y > x > z C) x > y > z
D) −2a + 11
D) y > z > x
3. Agar x2 y > 0 bo‘lsa, quyidagilarning qaysi biri 13. To‘g‘ri silindrning balandligi 5 cm va asosining
x va y ning barcha haqiqiy qiymatlarida to‘g‘ri radiusi 4 cm. Uning yon sirtidagi A va B
bo‘ladi? nuqtalar asos tekisligidan mos ravishda 2 va
x+y 3 cm balandlikda joylashgan. Agar AB
A) (x + y)2 > 0 B) >0
xy kesmaning uzunligi 5 cm bo‘lsa, silindr o‘qidan
C) x3 + y 3 > 0 D) x2 + y > 0 AB kesmagacha bo‘lgan eng yaqin masofani
  (cm) toping.
4. Agar f (x + 2) = log3 x2 − 6x + 27 + 6 bo‘lsa, √ √
f (2) ning qiymatini toping. √ 39 41 √
A) 10 B) C) D) 11
A) 6 + log3 19 B) 8 C) 6 + log3 7 D) 9 2 2
 
5. f (x) = 10 − x2 · ln x funksiyaning (4;7) 14. To‘g‘ri burchakli parallelepipedning qirralari
nuqtadan o‘tuvchi boshlang‘ich funksiyasi F (x) nisbati 2:1:3 kabi. Agar parallelepipedning to‘la
bo‘lsa, F (2) va F (3) larni taqqoslang. sirti 198 dm2 ga teng bo‘lsa, uning hajmini
A) F (2) = F (3) + 1 B) F (2) = F (3) (dm3 ) toping.
C) F (2) > F (3) D) F (2) < F (3) A) 148 B) 192 C) 162 D) 154
6. y = 3x2 − 6x + 7 kvadrat funksiyaning
ordinatalar o‘qiga nisbatan simmetrik 15. A va B aylanadagi nuqtalar bo‘lib, AB yoyning
funksiyasini aniqlang. markaziy burchagi 140◦ ga teng. Katta yoyda
olingan C nuqta uchun AC yoyni BC yoyga
A) y = 3x2 − 6x + 7 B) y = −3x2 + 6x − 7
nisbati 5 : 6 bo‘lsa, ∠ABCni toping.
C) y = −3x2 − 6x − 7 D) y = 3x2 + 6x + 7
√ √ A) 70◦ B) 50◦ C) 90◦ D) 60◦
a2 − 2a 5 − 4 + 5 √ √
3

7. √ ifodaning a = 5 − 3 2
a− 5 16. Agar A = {a, b, c, d, e} bo‘lsa, B ⊂ A (B = A,
bo‘lgandagi qiymatini toping. B = ∅) shartlarni qanoatlantiruvchi necha har
√ √
A) 5 B) 2 3 2 C) 1 D) 0 xil B to‘plam mavjud?
A) 14 B) 32 C) 16 D) 30
8. 2 cos2 x − cos x − 1 = 0 tenglamaning eng kichik
musbat yechimini toping.
17. To‘rtinchi hadi 20 ga teng bo‘lgan arifmetik
π π 3π 2π
A) B) C) D) progressiyaning dastlabki o‘n yettita hadi
4 6 4 3 yig‘indisi 680 ga teng. Progressiyaning oltinchi
9. Ifodani soddalashtiring (a ∈ (−2; −1)): hadini toping.
|a2 − 4| |a2 − 9| |a2 − 1| A) 24 B) 18 C) 23 D) 28
− + .
2−a a−3 1−a
A) a + 4 B) −a + 2 C) −3 (a + 2) 18. Bitta daftar 600 so‘m va u bitta qalamning
D) a + 2 narxidan 400 so‘mga qimmat. O‘quvchi
  3600 so‘mga daftarlar va qalamlar sotib oldi.
|x| + x 2 6x Quyida keltirilgan sonlardan qaysi biri xarid
10. − + 2 = 0 tenglama nechta
x−2 x−2 qilingan qalamlarning soni bo‘la oladi?
haqiqiy ildizga ega?
A) 5 B) 1 C) 3 D) 4
A) 3 B) 2 C) 0 D) 1


1
T-108 Matematika(8000824) - Sotish taqiqlanadi!

19. Rasmda markazi O nuqtada bo‘lgan aylanaga 4
24. f (x) = − 2 funksiyaning qiymatlar sohasini
A nuqtadan AB urinma o‘tkazilgan. AO kesma x
aylanani C nuqtada kesib o‘tadi. Agar toping.
aylananing kichik BC yoyi uzunligi 3 ga va A) (−∞; 0] B) (−∞; 0) ∪ (0; ∞)
radiusi 4 ga teng bo‘lsa, AC ni toping. C) [−2; ∞) D) (−∞; −2) ∪ (−2; ∞)
A 1 1
C 25. b = −a va c = bo‘lsa, a ni c orqali
B 10 10−b
ifodalang.
A) a = lg lg c B) a = 101−c C) a = lg c
O
D) a = c
26. 2 · 7 · 11 · 19 · 23 son quyidagi sonlardan qaysi
biriga ko‘paytirilsa, uning natural bo‘luvchilari
5 soni ikki marta ortadi?
A) 4(1 − cos 0, 75) B) −4
cos 0, 75 A) 11 B) 2 C) 7 D) 3
4
C) −4 D) 4 cos 0, 75 27. x = 3, 61(91), y = 3, 62, z = 3, 6(191) va
cos 0, 75
t = 3, 619(1) sonlarini kamaytirish tartibida
yozing.
20. Agar a, b, c musbat haqiqiy sonlar uchun
A) y > x > t > z B) y > t > z > x
ab = 14 va bc = 6 bo‘lsa, a + 2b + 3c eng kichik
C) x > z > y > t D) y > x > z > t
qiymatini toping.
28. Ikki shahar orasidagi masofa 126 km. Bu
A) 34 B) 16 C) 20 D) 18
masofa 1:6000000 masshtabli xaritada necha
  millimetrga teng bo‘ladi?
21. x2 + 9x = x2 + 9x − 20 tenglamaning haqiqiy
A) 0,21 B) 21 C) 2,1 D) 210
ildizlari yig‘indisini toping.
4, (2) + 4, (4) + 4, (6)
A) yechimga ega emas B) −10 C) −9 29. Hisoblang: .
4, (3) + 4, (5) + 4, (7)
D) 9
38 39 42 40
√ A) B) C) D)
39 40 43 41
22. f (x) = (x2 + x) · x2 + 1 funksiyaning x0 = 0
nuqtadagi hosilasini toping. 30. Uchlari A(3; 0), B(0; 2) nuqtalarda bo‘lgan
kesmani A uchidan boshlab hisoblaganda 4:3
A) 2 B) 1 C) 0 D) −1
nisbatda bo‘ladigan M nuqtaning
koordinatalarini toping.
23. Agar sin α · cos α = −0, 25 va 1, 6 < α < 3, 1      
12 13 13 12 9 8
bo’lsa, cos α − sin α ning qiymatini toping. A) ; B) ; C) ;
√ √ √
A) 1, 5 B) 2 C) − 2 D) − 1, 5
√ 7  7 7 7 7 7
8 9
D) ;
7 7




2


Matematika(8000848) - Sotish taqiqlanadi! T-108

MATEMATIKA
√
 sin x 10. Uchburchakning 3 va 4 teng bo‘lgan
1. √ dx integralni hisoblang.
x tomonlariga o‘tkazilgan medianalar o‘zaro
1 √ √ perpendikulyar bo‘lsa, bu uchburchakning
A) cos x + C B) 2 cos x + C uchinchi tomonini toping.
2 √ √
√ 1 √ A) 5 B) 2,5 C) 2,4 D) 6
C) −2 cos x + C D) − cos x + C
2 √
11. (3x − 8) −4x2 + 3x + 10 = 0 tenglama nechta
2. y = 2x to‘g‘ri chiziqqa parallel va
 1
 1 haqiqiy ildizga ega.
f (x) = 4x− 2 − 2x+1 · − 6x + 5 funksiya A) 3 B) 2 C) 1 D) 0
ln 2
grafigiga urinma bo‘lgan to‘g‘ri chiziq 12. y = −3x + 7 chiziqli funksiyaning x=1 to‘g‘ri
tenglamasini aniqlang. chiziqqa nisbatan simmetrigini toping.
A) y = 2x − 10 B) y = 2x − 11 A) y = 3x − 9 B) y = −3x − 1
C) y = 2x − 12 D) y = 2x − 16 C) y = 3x + 1 D) y = −3x + 9
3. Uchta sonning o‘rta arifmetigi 24, 3 ga teng. √ √
13. 2x2 + 6 − 3 x = 3 3 tenglamaning eng
Agar ulardan ikkitasi 34,8 va 18,9 bo‘lsa, katta ildizini toping.
uchinchi sonni toping. √ √ √
A) 3 B) 0, 5 3 C) 3 D) 2 3
A) 21,1 B) 19,8 C) 19,2 D) 18,6
14. sin 4x = sin 3x tenglamaning eng kichik musbat
4. Agar A (−2; 6; −9), B (−12; 6; −9), C (4; 6; 5) yechimini toping.
va D (14; −8; 15) nuqtalar berilgan bo‘lsa, 6π π 2π 4π
AB + BC + CD vektorning koordinatalarini A) B) C) D)
7 7 7 7
toping.
A) (10; −11; 8) B) (16; 14; −24) 3n2 + 2n − 18
15. Ushbu kasrning qiymati natural
C) (−16; 0; −14) D) (16; −14; 24) n
son bo‘ladigan n (n ∈ N ) ning barcha
31+log4 5 · 4log5 3 · 5log3 4 qiymatlari yig‘indisini toping.
5. Hisoblang:
3log5 4 · 4log3 5 · 5log4 3 A) 36 B) 39 C) 38 D) 33
A) 3 B) 4 C) 2 D) 1
16. Agar f (x) o‘zgarmas funksiya uchun f (2) = 3
6. Kasrning
√ maxrajini irratsionallikdan qutqaring: bo‘lsa, f (1) ni toping.
3
√ √ A) 3 B) 2 C) aniqlab bo‘lmaydi D) 1
2 3 − 13 − 1
√ √ √ √ 17. Algebraik ifodaning qiymatini toping.
1 − 2 3 − 13 1 − 2 3 − 13 0, 25ab − 0, 3b2 , bunda a=4 va b=3.
A) B)
√4 √ √2 √ A) 3 B) 0,3 C) −3 D) −0,3
1 − 2 3 + 13 1 − 2 3 + 13
C) D) 18. Ma’lum bir ishni birinchi ishchi 18 soatda,
2 4
ikkinchi ishchi 24 soatda bajaradi. Agar shu
3
7. 6 12 + 612 + 612
+ ... + 612 + 612 yig‘indining ishni birinchi ishchi 3 soat ishlaganidan keyin
4 unga ikkinchi ishchi qo‘shilib 4 soat birgalikda
32 ta
qismi quyidagilardan qaysi biriga teng? ishlasa, ishning qancha qismi bajarilmay
A) 215 · 313 B) 214 · 312 C) 4 · 612 qoladi?
D) 2 · 613 2 4 2 5
A) B) C) D)
9 9 3 8
3x+1 + 3x+2 + 3x+3
8. f (x) = funksiya berilgan 19. (a − 3) (a − 4) − 3 (a − 2) ifodaga qanday eng
5x+2 + 14 · 5x
bo‘lsa, 9 · f (−2) ni hisoblang. kichik butun son qo‘shilganda, ifodaning
A) 0,36 B) 25 C) 1,44 D) 9 qiymati ixtiyoriy a ∈ R uchun musbat bo‘ladi?
9. A, B va C sonli to‘plamlarning elementlari soni A) 7 B) 6 C) 8 D) 9
mos ravishda 10; 12 va 15 ta. A ∪ B ∪ C 20. Agar a eng katta musbat uch xonali son, b esa
to‘plamning elementlari soni eng kamida necha eng kichik manfiy to‘rt xonali son bo‘lsa,
bo‘la oladi? b − a ni hisoblang.
A) 15 B) 27 C) 22 D) 12 A) −9000 B) −1 C) −10998 D) −9099


1
T-108 Matematika(8000848) - Sotish taqiqlanadi!

21. Rasmda berilgan ma’lumotlarga ko‘ra x necha 26. B
gradus?



78◦
√
3 10 D√
◦
10
α + 26 5
5
α x
A C

ABC to‘g‘ri burchakli uchburchakning
A) 97◦ B) aniqlab bo‘lmaydi C) 102◦
perimetrini toping. (AD⊥BC)
D) 93◦ √ √
A) 2 3 + 2 10 B) 4 2 + 10
22. sin 2x = cos 3x tenglamaning eng kichik musbat √ √
C) 2 4 + 10 D) 3 4 + 10
yechimini toping.
π π 3π π 27. Tanga 7 marta tashlanganda 5 marta gerb va
A) B) C) D) 2 marta raqam tomoni tushishining
5 10 5 2
ehtimolligini toping.
23. Ifodani soddalashtiring (x > 0): 1 10 21 1
2 2 2 A) B) C) D)
+ + 32 49 128 128
x (x + 2) (x + 2) (x + 4) (x + 4) (x + 6)
6 12 2x + 12 28. Agar f (x) 13-darajali ko‘phad bo‘lsa,
A) 2 B) 2 C) 2 y = x14 · f (x) funksiyaning hosilasi nechanchi
x + 6x x + 6x x + 6x
24 darajali ko‘phad bo‘ladi?
D) 2 A) 52 B) 27 C) 26 D) 25
x + 6x
29. Quyidagi sonlardan nechtasi butun son?
24. Sakkizta haddan iborat arifmetik √ 2, 48
progressiyaning toq o‘rindagi hadlari yig‘indisi 1) 2 + 144; 2) 7, 12; 3) π − 1, 14; 4) −
1, 24
168 ga, juft o‘rindagi hadlari yig‘indisi 200 ga
A) 2 B) 3 C) 4 D) 1
teng. Shu progressiyaning oltinchi hadini
toping. 30. Katetlari uzunliklari 6 cm va 7 cm ga teng
bo‘lgan to‘g‘ri burchakli uchburchakning
A) 42 B) 58 C) 50 D) 66
gipotenuzasi atrofida to‘liq aylantirishdan hosil
25. To‘g‘ri burchakli parallelepipedning qirralari bo‘lgan jismning hajmini (cm3 ) toping.
nisbati 2:1:3 kabi. Agar parallelepipedning to‘la √ √ √
882π 85 588π 85 441 85
sirti 198 dm2 ga teng bo‘lsa, uning hajmini A) B) C)
85√ 85 85
(dm3 ) toping.
441π 85
A) 192 B) 154 C) 148 D) 162 D)
85




2


Matematika(8000872) - Sotish taqiqlanadi! T-108

MATEMATIKA
  √  √
1. 4x · ln 3xdx integralni hisoblang. 11. Hisoblang: 3 − 2 2 + 3 + 2 2
√ √ √ √
A) 2 − 1 B) 2 2 C) 2 + 1 D) 2
A) 2x2 ln 3x − 2x2 + C
12. n natural sonning qanday qiymatida
B) 4x2 ln 3x − 2x2 + C 1 13
2+ = tenglik o‘rinli bo‘ladi?
C) 2x2 ln 3x − x2 + C 2 5
1+
n
D) x2 ln 3x − 2x2 + C
A) 1 B) 4 C) 3 D) 2
2. (x0 ; y0 ) nuqta y = 3x2 − bx + 12 parabola √  x2 −10x+16
uchining koordinatalari bo‘lsa, y0 + 3x20 ning 13. 5−2 x−2
≥ 1 tengsizlikni yeching.
qiymatini toping. A) (2; 8) ∪ (8; ∞) B) (−∞; 8] C) [8; ∞)
A) 15 B) 9 C) 18 D) 12 D) (−∞; 2) ∪ (2; 8]
3. Tenglamani yeching: 14. Uchlari Oxy tekisligining (0; 0), (3; 0), (2; 3) va
x+3 x+3 x+3 x+3 49 (0; 3) nuqtalarida bo‘lgan trapetsiyani Oy o‘qi
2 + 2 + 2 + ... + 2 =
4 −1 6 −1 8 −1 100 − 1 101 atrofida aylantirishdan hosil bo‘lgan jismning
1 hajmini toping.
A) 0 B) −3 C) − D) 2 A) 18π B) 19π C) 7π D) 12π
3
√ 15. Tekislikda ixtiyoriy uchtasi bitta to‘g‘ri
2 2+ 3 chiziqda yotmaydigan 8 ta nuqta berilgan.
4. cos 2x = tenglamaning eng kichik
4 Uchlari shu nuqtalarda bo‘lgan jami nechta har
musbat yechimini toping.
xil uchburchak mavjud?
π 2π π π
A) B) C) D) A) 56 B) 50 C) 54 D) 52
24 3 12 3
    16. 2m + 3; 3m + 5; 4m + 7; ... hadlari berilgan
      
5. Agar a − b = 8 va a · b = 9 bo‘lsa, a + b ni arifmetik progressiyaning dastlabki to‘qqizta
toping. hadi yig‘indisi 153 ga teng. m ning qiymatini
√ toping.
A) 108 B) 11 C) 10 D) 9
A) −1 B) 1 C) 3 D) 2
6. f (x) = kx + 2 funksiya k ning qanday
17. Tengsizlikni yeching:
qiymatlarida kamayuvchi bo‘ladi?
log 1 (log2 (2 − x)) + 1 ≥ 0.
A) k ∈ R B) k < 0 C) k > 0 3

D) k = 2n − 1, n ∈ N A) [−6; 2) ∪ (2; ∞) B) [−6; 2) C) [−6; 1)
D) (1; 2)
7. Tenglamani yeching (x ga nisbatan):
18. Rasmda grafigi keltirilgan f (x) funksiya uchun
6x2 + (2ab − 3b) x = ab2
quyidagi tengliklardan qaysi biri to‘g‘ri?
ab b ab b ab b y
A) − ; B) ; C) − ;
3 2 3 2 2 3 4
ab b
y=




D) ;− 3
2 3
f(




 
x)




3 √ √
8. 2 2 : 2 ni hisoblang va natijani ratsional
ko‘rsatkichli daraja shaklida tasvirlang.
7 5 1 3 x
A) 2− 12 B) 2− 12 C) 2− 12 D) 2− 4 −3 −2 −1 0 1 2 3 4 5 6
−1
9. Agar 8 litr dengiz suvida o‘rtacha 300 g tuz
bo‘lsa, 5 m3 dengiz suvida o‘rtacha necha
A) f  (−1) + f (−1) = 0
kilogramm tuz bo‘ladi?
B) f  (−2) + f (−2) = 0
A) 224,5 B) 166 C) 187,5 D) 150,5 C) f  (−1) + f (−2) = 0
10. To‘g‘ri burchakli uchburchakning o‘tkir D) f  (−2) + f (−1) = 0
burchagi 60◦ . Shu burchakning bissektrisasi 19. A = {a; b; c; d; e; f } to‘plamning nechta qism
uzunligi 1 cm ga teng bo‘lsa, gipotenuzasi to‘plamlarida, b elementi bo‘lib, c elementi
uzunligini (cm) toping. qatnashmaydi?
√ √ √
A) 2 + 1 B) 2 C) 5 − 1 D) 3 A) 8 B) 28 C) 16 D) 32


1
T-108 Matematika(8000872) - Sotish taqiqlanadi!
  
 9  2
 > 2 4 tengsizlikning barcha butun
3 1 1

20.  m4 − m4 1 + m2
x − 3 7 25. 1 + 1 :
yechimlari yig‘indisini toping. 1 − m2 m4
1 0,5
A) 18 B) 15 C) 21 D) 12 : 1 + 2m− 2 + m−1 ifodaning m = 36−1
21. ABCD parallelogramda D o‘tmas burchak. bo‘lgandagi qiymatini toping.
E nuqta AB tomonda yotadi. Agar 1 6 1
A) 5 B) C) D)
AE:EB nisbat 2:3 kabi bo‘lsa, 6 7 7
BCDE to‘rtburchak yuzini DAE uchburchak
yuziga nisbatni toping. 1 2 3 4 5 6 7 8 9
11 11 26. · · · · · · · ·
A) 3 B) C) D) 4 10 10 10 10 10 10 10 10 10
4 3 ko‘paytmani standart shaklga keltiring.
22. Rasmda ABCD to‘g‘ri to‘rtburchak, BAD A) 3, 6288 · 10−3 B) 3, 6288 · 10−5
burchakning AP bissektrisasi tasvirlangan. C) 3, 6288 · 10−4 D) 3, 6288 · 10−6
Agar BP =4 va P C=5 bo‘lsa, AP CD
trapetsiyaning yuzini toping. 27. 4 m2 12 dm2 16 cm2 necha cm2 ga teng?
P
B C A) 43016 B) 40136 C) 41216 D) 52016


28. (8;0) nuqtadan y = 25 − (x − 5)2
funksiyaning grafigigacha bo‘lgan eng qisqa
A D
masofani toping.
A) 24 B) 27 C) 25 D) 28 √ √
A) 3 B) 5 C) 6 D) 2
23. Ifodani soddalashtiring:
4a2 − 16a + 16 (a − 2)2 29. 2513 + 16127 + 27 yig‘indi qanday raqam bilan
:
a+3 −a2 + 9 tugaydi?
A) 4a − 12 B) 12 − 4a C) 2a − 12 A) 3 B) 6 C) 8 D) 5
D) 6 − 2a
24. Uchburchakli piramidaning yon qirralari o‘zaro 2
perpendikulyar hamda uzunliklari 6; 7 va 30. Agar sin α = bo‘lsa,
5
8 dm ga teng. Piramidaning hajmini (dm3 )
cos6 α − 3 cos4 α + 3 cos2 α + sin6 α − 1 ning
toping.
qiymatini toping.
A) 63 B) 54 C) 64 D) 56 A) −2 B) 0 C) 1 D) −1




2


Matematika(8000896) - Sotish taqiqlanadi! T-108

MATEMATIKA
 √
|x − 3| = 3√ y + 2 9. Rasmda grafigi keltirilgan f (x) funksiya uchun
1. tenglamalar sistemasi
|y + 2| = 3 x − 3 quyidagi tengliklardan qaysi biri to‘g‘ri?
nechta haqiqiy yechimga ega? y
A) 1 B) 4 C) 2 D) 3 4




y=
3




f(
x)
2. Agar prizmaning qirralar soni yoqlari sonidan
24 taga ko‘p bo‘lsa, prizmaning diagonallari
soni uchlari sonidan nechtaga ko‘p? x
−3 −2 −1 0 1 2 3 4 5 6
A) 117 B) 104 C) 130 D) 91
−1


3. y = (x − 4) · (x − 1)2 funksiyaning ekstremum A) f  (−2) + f (−1) = 0
nuqtalaridan o‘tuvchi to‘g‘ri chiziq tenglamasini B) f  (−1) + f (−1) = 0
tuzing. C) f  (−1) + f (−2) = 0
A) y = 2 − 2x B) y = 2x − 2 D) f  (−2) + f (−2) = 0
C) y = −2x − 2 D) y = 2x + 2 10. To‘g‘ri burchakli parallelepipedning barcha
qirralari uzunliklari yig‘indisi 48 dm. Agar
√
parallelepipedning diagonali uzunligi 5 2 dm
4. Uchburchakning asosiga parallel to‘g‘ri
bo‘lsa, uning to‘la sirti yuzini (dm2 ) toping.
chiziqlar yon tomonini (uchidan boshlab
hisoblaganda) 1:2:3 nisbatda bo‘ladi. Bu to‘g‘ri A) 82 B) 94 C) 104 D) 108
chiziqlar uchburchakning yuzasini qanday 1 √
2a− 6 − ab
3
3
nisbatda bo‘ladi? 11. 2 1 √ +√3
ifodaning a = 64,
A) 1:4:18 B) 1:6:27 C) 1:8:27 D) 1:8:18 a3 b3 − 2 6 a a
b = 0, 4 dagi qiymatini toping.
2 1 1 1
A) B) C) D)
5 6 2 3
5. y ning qanday qiymatlarida a (−2; y; −9)
vektorning uzunligi 11 ga teng bo‘ladi? 12. A murakkab sonlar to‘plami va B juft sonlar
to‘plami bo‘lsa, A ∩ B to‘plamni aniqlang.
A) y = ±9 B) y = ±6 C) y = ±7
D) y = ±2 A) {x|x = 2n − 2, n ∈ N }
B) {x|x = 2n, n ∈ N }
C) {x|x = 2n + 2, n ∈ N } D) ∅
6. Faqat 3 ta natural bo‘luvchiga ega bo‘lgan ikki
1
xonali natural sonlarning eng kattasini toping. 13. xlog2 x−5 = tenglamaning ildizlari
64
A) 81 B) 51 C) 46 D) 49 ko‘paytmasini toping.
1
A) 64 B) 16 C) 32 D)
7. b ning qanday qiymatlarida 4
2b (3 − x) + x (2 − b) = 2b − 5x tenglamaning 14. Kasrning maxraji suratidan 8 ga ortiq bo‘lib,
ildizi 1 dan katta
 bo‘ladi?
   ularning yig‘indisi 30 ga teng. Bu kasrning
1 2
A) (−∞; −7) ∪ 2 ; ∞ B) ;4 suratidan 1 ni ayirib, maxrajiga 1 ni qo‘shsak,
  3  3  kasrning qiymati quyidagilardan qaysi biriga
2 1
C) −∞; ∪ (4; ∞) D) −7; 2 teng bo‘ladi?
3 3 5 3 1 2
A) B) C) D)
6 7 2 5
√ √
8. 2 5+x = 4 · 2 x−3 tenglamaning ildizi x0 bo‘lsa, 15. Agar a3 + a6 + a9 + ... + a3n = 736 va
x20 − 2x0 + 3 ni hisoblang. a2n+1 + an+2 = 23 bo’lsa, a1 ; a2 ; a3 ; ...; a3n
A) 13 B) 11 C) 10 D) 12 arifmetik progressiyaning hadlari sonini toping.
A) 189 B) 192 C) 213 D) 204


1
T-108 Matematika(8000896) - Sotish taqiqlanadi!
    3 1
16. Ifodani
 soddalashtiring:  23. a−2 −3 · a3 −1 · a−2 : a ifodaning a = −
1 1 1 6
+ + · dagi qiymatini toping.
a · (a + 1) (a + 1) · (a + 2) (a + 2) · (a + 3)
a2 + 3a 1 1
· A) −6 B) C) − D) 36
9 36 6
1 1
A) a B) C) a + 3 D) 24. Piyoda 3 soatda 7,8 km yo‘l yurdi. Agar piyoda
9 3
shu tezlik bilan yursa, 4 soatda necha km yo‘l
3n2 + 2n − 18
17. Ushbu kasrning qiymati natural yuradi?
n
son bo‘ladigan n (n ∈ N ) ning barcha A) 10,6 B) 10,4 C) 10,5 D) 10,8
qiymatlari yig‘indisini toping.
2  6
A) 33 B) 36 C) 38 D) 39 25. Integralni hisoblang: x2 − 1 · xdx
18. Rasmda ABC uchburchak va uning BD, CE −1
bissektrisalari tasvirlangan. Berilgan A) 36 · 7−1 B) 3 · 14−1
7 C) 37 · 7−1
ma’lumotlarga ko‘ra α necha gradus? D) 36 · 14−1
B
26. Rasmda A va B nuqtalar son o‘qida
tasvirlangan. 2A + B ning son qiymatini
E α
toping.
9, 5 birlik 7 birlik

x + 50o x 20o B -3 0 2,5 A
A D C
A) 8 B) 9,5 C) 12,5 D) 6,5
A) 105,5◦ B) 135,5◦ C) 112,5◦ D) 122,5◦
27. f (x) = kx + 3 funksiya k ning qanday
19. 2 cos2 x − cos x − 1 = 0 tenglamaning eng kichik qiymatlarida toq funksiya bo‘ladi?
musbat yechimini toping.
A) k ∈ R B) k > 0
π 2π 3π π
A) B) C) D) C) k ning hech bir qiymatida D) k < 0
6 3 4 4
√
20. Yuzasi 18 2 bo‘lgan to‘g‘ri burchakli x 1
trapetsiyaga ichki chizilgan aylananing radiusi 28. Tengsizlikni yeching: − ≤0
x−2 x
3 bo‘lsa, trapetsiyaning o‘rta chizig‘ini toping.
√ A) (2; +∞) B) (0; 2) C) (−∞; 0)
A) 6 B) 3 2 √ D) (0; 3)
C) berilgan ma’lumotlar yetarli emas D) 6 2
29. y = ax2 + bx + c kvadratik funksiyaning grafigi
21. 3 ta mergan bir-biriga bog‘liq bo‘lmagan holda
I, II va IV choraklarda yotsa, a, b va c larning
nishonga bir martadan o‘q uzishmoqda. Har
har birini nol bilan taqqoslang.
birining nishonga tekkizish ehtimolligi mos
ravishda 0,8; 0,7 va 0,6 ga teng. Nishonga faqat A) a > 0, b < 0, c ≤ 0
birinchi va ikkinchi merganlarning o‘qlari
tegishi hodisasining ehtimolligini toping. B) a < 0, b < 0, c ≥ 0
A) 0,7 B) 0,56 C) 0,336 D) 0,224 C) a < 0, b > 0, c ≥ 0
π 3π D) a > 0, b < 0, c ≥ 0
22. cos( − 8x) + 2 sin( + 4x) · sin(π + 4x) = 0
2 2
tenglamaning barcha yechimlarini toping. 30. Ifodani soddalashtiring:
 
π πk 9a4 b3 2 c3 d
A) x = + πk, k ∈ Z B) x = ,k∈Z − · −2 · 3 2
4 8 16c3 d2 3 a b
π 2
C) x = + πk, k ∈ Z D) (−∞; +∞) 3a b 3ab 3ab 3a2 b
2 A) B) C) − D) −
2d 2d 2d 2d




2


Matematika(8000920) - Sotish taqiqlanadi! T-108

MATEMATIKA

a2 + bc − ac − ab b 10. Magazinda birinchi kuni 76% tarvuz sotildi.
1. Agar 2 + c + b = 2 tenglikda
ab − bc + ac − c Ikkinchi kuni esa qolgan 54 ta tarvuz sotildi.
a = 18, b = −2 bo‘lsa, c ning qiymatini toping. Birinchi kuni nechta tarvuz sotilgan?
A) 9 B) −19 C) 11 D) 20 A) 168 B) 163 C) 171 D) 176
2. Soddalashtiring: (a < 0) 11. Masofa 5% ga orttirilib, tezlik 30% ga
√ a
3 −a + √ kamaytirilsa, harakatlanish vaqti necha foizga
−a ortadi?
√ √ √ √
A) 4 a B) 2 −a C) 2 a D) 4 −a A) 50 B) 45 C) 35 D) 25
3. Uchburchakli piramidaning yon qirralari o‘zaro
perpendikulyar hamda uzunliklari 6; 7 va 12. Agar 0 < a < 1 bo‘lsa, quyidagilardan qaysi
8 dm ga teng. Piramidaning hajmini (dm3 ) biri ma’noga ega?
toping. π
A) log2 loga log2 3 B) loga loga
A) 56 B) 64 C) 63 D) 54 4
√ √ C) log2 loga (a + 1) D) lg lg lg a
4. x2 · 3 x+2 − 9x2 = 6 · 3 x+2 − 54 tenglamaning
ildizlari kvadratlarining yig‘indisini toping. 13. Agar f (x) o‘zgarmas funksiya uchun f (2) = 3
bo‘lsa, f (1) ni toping.
A) 4 B) 10 C) 16 D) 12
A) 3 B) 1 C) 2 D) aniqlab bo‘lmaydi
5. Ifodani soddalashtiring:
5 (a − b) a2 − b2 14. Rasmda y = f (x) funksiya grafigi va unga
 2  :
3 a + b2 (a + b)2 − 2ab (2; 2) nuqtadan o‘tkazilgan urinmasi

5 5 5 tasvirlangan. Agar g (x) = x2 − 2 · f (x)
A) − B) C) − bo‘lsa, g (2) ni toping.
3 (a + b) 3 (a + b) 3 (a − b)
5 y
D)
3 (a − b)
6. 43 · 47 · 28 · 32 − 18 · 63 · 27 ayirma qanday
raqam bilan tugaydi? 2

A) 4 B) 6 C) 2 D) 8
7. Uchburchakning 3 va 4 teng bo‘lgan x
0 2 5
tomonlariga o‘tkazilgan medianalar o‘zaro
perpendikulyar bo‘lsa, bu uchburchakning
f(
uchinchi tomonini toping. x)
√ √
A) 2,4 B) 5 C) 6 D) 2,5 2 2 1 1
A) 9 B) 6 C) 9 D) 6
9m + 7 3 3 3 3
8. m ning qanday qiymatida ifodaning
6
2 15. 6 ta to‘g‘ri chiziqlar ko‘pi bilan tekislikni
qiymati 11 ga teng bo‘ladi? nechta qismga ajratadi?
3
A) 11 B) 13 C) 8 D) 7 A) 22 B) 21 C) 15 D) 16
9. a va b parallel to‘g‘ri chiziqlar. Rasmdan 16. B = ∅ va B ⊂ A. A va B to‘plamlarning
foydalanib α burchakning qiymatini toping. elementlari soni mos ravishda m va n ga teng.
a Agar n + 3m=18 bo‘lsa, A to‘plamning
10◦ elementlari sonini toping.
α A) 4 B) 2 C) 5 D) 3

17. ā (−1; 2), b (−2; 1) va c (−3; 2) vektorlar
162◦
berilgan. k ning qanday qiymatida 2ā − kb
b vektor c vektorga perpendikulyar bo‘ladi?
A) 18◦ B) 28◦ C) 24◦ 4 7 7 4
A) − B) − C) D)
D) aniqlab bo‘lmaydi 7 4 4 7


1
T-108 Matematika(8000920) - Sotish taqiqlanadi!

18. f (x) = ln xx−1 funksiyaning hosilasini toping. 23. x2 · cos x3 dx integralni hisoblang.
cos x3 sin x3
1 A) + C B) +C
A) f  (x) = ln x − + 1 3 3
x
cos x3 sin x3
B) f  (x) = ln x + 1 C) − + C D) − +C
3 3
2
C) f  (x) = ln x − +1 24. b2 ning qanday qiymatlarida f (x) = x2 + bx + 3
x funksiyaning grafigi abssissalar o‘qidan
1 yuqorida joylashadi?
D) f  (x) = ln x + +1
x A) b2 > 0 B) b2 < 12 C) b2 = 12
D) b2 > 12
19. Rasmda ABC uchburchak va uning BD, CE
25. Arifmetik progressiyaning ikkinchi va oltinchi
bissektrisalari tasvirlangan. Berilgan
hadlarining yig‘indisi 72 ga teng. Arifmetik
ma’lumotlarga ko‘ra α necha gradus?
progressiyaning ikkinchi hadining beshinchi
B 7
hadiga nisbati ga teng bo‘lsa, uning oltinchi
10
E α hadini toping.
A) 44 B) 42 C) 48 D) 40
26. Agar x = 2n + 1 (n − natural son) bo‘lsa,
x + 50o x 20o
(−1)x+1 + (−1)2x
ifodaning qiymatini
A D C (−1)x
aniqlang.
A) 122,5◦ B) 105,5◦ C) 135,5◦ D) 112,5◦
A) −2 yoki 0 B) −2 C) 2 D) 0
1 2 1
20. Tenglamani yeching: 27.  + = tenglama
    x3 + 2 + 3 x3 + 2 + 7 2
1, 4 · (2 + 0, 6) · 4 + 0, 62 · 16 + 0, 64 · x =
nechta haqiqiy ildizga ega?
0, 68 − 256
A) 1 B) 0 C) 4 D) 2
A) 16 − 0, 64 B) 0, 64 − 16 C) 1 D) −1 √
28. Uzunligi 128 ga teng bo‘lgan AB kesmaning
21. Tengsizlikni
 2 yeching:
 uchlari radiusi 5 ga, balandligi 8 ga teng
x + 2x + 1 (x − 3) (x + 4) silindrning pastki va yuqori asoslaridagi
< 0.
x2 − 4x + 4 aylanalarda yotadi. Silindr markaziy o‘qidan
AB kesmagacha bo‘lgan eng qisqa masofani
A) (−4; −1) ∪ (−1; 2) ∪ (2; 3) toping.
√ √
B) (−∞; −4) ∪ (3; ∞) A) 4 B) 17 C) 19 D) 3
   
C) (−∞; −4) ∪ (−1; 2) ∪ (3; ∞) 3π
29. 2 1 − sin 2α + ctg − α · cos 2α + 1
D) (−4; −1) ∪ (2; 3) 4
ifodaning α = 15◦ dagi qiymatini toping.
√
22. Ifodani soddalashtiring:
    A) 1 B) 0 C) −1 D) 2
14π 8π 30. Hisoblang:
sin α + sin α − + sin α +  
3 3 5
(0, (2) + 3, 6 (1)) : 1 − 1, 91 (6) + 42, 5.
A) cos α B) 1 C) 0 D) sin α 6
A) −3, 5 B) 0, 5 C) 3, 5 D) −0, 5




2


Matematika(8000944) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Hisoblang: 10n+1 − 4 · 10n
9. Kasrni qisqartiring:
7, 16 · (8, 21 − 6, 18) + 12, 84 · (7, 81 − 5, 78) 10n+1 + 5 · 10n
A) 40,6 B) 21,4 C) 20,3 D) 42,8 2 2 5 3
A) B) C) D)
2. Uzunligi 80 metr bo‘lgan sim uzunliklari 3 5 2 2
5:7:13 nisbatda bo‘lingan. Hosil bo‘lgan 10. Agar f (x) funksiya (−∞; +∞) da qat’iy
simlardan eng yengilining uzunligini (m) o‘suvchi funksiya bo‘lsa, y = 3f (x) − 8 funksiya
toping. uchun quyidagi mulohazalardan qaysi biri doim
A) 17 B) 16,4 C) 16 D) 16,6 to‘g‘ri bo‘ladi?
3. Muntazam piramida asosining tomoni 10 dm ga
A) qat’iy kamayuvchi
va ichki burchaklarining yig‘indisi 720◦ ga teng
bo‘lgan ko‘pburchakdan iborat. Agar B) dastlab o‘sadi, keyin kamayadi
piramidaning yon qirrasi 13 dm ga teng bo‘lsa, C) dastlab kamayadi, keyin o‘sadi
piramidaning yon sirti yuzini (dm2 ) toping.
D) qat’iy o‘suvchi
A) 300 B) 320 C) 340 D) 360
11. Tengsizlikni yeching:
4. Ikki natural sonning EKUKi 168 ga teng va
(3x − 12)2 · (4x − 12) ≥ (3x − 12) · (4x − 12)2
ularning nisbati 3:4 kabi bo‘lsa, kichik sonni
toping. A) [0; 3] ∪ [4; +∞) B) (−∞; 0] ∪ [3; 4]
C) [4; +∞) D) (−∞; 0]
A) 48 B) 36 C) 56 D) 42
2 12. log23 (x − 1) − 2log3 (x − 1) > 3 tengsizlikning
5. (3 − a) (a + 4) − a (−a − 6) ifodaning a = 2 barcha haqiqiy yechimlari to‘plamini toping.
5
bo‘lgandagi qiymatini toping.
A) (28; +∞)
3 2  
A) 21 B) 8 C) 10 D) 24 4
5 5 B) 1; ∪ (28; +∞)
  3
 x+1 5  11  
6. 2 3 −  < tengsizlikni yeching. 4
2 2 C) 1;
  3
1  
A) (0; 8) B) (8; +∞) C) −∞; 4
8 D) −∞; ∪ (28; +∞)
D) (−∞; 8) 3

7. a ning qanday qiymatlarida uzunliklari mos 13. A to‘plam 48 sonining butun bo‘luvchilaridan
ravishda a + 2; 4 va 2a − 1 bo‘lgan kesmalardan tashkil topgan bo‘lsa, A to‘plamning
uchburchak yasash mumkin? elementlari sonini aniqlang.
A) (0; 5) B) (0; 7) C) (1; 8) D) (1; 7) A) 10 B) 20 C) 18 D) 16
8. To‘g‘ri burchakli parallelepipedning A uchidan 2  2 6
chiquvchi 8; 9 va 12 dm qirralaridan mos 14. Integralni hisoblang: x − 1 · xdx
−1
ravishda A nuqtadan boshlab hisoblaganda
qirralari 3; 5 va 6 dm bo‘lgan piramida qirqib A) 37 · 14−1 B) 36 · 7−1 C) 36 · 14−1
olingan. (rasm) Qolgan qismining hajmini D) 37 · 7−1
(dm3 ) hisoblang. 15. 0, 372 + 3, 649 + 4, 8463 yig‘indining qiymatini
C1 D1 yuzdan birlar xonasigacha yaxlitlang.
B1 A1 A) 7,87 B) 8,84 C) 8,87 D) 7,84
16. a va b ning qanday qiymatlarida
L 8x − 12 a b
2 = + tenglik ayniyat
C D 16x − 9 4x + 3 4x − 3
M bo‘ladi?
B K A A) a = 3; b = −1 B) a = 1; b = 3
A) 774 B) 849 C) 819 D) 834 C) a = −3; b = 1 D) a = −1; b = −3


1
T-108 Matematika(8000944) - Sotish taqiqlanadi!
√
17. 
Agar a = 3 3 − 2 bo‘lsa,  24. 0, 1, 2, 3, 4, 5 raqamlardan jami nechta
a4 + 5a3 + 15a − 9 3 xonali sonlar tuzish mumkin?
+ 9a−4 :
a6 + 3a4 A) 180 B) 210 C) 125 D) 216
 5 −1
a + 2a4 
: − 4 ning qiymatini toping.
a+3 25. (x2 − 121)2 · (32 − 14x − x2 ) =
√ √   √
A) 5 B) 23 C) 12 3 D) 3 3 = 121 − x2 · 32 − 14x − x2 tenglikni nechta
18. A, B, C, D, E va F nuqtalar tartib bo‘yicha butun son qanoatlantiradi?
muntazam oltiburchakning uchlari bo‘lsa, A) 15 B) 14 C) 16 D) 18
quyidagi vektorlardan qaysi biri AD vektorga
teng? 26. Bitta daftar 600 so‘m va u bitta qalamning
    narxidan 400 so‘mga qimmat. O‘quvchi
A) 2 DC − DE B) −2 DC − DE 
C) 2 DC + DE D) −2 DC + DE 3600 so‘mga daftarlar va qalamlar sotib oldi.
Quyida keltirilgan sonlardan qaysi biri xarid
19. (24; 204] oraliqda 3 ga karrali bo‘lgan barcha qilingan qalamlarning soni bo‘la oladi?
natural sonlar yig‘indisi qanday raqam bilan
tugaydi? A) 4 B) 3 C) 5 D) 1
A) 2 B) 6 C) 0 D) 5 27. f (x) = (k + 2) x + 2 funksiya k ning qanday
20. Ikki to‘g‘ri chiziqning kesishishidan hosil qiymatlarida o‘suvchi bo‘ladi?
4 A) k < −2 B) k < 0 C) k ∈ R
bo‘lgan o‘tmas burchak sinusi ga teng bo‘lsa,
5 D) k > −2
o‘tkir burchak tangensini toping.
3 3 3 4 28. Agar a = 13 − x2 , b = x2 − 3 va
A) B) − C) D)
4 5 5 3 a, b ∈ N bo‘lsa, ab eng katta qiymatini toping.
√ √
mn · 4 m m2 + 4 A) 9 B) 25 C) 16 D) 24
21. √4
− 2 ifodaning m = 6
(m + 2) ·√ m−1 n2 m − 4
29. Tenglamani
 yeching:

va n = 4 3 bo‘lgandagi qiymatini toping. √
√ √ 2 cos 2πx −
π
+ 2=0
A) 2 B) −0, 5 C) −2 3 D) 3 3
√
22. f (x) = ln x2 − 4x + 5 + 3x funksiyaning
x0 = 0 nuqtadagi hosilasini toping. 13 5
A) x1 = − + k, k ∈ Z; x2 = + k, k ∈ Z
2 2 2 3 6 6
A) 4 B) 3 C) 2 D) 2 13 5
5 5 5 5 B) x1 = − + k, k ∈ Z; x2 = + k, k ∈ Z
23. cos4 13x − sin4 13x = cos 24x tenglamaning 12 12
barcha yechimlarini toping. 13 5
C) x1 = − + k, k ∈ Z; x2 = + k, k ∈ Z
24 24
A) x = πk, k ∈ Z 13 5
D) x1 = + k, k ∈ Z; x2 = − + k, k ∈ Z
B) x =
πk
, k∈Z 24 24
25
πk 30. Uchburchakning 3 va 4 teng bo‘lgan
C) x = , k∈Z tomonlariga o‘tkazilgan medianalar o‘zaro
4
perpendikulyar bo‘lsa, bu uchburchakning
πk uchinchi tomonini toping.
D) x = , k∈Z √ √
5
A) 6 B) 2,5 C) 5 D) 2,4




2


Matematika(8000968) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Rasmda ABC teng yonli (AB = BC) 9. Hisoblang: 0, 04 · 10−8 · 2, 3 · 1012 .
uchburchak tasvirlangan. Bunda BD⊥AC, A) 920 B) 92 C) 9,2 D) 9200
DE⊥BC va EF ||AC. Agar AB=11 va CD=5
bo‘lsa, EF ni toping. 10. Rasmda f (x) funksiyaning grafigi tasvirlangan.
B Agar g (x) = (2x − 7)7 · f (x) bo‘lsa, g (3) ni
toping.
y


G




x)
F E 2




f(
A D C 1
840 1000 960 810 3
x
A) B) C) D)
121 121 121 121
2. Ushbu  
3xyz x−1 y−1 z−1
− + + : A) 14 B) 7 C) −14 D) −7
xy + yz + zx  x y z
1 1 1 x
: + + ifodaning x = 0, 1; y = 5;z = 8 11. dx integralni hisoblang.
x y z
dagi qiymatini toping. (x2 + 4)3
A) 40 B) 13,1 C) 4 D) 1 −1 −2
A) +C B) +C
3. Hisoblang: x2 + 4 x2 + 4
 2   2
5√ 10 1 2
72 · − 15 + (−45) · −2 + C) +C D) +C
6 3 x2 + 4 x2 + 4
1 √ 3
+ · 3 −312 12. Ko‘phadlarni ko‘paytiring: (3a + 4) · (4a − 3)
6
A) 12a2 − 7a − 12 B) 12a2 + 25a − 12
A) 98 B) 23 C) 106 D) 1298
C) 12a2 − 25a − 12 D) 12a2 + 7a − 12
4. 0, 009 · 0, 02 · 106 ko‘paytmani standart shaklga
keltiring. 13. Agar to‘g‘ri burchakli
√ uchburchakning √
A) 1, 8 · 10 B) 1, 8 · 10−2 C) 1, 8 · 10−1 katetlaridan biri 2 2 ga, gipotenuzasi 4 5 ga
D) 1, 8 · 102 teng bo‘lsa, gipotenuzaga tushurilgan
bissektrisa uzunligini toping.
5. Kasrning maxraji suratidan 8 ga ortiq bo‘lib, √
ularning yig‘indisi 30 ga teng. Bu kasrning A) 2 3 B) 3 C) 4 D) 6
suratidan 1 ni ayirib, maxrajiga 1 ni qo‘shsak,
kasrning qiymati quyidagilardan qaysi biriga 14. Agar f (x) = (3x − 2)18 bo‘lsa, f  (1) ni
teng bo‘ladi? hisoblang.
5 1 3 2 A) 36 B) 54 C) 18 D) 27
A) B) C) D)
6 2 7 5
15. Agar ABC uchburchakning burchaklari
6. Ketma-ketlikning istalgan 2 ta ketma-ket ∠A : ∠B : ∠C = 2 : 3 : 4 shartlarni
hadining yig‘indisi 10 ga teng. Agar uchinchi qanoatlantirsa, uchburchakning qaysi tomoni
hadi 7 ga teng bo‘lsa, ketma-ketlikning eng katta bo‘ladi?
dastlabki to‘qqizta hadi yig‘indisini toping.
A) AC B) BC C) aniqlab bo‘lmaydi
A) 47 B) 45 C) 43 D) 37 D) AB
7. 6 kishidan 4 ta kishini va bu 4 kishidan 2
kishini necha xil usulda tanlab olish mumkin? 16. x2 + ax = 1 tenglamaning x1 va x2 ildizlari
x1 x2
A) 90 B) 144 C) 120 D) 60 + = −18 tenglikni qanoatlantirsa,
x2 x1
8. 43 · 47 · 28 · 32 − 18 · 63 · 27 ayirma qanday
a2 − 2 ning qiymatini toping.
raqam bilan tugaydi?
A) 2 B) 14 C) 7 D) 34
A) 8 B) 6 C) 2 D) 4


1
T-108 Matematika(8000968) - Sotish taqiqlanadi!

2
4x −5x+6 − 1 24. [1; 200] sonlar to‘plamida nechta natural son
17. = 1 tenglamaning ildizlari
x2 −4x+4 6 ga (qoldiqsiz) bo‘linib, 9 ga (qoldiqsiz)
2 −1
yig‘indisi (yoki ildizi, agar u bitta bo‘lsa) bo‘linmaydi?
12 dan qanchaga kam? A) 11 B) 44 C) 33 D) 22
A) 6 B) 8 C) 4 D) 10 25. Silindrning balandligi 5 ga, o‘q kesimining
 2 √ diagonali 13 ga teng. Silindr asosining radiusini
18. x − 2x − 24 10x − x2 < 0 tengsizlikning
toping.
eng katta butun yechimini toping. √ √
A) 5 B) 9 C) 7 D) 6 A) 6 B) 4 3 C) 6 2 D) 12
  √ √
π π 26. 3 x − 2 − 3 x − 9 = 1 tenglamaning ildizlari
19. Hisoblang: log 3 cos + sin − yig‘indisini toping.
 4 12 12
π π A) 9 B) 1 C) 11 D) 10
− log 4 cos − sin
3 12 12 27. Agar ā (x; 2) va b (5; y) o‘zaro kollinear
1 1 vektorlar bo‘lsa, 2xy − 3 ning qiymatini toping.
A) 1 B) C) 0 D) −
2 2 A) 17 B) 3 C) 13 D) 7
20. 540 soni 25%ga oshirildi. Hosil bo‘lgan sonning 1  
28. 1 + cos−1 2α + tg 2α 1 − cos−1 2α + tg 2α
20%ini toping. 2
A) 125 B) 155 C) 130 D) 135 ifodaning α = 15◦ dagi qiymatini toping.
√ 1 √ 2
21. Uchburchakli piramida asosining ikki tomoni 6 A) 3 B) √ C) 2 3 D) √
va 7 dm bo‘lib, ular orasidagi burchak 45◦ ga 3 3
teng. Agar piramidaning 8 dm bo‘lgan yon 29. Koordinata o‘qlarining (3; 0) va (0; 4)
qirrasi asos tekisligi bilan 30◦ li burchak tashkil nuqtalaridan o‘tadigan chiziqli fuksiyani toping.
etsa, uning hajmini (dm3 ) toping. 4 4
√ √ √ √ A) y = x − 4 B) y = − x + 4
A) 14 2 B) 28 2 C) 56 2 D) 7 2 3 3
1 3 3 3 3 5 1 4 4
22. Hisoblang: 1 · 3 + 2 · 3 − 3 · 3 − 1 C) y = x + 4 D) y = − x − 4
2 5 4 5 5 6 2 3 3
√  2 
A) −0, 5 B) −1, 5 C) 0 D) 0,5 30. y = 6 − x + log(4−x) x − 4 funksiyaning
23. y = −3x + 7 chiziqli funksiyaning y = x to‘g‘ri aniqlanish sohasini toping.
chiziqqa nisbatan simmetrigini toping.
A) (−∞; −2) ∪ (2; 3) ∪ (3; 4)
−7 + x 7−x
A) y = B) y = B) (2; 3) ∪ (3; 4) ∪ (4; 6)
3 3
−7 − x 7+x C) (−∞; −2) ∪ (2; 4)
C) y = D) y =
3 3
D) (2; 4)




2


Matematika(8000992) - Sotish taqiqlanadi! T-108

MATEMATIKA
√
 sin x  √ √  π π
1. √ dx integralni hisoblang. 8. A = − 3; 3 , B = − ; va
x 2 2
√
√ 1 √ √ 7
A) 2 cos x + C B) − cos x + C C = − 5; bo‘lsa, (A ∪ B) ∩ C to‘plamni
2 2
√ 1 √ aniqlang.
C) −2 cos x + C D) cos x + C √
2 √ 7 π π
A) − 3; B) − ;
2. 0, 1, 2, 3, 4, 5 raqamlardan jami nechta 2 2 2
 √ √   √ √ 
3 xonali sonlar tuzish mumkin? C) − 3; 3 D) − 5; 3
A) 216 B) 180 C) 210 D) 125 9. ā (−1; 2), b (−2; 1) va c (−3; 2) vektorlar
berilgan. k ning qanday qiymatida 2ā − kb
3
3. 6 12 + 612 + 612
+ ... + 612 + 612 yig‘indining vektor c vektorga perpendikulyar bo‘ladi?
4 4 7 7 4
32 ta
A) − B) − C) D)
qismi quyidagilardan qaysi biriga teng? 7 4 4 7
A) 4 · 612 B) 2 · 613 C) 214 · 312 10. Rasmda qaysi funksiyaning grafigi
D) 215 · 313 tasvirlangan?
4. Hisoblang: y
1 sin 112◦
+ − cos 7◦ · cos 14◦ · cos 28◦ · cos 56◦ .
2 16 sin 7◦
1 3
A) 0 B) C) D) 1
2 4

5. Rasmda f (x) = ax2 + bx + c funksiyaning
grafigi va unga o‘tkazilgan urinma tasvirlangan
bo‘lsa, a ni toping.
y 1
x
0 1
6


A) f (x) = 2|x| − 1 B) f (x) = |x + 1| + 1
C) f (x) = 2|x + 1| + 1 D) f (x) = 3|x + 2|
11. Piramida balandligining o‘rtasidan asosga
2 parallel tekislik o‘tkazilgan va hosil bo‘lgan
kesim yuzi 27 ga teng. Agar berilgan
x piramidaning balandligi 10 ga teng bo‘lsa,
0 3 6
uning hajmini toping.
f (x)
A) 400 B) 340 C) 360 D) 320
2 5 1 4 12. Agar x = 10√bo‘lsa,
A) − B) − C) − D) −
3 9 3 9 (4 − x)−1 · x3 − 9x2 + 24x − 16 ifodaning
qiymatini toping.
6. To‘g‘ri burchakli uchburchakning o‘tkir A) −3 B) 2 C) −2 D) 3
burchagi 60◦ . Shu burchakning bissektrisasi
uzunligi 1 cm ga teng bo‘lsa, gipotenuzasi 13. 1 dan 120 gacha (120 ning o‘zi ham) bo‘lgan
uzunligini (cm) toping. natural sonlar orasida 3 ga ham, 5 ga ham
√ √ √ bo‘linmaydiganlari nechta?
A) 3 B) 5 − 1 C) 2 + 1 D) 2
A) 61 B) 60 C) 56 D) 64
7. Soddalashtiring: 3a − (5a − (3a − (2a + b))) 14. x4 · 5x + 25 ≥ 25x4 + 5x tengsizlikni yeching.
A) −a + b B) a − b C) a + b D) −a − b A) [−1; 1] ∪ [2; ∞) B) (−∞; 1] ∪ [1; ∞)
C) (−∞; −1] ∪ [1; 2] D) (−∞; 1] ∪ [2; ∞)


1
T-108 Matematika(8000992) - Sotish taqiqlanadi!

15. Muntazam to‘rtburchakli kesik piramida 24. Rasmda ABCD parallelogramm tasvirlangan.
asoslarining tomonlari 9 cm va 15 cm. Kesik G nuqta BE va DF kesmalarning kesishish
piramidaning diagonali 18 cm bo‘lsa, uning nuqtasi. Agar BF = F C va CE = ED bo‘lsa,
balandligini (cm) toping. SABCD
ni toping.
A) 6 B) 7 C) 8 D) 9 SABGD
F
B C
6x > x2 G
16. tengsizliklar sistemasining butun
4x2 ≤ 25 E
yechimlari yig‘indisini toping.
A) 4 B) 7 C) 12 D) 3 A D
3 5
A) B) 1 C) D) 2
1 6 2 3
17. = 2 tenglamaning ildizlari
|x| x + 2x
ko‘paytmasini toping.
A) −8 B) −32 C) 4 D) 0

18. Quyidagi sonlardan nechtasi butun son?
 √ 2, 48 25. Tenglamani yeching:
1) 2 + 144; 2) 7, 12; 3) π − 1, 14; 4) −
1, 24 x+3 x+3 x+3 x+3 49
2 + 2 + 2 + ... + 2 =
A) 2 B) 3 C) 1 D) 4 4 −1 6 −1 8 −1 100 − 1 101
1
19. Agar n va m natural sonlar uchun A) − B) 2 C) 0 D) −3
3
6n − 4m 1 2
= 1 tenglik bajarilsa, +
n n m
ifodaning eng katta qiymatini toping.
6 7 9 13
A) B) C) D)
10 10 10 20
√
20. Quyidagi jumlalardan qaysilari noto‘g‘ri? 26. Hisoblang: 20192 − 2017 · 2021
1) agar natural son 6 ga bo‘linsa, u holda 12 ga A) 18 B) 2 C) 8 D) 12
ham bo‘linadi; 2) agar natural son 12 ga
bo‘linsa, u holda 6 ga ham bo‘linadi; 3) agar
natural son 12 ga bo‘linmasa, u holda 6 ga ham
bo‘linmaydi; 4) agar natural son 6 ga
bo‘linmasa, u holda 12 ga ham bo‘linmaydi.
27. y = f (x) funksiya grafigidan foydalanib, (−2; 6)
A) 2, 3 B) 1, 2 C) 1, 3 D) 3, 4
oraliqda f (x) · f  (x) = 0 tenglamaning barcha
21. Agar cos 34◦ = a va sin 31◦ = b bo‘lsa, yechimlari to‘plamini toping.
sin 22◦ + sin 28◦ ni a va b orqali ifodalang.
    y
A) a2 − b2 B) 2 a2 − b2 C) 2 b2 − a2
3
D) b2 − a2
x)
f(
=




22. Bitta daftar 600 so‘m va u bitta qalamning
y




1
narxidan 400 so‘mga qimmat. O‘quvchi
4
3600 so‘mga daftarlar va qalamlar sotib oldi. x
−3 −2 −1 0 1 2 3 5 6
Quyida keltirilgan sonlardan qaysi biri xarid
−1
qilingan qalamlarning soni bo‘la oladi?
A) 5 B) 1 C) 3 D) 4 A) {−1; 3; 5} B) {−1; 2; 3; 4; 5}
C) {−1; 1; 3; 4; 5} D) {−1; 0; 2; 3; 5}
23. Ixtiyoriy uchtasi bir to‘g‘ri chiziqda yotmagan
10 ta nuqtani o‘zaro tutashtirib ko‘pi bilan
nechta har xil kesma hosil qilish mumkin?
A) 10 B) 55 C) 90 D) 45



2
 Matematika(8000992) - Sotish taqiqlanadi! T-108

28. Rasmda ishchilar tomonidan 10 kunda 29. Agar a · c < 0 bo‘lsa, y = ax2 + bx + c kvadrat
tayyorlangan detallarning diagrammasi funksiyaning grafigi qaysi choraklarda yotadi?
tasvirlangan. Ishchilar bu 10 kunda o‘rtacha A) I, II, III va IV B) I, III va IV
kuniga nechtadan detal tayyorlagan? (bu yerda C) II, III va IV D) I, II va III
t − kunlar, a − detallar soni)
a
1400 1400



1200 1200 1200



1000 1000 1000



800 800

30. Tengsizlikni yeching:
25log 5 (x−2) + (x − 2)2 > 32.
1 2 3 4 5 6 7 8 9 10
t
A) (2; 6) B) (−∞; −2) ∪ (6; ∞)
A) 1080 B) 1120 C) 1100 D) 1160 C) (2; 6) ∪ (6; ∞) D) (6; ∞)




3


Matematika(8001016) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. 4x2 ≤ x2 − 12x + 36 ≤ 25 qo‘sh tengsizlikni 11. a (−12; 13; −15) vektorning Oxy tekisligidagi
qanoatlantiruvchi butun sonlar nechta? proyeksiyasi bo‘lgan vektorni toping.
A) 4 B) 2 C) 3 D) 1 A) p (−12; 0; −15) B) p (−12; 13; 0)
C) p (0; 13; −15) D) p (0; 0; −15)
2. Agar a, b, c musbat haqiqiy sonlar uchun
ab = 14 va bc = 6 bo‘lsa, a + 2b + 3c eng kichik 12. Rasmda A va B nuqtalar son o‘qida
qiymatini toping. tasvirlangan. 2A + B ning son qiymatini
toping.
A) 18 B) 20 C) 34 D) 16
9, 5 birlik 7 birlik
1 √
2a− 6 − ab
3
3
3. 2 1 √ +√
3
ifodaning a = 64, B -3 0 2,5 A
a3 b3 − 2 a 6 a
b = 0, 4 dagi qiymatini toping. A) 8 B) 12,5 C) 9,5 D) 6,5
1 1 2 1 13. To‘g‘ri to‘rtburchak shaklidagi yer maydonning
A) B) C) D)
3 6 5 2 to‘rtta tomoni 360 m uzunlikdagi devor bilan
4. Tekislikda ixtiyoriy uchtasi bitta to‘g‘ri chiziqda o‘ralgan. Bu yer maydonining eng katta yuzasi
yotmaydigan A, B, C, D, M va N nuqtalarni necha m2 bo‘ladi?
uchburchaklarning uchlari deb hisoblasak, A) 81000 B) 8100 C) 3240 D) 32400
nechta uchburchakda B nuqta qatnashadi? 4 2 8−x
14. x ning qanday qiymatida ; va lar
A) 15 B) 9 C) 10 D) 12 x−3 3 x−3
berilgan tartibda arifmetik progressiyaning
5. y = −3x + 7 chiziqli funksiyaning abssissalar ketma-ket hadlari bo‘ladi?
o‘qiga nisbatan simmetrigini toping. 3 6 3 6
A) 4 B) 4 C) 6 D) 6
A) y = −3x − 7 B) y = 3x − 7 7 7 7 7
C) y = −3x + 7 D) y = 3x + 7 1 2 3 4 5 6 7 8 9
 √  15. · · · · · · · ·
6. y = log(1−2x) 2 − 3 − x funksiyaning 10 10 10 10 10 10 10 10 10
aniqlanish sohasini toping. ko‘paytmani standart shaklga keltiring.
A) (0; 0, 5) ∪ (0, 5; 3] B) (0; 0, 5) A) 3, 6288 · 10−6 B) 3, 6288 · 10−4
C) (−1; 0, 5) D) (−1; 0) ∪ (0; 0, 5) C) 3, 6288 · 10−5 D) 3, 6288 · 10−3
16. Piramida balandligining o‘rtasidan asosga
7. To‘g‘ri burchakli uchburchak o‘tkir parallel tekislik o‘tkazilgan va hosil bo‘lgan
burchaklarining bissektrisalari kesishishidan kesim yuzi 27 ga teng. Agar berilgan
hosil bo‘lgan o‘tkir burchakni toping. piramidaning balandligi 10 ga teng bo‘lsa,
A) 15◦ B) 45◦ C) 60◦ D) 30◦ uning hajmini toping.
8. 1 gektar maydonga o‘rtacha 0,6 sentner zig‘ir A) 360 B) 400 C) 320 D) 340

urug‘i ekiladi. 1:10000 masshtabli xaritada
3
bo‘yi 20 cm va eni 12 cm bo‘lgan to‘g‘ri 17. f (x) = funksiyaning aniqlanish
6−x
to‘rtburchak shaklidagi yer maydoniga zig‘ir
urug‘i ekish uchun o‘rtacha necha sentner kerak sohasiga tegishli natural sonlar nechta?
bo‘ladi? A) 5 B) 3 C) 6 D) 4

A) 400 B) 40 C) 14,4 D) 144 x + 2, x ≤ −1
18. Agar f (x) = bo‘lsa,
x2 , x > −1
9. Uchburchakning 3 va 4 teng bo‘lgan
0 3
tomonlariga o‘tkazilgan medianalar o‘zaro 6x · f (x)dx integralni hisoblang.
perpendikulyar bo‘lsa, bu uchburchakning −2
uchinchi tomonini toping. A) −8,8 B) −7,8 C) −8,4 D) −4,8
√ √
A) 6 B) 2,4 C) 5 D) 2,5 19. x va y lar uchun
y 2 + 2x (x + y) + 3 (2x + 3) = 0 tenglik o‘rinli
10. (2x − 1)2 · (2x + 1)2 algebraik ifoda x2 + y 2
quyidagilardan qaysi biriga aynan teng? bo‘lsa, ifodaning qiymatini toping.
6
A) 16x4 + 8x2 + 1 B) 16x4 − 4x2 + 1 4
C) 16x4 − 8x2 + 1 D) 16x4 + 4x2 + 1 A) 3 B) 2 C)
3
D) 1



1
T-108 Matematika(8001016) - Sotish taqiqlanadi!

1
20. A = {x| x = 4n + 3, n ∈ N }, 2
25. 3 log0,25 3 − 0, 251+cos (5π−3x) ifodaning eng
B = {x| x = 6n + 5, n ∈ N } bo‘lsa, A ∩ B kichik qiymatini toping.
to‘plamni aniqlang. 3 1 3
A) B) − C) − D) 0
16 4 4
A) {x| x = 24n − 1, n ∈ N }
26. a va b raqamlar yig‘indisi 13 ga qoldiqsiz
B) {x| x = 12n + 11, n ∈ N } bo‘linadi. Agar aba ko‘rinishdagi uch xonali
C) {x| x = 12n − 1, n ∈ N } sonlarni 13 ga bo‘lganda bir xil qoldiq qolsa,
D) {x| x = 24n − 13, n ∈ N } shu qoldiqni toping.
    A) 4 B) 2 C) 6 D) 0
21. x2 − 5x − 4 · x2 − 5x + 3 − 8 = 0
27. Hisoblang:
tenglamaning haqiqiy ildizlari yig‘indisini
(tg 435◦ − tg 375◦ ) · sin2 70◦ · sin2 50◦ · sin2 10◦ :
toping.
: sin 120◦
A) 4 B) 5 C) 1 D) 10 1 1 1
A) 1 B) C) D)
22. a va b ning qanday qiymatlarida 4 8 16
8x − 12 a b 28. 5 ta sonning o‘rta arifmetigi 13 ga teng. Shu
2 = + tenglik ayniyat
16x − 9 4x + 3 4x − 3 sonlarga qaysi son qo‘shilsa ularning o‘rta
bo‘ladi? arifmetigi 14 ga teng bo‘ladi?
A) a = −3; b = 1 B) a = 1; b = 3 A) 17 B) 19 C) 21 D) 18
C) a = 3; b = −1 D) a = −1; b = −3 √ √
29. Tomonlari 3 3; 4 va 2 6 ga teng bo‘lgan
  uchburchakning turini aniqlang.
2 7
23. Hisoblang: 3− + 1+ A) o‘tmas burchakli B) o‘tkir burchakli
9 9
C) to‘g‘ri burchakli D) aniqlab bo‘lmaydi
5 4
A) B) 3 C) D) 4 30. Uchburchakli piramida asosining tomonlari
3 3 9 dm, 10 dm va 17 dm ga teng. Piramidaning
√
24. 6x − x2 · (2x − 5) > 0 tengsizlikni nechta barcha yon yoqlari asos tekisligi bilan 45◦ li
butun son qanoatlantiradi? burchak tashkil etsa, uning hajmini (dm3 )
toping.
A) 3 B) 4 C) cheksiz ko‘p D) 0
A) 26 B) 28 C) 24 D) 22




2


Matematika(8001040) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Algebraik ifodaning qiymatini toping. 10. To‘g‘ri burchakli parallelepipedning bir uchidan
0, 25ab − 0, 3b2 , bunda a=4 va b=3. chiquvchi qirralari a; b va c bo‘lib,
C) −0,3 D) −3 1 1 1 1
A) 0,3 B) 3 + + = tenglikni qanoatlantiradi. Agar
a b c 2
2. 
f (x) = 24tgx − 24x + 6π + 11 funksiyaning parallelepiped to‘la sirtining yuzi 288 bo‘lsa,
π π
− ; kesmadagi eng katta qiymatini toping. uning hajmini toping.
4 4
√ A) 144 B) 432 C) 576 D) 288
A) 14√3 + 11 B) 35 C) 24
D) 12 3 + 13 11. Hisoblang:
   
7 3 1 5
2 2020 − 2019 : 2019 − 2018
3. Agar sin α = − bo‘lsa, 8 8 3 6
5
A) 4 B) 1 C) 3 D) 2
sin 2α − sin 3α + sin 5α
ning qiymatini toping.
1 + cos α − 2 sin2 2α 12. Tenglamani yeching:
2 2 4 5 3 · 2x−2 − 5 · 2x−4 = 18 − 2x−3
A) − B) C) − D)
5 5 5 4 A) −2 B) 3 C) 5 D) 4
4. f (x) = (x − 1)20 · (cos x + sin x) funksiyaning 13. Farxod, Anvar va Jahongir birgalikda 57,8 kg
x0 = 0 nuqtadagi hosilasini toping. uzum yig‘ishdi. Anvar Farxodga nisbatan 2,4
A) −19 B) 19 C) −20 D) 20 kg ko‘p, Jahongir esa Farxod bilan Anvarning
5. Tenglamani yeching: birgalikdagi yig‘ganidan 20,6 kg kam yig‘gan.
x−2 x−2 x−2 x−2 1 Anvar va Jahongir birgalikda necha kg uzum
+ + + =1 yig‘ishgan?
3·5 5·7 7·9 9 · 11 11
A) 14 B) 11 C) 8 D) 4 A) 36,8 B) 40,2 C) 38,8 D) 39,4
6. Rasmda to‘g‘ri to‘rtburchak teng bo‘laklarga 14. a(−2; 6; 3) vektor bilan yo‘nalishi bir xil bo‘lgan
bo‘lingan. To‘g‘ri to‘rtburchakning necha foizi birlik vektorning koordinatalarini toping.
   
bo‘yalgan? 2 −6 −3 2 6 3
A) ; ; B) ; ;
 7 7 7  7 7 7 
2 6 3 2 6 3
C) − ; ; D) − ; ; −
7 7 7 7 7 7
15. Agar a = 63x−2y va b = 63x+2y bo‘lsa,
4 · 6x + 3 · 6y ni a va b orqali ifodalang.
 
√4 a √4 a
A) 4 · ab + 3 · 6
B) 4 · ab + 3 · 3
b b
 
√ b √ b
C) 4 · 6 ab + 3 · 4 D) 4 · 3 ab + 3 ·
A) 52,5 B) 57 C) 55 D) 57,5 a a
 
2 7 16. Rasmda ABC uchburchak va uning BD
7. Hisoblang: 3− + 1+
9 9 medianasi tasvirlangan. Agar AC=2BD va
∠CAB = 22◦ bo‘lsa, ACB burchakni toping.
4 5
A) B) C) 3 D) 4 B
3 3
a 9
8. a va b natural sonlar uchun = bo‘lsa, u A C
5 b+2 D
holda a + b ifodaning eng katta qiymatini
toping. A) 58◦ B) 62◦ C) 52◦ D) 68◦
A) 16 B) 44 C) 45 D) 12 17. Tog‘ning cho‘qqisiga 8 ta yo‘l olib boradi.
9. cos 5x = cos (5 + x) tenglamaning eng kichik Borgan yo‘lidan qaytmaslik sharti bilan
musbat yechimini toping. tog‘ning cho‘qqisiga jami necha xil usulda borib
5 5 5 π 5 kelish mumkin?
A) B) C) D) − A) 28 B) 56 C) 21 D) 42
3 4 6 3 6


1
T-108 Matematika(8001040) - Sotish taqiqlanadi!

 −1
18. Yon tomonining uzunligi 5 dm bo‘lgan teng a3 b + 2a2 b − 3ab 1 − a2
25. · + 2b
yonli trapetsiyaga doira ichki chizilgan. Agar a3 + 5a2 + 6a a2 + 3a + 2
trapetsiyaning yuzi 20 dm2 bo‘lsa, doiraning 1
yuzini (cm2 ) toping. ifodaning a = , b = −6 dagi qiymatini toping.
3
A) 20π B) 40π C) 16π D) 400π 1 1
A) B) −6 C) −6 D) 9
19. F (x) funksiya f (x) = x2 − x + 2 funksiyaning 3 3
boshlang‘ich funksiyasi. F (x) funksiyaning
[0; 2] kesmadagi eng kichik qiymati 2 ga teng
26. 1 dan 120 gacha (120 ning o‘zi ham) bo‘lgan
bo‘lsa, uning [0; 2] kesmadagi eng katta
natural sonlar orasida 3 ga ham, 5 ga ham
qiymatini toping.
bo‘linmaydiganlari nechta?
2 2 1 1
A) 6 B) 5 C) 6 D) 5 A) 56 B) 60 C) 61 D) 64
3 3 3 3
20. 2 · 7 · 11 · 19 · 23 son quyidagi sonlardan qaysi
biriga ko‘paytirilsa, uning natural bo‘luvchilari 27. Rasmdan foydalanib, ((A ∩ B) ∪ C) ∩ D
soni ikki marta ortadi? to‘plamning elementlari sonini toping.
A) 11 B) 7 C) 2 D) 3 D
A B C
x3 9x d
21. ≤ tengsizlikning butun yechimlari a
c
m
x−2 x−2 b
l n
sonini toping. e
k, p, q
A) 4 B) 7 C) 6 D) 5
22. y = −3x + 7 chiziqli funksiyaning x=1 to‘g‘ri A) 4 B) 3 C) 0 D) 1
chiziqqa nisbatan simmetrigini toping.
A) y = −3x + 9 B) y = 3x − 9 28. Agar 0 < a < 1 bo‘lsa, quyidagilardan qaysi
C) y = −3x − 1 D) y = 3x + 1 biri ma’noga ega?
23. f (x) = x2 − 5x − 6 funksiyaning nollari A) log2 loga (a + 1) B) log2 loga log2 3
yig‘indisini toping. π
C) lg lg lg a D) loga loga
A) 0 B) 5 C) −6 D) −5 4
24. To‘g‘ri to‘rtburchak shaklidagi qog‘ozning A,
 
B, C va D uchlaridan tomonlari bo‘ylab,  2 
29. 24x −1 − 5 = 3 tenglama nechta haqiqiy
tomoni 10 cm bo‘lgan to‘rtta kvadrat kesib
olingan. Qolgan shakldan hajmi 4,5 dm3 ga ildizga ega?
teng bo‘lgan usti ochiq parallelepiped yasalgan. A) 4 B) 1 C) 3 D) 2
Parallelepiped asosining bir tomoni
ikkinchisidan 15 cm ortiq bo‘lsa, ABCD to‘g‘ri 30. Silindrning balandligi 5 ga, o‘q kesimining
to‘rtburchak shaklidagi qog‘ozning yuzasi necha
diagonali 13 ga teng. Silindr asosining radiusini
сm2 bo‘lgan?
toping.
A) 2700 B) 2200 C) 1750 D) 1350 √ √
A) 6 2 B) 6 C) 4 3 D) 12




2


Matematika(8001064) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Farxod, Anvar va Jahongir birgalikda 57,8 kg 11. Rasmda f  (x) kvadrat funksiyaning grafigi
uzum yig‘ishdi. Anvar Farxodga nisbatan 2,4 tasvirlangan. Uning boshlang‘ich funksiyasi
kg ko‘p, Jahongir esa Farxod bilan Anvarning uchun f (0) = 0 bo‘lsa, u holda f (2) ni toping.
birgalikdagi yig‘ganidan 20,6 kg kam yig‘gan.
Anvar va Jahongir birgalikda necha kg uzum y

yig‘ishgan?
6
A) 39,4 B) 38,8 C) 36,8
D) 40,2 f  (x)
 −2
1 + mn−1 m−1 mn−1 n
2. −1 · −1 −1 : ·
(mn) m n−n m n − m m
ifodaning m = 4 va n = 2, 5 bo‘lgandagi
qiymatini toping. x
0 1 2
A) 1,6 B) −1, 5 C) 10 D) 16
3. Ikkita to‘g‘ri chiziq kesishganidan hosil bo‘lgan A) 0 B) 2 C) 3 D) 1
burchaklardan biri ikkinchisidan 36◦ ga katta
bo‘lsa, ularning nisbatini toping.
12. Biri ikkinchisidan 3 marta katta bo‘lgan ikki
A) 3:2 B) 6:5 C) 5:4 D) 4:3 sonning yig‘indisi 9,64 ga teng. Shu sonlarning
4. x2 + ax = 1 tenglamaning x1 va x2 ildizlari kichigini toping.
x1 x2
+ = −18 tenglikni qanoatlantirsa, A) 2,21 B) 2,31 C) 2,16 D) 2,41
x2 x1
a2 − 2 ning qiymatini toping.
13. Piramidaning asosi to‘g‘ri burchakli
A) 2 B) 7 C) 14 D) 34 uchburchakdan iborat bo‘lib, uning
5. ABCD parallelogrammning uchlari gipotenuzasi
√ 2 dm. Piramidaning har bir yon
A (−2; 6; −9), B (−12; 6; 5) va C (4; 6; 5) qirrasi 5 dm bo‘lib, ular asos tekisligi bilan α
−−→
nuqtalar bo‘lsa, BD vektorning koordinatalari burchak tashkil qiladi. tg α ni toping.
√
yig‘indisini toping. 1 5
A) B) 1 C) 2 D)
A) 12 B) −16 C) −12 D) 16 2 2
π π
6. tg( − x) · ctg(x − ) = 0 tenglamaning eng
4 6 14. 2513 + 16127 + 27 yig‘indi qanday raqam bilan
katta manfiy yechimini toping. tugaydi?
π 3π π π A) 6 B) 8 C) 3 D) 5
A) − B) − C) − D) −
3 4 6 4
   
243x 5 · 27x 1 2 3 1 3 4
7. Agar 3x = 2 bo‘lsa, + − 81x ning 15. 2 a b · −3 a b ifodani
32 8 4 3
qiymatini toping. soddalashtiring.
A) −9 B) −10 C) −5 D) −2 1 1 1
A) −7 a5 b7 B) −7 a5 b7 C) −7 a5 b7
4 2 8−x 3 4 12
8. x ning qanday qiymatida ; va lar 1 5 7
x−3 3 x−3 D) −7 a b
berilgan tartibda arifmetik progressiyaning 2
ketma-ket hadlari bo‘ladi?
6 3 3 6 16. 25log 5 x − 5 · 2log2 x = 24 tenglamaning ildizi x0
A) 6 B) 4 C) 6 D) 4
7 7 7 7 bo‘lsa, x20 − 5x0 + 7 ning qiymatini toping.
9. Agar f (x) = kx + 3 funksiya uchun f (2) = −3 A) 32 B) 31 C) 30 D) 33
munosabat o‘rinli bo‘lsa, f (−2) ni toping.
A) 6 B) 3 C) 0 D) 9 17. cos 5x = cos (5 + x) tenglamaning eng kichik
√  x2 −10x+16 musbat yechimini toping.
10. 5−2 x−2
≥ 1 tengsizlikni yeching. 5 5 5 π 5
A) B) C) D) −
A) [8; ∞) B) (−∞; 8] C) (2; 8) ∪ (8; ∞) 4 3 6 3 6
D) (−∞; 2) ∪ (2; 8]


1
T-108 Matematika(8001064) - Sotish taqiqlanadi!

18. Rasmda ABC uchburchakka aylana ichki 23. 3 ta mergan bir-biriga bog‘liq bo‘lmagan holda
chizilgan. Agar AB=14, BC=13 va AC=15 nishonga bir martadan o‘q uzishmoqda. Har
bo‘lsa, aylana markazi O nuqtadan birining nishonga tekkizish ehtimolligi mos
A nuqtagacha bo‘lgan masofani toping. ravishda 0,8; 0,7 va 0,6 ga teng. Nishonga faqat
B birinchi va ikkinchi merganlarning o‘qlari
tegishi hodisasining ehtimolligini toping.
A) 0,336 B) 0,7 C) 0,56 D) 0,224
x3 9x
O 24. ≤ tengsizlikning butun yechimlari
x−2 x−2
sonini toping.
A C
√ √ √ √ A) 7 B) 6 C) 4 D) 5
A) 84 B) 80 C) 52 D) 65
25. Rasmda y = f (x) funksiya grafigi va unga
(3; 2) nuqtadan o‘tkazilgan urinmasi
1 2 2 1 tasvirlangan. Agar g (x) = (x − 2) · f (x)
19. a = 0, 6 3 · 1, 3− 5 , b = 0, 7− 3 · 0, 3− 5 va
1 2 bo‘lsa, g  (3) ni toping.
c = 1, 8 3 · 0, 3− 5 sonlardan qaysilari 1 dan
y
katta?
4
A) b va c B) faqat b C) a va b D) a va c



20. Rasmda y = f (x) funksiyaning grafigi 2
f (x)
tasvirlangan. Quyidagi tengsizliklardan qaysi 1
biri to‘g‘ri? x
y 0 3

4
y=




3 2 1 1 2
f(




A) 1 B) 2 C) 1 D) 2
x)




3 3 3 3
26. α tekislik va uni kesib o‘tmaydigan AB kesma
x berilgan. Kesmaning uchlaridan α tekislikkacha
−3 −2 −1 1 2 3 4 5 6 bo‘lgan masofalar AA1 =18 cm, BB1 =13 cm
−1
bo‘lsa, AB kesmani A uchidan boshlab
hisoblaganda 3:2 nisbatda bo‘luvchi C
A) f  (5) · f (2) > 0 B) f  (4) · f (3) > 0 nuqtadan α tekislikkacha bo‘lgan masofani
C) f  (4) · f (5) > 0 D) f  (1) · f (3) > 0 (cm) toping.
A) 14 B) 15,5 C) 15 D) 16
21. y = −x2 + bx + c kvadrat funksiyaning eng 27. Teng yonli uchburchakning perimetri 32 cm ga
katta qiymati −2 ga teng va unga x = 2 teng. Agar teng tomonlarining o‘rtalarini
nuqtada erishadi. bc ni toping. tutashtiruvchi kesma uzunligi 6 cm bo‘lsa,
uchburchakning yuzini (cm2 ) toping.
A) −18 B) 18 C) 24 D) −24
A) 42 B) 56 C) 54 D) 48
28. 0,6(8) son 0,(31) sondan necha marta katta?
22. A = {x| sin x = 0, x ∈ Z} to‘plamga teng
A) 3,(3) B) 2,(2) C) 2,2 D) 2
bo‘lgan to‘plamni aniqlang.  2 2
29. x − 7x + 13 − (x − 3) · (x − 4) − 3 = 0
A) {x| x = πk, k ∈ R} tenglamaning haqiqiy ildizlari ko‘paytmasini
B) {x| xn = 0, n ∈ N } toping.
C) {x| x = πk, k ∈ N } A) 14 B) 154 C) 11 D) 49

D) {x| x = πn, n ∈ Z} 30. 15 · 221 · 517 ko‘paytma nechta nol bilan
tugaydi?
A) 18 B) 22 C) 21 D) 19



2


Matematika(8001088) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Ifodani soddalashtiring: 10. Rasmda ABCD parallelogramm tasvirlangan.
4a2 − 16a + 16 (a − 2)2 G nuqta BE va DF kesmalarning kesishish
:
a+3 −a2 + 9 nuqtasi. Agar BF = F C va CE = ED bo‘lsa,
SABCD
A) 4a − 12 B) 12 − 4a C) 6 − 2a ni toping.
D) 2a − 12 SABGD
F
B C
2. ABC uchburchakning BD medianasidagi E va G
F nuqtalar (E nuqta B uchiga yaqin E
joylashgan) medianani teng uchta qismga
bo‘ladi. Agar ABC uchburchakning yuzi 36 ga A D
teng bo‘lsa, AEB uchburchakning yuzini 3 5
toping. A) 2 B) C) D) 1
2 3
A) 4 B) 12 C) 9 D) 6

3. Agar tg α + ctg α = 3 bo‘lsa, 11. Konusning to‘la sirti 24 ga teng. Agar konus
tg 2 α − 2 tg α + ctg α ifodaning qiymatini toping. o‘q kesimi muntazam uchburchakdan iborat
bo‘lsa, konus asosining yuzini toping.
A) 4 B) 2 C) 1 D) 3
A) 6 B) 12 C) 9,6 D) 8
5 2
4. 2019 − 2017 ni hisoblang.
26 13 12. Hisoblang: 70 · 10−5 + 1, 8 · 10−4
53 27 51 24 A) 88 · 10−6 B) 8, 8 · 10−4 C) 8, 8 · 10−3
A) B) C) D)
26 13 26 13 D) 0, 88 · 10−1

3x + 2
5. k ning qanday qiymatlarida =k+2 6
4x − 3 13. (x − 5)4 · xdx integralni hisoblang.
tenglamaning ildizi 1 dan kichik bo‘ladi? 5

A) (−∞; −1, 25) ∪ (3; ∞) B) (−1, 25; 3) 1 1 1 1
A) 1 B) 1 C) 1 D) 1
C) (−3; 1, 25) D) (−∞; −3) ∪ (1, 25; ∞) 7 9 6 8

6. Ifodani soddalashtirting:   
sin 4α cos 2α sin 2α 14. (3x − 2)2 + 3 (3x − 2)3 + 4 (3x − 2)4 ≥ 4
· − + 1.
1 + cos 4α 1 + cos 2α 1 + cos 2α tengsizlikning eng katta manfiy butun yechimi
A) cos α + 1 B) sin α + 1 C) tg α + 1 bilan eng kichik musbat butun yechimi
D) 1 yig‘indisini toping.
A) 4 B) tengsizlik yechimga ega emas C) 3
7. (an ) arifmetik progressiyaning dastlabki o‘n D) 1
ikkita hadining yig‘indisi 432 ga teng. Agar
a9 − a5 = 16 bo‘lsa, to‘rtinchi hadini toping.
15. Magazinda birinchi kuni 76% tarvuz sotildi.
A) 26 B) 22 C) 24 D) 28 Ikkinchi kuni esa qolgan 54 ta tarvuz sotildi.
Birinchi kuni nechta tarvuz sotilgan?
8. ABCD parallelogrammning uchlari
A (−2; 6; −9), B (−12; 6; 5) va C (4; 6; 5) A) 168 B) 171 C) 176 D) 163
−−→
nuqtalar bo‘lsa, BD vektorning koordinatalari
yig‘indisini toping. 2 3
16. f (x) = 3 + 3 + 14 funksiyaning
A) 16 B) −12 C) 12 D) −16 (x − 2) x
kamayish oraliqlarini aniqlang.
9. Agar ABC uchburchakning tomonlari
AB : AC : BC = 5 : 3 : 4 nisbatda bo‘lsa, A) (0; 2) ∪ (2; ∞)
uchburchakning qaysi burchagi eng katta B) (−∞; 0) ∪ (0; 2) ∪ (2; ∞)
bo‘ladi?
C) (−∞; 0) ∪ (2; ∞)
A) ∠ ACB B) ∠ ABC
D) (−∞; 0) ∪ (0; 2)
C) aniqlab bo‘lmaydi D) ∠ BAC



1
T-108 Matematika(8001088) - Sotish taqiqlanadi!

lg 3+lg 5
17. Beshta bir xil qog‘ozchaning har biriga quyidagi 24. Hisoblang: 5 lg 25−lg 5
harflardan biri takrorlanmasdan yozilgan: A, A) 10 B) 5 C) 1 D) 15
T, N, S, O. Qog‘ozchalar qutiga solingan va
yaxshilab aralashtirilgan. Qutiga qaramasdan
25. Ifodani soddalashtiring:
bittalab olingan va olingan tartibda o‘qilganda √ √ −1  √ 
4
m−4 4
m+4 44m
SON so‘zi hosil bo‘lish ehtimolligini toping. √ −√ · √
1 1 1 1
4
m+4 4
m−4 4
m−4
A) B) C) D) √
40 30 120 60
4
m+4 √
A) − B) − 4 m − 4
18. Hisoblang: 4 √
7, 16 · (8, 21 − 6, 18) + 12, 84 · (7, 81 − 5, 78) √ 4
m+4
C) −4 ( m + 4) D)
4
4
A) 42,8 B) 21,4 C) 20,3 D) 40,6
√
3
√3
x4 − 9 x2 − 4 26. y = −3x + 7 chiziqli funksiyaning ordinatalar
√
19. 3 − √ = 7 tenglamaning ildizlari
x2 − 3
3
x+2 o‘qiga nisbatan simmetrigini toping.
yig‘indisini toping. A) y = 3x + 7 B) y = −3x + 7
A) 7 B) 8 C) 19 D) −1 C) y = 3x − 7 D) y = −3x − 7
20. f (x) = (x − 3)2 + 5 parabola uchining
koordinatalari yig‘indisini toping. 25
27. Radiusi bo‘lgan sferaga balandligi 8 ga teng
A) 8 B) −8 C) 2 D) −2 4
bo‘lgan konus ichki chizilgan. Konusning
21. A = {x| x ≥ 2, x ∈ Z}, B = {x| x < 8, x ∈ Q}
hajmini toping.
bo‘lsa, A ∩ B to‘plamning elementlari sonini
aniqlang. A) 144π B) 96π C) 72π D) 192π
A) 8 B) 7 C) ∞ D) 6 1 √
 √ −2x 2a− 6 −
3
ab 3
22. 9−4x−3 = 91,5 · 9 3 tenglamani yeching. 28. 2 1 √ +√
3
ifodaning a = 64,
a3 b3 − 2 a 6 a
A) 3 B) −3 C) −2 D) 2
b = 0, 4 dagi qiymatini toping.
23. y = f (x) funksiya grafigidan foydalanib, (−2; 6) 1 1 2 1
oraliqda f (x) · f  (x) = 0 tenglamaning barcha A)
2
B)
6
C)
5
D)
3
yechimlari to‘plamini toping.
29. A aralashmaning bir kilogrammi 12000 so‘m, B
y
aralashmaning bir kilogrammi 18000 so‘m. A
3
va B aralashmalardan mos ravishda 4:1
x)
f(




nisbatda tayyorlangan 1 kg aralashmaning
=
y




narxini (so‘m) aniqlang.
1
4 A) 12800 B) 13200 C) 14200 D) 14800
x
−3 −2 −1 0 1 2 3 5 6
−1 30. Ikki natural sonning EKUKi va EKUBi mos
ravishda 420 va 35 ga teng bo‘lsa, ularning
A) {−1; 3; 5} B) {−1; 2; 3; 4; 5} ko‘paytmasi 352 dan necha marta katta?
C) {−1; 1; 3; 4; 5} D) {−1; 0; 2; 3; 5}
A) 16 B) 10 C) 15 D) 12




2


Matematika(8001112) - Sotish taqiqlanadi! T-108

MATEMATIKA
 
1. f (x) = 13x5 + 6x3 − 27 funksiya berilgan  √ √  π π
10. A = − 3; 3 , B = − ; va
bo‘lsa, f (f (x)) funksiyaning darajasi toping.  2 2
√ 
A) 25 B) 10 C) 15 D) 9 √ 7
C = − 5; bo‘lsa, (A ∪ B) ∩ C to‘plamni
2
2. Qisqarmaydigan oddiy kasrning maxraji
aniqlang.
suratidan 3 birlikka katta. Agar kasrning  
π π  √ √ 
suratiga 1, maxrajiga 2 qo‘shilsa, hosil bo‘lgan A) − ; B) − 5; 3
2 2 2 
kasrning qiymati ga teng bo‘ladi. Berilgan √ 
3  √ √  √ 7
C) − 3; 3 D) − 3;
kasrning maxraji quyidagi sonlardan qaysi 2
biriga qoldiqsiz bo‘linadi?  √ 2 √
A) 5 B) 3 C) 8 D) 6 11. Hisoblang: 11 − 6 2 − 2 + 2 2.
√
3. Bir nuqtadan tekkislikka ikkita og‘ma A) 3 B) 1 C) 4 D) −2 2
o‘tkazilgan. Og‘malarning uzunliklari 17:10 12. a sonining 24%i 108 ning 18%iga teng bo‘lsa,
kabi nisbatda va ularning mos ravishda a ni toping.
proyeksiyalari esa 5:2 nisbatda. Agar og‘malar A) 72 B) 88 C) 76 D) 81
va ularning proyeksiyalari uzunliklari natural
13. 4x · ln 3xdx integralni hisoblang.
sonlar bo‘lsa, quyidagi sonlardan qaysi biri
berilgan nuqtadan tekislikkacha bo‘lgan A) 2x2 ln 3x − 2x2 + C
masofaning uzunligi bo‘la oladi?
B) 4x2 ln 3x − 2x2 + C
A) 7 B) 6 C) 9 D) 8
C) x2 ln 3x − 2x2 + C
4. Hisoblang:
12, 4 : 3, 1 + (1, 2 · 8, 5 − 6, 3 · 2, 8) : 0, 3. D) 2x2 ln 3x − x2 + C
14. 3 ta turli lavozimga nomzodlari ko‘rsatilgan 5
A) −16, 6 B) −18, 6 C) −20, 8 D) −24, 8
kishidan 3 kishini necha xil usul bilan saylash
mumkin?
5. (7; −12) nuqtaning ordinatalar o‘qiga nisbatan A) 70 B) 60 C) 56 D) 64
simmetrik bo‘lgan nuqtasini toping.
15. x2 + ax = 1 tenglamaning x1 va x2 ildizlari
A) (−7; −12) B) (−7; 12) C) (12; −7) x1 x2
D) (7; 12) + = −18 tenglikni qanoatlantirsa,
x2 x1
6. Piramida asosining diagonallari soni a2 − 2 ning qiymatini toping.
piramidaning qirralar soniga teng. A) 34 B) 14 C) 2 D) 7
Piramidaning yoqlari soni bilan uchlari soni 16. −1, 25 soniga qarama-qarshi bo‘lgan sonning
yig‘indisini toping. teskarisi 0, 1 dan qanchaga katta?
A) 8 B) 16 C) 14 D) 12 A) 0,7 B) 0,4 C) 0,3 D) 1,15
7. Tengsizlikni yeching: 17. Agar sin4 x − cos4 x = m bo‘lsa, cos2 x ni m
25log5 (x−2) + (x − 2)2 > 32. orqali ifodalang.
A) (−∞; −2) ∪ (6; ∞) B) (6; ∞) m−1 1−m 1+m
A) B) C)
C) (2; 6) ∪ (6; ∞) D) (2; 6) 2 2 2
m+1
8. Soddalashtiring: D) −
2
sin(log 2 3 + log3 2) + sin(log2 3 − log3 2)
− 18. Ko‘paytuvchilarga ajrating: (a + b)2 − c2
sin(log2 3 − log3 2) − sin(log2 3 + log3 2)
2 tg log3 2 − tg log2 3 A) (a + b − c) · (a + b + c)
− .
tg log3 2 B) (a − b − c) · (a + b + c)
A) 1 B) −2 C) −1 D) 0 C) (a + b − c) · (a − b − c)
D) (a + b − c) · (a − b + c)
9. Arifmetik progressiyaning dastlabki o‘n ikkita 19. 43 · 47 · 28 · 32 − 18 · 63 · 27 ayirma qanday
hadining yig‘indisi 168 bo‘lsa, a5 + a8 ni toping. raqam bilan tugaydi?
A) 28 B) 13 C) 56 D) 14 A) 6 B) 8 C) 4 D) 2


1
T-108 Matematika(8001112) - Sotish taqiqlanadi!

20. f (x) = 3x + b funksiya b ning qanday 26. x2 − 5x − 4 · x2 − 5x + 3 − 8 = 0
qiymat(lar)ida toq funksiya bo‘ladi? tenglamaning haqiqiy ildizlari yig‘indisini
A) b = 2n − 1, n ∈ N B) b < 0 C) b = 0 toping.
D) b > 0 A) 4 B) 1 C) 5 D) 10
27. To‘g‘ri
√ burchakli uchburchakning katta kateti
21. Agar qo‘shni burchaklar ayirmasi 12◦ bo‘lsa,
4 2 ga teng, kichik kateti gepotenuzasidan
shu burchaklardan kattasinining gradus
3 marta kichik. Uchburchakka ichki chizilgan
o‘lchovini aniqlang.
aylananing uzunligini toping.
A) 84◦ B) 72◦ C) 96◦ D) 108◦ √ √
A) 2 2 − 1 π B) 4 2 − 1 π
√ √
22. y = x3 − x2 − x − 2 funksiya Ox o‘qi bilan C) 4 2 + 1 π D) 2 2 2 + 1 π
kesishgan burchak tangensini toping. 3x − p
28. = 0 tenglama yechimga ega bo‘ladigan
A) 6 B) 5 C) 7 D) 4 x−2
p ning barcha qiymatlarini toping.
x2 − 3x + 4 A) (0; 9) ∪ (9; ∞) B) (−∞; 9) ∪ (9; ∞)
23. ≤ 0 tengsizlikning natural
x2 − 10 · (x − 1) C) (9; ∞) D) (0; 2) ∪ (2; ∞)
yechimlari yig‘indisini toping.
29. m2 − n−1 m + n−2 m−1 + n − m (mn)−2
A) 3 B) 6 C) 4 D) 5 3
ifodaning m = , n = 0, (4) dagi qiymatini
4 3 3 4
24. −x3 · x2 : −x5 ifodaning x = −2 dagi toping.
qiymatini toping. 3
A) 8 B) −8 C) 0, 5 D) −4 A) 0,25 B) 4 C) 1 D) 1
4
25. y = f (x) funksiya grafigidan foydalanib, (−2; 6) 30. Rasmda markazi O nuqtada bo‘lgan aylanaga
oraliqda f (x) · f  (x) = 0 tenglamaning barcha A nuqtadan AB urinma o‘tkazilgan. AO kesma
yechimlari to‘plamini toping. aylanani C nuqtada kesib o‘tadi. Agar
aylananing kichik BC yoyi uzunligi 3 ga va
y
radiusi 4 ga teng bo‘lsa, AC ni toping.
A
3
x)




B C
f(
=
y




1
4 O
x
−3 −2 −1 0 1 2 3 5 6
−1

A) {−1; 0; 2; 3; 5} B) {−1; 3; 5} A) 4 cos 0, 75 B) 4(1 − cos 0, 75)
C) {−1; 2; 3; 4; 5} D) {−1; 1; 3; 4; 5} 5 4
C) − 4 D) −4
cos 0, 75 cos 0, 75




2


Matematika(8001136) - Sotish taqiqlanadi! T-108

MATEMATIKA
 3
512 · 24  −3 −5 11. Rasmda berilgan ABC uchburchakda AD
1. Hisoblang:  2 · 2−4 ·4 bissektrisa. Agar ∠ADC = 113◦ bo‘lsa, B
7
2 · 128
burchak C burchakdan necha gradusga katta?
1 B
A) 8 B) 4 C) D) 1
2
2. Ikkita natural sonning yig‘indisi 15 ga teng D
bo‘lsa, ularning ko‘paytmasi quyidagi sonlardan
qaysi biriga teng bo‘lishi mumkin?
A) 36 B) 35 C) 34 D) 37
  A C
2x − x2 − 4 (x + 3)
3. > 0 tengsizlikni yeching. A) 46◦ B) 67◦ C) 23◦ D) 47◦
x2 − 9
A) (2; 3) B) (−∞; 2) ∪ (2; 3) C) (−∞; 3) 12. Hisoblang:
5
D) (−∞; −3) ∪ (−3; 3) (0, (2) + 3, 6 (1)) : 1 − 1, 91 (6) + 42, 5.
6
4. Ma’lum bir ishni birinchi ishchi 18 soatda, A) 0, 5 B) −3, 5 C) 3, 5 D) −0, 5
ikkinchi ishchi 24 soatda bajaradi. Agar shu
13. Qirralari 2 dm, 3 dm va 4 dm bo‘lgan to‘g‘ri
ishni birinchi ishchi 3 soat ishlaganidan keyin
burchakli parallelepiped shaklidagi quti ichiga
unga ikkinchi ishchi qo‘shilib 4 soat birgalikda
eng ko‘pi bilan qirrasi 7 cm bo‘lgan kublardan
ishlasa, ishning qancha qismi bajarilmay
nechtasini joylashtirish mumkin?
qoladi?
2 5 4 2 A) 45 B) 40 C) 69 D) 42
A) B) C) D) 14. Agar log20 250 = m bo‘lsa, log2 5 ni m orqali
3 8 9 9
ifodalang.
x2 − x 6 2m − 1 1 − 3m 1 − 2m
5. f (x) = va g(x) = + 5 berilgan. A) B) C)
2 x−5 m−3 m−2 m−3
Agar a = f (5), b = g(6) bo‘lsa, quyidagi 2m − 3
tengsizlikalardan qaysi biri to‘g‘ri? D)
m−2
A) 10a<9b B) 12a<11b C) 9a<8b −−→
D) 13a>12b 15. ABCD parallelogramm uchun AB (3; 5; −7) va
−−→
AD (−11; 7; 3). Parallelogramm
6. Hisoblang:
diagonallarining keshishgan nuqtasi O bo‘lsa,
−2019 + 2019 − 2019
 + ... + 2019 − 2019 −→
OA vektorning koordinatalari yig‘indisini
2019 ta
toping.
A) 0 B) −2019 C) 2019 D) 2018
A) 0 B) −1 C) 2 D) 1
7. 540 soni 25%ga oshirildi. Hosil bo‘lgan sonning  x+1 
20%ini toping. 7 − 1 · (2x − 4)
16. > 0 tengsizlikni yeching.
x−2
A) 125 B) 135 C) 130 D) 155
8. f (x) = (x − 3)2 + 1 parabola uchining A) (2; +∞)
koordinatalari ko‘paytmasini toping. B) (−1; 2) ∪ (2; +∞)
A) −3 B) 4 C) −2 D) 3 C) (−1; +∞)
2 D) (−∞; −1) ∪ (2; +∞)
9. Agar sin α = bo‘lsa,
5 17. Agar A = {x| x = 4n, n ∈ N },
cos6 α − 3 cos4 α + 3 cos2 α + sin6 α − 1 ning
B = {x| x = 4n + 2, n ∈ N } bo‘lsa, A ∪ B
qiymatini toping.
to‘plamni aniqlang.
A) 0 B) −1 C) 1 D) −2
2  2 6 A) {x| x = 4n, n ∈ N }
10. Integralni hisoblang: x − 1 · xdx B) {x| x = 2n, n ∈ N }
−1
A) 36 · 14−1 B) 37 · 14−1 C) 37 · 7−1 C) {x| x = 2n + 2, n ∈ N }
D) 36 · 7−1 D) {x| x = 4n − 2, n ∈ N }


1
T-108 Matematika(8001136) - Sotish taqiqlanadi!

18. Cheksiz kamayuvchi
√  geometrik progressiyaning
√ 24. (x + 1) · (|x| − 1) = 3 tenglama nechta haqiqiy
yig‘indisi 9 3 + 1 ga, birinchi hadi 6 3 ga ildizga ega?
teng. Uning uchinchi hadini toping. A) 0 B) 1 C) 4 D) 2
√ √ √
A) 6 B) 3 3 C) 3 D) 2 3
19. ABCD parallelogrammning BC, CD 25. Oltiburchakli prizmada nechta turli diagonal
tomonlarida mos ravishda yotuvchi M , o‘tkazish mumkin?
N nuqtalar BC : M C = 5 : 3 va A) 12 B) 18 C) 24 D) 9
DC : N C = 3 : 1 shartlarni qanoatlantiradi.
Agar parallelogrammning yuzi 35 ga teng 26. Ifodani soddalashtiring (a > 0):
2 a−1 1 1
bo‘lsa, BM N D to‘rtburchakning yuzini toping. √ ·√ ·√ ·√
16
a+1 8
a+1 4
a+1 a+1
A) 14 B) 12 C) 15 D) 16 √  2  √
A) 2 ( a − 1) B) 2 a − 1
16
C) 16 a − 1
20. O‘tmas burchagi α ga teng rombga ichki √
D) 16 a + 1
chizilgan aylananing uzunligi L ga teng bo‘lsa,
rombning yuzasini toping.  2
27. x2 − 7x + 13 − (x − 3) · (x − 4) − 3 = 0
L2 L2 2L2 tenglamaning haqiqiy ildizlari ko‘paytmasini
A) 2 B) C) · cos α
π sin α 2πsin2 α π2 toping.
L2
D) 2 · sin α A) 49 B) 14 C) 11 D) 154
π
21. Ifodani soddalashtiring: (x + 8)4 + (x − 6)4
28. f (x) = funksiyaning eng
4a2 − 16a + 16 (a − 2)2 2
:
a+3 −a2 + 9 kichik qiymatini toping.
A) 6 − 2a B) 2a − 12 C) 12 − 4a 84 + 64
A) B) 84 C) 74 D) 64
D) 4a − 12 2
22. Tekislikda ixtiyoriy uchtasi bitta to‘g‘ri chiziqda
yotmaydigan A, B, C, D, M va N nuqtalarni 29. f (x) = (x − 1)20 · (cos x + sin x) funksiyaning
uchburchaklarning uchlari deb hisoblasak, x0 = 0 nuqtadagi hosilasini toping.
nechta uchburchakda B nuqta qatnashadi? A) −19 B) 20 C) 19 D) −20
A) 10 B) 9 C) 12 D) 15
1
4 3π 30. (2x − 3)2 − 4 (2 − x)2 − 3 x − 1 ifodaning
23. Agar sin α = − va α ∈ ; 2π bo‘lsa, 3
5 2 2
α x= dagi qiymatini toping.
sin2 ning qiymatini toping. 3
2 1 1
A) 0,4 B) 0,8 C) 0,1 D) 0,2 A) 2 B) −1 C) −2 D) −3
3 3




2


Matematika(8001160) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. Quyida berilgan sonlardan eng kattasini toping. 2 3
8. f (x) = 3 + + 14 funksiyaning
47 7 23 5 (x − 2) x3
A) B) C) D) kamayish oraliqlarini aniqlang.
72 12 36 9
A) (0; 2) ∪ (2; ∞)
2. Toza suvga tuz aralashtirilgandan so‘ng massasi
850 gramm bo‘ldi. Agar tuzning massasi toza B) (−∞; 0) ∪ (0; 2) ∪ (2; ∞)
suvning massasidan 75% ga kam bo‘lsa, toza C) (−∞; 0) ∪ (0; 2)
suvning massasi necha gramm bo‘lgan?
D) (−∞; 0) ∪ (2; ∞)
A) 640 B) 660 C) 680 D) 620
9. Merganning nishonga tekkizish ehtimoli 0,8 ga
 (x − 2)dx teng. U nishonga 3 marta o‘q uzganda barcha
3. 2 integralni hisoblang.
x − 4x + 17 o‘qlari nishonga tegishining ehtimolligini
 2
A) ln  x2 − 4x + 17 + C toping.
B) ln x2 − 4x + 17 + C A) 0,512 B) 0,912 C) 0,72 D) 0,8
√
C) ln x2 − 4x + 17 + C
 −2
D) ln x2 − 4x + 17 +C 10. Mis, rux va qo‘rg‘oshindan iborat bo‘lgan
15 kg li qotishmaning tarkibida 20% mis bo‘lib,
4. Ifodani soddalashtiring: rux va qo‘rg‘oshinning og‘irliklari mos ravishda
5 (a − b) a2 − b2 5:1 nisbatda. Qotishmadagi ruxning og‘irligi
 2 
2 :
3 a +b (a + b)2 − 2ab misning og‘irligidan necha kilogrammga ko‘p?
5 5 5 A) 7 B) 4,5 C) 5 D) 6
A) B) − C)
3 (a + b) 3 (a + b) 3 (a − b) √
5 11. 5 − 11x − 3x2 ≥ 1 tengsizlikning butun
D) −
3 (a − b) yechimlari sonini toping.
A) 5 B) 3 C) 2 D) 4
5. A = {x| x2 ≤ 64, x ∈ R},
B = {x| x2 > 4, x ∈ N } bo‘lsa, A ∩ B 12. Ixtiyoriy uchtasi bitta to‘g‘ri chiziqda
to‘plamni aniqlang. yotmaydigan A, B, C va D nuqtalar berilgan.
−−
→ −−→
A) {2; 3; 4; 5; 6; 7; 8} B) {3; 4; 5; 6; 7; 8} Agar AB = 0, 8DC bo‘lsa, ABCD to‘rtburchak
C) (2; 8] D) [2; 8] turini aniqlang.
A) kvadrat B) trapetsiya
6. |x − 7| · log2 (x − 2) = 3 · (x − 7) tenglamaning C) parallelogramm D) to‘g‘ri to‘rtburchak
ildizlari yig‘indisini toping.
1 1 1 13. Ushbu  
A) 9 B) 17 C) 17 D) 19
8 8 8 3xyz x−1 y−1 z−1
− + + :
xy + yz + zx  x y z
7. Rasmda tasvirlangan to‘g‘ri prizmaning 1 1 1
: + + ifodaning x = 0, 1; y = 5;z = 8
hajmini (dm3 ) toping. x y z
80cm dagi qiymatini toping.
A) 40 B) 13,1 C) 4 D) 1

14. ABCD trapetsiyaning AB katta asosida
cm
140




E nuqta olingan. DE kesma BC yon tomoniga
parallel. Agar BCDE to‘rtburchak yuzining
20cm AED uchburchak yuziga nisbati 6:5 kabi
bo‘lsa, AE:EB nisbatni toping.
50cm 3 5 5 3
A) B) C) D)
A) 169 B) 156 C) 196 D) 182 5 6 3 2



1
T-108 Matematika(8001160) - Sotish taqiqlanadi!

15. Quyidagi jumlalardan qaysilari noto‘g‘ri? 23. Sharga tashqi chizilgan kesik konus asosining
1) agar natural son 6 ga bo‘linsa, u holda 12 ga radiuslari 3 va 6 ga teng. Kesik konus to‘la
ham bo‘linadi; 2) agar natural son 12 ga sirtining shar sirtiga nisbatini toping.
bo‘linsa, u holda 6 ga ham bo‘linadi; 3) agar 7 7 14 14
A) B) C) D)
natural son 12 ga bo‘linmasa, u holda 6 ga ham 4 6 3 9
bo‘linmaydi; 4) agar natural son 6 ga
bo‘linmasa, u holda 12 ga ham bo‘linmaydi. 24. Agar ABC uchburchakning burchaklari
∠A : ∠B : ∠C = 2 : 3 : 4 shartlarni
A) 3, 4 B) 1, 3 C) 1, 2 D) 2, 3
√ qanoatlantirsa, uchburchakning qaysi tomoni
16. f (x) = (2x + 1)5 · x6 + 16 funksiyaning eng katta bo‘ladi?
x0 = 0 nuqtadagi hosilasini toping. A) aniqlab bo‘lmaydi B) AB C) AC
A) 10 B) 40 C) 20 D) 5 D) BC
17. Ifodani soddalashtiring (a > 0):
2 a−1 1 1 25. Tenglamani yeching:   
√ ·√ ·√ ·√ 1, 4 · (2 + 0, 6) · 4 + 0, 62 · 16 + 0, 64 · x =
16
a+1 8
a+1 4
a+1 a+1
√ √ √ 0, 68 − 256
A) 2 ( 16 a −1) B) 16 a − 1 C) 16 a + 1
D) 2 a2 − 1 A) −1 B) 16 − 0, 64 C) 0, 64 − 16 D) 1
 
18. Soatning soat mili 14◦ burilganda minut mili  2 
26. 24x −1 − 5 = 3 tenglama nechta haqiqiy
necha gradus burchakka buriladi?
ildizga ega?
A) 84◦ B) 360◦ C) 720◦ D) 168◦
A) 4 B) 3 C) 2 D) 1
19. Hadlari xn = 4n2 + cn + 2 formula bilan
berilgan ketma-ketlikda x4 − x2 = 52 bo‘lsa, bu 27. Agar a · c < 0 bo‘lsa, y = ax2 + bx + c kvadrat
ketma-ketlikning uchinchi hadini toping. funksiyaning grafigi qaysi choraklarda yotadi?
A) 56 B) 52 C) 44 D) 50 A) I, II va III B) I, II, III va IV
0, 0432 0, 099 0, 128 C) I, III va IV D) II, III va IV
20. Hisoblang: + + .
0, 16 0, 3 0, 008 28. f (x) = (x − 3)2 + 5 parabola uchining
A) 19,57 B) 2,2 C) 16,6 D) 22 koordinatalari yig‘indisini toping.
21. 3 · 92x + 2 · 9x − 1 ≤ 0 tengsizlikni yeching. A) 2 B) 8 C) −2 D) −8

A) (−∞; 2) 29. 0, 009 · 0, 02 · 106 ko‘paytmani standart shaklga
B) (−∞; −0, 5] keltiring.
A) 1, 8 · 10−2 B) 1, 8 · 102 C) 1, 8 · 10
C) [0, 5; +∞)
D) 1, 8 · 10−1
D) (−∞; 2) ∪ [3; +∞)
  30. Soddalashtiring:
1 π
22. Agar sin α = √ va α ∈ 0; bo‘lsa, sin(log2 3 + log3 2) + sin(log2 3 − log3 2)
10 2 −
sin(log2 3 − log3 2) − sin(log2 3 + log3 2)
tg 2α ning qiymatini toping. 2 tg log3 2 − tg log2 3
3 1 3 3 − .
A) B) C) − D) tg log3 2
8 3 4 4
A) −2 B) 1 C) 0 D) −1




2


Matematika(8001184) - Sotish taqiqlanadi! T-108

MATEMATIKA

1. a va b ning qanday qiymatlarida 10. ABCD qavariq to‘rtburchakka aylana ichki
8x − 12 a b chizilgan. Agar AB = 8 va BC = 12 bo‘lsa,
= + tenglik ayniyat
16x2 − 9 4x + 3 4x − 3 CD − AD ayirmani toping.
bo‘ladi? A) 4 B) aniqlab bo‘lmaydi C) 2 D) 3
A) a = 1; b = 3 B) a = −3; b = 1
11. Agar f (x) = kx + 3 funksiya uchun f (2) = −3
C) a = −1; b = −3 D) a = 3; b = −1
munosabat o‘rinli bo‘lsa, f (−2) ni toping.
2. Hisoblang: sin6 1 − 3 sin4 1 + 3 sin2 1 + cos6 1 + 1 A) 6 B) 3 C) 9 D) 0
A) −2 B) 0 C) −1 D) 2 12. Bir nechta natural sonlarning yig‘indisi 47 ga
3. ABCD parallelogrammda C o‘tkir burchak. teng. Agar shu sonlarning har biri 2 ga ortirilib
E nuqta AB tomonda yotadi. yig‘indisi hisoblansa, u 63 ga teng bo‘ladi.
AECD to‘rtburchak yuzining Yig‘indida nechta son qatnashgan?
BCE uchburchak yuziga nisbati 5:2 kabi A) 6 B) 8 C) 7 D) 9
bo‘lsa, AE:EB nisbatni toping.   
3 3 2 4 13. (3x − 2)2 + 3 (3x − 2)3 + 4 (3x − 2)4 ≥ 4
A) B) C) D) tengsizlikning eng katta manfiy butun yechimi
2 4 3 3
bilan eng kichik musbat butun yechimi
4. Uchburchakli piramida asosining ikki tomoni 6 yig‘indisini toping.
va 7 dm bo‘lib, ular orasidagi burchak 45◦ ga
A) 4 B) 1 C) 3
teng. Agar piramidaning 8 dm bo‘lgan yon
D) tengsizlik yechimga ega emas
qirrasi asos tekisligi bilan 30◦ li burchak tashkil
etsa, uning hajmini (dm3 ) toping. 14. Rasmdan foydalanib, ((A ∩ B) ∪ C) ∩ D
√ √ √ √ to‘plamning elementlari sonini toping.
A) 7 2 B) 14 2 C) 28 2 D) 56 2
D
5. Agar qisqarmaydigan kasrning surati 3 ga A B C
6 a d m
orttirilsa, kasrning qiymati ga, maxraji 2 ga c
7 b
l n
e
3
kamaytirilsa, kasrning qiymati ga teng k, p, q
4
7 A) 1 B) 4 C) 0 D) 3
bo‘ladi. Berilgan kasrning qismini toping.
27
15. y = 2x2 − 8x + 11 parabola uchining
1 2 3 1
A) B) C) D) koordinatalari yig‘indisini toping.
6 3 4 12
A) 5 B) 6 C) 7 D) 8
6. Agar x = 10√bo‘lsa, 16. (5; −8) nuqtaning (−4; 9) nuqtaga nisbatan
(4 − x)−1 · x3 − 9x2 + 24x − 16 ifodaning
simmetrik bo‘lgan nuqtasini toping.
qiymatini toping.
A) (−13; 23) B) (−13; 26) C) (−13; 24)
A) −2 B) 3 C) −3 D) 2
D) (−14; 14)
7. 34974 sonning raqamalari joylarini almashtirib 17. (an ) arifmetik progressiyaning dastlabki o‘n
jami nechta har xil 5 xonali son hosil qilish ikkita hadining yig‘indisi 432 ga teng. Agar
mumkin? a9 − a5 = 16 bo‘lsa, to‘rtinchi hadini toping.
A) 120 B) 30 C) 20 D) 60 A) 28 B) 24 D) 22C) 26
1  
8. Agar lg (x + 3) − lg = 1 bo‘lsa, x ni toping. 4 3π
x 18. Agar sin α = − va α ∈ ; 2π bo‘lsa,
5 2
A) 5 B) 2 C) −5 D) −2 α
sin2 ning qiymatini toping.
9. To‘g‘ri to‘rtburchak shaklidagi yer maydonning 2
to‘rtta tomoni 360 m uzunlikdagi devor bilan A) 0,4 B) 0,2 C) 0,1 D) 0,8
o‘ralgan. Bu yer maydonining eng katta yuzasi 19. Hisoblang:
necha m2 bo‘ladi? 139 · 163 − 160 · 139 + 141 · 175 − 172 · 141
A) 81000 B) 8100 C) 32400 D) 3240 A) 870 B) 852 C) 864 D) 840


1
T-108 Matematika(8001184) - Sotish taqiqlanadi!
√   √  
20. Agar x2 − 3−2 x− 4+2 3=0 5x + 6
25. y = ln funksiyaning grafigiga
tenglamaning ildizlari x1 va x2 bo‘lsa, u holda 2x + 15
|x1 − x2 | ni toping. abssissasi x0 = 3 bo‘lgan nuqtadan urinma
√ √ √ √ o‘tkazilgan. Bu urinma va koordinata o‘qlari
A) 2 B) 7 C) 11 D) 3
hosil qilgan uchburchakning yuzini toping.
3 9 9 3
21. f (x) = (sin x + cos x)2 funksiyaning A) B) C) D)
14 14 7 7
boshlang‘ich funksiyasini toping. √ √
26. 2 5+x = 4 · 2 x−3 tenglamaning ildizi x0 bo‘lsa,
1 x20 − 2x0 + 3 ni hisoblang.
A) F (x) = x − cos 2x + C
2 A) 10 B) 12 C) 13 D) 11
1 27. Hisoblang:
B) F (x) = x + cos 2x + C
2 2, 2 + 2, 2 + ... + 2, 2 + 1, 1 + 1, 1 + ... + 1, 1
1 8 ta 16 ta
C) F (x) = −x − cos 2x + C
2 A) 70,4 B) 52,8 C) 17,6 D) 35,2
1 28. Ifodani soddalashtiring:
 
D) F (x) = −x + cos 2x + C
2 9a4 b3 2 c3 d
− · −2 · 3 2
16c3 d2 3 a b
x − 25 x2 − 6 3ab 3a2 b 3ab 3a2 b
22. √ +√ ifodaning x = 6 dagi A) − B) C) D) −
5+ x 6−x 2d 2d 2d 2d
qiymatini toping.
√ 29. Piramida asosining diagonallari soni
A) 1 B) −11 C) −1 D) −2 6 piramidaning qirralar soniga teng.
Piramidaning yoqlari soni bilan uchlari soni
23. Hisoblang:
√ √
√ √ √ yig‘indisini toping.
19 + 2 · 38 + 57 − 6 − 2 A) 12 B) 14 C) 16 D) 8
√ √
3+ 2 30. To‘g‘ri
√ burchakli uchburchakning katta kateti
A) 17 B) 15 C) 19 D) 18 4 2 ga teng, kichik kateti gepotenuzasidan
3 marta kichik. Uchburchakka ichki chizilgan
24. 9, 142 + 2, 76 · 0, 86 − 9, 14 · 6, 38 ni hisoblang. aylananing uzunligini toping.
√   √ 
A) 27,6 B) 8,6 C) 2,76 D) 91,4 A) 4 2 − 1 π B) 2 2 2 + 1 π
√  √ 
C) 2 2 − 1 π D) 4 2 + 1 π




2