Matematika. Milliy sertifikat imtihoniga tayyorgarlik: variantlar to‘plami (2025–2026)

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Matematika. Milliy sertifikat imtihoniga tayyorgarlik: variantlar to‘plami (2025–2026)

Sotib olish

Imtihon tuzilishi va yo'riqnoma
• Imtihon Bilimni baholash agentligi tomonidan an'anaviy (qog'oz) shaklda o'tkaziladi: 45 ta
topshiriq, 150 daqiqa. Har bir variant xuddi shu tuzilishda: 32 ta Y-1, 3 ta Y-2 va 10 ta ochiq
(a/b) topshiriq.
• Ballar: Y-1 — 1,3 yoki 2,2; Y-2 — 2,2; ochiq topshiriq — a) 1,5 + b) 1,7 = 3,2 ball. Yakuniy natija
Rash modeli bo'yicha hisoblanadi; sertifikat uchun kamida 46 ball kerak (C), 70 dan yuqori —
A+.
• Noto'g'ri javob uchun ball ayirilmaydi — barcha topshiriqlarga javob bering. Ochiq
topshiriqlarda kasr javobni qisqarmas kasr ko'rinishida, π li javoblarni π orqali yozing.
• Har bir topshiriq ostida to'g'ri javob yashil rangda berilgan; hujjat oxirida har bir variant uchun
javoblar kaliti bor. Tavsiya: variantni 150 daqiqa ichida javoblarga qaramasdan yeching, so'ng
kalit bilan tekshiring.
• Muhim: rasmiy imtihon savollari ochiq e'lon qilinmaydi. Bu to'plam rasmiy spetsifikatsiya
(topshiriq turlari va mazmun sohalari) asosida tuzilgan mashq variantlaridir. Barcha hisoblash
javoblari dastur yordamida tekshirilgan. Imtihon tartibidagi o'zgarishlarni uzbmb.uz da kuzatib
boring.
Har bir variant tuzilishi
Topshiriqlar Turi Izoh
1–32 Y-1 (yopiq) To'rt variantdan bitta to'g'ri javobni tanlang
33–35 Y-2 (moslashtirish) Chap ustundagi 4 ta ifodani o'ng ustundagi 6 ta
qiymatdan mosiga juftlang
36–45 O (ochiq) a) va b) bandlarga qisqa javobni o'zingiz yozasiz; faqat
yakuniy javob baholanadi
Matematika — milliy sertifikat mashq variantlari | 2

Mundarija
№ Variant Topshiriqlar
1 1-variant 1–45
2 2-variant 46–90
3 3-variant 91–135
4 4-variant 136–180
5 5-variant 181–225
6 6-variant 226–270
7 7-variant 271–315
8 8-variant 316–360
9 9-variant 361–405
10 10-variant 406–450
11 11-variant 451–495
12 12-variant 496–540
13 13-variant 541–585
14 14-variant 586–630
15 15-variant 631–675
16 16-variant 676–720
17 17-variant 721–765
18 18-variant 766–810
19 19-variant 811–855
20 20-variant 856–900
21 21-variant 901–945
22 22-variant 946–990
23 23-variant 991–1035
Jami topshiriqlar 1035
Javoblar kaliti (hujjat oxirida)
Matematika — milliy sertifikat mashq variantlari | 3

1-variant
Y-1 • bitta to'g'ri javob
1. Silindr hajmi formulasi qaysi?
A) V = 2πrh
B) V = πr²h
C) V = 1/3 · πr²h
D) V = 4/3 · πr³
To'g'ri javob: B) V = πr²h✔
2. Uchburchak yuzini toping.
Asosi 4, unga tushirilgan balandlik 10
A) 20
B) 40
C) 14
D) 21
To'g'ri javob: A) 20
✔
3. Tenglamalar sistemasini yeching va x + y ni toping.
{ 2x + 4y = 30; 3x − 2y = -19 }
A) -8
B) 9
C) 7
D) -9
To'g'ri javob: C) 7
✔
4. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 4, q = 3, n = 5
A) 488
B) 481
C) 324
D) 484
To'g'ri javob: D) 484
✔
5. EKUKni toping.
EKUK(73; 73)
A) 146
B) 73
C) 5329
D) 74
To'g'ri javob: B) 73
✔
6. log₃81 ni hisoblang.
A) 3
B) 27
C) 4
D) 5
To'g'ri javob: C) 4
✔
Matematika — milliy sertifikat mashq variantlari | 4

7. Trapetsiya yuzini toping.
Asoslari 15 va 8, balandligi 3
A) 69
B) 69/2
C) 360
D) 75/2
To'g'ri javob: B) 69/2✔
8. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 7, d = -4, n = 17
A) -429
B) -57
C) -442
D) -425
To'g'ri javob: D) -425
✔
9. Hisoblang.
1/12 + 3/12
A) 1/48
B) 1/6
C) 49/144
D) 1/3
To'g'ri javob: D) 1/3
✔
10. (4^4)^3 ni hisoblang.
A) 16777217
B) 16384
C) 16777216
D) 768
To'g'ri javob: C) 16777216
✔
11. Tenglama ildizlari yig'indisini toping.
|x + 3| = 8
A) 8
B) 6
C) 5
D) -6
To'g'ri javob: D) -6
✔
12. Hisoblang.
√64 + √169
A) 20
B) 15
C) 21
D) 104
To'g'ri javob: C) 21
✔
Matematika — milliy sertifikat mashq variantlari | 5

13. Tenglamalar sistemasini yeching va x + y ni toping.
{ x + 3y = 18; 2x − 3y = -36 }
A) -14
B) 2
C) -48
D) 4
To'g'ri javob: B) 2✔
14. Vektor uzunligini toping.
(-9; 12)
a⃗
A) 15
B) 16
C) 3
D) 21
To'g'ri javob: A) 15
✔
15. Hisoblang.
√121 + √196
A) 154
B) 25
C) 24
D) 17
To'g'ri javob: B) 25
✔
16. Ifodaning qiymatini toping.
log₃3 + log₃81
A) 5
B) 4
C) 243
D) 6
To'g'ri javob: A) 5
✔
17. Hisoblang.
6/3 + 7/10
A) 27/10
B) 1
C) 41/15
D) 7/5
To'g'ri javob: A) 27/10
✔
18. Tengsizlikning butun yechimlari sonini toping.
x² + 8x + 15 < 0
A) 2
B) 0
C) 3
D) 1
To'g'ri javob: D) 1
✔
Matematika — milliy sertifikat mashq variantlari | 6

19. f'(x₀) ni toping.
f(x) = 3x³ + x² + x − 1, x₀ = 4
A) 211
B) 152
C) 153
D) 155
To'g'ri javob: C) 153✔
20. Ifodaning qiymatini toping.
5^3 · 5^4 : 5^2
A) 3130
B) 9765625
C) 3125
D) 78125
To'g'ri javob: C) 3125
✔
21. Ifodaning qiymatini toping.
tg 45° + sin 0°
A) 2
B) 0
C) 1
D) 3
To'g'ri javob: C) 1
✔
22. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 4, q = 3, n = 6
A) 1453
B) 972
C) 1460
D) 1456
To'g'ri javob: D) 1456
✔
23. Tenglama ildizlari yig'indisini toping.
x² − 7x + 10 = 0
A) 8
B) 10
C) -7
D) 7
To'g'ri javob: D) 7
✔
24. EKUKni toping.
EKUK(14; 43)
A) 602
B) 1
C) 1204
D) 616
To'g'ri javob: A) 602
✔
Matematika — milliy sertifikat mashq variantlari | 7

25. Uchburchakning ikki burchagi 74° va 40°. Uchinchi burchagini toping.
A) 76°
B) 66°
C) 114°
D) 246°
To'g'ri javob: B) 66°✔
26. Trapetsiya yuzini toping.
Asoslari 3 va 12, balandligi 7
A) 252
B) 119/2
C) 105
D) 105/2
To'g'ri javob: D) 105/2
✔
27. (a + b)² nimaga teng?
A) a² + b²
B) a² + 2ab + b²
C) a² − 2ab + b²
D) 2a + 2b
To'g'ri javob: B) a² + 2ab + b²
✔
28. cos 180° ning qiymatini toping.
A) √3/2
B) 2
C) −1
D) 0
To'g'ri javob: C) −1
✔
29. Tenglamaning katta ildizini toping.
x² − 2x − 15 = 0
A) 5
B) -5
C) 6
D) -3
To'g'ri javob: A) 5
✔
30. Tenglama ildizlari yig'indisini toping.
x² + 3x − 54 = 0
A) 3
B) -3
C) -54
D) -2
To'g'ri javob: B) -3
✔
31. Ehtimollikni toping.
Qutida 3 ta oq va 2 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 3/5
B) 1/5
C) 2/5
D) 3/2
To'g'ri javob: A) 3/5
✔
Matematika — milliy sertifikat mashq variantlari | 8

32. Trapetsiya yuzini toping.
Asoslari 9 va 12, balandligi 7
A) 756
B) 147/2
C) 161/2
D) 147
To'g'ri javob: B) 147/2✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) 8/6 + 8/3 a) 4/3
2) 3/2 + 8/9 b) 26/15
3) 9/4 + 5/7 c) 4
4) 7/5 + 4/12 d) 83/28
e) 29/22
f) 43/18
A) 1–b, 2–f, 3–c, 4–d
B) 1–c, 2–d, 3–f, 4–b
C) 1–c, 2–f, 3–a, 4–b
D) 1–c, 2–f, 3–d, 4–b
To'g'ri javob: D) 1–c, 2–f, 3–d, 4–b
✔
34. Har bir ifodaga uning qiymatini moslang.
1) √25 + √144 a) 6
2) √49 + √49 b) 13
3) √196 + √16 c) 18
4) √196 + √121 d) 17
e) 25
f) 14
A) 1–d, 2–f, 3–a, 4–e
B) 1–d, 2–a, 3–c, 4–e
C) 1–d, 2–b, 3–c, 4–e
D) 1–d, 2–f, 3–c, 4–e
To'g'ri javob: D) 1–d, 2–f, 3–c, 4–e
✔
35. Har bir ifodaga uning qiymatini moslang.
1) log₃81 + log₃9 a) 7
2) log₃3 + log₃81 b) 6
3) log₂2 + log₂2 c) 5
4) log₃9 + log₃9 d) 2
e) 3
f) 4
Matematika — milliy sertifikat mashq variantlari | 9

$A) 1–b, 2–c, 3–d, 4–e B) 1–d, 2–b, 3–f, 4–c C) 1–f, 2–c, 3–d, 4–b D) 1–b, 2–c, 3–d, 4–f To'g'ri javob: D) 1–b, 2–c, 3–d, 4–f✔ O • ochiq topshiriq (qisqa javob) 36. Ko'rsatkichli tenglamani yeching. Javobni yozing. a) 5^(x − 3) = 125 b) 3^(x − 4) = 27 Javob: a) 6; b) 7 ✔ 37. Trapetsiya yuzini toping. Javobni yozing. a) Asoslari 8 va 3, balandligi 9 b) Asoslari 12 va 9, balandligi 10 Javob: a) 99/2; b) 105 ✔ 38. Vektorlarning skalyar ko'paytmasini toping. Javobni yozing. a) (-4; 4), (6; 6) a⃗ b ⃗ b) (-6; 6), (3; -2) a⃗ b ⃗ Javob: a) 0; b) -30 ✔ 39. Trapetsiya yuzini toping. Javobni yozing. a) Asoslari 4 va 8, balandligi 5 b) Asoslari 13 va 11, balandligi 10 Javob: a) 30; b) 120 ✔ 40. f'(x₀) ni toping. Javobni yozing. a) f(x) = 3x³ + x² − 5x + 9, x₀ = 0 b) f(x) = 2x³ + 3x² − 4x + 5, x₀ = -2 Javob: a) -5; b) 8 ✔ 41. f'(x₀) ni toping. Javobni yozing. a) f(x) = 2x³ + 4x² + 4x − 3, x₀ = 0 b) f(x) = 2x³ + x² + 5x + 7, x₀ = 3 Javob: a) 4; b) 65 ✔ 42. EKUBni toping. Javobni yozing. a) EKUB(23; 15) b) EKUB(79; 40) Javob: a) 1; b) 1 ✔ 43. Ifodaning qiymatini toping. Javobni yozing. a) log₃3 + log₃9 b) log₅625 + log₅125 Javob: a) 3; b) 7 ✔ 44. Tenglamalar sistemasini yeching va x + y ni toping. Javobni yozing. a) { x + 4y = -35; 4x − 2y = 4 } b) { x + 2y = 3; 4x − 3y = -21 } Javob: a) -11; b) 0 ✔ Matematika — milliy sertifikat mashq variantlari | 10$

45. Ifodaning qiymatini toping. Javobni yozing.
a) cos 180° + sin 90°
b) cos 60° + sin 30°
Javob: a) 0; b) 1✔
Matematika — milliy sertifikat mashq variantlari | 11

2-variant
Y-1 • bitta to'g'ri javob
1. Tenglamalar sistemasini yeching va x + y ni toping.
{ 3x + 2y = 16; 2x − 2y = -6 }
A) 9
B) -3
C) 10
D) 7
To'g'ri javob: D) 7✔
2. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 6, 4, 3
A) 78
B) 108
C) 13
D) 72
To'g'ri javob: D) 72
✔
3. Ifodaning qiymatini toping.
log₅125 + log₅625
A) 7
B) 78125
C) 12
D) 8
To'g'ri javob: A) 7
✔
4. tg 45° ning qiymatini toping.
A) 1
B) √3/2
C) √2/2
D) 2
To'g'ri javob: A) 1
✔
5. A va B nuqtalar orasidagi masofani toping.
A(-4; 2), B(-12; -13)
A) 23
B) 19
C) 7
D) 17
To'g'ri javob: D) 17
✔
6. Radiusi 5 ga teng aylananing uzunligini toping.
A) 10π
B) 20π
C) 5π
D) 25π
To'g'ri javob: A) 10π
✔
Matematika — milliy sertifikat mashq variantlari | 12

7. EKUBni toping.
EKUB(81; 54)
A) 135
B) 54
C) 162
D) 27
To'g'ri javob: D) 27✔
8. Ifodaning qiymatini toping.
cos 0° + sin 0°
A) 0
B) 1
C) −1
D) 2
To'g'ri javob: B) 1
✔
9. (ln x)' hosilasi nimaga teng?
A) ln x
B) x
C) eˣ
D) 1/x
To'g'ri javob: D) 1/x
✔
10. Tenglama ildizlari yig'indisini toping.
|x + 7| = 5
A) -2
B) 14
C) -14
D) 5
To'g'ri javob: C) -14
✔
11. A va B nuqtalar orasidagi masofani toping.
A(-3; -1), B(-8; -13)
A) 17
B) 7
C) 15
D) 13
To'g'ri javob: D) 13
✔
12. Shar sirti yuzi formulasi qaysi?
A) S = 4/3 · πr³
B) S = πr²
C) S = 4πr²
D) S = 2πr
To'g'ri javob: C) S = 4πr²
✔
Matematika — milliy sertifikat mashq variantlari | 13

13. Aniq integralni hisoblang.
∫₀^1 (2x − 1) dx
A) 0
B) 3
C) 1
D) 2
To'g'ri javob: A) 0✔
14. Tenglamaning katta ildizini toping.
x² − 9x + 8 = 0
A) -8
B) 8
C) 9
D) 1
To'g'ri javob: B) 8
✔
15. Masalani yeching.
Mahsulot narxi 3700 so'm edi. Narx 30% ga oshirildi. Yangi narx necha so'm?
A) 4810
B) 2590
C) 3730
D) 1110
To'g'ri javob: A) 4810
✔
16. Uchburchak yuzini toping.
Asosi 9, unga tushirilgan balandlik 17
A) 153/2
B) 153
C) 26
D) 155/2
To'g'ri javob: A) 153/2
✔
17. Ifodaning qiymatini toping.
cos 60° + cos 180°
A) −1/2
B) −3/2
C) −5/2
D) 3/2
To'g'ri javob: A) −1/2
✔
18. Hisoblang.
7/10 + 9/4
A) 119/40
B) 8/7
C) 63/40
D) 59/20
To'g'ri javob: D) 59/20
✔
Matematika — milliy sertifikat mashq variantlari | 14

19. EKUKni toping.
EKUK(58; 56)
A) 2
B) 3248
C) 1624
D) 1682
To'g'ri javob: C) 1624✔
20. Ifodaning qiymatini toping.
log₃27 + log₃3
A) 3
B) 5
C) 81
D) 4
To'g'ri javob: D) 4
✔
21. O'rinlashtirishlar sonini toping.
A(8; 2)
A) 28
B) 8
C) 64
D) 56
To'g'ri javob: D) 56
✔
22. Aylana uzunligini toping (π orqali).
Radius R = 2
A) 2π
B) 8π
C) 5π
D) 4π
To'g'ri javob: D) 4π
✔
23. Hisoblang.
2/3 + 4/7
A) 26/21
B) 9/7
C) 3/5
D) 8/21
To'g'ri javob: A) 26/21
✔
24. Ifodaning qiymatini toping.
3^6 · 3^4 : 3^5
A) 246
B) 243
C) 1162261467
D) 59049
To'g'ri javob: B) 243
✔
Matematika — milliy sertifikat mashq variantlari | 15

25. To'g'ri burchakli uchburchakning gipotenuzasi 17, bir kateti 8. Ikkinchi katetini toping.
A) 15
B) 13
C) 9
D) 16
To'g'ri javob: A) 15✔
26. A va B nuqtalar orasidagi masofani toping.
A(2; 2), B(11; -10)
A) 17
B) 21
C) 15
D) 3
To'g'ri javob: C) 15
✔
27. Ifodaning qiymatini toping.
sin 90° + sin 30°
A) 1/2
B) −1/2
C) 5/2
D) 3/2
To'g'ri javob: D) 3/2
✔
28. Radiusi 7 ga teng aylananing uzunligini toping.
A) 49π
B) 14π
C) 28π
D) 7π
To'g'ri javob: B) 14π
✔
29. Uchburchak yuzini toping.
Asosi 18, unga tushirilgan balandlik 16
A) 288
B) 34
C) 144
D) 145
To'g'ri javob: C) 144
✔
30. "Algoritm" atamasi qaysi olim nomidan kelib chiqqan?
A) Beruniy
B) Forobiy
C) Al-Xorazmiy
D) Ulug'bek
To'g'ri javob: C) Al-Xorazmiy
✔
31. Guruhlashlar sonini toping.
C(6; 3)
A) 120
B) 18
C) 20
D) 15
To'g'ri javob: C) 20
✔
Matematika — milliy sertifikat mashq variantlari | 16

32. Tengsizlikning butun yechimlari sonini toping.
x² + x − 12 < 0
A) 8
B) 5
C) 6
D) 7
To'g'ri javob: C) 6✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) log₂8 + log₂16 a) 4
2) log₅25 + log₅5 b) 6
3) log₃3 + log₃3 c) 7
4) log₂8 + log₂2 d) 8
e) 3
f) 2
A) 1–a, 2–c, 3–f, 4–e
B) 1–c, 2–e, 3–f, 4–d
C) 1–c, 2–e, 3–f, 4–a
D) 1–e, 2–c, 3–a, 4–f
To'g'ri javob: C) 1–c, 2–e, 3–f, 4–a
✔
34. Har bir ifodaga uning qiymatini moslang.
1) C(7; 2) a) 336
2) A(5; 2) b) 70
3) A(8; 3) c) 20
4) C(8; 4) d) 5040
e) 1680
f) 21
A) 1–f, 2–c, 3–a, 4–b
B) 1–c, 2–f, 3–a, 4–b
C) 1–e, 2–c, 3–a, 4–b
D) 1–f, 2–a, 3–c, 4–b
To'g'ri javob: A) 1–f, 2–c, 3–a, 4–b
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √25 + √25 a) 13
2) √25 + √100 b) 5
3) √16 + √49 c) 15
4) √64 + √25 d) 11
e) 10
f) 4
Matematika — milliy sertifikat mashq variantlari | 17

A) 1–e, 2–c, 3–d, 4–a
B) 1–b, 2–c, 3–d, 4–a
C) 1–e, 2–a, 3–d, 4–c
D) 1–d, 2–c, 3–e, 4–a
To'g'ri javob: A) 1–e, 2–c, 3–d, 4–a✔
O • ochiq topshiriq (qisqa javob)
36. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) x² + 10x + 9 = 0
b) x² + 9x = 0
Javob: a) -10; b) -9
✔
37. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 3, q = 2, n = 5
b) b₁ = 4, q = 2, n = 4
Javob: a) 93; b) 60
✔
38. Vektorlarning skalyar ko'paytmasini toping. Javobni yozing.
a) (2; -6), (-4; 5)
a⃗ b ⃗
b) (-5; 6), (-1; 3)
a⃗ b ⃗
Javob: a) -38; b) 23
✔
39. EKUBni toping. Javobni yozing.
a) EKUB(86; 66)
b) EKUB(90; 58)
Javob: a) 2; b) 2
✔
40. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x + 9| = 3
b) |x − 3| = 3
Javob: a) -18; b) 6
✔
41. Tengsizlikning butun yechimlari sonini toping. Javobni yozing.
a) x² − 2x − 24 < 0
b) x² − 5x − 36 < 0
Javob: a) 9; b) 12
✔
42. Tenglamalar sistemasini yeching va x + y ni toping. Javobni yozing.
a) { 4x + 5y = -21; x − y = 6 }
b) { 2x + 5y = 23; 3x − y = -8 }
Javob: a) -4; b) 4
✔
43. A va B nuqtalar orasidagi masofani toping. Javobni yozing.
a) A(2; 4), B(-4; -4)
b) A(3; 3), B(12; -9)
Javob: a) 10; b) 15
✔
44. Tenglamani yeching. Javobni yozing.
a) 5(x + 17) = 2x + 76
b) 7(x − 7) = 2x − 79
Javob: a) -3; b) -6
✔
Matematika — milliy sertifikat mashq variantlari | 18

45. Aniq integralni hisoblang. Javobni yozing.
a) ∫₀^1 (4x + 5) dx
b) ∫₀^3 (2x − 1) dx
Javob: a) 7; b) 6✔
Matematika — milliy sertifikat mashq variantlari | 19

3-variant
Y-1 • bitta to'g'ri javob
1. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 2, 6, 5
A) 13
B) 62
C) 104
D) 60
To'g'ri javob: D) 60✔
2. Hisoblang.
√225 + √169
A) 19
B) 195
C) 27
D) 28
To'g'ri javob: D) 28
✔
3. Aylana uzunligini toping (π orqali).
Radius R = 10
A) 10π
B) 20π
C) 100π
D) 40π
To'g'ri javob: B) 20π
✔
4. Ehtimollikni toping.
Qutida 4 ta oq va 2 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 2/3
B) 1/6
C) 2
D) 1/3
To'g'ri javob: A) 2/3
✔
5. Ifodaning qiymatini toping.
3^5 · 3^6 : 3^2
A) 22876792454961
B) 19683
C) 19686
D) 177147
To'g'ri javob: B) 19683
✔
6. Logarifmik tenglamani yeching.
log₁₀(x − 3) = 3
A) 1003
B) 1000
C) 997
D) 33
To'g'ri javob: A) 1003
✔
Matematika — milliy sertifikat mashq variantlari | 20

7. Uchburchak yuzini toping.
Asosi 18, unga tushirilgan balandlik 10
A) 91
B) 28
C) 90
D) 180
To'g'ri javob: C) 90✔
8. Vektorlarning skalyar ko'paytmasini toping.
(-2; -2), (0; 3)
a⃗ b ⃗
A) -4
B) -6
C) -5
D) 6
To'g'ri javob: B) -6
✔
9. Ifodaning qiymatini toping.
3^6 · 3^4 : 3^1
A) 59049
B) 94143178827
C) 19683
D) 19686
To'g'ri javob: C) 19683
✔
10. Parabola uchining ordinatasini toping.
y = x² − 4x + 1
A) -3
B) 1
C) 2
D) -2
To'g'ri javob: A) -3
✔
11. Ko'rsatkichli tenglamani yeching.
5^(x − 1) = 625
A) 6
B) 5
C) 3
D) 4
To'g'ri javob: B) 5
✔
12. Guruhlashlar sonini toping.
C(8; 2)
A) 8
B) 28
C) 56
D) 16
To'g'ri javob: B) 28
✔
Matematika — milliy sertifikat mashq variantlari | 21

13. Vektor uzunligini toping.
(3; 4)a⃗
A) 1
B) 6
C) 5
D) 7
To'g'ri javob: C) 5
✔
14. Uchburchak yuzini toping.
Asosi 12, unga tushirilgan balandlik 6
A) 36
B) 18
C) 72
D) 37
To'g'ri javob: A) 36
✔
15. f(x) = 5x + 5 bo'lsa, f(0) ni toping.
A) 5
B) 7
C) 2
D) 3
To'g'ri javob: A) 5
✔
16. Tenglamani yeching: 7x + 5 = 12
A) 1
B) -2
C) -1
D) 4
To'g'ri javob: A) 1
✔
17. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 5, q = 3, n = 3
A) 62
B) 45
C) 65
D) 70
To'g'ri javob: C) 65
✔
18. A va B nuqtalar orasidagi masofani toping.
A(3; 0), B(10; 24)
A) 27
B) 25
C) 31
D) 17
To'g'ri javob: B) 25
✔
Matematika — milliy sertifikat mashq variantlari | 22

19. EKUKni toping.
EKUK(14; 76)
A) 546
B) 1064
C) 2
D) 532
To'g'ri javob: D) 532✔
20. Tengsizlikni yeching: 6x + 6 > 8
A) x < 1/3
B) x > 7/3
C) x > 1/3
D) x > 4/3
To'g'ri javob: C) x > 1/3
✔
21. Son 9 ga bo'linishi uchun qanday shart bajarilishi kerak?
A) Toq bo'lishi kerak
B) Oxirgi raqami 9 bo'lishi kerak
C) 3 ga bo'linishi yetarli
D) Raqamlari yig'indisi 9 ga bo'linishi kerak
To'g'ri javob: D) Raqamlari yig'indisi 9 ga bo'linishi kerak
✔
22. Masalani yeching.
Mahsulot narxi 3000 so'm edi. Narx 10% ga oshirildi. Yangi narx necha so'm?
A) 3300
B) 2700
C) 3010
D) 300
To'g'ri javob: A) 3300
✔
23. Aylana uzunligi formulasi qaysi?
A) C = πr²
B) C = 4r
C) C = 2πr
D) C = r²
To'g'ri javob: C) C = 2πr
✔
24. Logarifmik tenglamani yeching.
log₂(x − 3) = 1
A) -1
B) 5
C) 6
D) 2
To'g'ri javob: B) 5
✔
25. Ifodaning qiymatini toping.
log₃81 + log₃81
A) 6561
B) 8
C) 9
D) 16
To'g'ri javob: B) 8
✔
Matematika — milliy sertifikat mashq variantlari | 23

26. A va B nuqtalar orasidagi masofani toping.
A(0; 2), B(8; -13)
A) 19
B) 23
C) 7
D) 17
To'g'ri javob: D) 17✔
27. Hisoblang.
√49 + √225
A) 21
B) 105
C) 16
D) 22
To'g'ri javob: D) 22
✔
28. Guruhlashlar sonini toping.
C(5; 2)
A) 10
B) 20
C) 5
D) 11
To'g'ri javob: A) 10
✔
29. Tenglamaning katta ildizini toping.
x² + 4x − 21 = 0
A) 3
B) 4
C) -3
D) -7
To'g'ri javob: A) 3
✔
30. Geometrik progressiyaning n-hadi formulasi qaysi?
A) b = b₁ + (n − 1)q
ₙ
B) b = b₁ · qⁿ
ₙ
C) b = n · q
ₙ
D) b = b₁ · qⁿ⁻¹
ₙ
To'g'ri javob: D) bₙ = b₁ · qⁿ⁻¹
✔
31. f(x₀) qiymatini toping.
f(x) = 4x² − 4x + 7, x₀ = -4
A) -13
B) 91
C) 87
D) -87
To'g'ri javob: C) 87
✔
Matematika — milliy sertifikat mashq variantlari | 24

32. Tenglamaning katta ildizini toping.
x² + 4x = 0
A) -4
B) 2
C) 0
D) 1
To'g'ri javob: C) 0✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) tg 45° + sin 30° a) 1/2
2) cos 60° + tg 0° b) −1/2
3) sin 270° + cos 60° c) 3/2
4) sin 270° + tg 0° d) 1
e) 2
f) −1
A) 1–c, 2–b, 3–f, 4–a
B) 1–c, 2–a, 3–b, 4–f
C) 1–d, 2–a, 3–b, 4–f
D) 1–c, 2–a, 3–f, 4–b
To'g'ri javob: B) 1–c, 2–a, 3–b, 4–f
✔
34. Har bir ifodaga uning qiymatini moslang.
1) A(7; 4) a) 60
2) C(9; 2) b) 72
3) A(7; 2) c) 840
4) C(6; 2) d) 36
e) 42
f) 15
A) 1–c, 2–f, 3–e, 4–d
B) 1–c, 2–d, 3–f, 4–e
C) 1–c, 2–d, 3–e, 4–b
D) 1–c, 2–d, 3–e, 4–f
To'g'ri javob: D) 1–c, 2–d, 3–e, 4–f
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √225 + √144 a) 15
2) √49 + √49 b) 14
3) √16 + √4 c) 6
4) √121 + √64 d) 27
e) 26
f) 19
Matematika — milliy sertifikat mashq variantlari | 25

A) 1–d, 2–c, 3–b, 4–f
B) 1–d, 2–f, 3–c, 4–b
C) 1–d, 2–b, 3–c, 4–f
D) 1–f, 2–b, 3–c, 4–d
To'g'ri javob: C) 1–d, 2–b, 3–c, 4–f✔
O • ochiq topshiriq (qisqa javob)
36. Ehtimollikni toping. Javobni yozing.
a) Qutida 6 ta oq va 7 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 5 ta oq va 3 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 6/13; b) 5/8
✔
37. Vektor uzunligini toping. Javobni yozing.
a) (-5; -12)
a⃗
b) (-5; 12)
a⃗
Javob: a) 13; b) 13
✔
38. EKUBni toping. Javobni yozing.
a) EKUB(60; 32)
b) EKUB(11; 30)
Javob: a) 4; b) 1
✔
39. Uchburchak yuzini toping. Javobni yozing.
a) Asosi 11, unga tushirilgan balandlik 6
b) Asosi 10, unga tushirilgan balandlik 7
Javob: a) 33; b) 35
✔
40. Logarifmik tenglamani yeching. Javobni yozing.
a) log₃(x − 9) = 4
b) log₁₀(x − 8) = 3
Javob: a) 90; b) 1008
✔
41. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 3, q = -2, n = 6
b) b₁ = 3, q = 2, n = 5
Javob: a) -63; b) 93
✔
42. Vektorlarning skalyar ko'paytmasini toping. Javobni yozing.
a) (2; 3), (-6; 1)
a⃗ b ⃗
b) (0; 3), (-5; 1)
a⃗ b ⃗
Javob: a) -9; b) 3
✔
43. f(x₀) qiymatini toping. Javobni yozing.
a) f(x) = −4x² + 5x − 3, x₀ = -1
b) f(x) = x² + 6x − 3, x₀ = 4
Javob: a) -12; b) 37
✔
44. Trapetsiya yuzini toping. Javobni yozing.
a) Asoslari 7 va 15, balandligi 7
b) Asoslari 3 va 2, balandligi 10
Javob: a) 77; b) 25
✔
Matematika — milliy sertifikat mashq variantlari | 26

45. Ehtimollikni toping. Javobni yozing.
a) Qutida 3 ta oq va 6 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 6 ta oq va 7 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 1/3; b) 6/13✔
Matematika — milliy sertifikat mashq variantlari | 27

4-variant
Y-1 • bitta to'g'ri javob
1. Kosinuslar teoremasi qanday ifodalanadi?
A) a = b · cosA
B) a / sinA = 2R
C) a² = b² + c² − 2bc·cosA
D) a² = b² + c²
To'g'ri javob: C) a² = b² + c² − 2bc·cosA✔
2. Algebra fanining asoschisi hisoblangan vatandoshimiz kim?
A) Ibn Sino
B) Mirzo Ulug'bek
C) Muhammad ibn Muso al-Xorazmiy
D) Abu Rayhon Beruniy
To'g'ri javob: C) Muhammad ibn Muso al-Xorazmiy
✔
3. Viyet teoremasiga ko'ra x² + px + q = 0 tenglama ildizlari ko'paytmasi nimaga teng?
A) p
B) −q
C) q
D) −p
To'g'ri javob: C) q
✔
4. Tenglama ildizlari yig'indisini toping.
x² − 5x − 14 = 0
A) 6
B) -14
C) -5
D) 5
To'g'ri javob: D) 5
✔
5. Hisoblang.
1/8 + 2/12
A) 1/48
B) 7/24
C) 3/20
D) 29/96
To'g'ri javob: B) 7/24
✔
6. 2x² + 3x − 4 = 0 tenglamaning diskriminantini toping.
A) 45
B) 41
C) 37
D) -23
To'g'ri javob: B) 41
✔
Matematika — milliy sertifikat mashq variantlari | 28

$7. Ifodaning qiymatini toping. cos 0° + cos 90° A) 0 B) 1 C) 2 D) −1 To'g'ri javob: B) 1✔ 8. Tenglamalar sistemasini yeching va x + y ni toping. { 2x + 2y = -22; 5x − 4y = -28 } A) -5 B) -9 C) 24 D) -11 To'g'ri javob: D) -11 ✔ 9. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. b₁ = 3, q = 2, n = 5 A) 48 B) 91 C) 96 D) 93 To'g'ri javob: D) 93 ✔ 10. Hisoblang. 2/5 + 8/4 A) 4/5 B) 49/20 C) 10/9 D) 12/5 To'g'ri javob: D) 12/5 ✔ 11. Aniq integralni hisoblang. ∫₀^1 (4x + 3) dx A) 7 B) 5 C) 6 D) 10 To'g'ri javob: B) 5 ✔ 12. f(x₀) qiymatini toping. f(x) = −3x² + 5x − 1, x₀ = -1 A) -12 B) 9 C) 7 D) -9 To'g'ri javob: D) -9 ✔ Matematika — milliy sertifikat mashq variantlari | 29$

13. 120 ning 40% ini toping.
A) 48
B) 40
C) 58
D) 64
To'g'ri javob: A) 48✔
14. Uchburchak ichki burchaklarining yig'indisi necha gradus?
A) 180°
B) 360°
C) 270°
D) 90°
To'g'ri javob: A) 180°
✔
15. Arifmetik progressiyada a₁ = 3, d = 1. Dastlabki 9 ta had yig'indisini toping.
A) 58
B) 63
C) 69
D) 65
To'g'ri javob: B) 63
✔
16. Ifodaning qiymatini toping.
log₅625 + log₅625
A) 8
B) 390625
C) 16
D) 9
To'g'ri javob: A) 8
✔
17. Aniq integralni hisoblang.
∫₀^1 (8x) dx
A) 4
B) 8
C) 5
D) 6
To'g'ri javob: A) 4
✔
18. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 9, 8, 7
A) 504
B) 382
C) 513
D) 24
To'g'ri javob: A) 504
✔
19. Tenglamani yeching: 9x − 10 = 8
A) 0
B) 4
C) 2
D) -2
To'g'ri javob: C) 2
✔
Matematika — milliy sertifikat mashq variantlari | 30

20. Uchburchak yuzini toping.
Asosi 20, unga tushirilgan balandlik 11
A) 110
B) 31
C) 220
D) 111
To'g'ri javob: A) 110✔
21. Uchburchak yuzini toping.
Asosi 13, unga tushirilgan balandlik 6
A) 19
B) 40
C) 78
D) 39
To'g'ri javob: D) 39
✔
22. Ifodaning qiymatini toping.
2^5 · 2^6 : 2^5
A) 64
B) 66
C) 33554432
D) 2048
To'g'ri javob: A) 64
✔
23. Logarifmik tenglamani yeching.
log₃(x − 2) = 2
A) 8
B) 7
C) 11
D) 9
To'g'ri javob: C) 11
✔
24. Silindr hajmini toping (π orqali).
Asos radiusi 6, balandligi 4
A) 24π
B) 288π
C) 144π
D) 48π
To'g'ri javob: C) 144π
✔
25. Tenglamani yeching.
4(x + 2) = 2x + 28
A) -10
B) 10
C) 8
D) 11
To'g'ri javob: B) 10
✔
Matematika — milliy sertifikat mashq variantlari | 31

26. Qavariq 10-burchakning ichki burchaklari yig'indisini toping.
A) 2880°
B) 1620°
C) 1440°
D) 1800°
To'g'ri javob: C) 1440°✔
27. Ehtimollikni toping.
Qutida 3 ta oq va 6 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 1/9
B) 1/2
C) 1/3
D) 2/3
To'g'ri javob: C) 1/3
✔
28. Masalani yeching.
Mahsulot narxi 2900 so'm edi. Narx 30% ga oshirildi. Yangi narx necha so'm?
A) 2030
B) 2930
C) 3770
D) 870
To'g'ri javob: C) 3770
✔
29. Aniq integralni hisoblang.
∫₀^2 (2x + 6) dx
A) 16
B) 18
C) 32
D) 10
To'g'ri javob: A) 16
✔
30. Tenglamani yeching.
5(x − 1) = x − 45
A) -9
B) -10
C) -12
D) 10
To'g'ri javob: B) -10
✔
31. EKUBni toping.
EKUB(46; 80)
A) 2
B) 34
C) 1840
D) 4
To'g'ri javob: A) 2
✔
Matematika — milliy sertifikat mashq variantlari | 32

32. Ifodaning qiymatini toping.
log₃9 + log₃9
A) 4
B) 81
C) 6
D) 5
To'g'ri javob: A) 4✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) A(9; 4) a) 3024
2) C(6; 4) b) 120
3) A(5; 4) c) 1680
4) A(9; 3) d) 504
e) 15
f) 20
A) 1–a, 2–c, 3–b, 4–d
B) 1–e, 2–a, 3–d, 4–b
C) 1–a, 2–e, 3–b, 4–d
D) 1–a, 2–e, 3–b, 4–c
To'g'ri javob: C) 1–a, 2–e, 3–b, 4–d
✔
34. Har bir ifodaga uning qiymatini moslang.
1) cos 180° + cos 60° a) 1/2
2) cos 0° + tg 45° b) −1
3) sin 90° + tg 0° c) −1/2
4) cos 60° + cos 90° d) 2
e) 1
f) 3/2
A) 1–e, 2–d, 3–c, 4–a
B) 1–c, 2–f, 3–e, 4–a
C) 1–c, 2–d, 3–e, 4–a
D) 1–c, 2–d, 3–f, 4–a
To'g'ri javob: C) 1–c, 2–d, 3–e, 4–a
✔
35. Har bir ifodaga uning qiymatini moslang.
1) tg 45° + cos 90° a) −1
2) cos 180° + sin 270° b) 0
3) sin 30° + sin 90° c) 1/2
4) tg 0° + cos 90° d) −2
e) 3/2
f) 1
Matematika — milliy sertifikat mashq variantlari | 33

A) 1–b, 2–d, 3–f, 4–e
B) 1–f, 2–d, 3–e, 4–b
C) 1–e, 2–d, 3–f, 4–b
D) 1–c, 2–d, 3–e, 4–b
To'g'ri javob: B) 1–f, 2–d, 3–e, 4–b✔
O • ochiq topshiriq (qisqa javob)
36. Tenglamani yeching. Javobni yozing.
a) 5(x + 18) = x + 138
b) 7(x + 17) = x + 47
Javob: a) 12; b) -12
✔
37. f(x₀) qiymatini toping. Javobni yozing.
a) f(x) = 4x² + 2x − 6, x₀ = -1
b) f(x) = −2x² − 5x + 4, x₀ = -1
Javob: a) -4; b) 7
✔
38. Hisoblang. Javobni yozing.
a) √169 + √144
b) √64 + √100
Javob: a) 25; b) 18
✔
39. EKUBni toping. Javobni yozing.
a) EKUB(8; 90)
b) EKUB(56; 65)
Javob: a) 2; b) 1
✔
40. Masalani yeching. Javobni yozing.
a) Narx 2500 so'm. Avval 20% ga oshirildi, so'ng 25% ga kamaytirildi. Oxirgi narx necha so'm?
b) Narx 3200 so'm. Avval 50% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
Javob: a) 2250; b) 4320
✔
41. Hisoblang. Javobni yozing.
a) 6/12 + 9/3
b) 8/7 + 5/4
Javob: a) 7/2; b) 67/28
✔
42. Masalani yeching. Javobni yozing.
a) Narx 2800 so'm. Avval 15% ga oshirildi, so'ng 25% ga kamaytirildi. Oxirgi narx necha so'm?
b) Narx 400 so'm. Avval 10% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
Javob: a) 2415; b) 396
✔
43. Masalani yeching. Javobni yozing.
a) Mahsulot narxi 2600 so'm edi. Narx 30% ga oshirildi. Yangi narx necha so'm?
b) Narx 1400 so'm. Avval 20% ga oshirildi, so'ng 20% ga kamaytirildi. Oxirgi narx necha so'm?
Javob: a) 3380; b) 1344
✔
44. Masalani yeching. Javobni yozing.
a) Narx 3100 so'm. Avval 40% ga oshirildi, so'ng 25% ga kamaytirildi. Oxirgi narx necha so'm?
b) Mahsulot narxi 1000 so'm edi. Narx 20% ga oshirildi. Yangi narx necha so'm?
Javob: a) 3255; b) 1200
✔
Matematika — milliy sertifikat mashq variantlari | 34

45. Tenglamani yeching. Javobni yozing.
a) 7(x − 13) = 2x − 51
b) 5(x − 7) = 3x − 49
Javob: a) 8; b) -7✔
Matematika — milliy sertifikat mashq variantlari | 35

5-variant
Y-1 • bitta to'g'ri javob
1. Vektor uzunligini toping.
(-9; -12)a⃗
A) 15
B) 3
C) 16
D) 21
To'g'ri javob: A) 15
✔
2. f'(x₀) ni toping.
f(x) = 3x³ + x² − x + 9, x₀ = 4
A) 151
B) 213
C) 153
D) 150
To'g'ri javob: A) 151
✔
3. f'(x₀) ni toping.
f(x) = 3x³ + 3x² − 4x − 6, x₀ = 0
A) 2
B) -5
C) -4
D) -6
To'g'ri javob: C) -4
✔
4. Vektorlarning skalyar ko'paytmasini toping.
(-4; 0), (4; 3)
a⃗ b ⃗
A) -12
B) 16
C) -16
D) -15
To'g'ri javob: C) -16
✔
5. Doira yuzini toping (π orqali).
Radius R = 8
A) 16π
B) 8π
C) 64π
D) 128π
To'g'ri javob: C) 64π
✔
6. Tenglamani yeching.
5(x + 1) = 3x + 15
A) 5
B) -5
C) 6
D) 3
To'g'ri javob: A) 5
✔
Matematika — milliy sertifikat mashq variantlari | 36

7. Uchburchak yuzini toping.
Asosi 15, unga tushirilgan balandlik 6
A) 46
B) 45
C) 21
D) 90
To'g'ri javob: B) 45✔
8. (a − b)² nimaga teng?
A) a² − b²
B) a² + b²
C) a² + 2ab + b²
D) a² − 2ab + b²
To'g'ri javob: D) a² − 2ab + b²
✔
9. Vektor uzunligini toping.
(-5; -12)
a⃗
A) 14
B) 13
C) 7
D) 17
To'g'ri javob: B) 13
✔
10. Parabola uchining ordinatasini toping.
y = x² − 2x + 1
A) 2
B) 0
C) 1
D) 3
To'g'ri javob: B) 0
✔
11. Tenglama ildizlari yig'indisini toping.
x² − 3x − 4 = 0
A) -4
B) -3
C) 3
D) 4
To'g'ri javob: C) 3
✔
12. Kvadrat tenglama ax² + bx + c = 0 ning diskriminanti qanday hisoblanadi?
A) D = b² + 4ac
B) D = b² − 4ac
C) D = 4ac − b²
D) D = b − 4ac
To'g'ri javob: B) D = b² − 4ac
✔
Matematika — milliy sertifikat mashq variantlari | 37

13. Tenglamani yeching.
6(x + 14) = 3x + 66
A) -6
B) -5
C) 6
D) -8
To'g'ri javob: A) -6✔
14. f(x) = x² − 2x − 9 funksiyaning x = -2 nuqtadagi hosilasini toping.
A) -4
B) -1
C) -6
D) 0
To'g'ri javob: C) -6
✔
15. Tenglama ildizlari yig'indisini toping.
|x − 0| = 3
A) 1
B) 0
C) 3
D) 2
To'g'ri javob: B) 0
✔
16. Logarifmik tenglamani yeching.
log₅(x − 4) = 2
A) 21
B) 14
C) 29
D) 25
To'g'ri javob: C) 29
✔
17. logₐ1 nimaga teng?
A) 0
B) a
C) Aniqlanmagan
D) 1
To'g'ri javob: A) 0
✔
18. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -9, d = 6, n = 12
A) 57
B) 276
C) 288
D) 294
To'g'ri javob: C) 288
✔
Matematika — milliy sertifikat mashq variantlari | 38

19. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 7, d = 0, n = 5
A) 30
B) 35
C) 36
D) 7
To'g'ri javob: B) 35✔
20. Logarifmik tenglamani yeching.
log₂(x − 6) = 4
A) 22
B) 14
C) 10
D) 16
To'g'ri javob: A) 22
✔
21. Parabola uchining ordinatasini toping.
y = x² − 12x + 29
A) 6
B) -7
C) 29
D) -6
To'g'ri javob: B) -7
✔
22. Uchburchak yuzini toping.
Asosi 10, unga tushirilgan balandlik 11
A) 55
B) 21
C) 110
D) 56
To'g'ri javob: A) 55
✔
23. f(x₀) qiymatini toping.
f(x) = 2x² + 4x − 2, x₀ = -2
A) -2
B) 0
C) 2
D) -1
To'g'ri javob: A) -2
✔
24. Ifodaning qiymatini toping.
2^2 · 2^3 : 2^3
A) 32
B) 4
C) 6
D) 8
To'g'ri javob: B) 4
✔
Matematika — milliy sertifikat mashq variantlari | 39

25. Muqarrar hodisaning ehtimoli nimaga teng?
A) 0
B) 100
C) 1
D) 0,5
To'g'ri javob: C) 1✔
26. Ifodaning qiymatini toping.
2^5 · 2^5 : 2^5
A) 1024
B) 32
C) 1048576
D) 34
To'g'ri javob: B) 32
✔
27. Tengsizlikning butun yechimlari sonini toping.
x² − 11x + 24 < 0
A) 3
B) 4
C) 5
D) 6
To'g'ri javob: B) 4
✔
28. x² − 10x + 25 = 0 tenglama ildizlarining ko'paytmasini toping.
A) 26
B) -25
C) 10
D) 25
To'g'ri javob: D) 25
✔
29. Aylana uzunligini toping (π orqali).
Radius R = 9
A) 81π
B) 36π
C) 18π
D) 9π
To'g'ri javob: C) 18π
✔
30. Ifodaning qiymatini toping.
sin 30° + tg 0°
A) 1/2
B) 5/2
C) −3/2
D) −1/2
To'g'ri javob: A) 1/2
✔
31. Mirzo Ulug'bek trigonometriyada qaysi qiymatni yuqori aniqlikda hisoblagan?
A) √2
B) e soni
C) sin 1°
D) π soni
To'g'ri javob: C) sin 1°
✔
Matematika — milliy sertifikat mashq variantlari | 40

32. f(x) = 5x − 4 bo'lsa, f(-1) ni toping.
A) -8
B) -10
C) -9
D) -13
To'g'ri javob: C) -9✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) Radius R = 3 a) 12π
2) Radius R = 15 b) 225π
3) Radius R = 11 c) 22π
4) Radius R = 6 d) 6π
e) 20π
f) 9π
A) 1–f, 2–b, 3–c, 4–a
B) 1–b, 2–f, 3–c, 4–a
C) 1–f, 2–b, 3–e, 4–a
D) 1–c, 2–b, 3–f, 4–a
To'g'ri javob: A) 1–f, 2–b, 3–c, 4–a
✔
34. Har bir ifodaga uning qiymatini moslang.
1) Radius R = 2 a) 225π
2) Radius R = 6 b) 64π
3) Radius R = 15 c) 20π
4) Radius R = 10 d) 25π
e) 36π
f) 4π
A) 1–c, 2–f, 3–e, 4–a
B) 1–f, 2–e, 3–a, 4–c
C) 1–f, 2–e, 3–a, 4–d
D) 1–f, 2–e, 3–b, 4–c
To'g'ri javob: B) 1–f, 2–e, 3–a, 4–c
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √9 + √225 a) 18
2) √121 + √25 b) 19
3) √196 + √144 c) 15
4) √16 + √225 d) 26
e) 16
f) 27
Matematika — milliy sertifikat mashq variantlari | 41

A) 1–e, 2–a, 3–d, 4–b
B) 1–a, 2–e, 3–b, 4–d
C) 1–e, 2–b, 3–a, 4–d
D) 1–a, 2–e, 3–d, 4–b
To'g'ri javob: D) 1–a, 2–e, 3–d, 4–b✔
O • ochiq topshiriq (qisqa javob)
36. f(x₀) qiymatini toping. Javobni yozing.
a) f(x) = −3x² − 3x + 5, x₀ = 0
b) f(x) = 2x² − 2, x₀ = -2
Javob: a) 5; b) 6
✔
37. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 2, q = 3, n = 5
b) b₁ = 3, q = -2, n = 6
Javob: a) 242; b) -63
✔
38. Ifodaning qiymatini toping. Javobni yozing.
a) 5^4 · 5^2 : 5^3
b) 2^3 · 2^5 : 2^5
Javob: a) 125; b) 8
✔
39. Tenglamani yeching. Javobni yozing.
a) 7(x − 1) = x − 43
b) 3(x + 17) = x + 73
Javob: a) -6; b) 11
✔
40. Tenglamani yeching. Javobni yozing.
a) 5(x − 6) = x − 6
b) 7(x + 6) = 3x + 2
Javob: a) 6; b) -10
✔
41. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 4, q = 3, n = 4
b) b₁ = 5, q = 3, n = 6
Javob: a) 160; b) 1820
✔
42. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x + 6| = 1
b) |x + 8| = 6
Javob: a) -12; b) -16
✔
43. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) a₁ = 2, d = 5, n = 9
b) a₁ = 1, d = 6, n = 12
Javob: a) 198; b) 408
✔
44. Aniq integralni hisoblang. Javobni yozing.
a) ∫₀^2 (2x + 2) dx
b) ∫₀^2 (4x + 5) dx
Javob: a) 8; b) 18
✔
Matematika — milliy sertifikat mashq variantlari | 42

45. Tenglamalar sistemasini yeching va x + y ni toping. Javobni yozing.
a) { 4x + 2y = -26; 4x − 2y = -22 }
b) { x + y = 8; 3x − 4y = -11 }
Javob: a) -7; b) 8✔
Matematika — milliy sertifikat mashq variantlari | 43

6-variant
Y-1 • bitta to'g'ri javob
1. Silindr hajmini toping (π orqali).
Asos radiusi 2, balandligi 9
A) 18π
B) 36π
C) 37π
D) 72π
To'g'ri javob: B) 36π✔
2. Masalani yeching.
Narx 1300 so'm. Avval 30% ga oshirildi, so'ng 20% ga kamaytirildi. Oxirgi narx necha so'm?
A) 1452
B) 1300
C) 1352
D) 1430
To'g'ri javob: C) 1352
✔
3. Tenglamalar sistemasini yeching va x + y ni toping.
{ x + 2y = -5; x − y = -8 }
A) -4
B) -6
C) -8
D) -7
To'g'ri javob: B) -6
✔
4. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 3, q = 3, n = 4
A) 120
B) 81
C) 117
D) 123
To'g'ri javob: A) 120
✔
5. f(x) = 4x + 5 bo'lsa, f(-4) ni toping.
A) -15
B) -14
C) -11
D) -10
To'g'ri javob: C) -11
✔
6. Hisoblang.
3/4 + 8/3
A) 11/7
B) 2
C) 7/2
D) 41/12
To'g'ri javob: D) 41/12
✔
Matematika — milliy sertifikat mashq variantlari | 44

7. f'(x₀) ni toping.
f(x) = 3x² + 6x − 7, x₀ = 3
A) 30
B) 24
C) 23
D) 38
To'g'ri javob: B) 24✔
8. Tenglamaning katta ildizini toping.
x² + 13x + 42 = 0
A) -7
B) 6
C) -5
D) -6
To'g'ri javob: D) -6
✔
9. EKUBni toping.
EKUB(50; 88)
A) 2
B) 38
C) 2200
D) 4
To'g'ri javob: A) 2
✔
10. Hisoblang.
2/4 + 9/2
A) 5
B) 41/8
C) 11/6
D) 9/4
To'g'ri javob: A) 5
✔
11. Tengsizlikning butun yechimlari sonini toping.
x² − x − 2 < 0
A) 3
B) 1
C) 2
D) 4
To'g'ri javob: C) 2
✔
12. C(6;3) — 6 ta elementdan 3 tadan guruhlashlar sonini toping.
A) 18
B) 26
C) 20
D) 120
To'g'ri javob: C) 20
✔
Matematika — milliy sertifikat mashq variantlari | 45

13. A va B nuqtalar orasidagi masofani toping.
A(-4; 0), B(-1; -4)
A) 1
B) 5
C) 6
D) 7
To'g'ri javob: B) 5✔
14. Tenglama ildizlari yig'indisini toping.
|x − 8| = 6
A) 16
B) 14
C) 6
D) -16
To'g'ri javob: A) 16
✔
15. Kesma o'rtasining koordinatalari qanday topiladi?
A) ((x₁ + x₂)/2; (y₁ + y₂)/2)
B) (x₁ · x₂; y₁ · y₂)
C) (x₁ − x₂; y₁ − y₂)
D) (x₁ + x₂; y₁ + y₂)
To'g'ri javob: A) ((x₁ + x₂)/2; (y₁ + y₂)/2)
✔
16. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 3, q = 3, n = 3
A) 36
B) 27
C) 42
D) 39
To'g'ri javob: D) 39
✔
17. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 2, q = -2, n = 4
A) -8
B) -10
C) -16
D) -9
To'g'ri javob: B) -10
✔
18. Aniq integralni hisoblang.
∫₀^3 (8x − 3) dx
A) 27
B) 30
C) 21
D) 54
To'g'ri javob: A) 27
✔
Matematika — milliy sertifikat mashq variantlari | 46

19. f'(x₀) ni toping.
f(x) = x³ + x² + 2x + 3, x₀ = -3
A) 23
B) -21
C) 22
D) 25
To'g'ri javob: A) 23✔
20. f(x) = 5x² − x + 9 funksiyaning x = 2 nuqtadagi hosilasini toping.
A) 19
B) 9
C) 27
D) 21
To'g'ri javob: A) 19
✔
21. Aylana uzunligini toping (π orqali).
Radius R = 7
A) 28π
B) 49π
C) 14π
D) 7π
To'g'ri javob: C) 14π
✔
22. EKUBni toping.
EKUB(27; 36)
A) 63
B) 108
C) 18
D) 9
To'g'ri javob: D) 9
✔
23. EKUKni toping.
EKUK(66; 25)
A) 1
B) 1650
C) 1716
D) 3300
To'g'ri javob: B) 1650
✔
24. Tengsizlikni yeching: 6x − 4 > -9
A) x > -5/6
B) x > 1/6
C) x > -13/6
D) x < -5/6
To'g'ri javob: A) x > -5/6
✔
Matematika — milliy sertifikat mashq variantlari | 47

25. Guruhlashlar sonini toping.
C(8; 3)
A) 24
B) 336
C) 56
D) 28
To'g'ri javob: C) 56✔
26. Tenglamalar sistemasini yeching: x + y = 2, x − y = -10. x ni toping.
A) 6
B) -4
C) -5
D) 2
To'g'ri javob: B) -4
✔
27. A va B nuqtalar orasidagi masofani toping.
A(-1; 4), B(-4; 0)
A) 1
B) 6
C) 5
D) 7
To'g'ri javob: C) 5
✔
28. f(x₀) qiymatini toping.
f(x) = 3x² − 2x + 4, x₀ = 2
A) 8
B) 15
C) 12
D) -12
To'g'ri javob: C) 12
✔
29. Uchburchak yuzini toping.
Asosi 7, unga tushirilgan balandlik 17
A) 119
B) 119/2
C) 24
D) 121/2
To'g'ri javob: B) 119/2
✔
30. Hisoblang.
6/10 + 6/3
A) 12/13
B) 79/30
C) 6/5
D) 13/5
To'g'ri javob: D) 13/5
✔
Matematika — milliy sertifikat mashq variantlari | 48

31. Hisoblang.
√64 + √144
A) 14
B) 20
C) 19
D) 96
To'g'ri javob: B) 20✔
32. a² − b² ifoda nimaga teng?
A) (a − b)(a + b)
B) a² + 2ab + b²
C) (a + b)²
D) (a − b)²
To'g'ri javob: A) (a − b)(a + b)
✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) √64 + √64 a) 16
2) √225 + √16 b) 21
3) √144 + √169 c) 9
4) √16 + √25 d) 25
e) 13
f) 19
A) 1–c, 2–a, 3–f, 4–d
B) 1–a, 2–f, 3–d, 4–c
C) 1–a, 2–c, 3–d, 4–f
D) 1–a, 2–f, 3–d, 4–b
To'g'ri javob: B) 1–a, 2–f, 3–d, 4–c
✔
34. Har bir ifodaga uning qiymatini moslang.
1) 3^4 · 3^6 : 3^3 a) 5764801
2) 7^4 · 7^6 : 7^2 b) 1953125
3) 7^5 · 7^5 : 7^5 c) 78125
4) 5^6 · 5^6 : 5^3 d) 81
e) 16807
f) 2187
A) 1–f, 2–a, 3–e, 4–b
B) 1–b, 2–a, 3–e, 4–f
C) 1–a, 2–b, 3–e, 4–f
D) 1–f, 2–b, 3–e, 4–a
To'g'ri javob: A) 1–f, 2–a, 3–e, 4–b
✔
35. Har bir ifodaga uning qiymatini moslang.
1) Radius R = 11 a) 121π
2) Radius R = 2 b) 81π
3) Radius R = 8 c) 4π
Matematika — milliy sertifikat mashq variantlari | 49

4) Radius R = 10 d) 16π
e) 64π
f) 20π
A) 1–e, 2–a, 3–c, 4–f
B) 1–a, 2–e, 3–c, 4–f
C) 1–a, 2–c, 3–e, 4–f
D) 1–a, 2–c, 3–e, 4–d
To'g'ri javob: C) 1–a, 2–c, 3–e, 4–f✔
O • ochiq topshiriq (qisqa javob)
36. To'g'ri burchakli parallelepiped hajmini toping. Javobni yozing.
a) O'lchamlari 2, 8, 7
b) O'lchamlari 5, 9, 7
Javob: a) 112; b) 315
✔
37. Tenglamaning katta ildizini toping. Javobni yozing.
a) x² − 17x + 72 = 0
b) x² − 1 = 0
Javob: a) 9; b) 1
✔
38. f'(x₀) ni toping. Javobni yozing.
a) f(x) = 2x³ + 5x² + 6, x₀ = 3
b) f(x) = 3x³ + x² − 2x, x₀ = 3
Javob: a) 84; b) 85
✔
39. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x − 0| = 4
b) |x + 5| = 8
Javob: a) 0; b) -10
✔
40. Tenglamani yeching. Javobni yozing.
a) 4(x + 16) = x + 79
b) 5(x + 4) = 2x + 41
Javob: a) 5; b) 7
✔
41. Tenglamaning katta ildizini toping. Javobni yozing.
a) x² − 2x − 3 = 0
b) x² − 4x = 0
Javob: a) 3; b) 4
✔
42. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) a₁ = -10, d = 3, n = 16
b) a₁ = -2, d = 2, n = 12
Javob: a) 200; b) 108
✔
43. Trapetsiya yuzini toping. Javobni yozing.
a) Asoslari 10 va 14, balandligi 3
b) Asoslari 14 va 11, balandligi 4
Javob: a) 36; b) 50
✔
Matematika — milliy sertifikat mashq variantlari | 50

44. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) a₁ = -9, d = -2, n = 9
b) a₁ = 0, d = 4, n = 11
Javob: a) -153; b) 220✔
45. EKUBni toping. Javobni yozing.
a) EKUB(8; 76)
b) EKUB(10; 76)
Javob: a) 4; b) 2
✔
Matematika — milliy sertifikat mashq variantlari | 51

7-variant
Y-1 • bitta to'g'ri javob
1. Tenglamalar sistemasini yeching va x + y ni toping.
{ x + 2y = 12; 5x − 2y = -12 }
A) -6
B) 8
C) 0
D) 6
To'g'ri javob: D) 6✔
2. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 3, d = 3, n = 7
A) 87
B) 21
C) 84
D) 77
To'g'ri javob: C) 84
✔
3. Logarifmik tenglamani yeching.
log₁₀(x − 2) = 1
A) 8
B) 13
C) 12
D) 10
To'g'ri javob: C) 12
✔
4. Vektorlarning skalyar ko'paytmasini toping.
(1; -6), (4; 0)
a⃗ b ⃗
A) 24
B) 5
C) -4
D) 4
To'g'ri javob: D) 4
✔
5. x² + 7x + 12 = 0 tenglama ildizlarining ko'paytmasini toping.
A) -12
B) 12
C) 13
D) -7
To'g'ri javob: B) 12
✔
6. √64 ni hisoblang.
A) 7
B) 9
C) 32
D) 8
To'g'ri javob: D) 8
✔
Matematika — milliy sertifikat mashq variantlari | 52

7. Uchburchak yuzini toping.
Asosi 14, unga tushirilgan balandlik 16
A) 30
B) 112
C) 224
D) 113
To'g'ri javob: B) 112✔
8. 200 ning 10% ini toping.
A) 21
B) 18
C) 26
D) 20
To'g'ri javob: D) 20
✔
9. Trapetsiya yuzini toping.
Asoslari 14 va 10, balandligi 10
A) 130
B) 120
C) 1400
D) 240
To'g'ri javob: B) 120
✔
10. f'(x₀) ni toping.
f(x) = 2x³ + 5x² − 3x − 6, x₀ = -1
A) -8
B) -7
C) 0
D) 3
To'g'ri javob: B) -7
✔
11. Ehtimollikni toping.
Qutida 6 ta oq va 9 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 2/3
B) 2/5
C) 1/15
D) 3/5
To'g'ri javob: B) 2/5
✔
12. f(x) = 4x + 8 bo'lsa, f(-1) ni toping.
A) 4
B) 8
C) 2
D) 0
To'g'ri javob: A) 4
✔
Matematika — milliy sertifikat mashq variantlari | 53

13. f'(x₀) ni toping.
f(x) = 3x³ + 2x² − 2x + 4, x₀ = 4
A) 162
B) 220
C) 157
D) 158
To'g'ri javob: D) 158✔
14. ∫ x dx nimaga teng?
A) x²/2 + C
B) 2x + C
C) x² + C
D) 1 + C
To'g'ri javob: A) x²/2 + C
✔
15. Uchburchak yuzini toping.
Asosi 6, unga tushirilgan balandlik 11
A) 33
B) 34
C) 17
D) 66
To'g'ri javob: A) 33
✔
16. 1 radian taxminan necha gradusga teng?
A) 3,14°
B) 90°
C) 57,3°
D) 180°
To'g'ri javob: C) 57,3°
✔
17. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 5, q = 3, n = 5
A) 605
B) 405
C) 602
D) 610
To'g'ri javob: A) 605
✔
18. Trapetsiya yuzini toping.
Asoslari 2 va 2, balandligi 4
A) 9
B) 12
C) 16
D) 8
To'g'ri javob: D) 8
✔
19. Parallelogramm yuzi formulasi qaysi?
A) S = a²
B) S = a · h
C) S = a · h / 2
D) S = (a + b) · h / 2
To'g'ri javob: B) S = a · h
✔
Matematika — milliy sertifikat mashq variantlari | 54

20. Konus hajmi formulasi qaysi?
A) V = 4/3 · πr³
B) V = πrh
C) V = πr²h
D) V = 1/3 · πr²h
To'g'ri javob: D) V = 1/3 · πr²h✔
21. Tengsizlikni yeching: 3x − 8 > 8
A) x > 0
B) x > 16/3
C) x < 16/3
D) x > 19/3
To'g'ri javob: B) x > 16/3
✔
22. x² + 6x = 0 tenglama ildizlarining ko'paytmasini toping.
A) 0
B) 1
C) -6
D) 3
To'g'ri javob: A) 0
✔
23. O'rinlashtirishlar soni A ᵏ qanday hisoblanadi?
ₙ
A) n! / (n − k)!
B) n!
C) nᵏ
D) n! / (k!(n − k)!)
To'g'ri javob: A) n! / (n − k)!
✔
24. Tenglamani yeching.
5(x + 3) = 3x + 9
A) -3
B) -2
C) -5
D) 3
To'g'ri javob: A) -3
✔
25. Logarifmik tenglamani yeching.
log₃(x − 8) = 3
A) 17
B) 27
C) 35
D) 19
To'g'ri javob: C) 35
✔
26. Masalani yeching.
Narx 1400 so'm. Avval 10% ga oshirildi, so'ng 25% ga kamaytirildi. Oxirgi narx necha so'm?
A) 1400
B) 1190
C) 1155
D) 1255
To'g'ri javob: C) 1155
✔
Matematika — milliy sertifikat mashq variantlari | 55

27. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 4, d = 2, n = 8
A) 88
B) 80
C) 90
D) 18
To'g'ri javob: A) 88✔
28. f(x) = 3x + 7 bo'lsa, f(4) ni toping.
A) 15
B) 23
C) 19
D) 16
To'g'ri javob: C) 19
✔
29. Masalani yeching.
Mahsulot narxi 2200 so'm edi. Narx 15% ga oshirildi. Yangi narx necha so'm?
A) 330
B) 2215
C) 2530
D) 1870
To'g'ri javob: C) 2530
✔
30. Hisoblang.
4/11 + 5/11
A) 20/121
B) 100/121
C) 9/22
D) 9/11
To'g'ri javob: D) 9/11
✔
31. Hisoblang.
√64 + √81
A) 72
B) 17
C) 12
D) 16
To'g'ri javob: B) 17
✔
32. Tub son nima?
A) Ikkidan ortiq bo'luvchisi bor son
B) Faqat 1 ga va o'ziga bo'linadigan, 1 dan katta natural son
C) 1 ga bo'linmaydigan son
D) Faqat juft son
To'g'ri javob: B) Faqat 1 ga va o'ziga bo'linadigan, 1 dan katta natural son
✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) A(8; 4) a) 20
2) A(9; 3) b) 72
3) C(9; 4) c) 126
Matematika — milliy sertifikat mashq variantlari | 56

4) C(7; 3) d) 504
e) 1680
f) 35
A) 1–e, 2–d, 3–c, 4–f
B) 1–e, 2–d, 3–c, 4–a
C) 1–c, 2–d, 3–e, 4–f
D) 1–d, 2–f, 3–c, 4–e
To'g'ri javob: A) 1–e, 2–d, 3–c, 4–f✔
34. Har bir ifodaga uning qiymatini moslang.
1) C(8; 2) a) 10
2) C(8; 3) b) 28
3) C(6; 3) c) 120
4) C(5; 3) d) 56
e) 20
f) 70
A) 1–b, 2–d, 3–e, 4–a
B) 1–b, 2–d, 3–e, 4–f
C) 1–b, 2–e, 3–d, 4–a
D) 1–b, 2–d, 3–a, 4–e
To'g'ri javob: A) 1–b, 2–d, 3–e, 4–a
✔
35. Har bir ifodaga uning qiymatini moslang.
1) log₃3 + log₃3 a) 6
2) log₂4 + log₂16 b) 2
3) log₅25 + log₅25 c) 4
4) log₂8 + log₂4 d) 3
e) 5
f) 9
A) 1–b, 2–a, 3–e, 4–c
B) 1–b, 2–a, 3–c, 4–e
C) 1–e, 2–c, 3–b, 4–a
D) 1–d, 2–a, 3–c, 4–e
To'g'ri javob: B) 1–b, 2–a, 3–c, 4–e
✔
O • ochiq topshiriq (qisqa javob)
36. Aylana uzunligini toping (π orqali). Javobni yozing.
a) Radius R = 12
b) Radius R = 15
Javob: a) 24π; b) 30π
✔
37. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) x² + 5x = 0
b) x² + 6x − 7 = 0
Javob: a) -5; b) -6
✔
Matematika — milliy sertifikat mashq variantlari | 57

38. To'g'ri burchakli parallelepiped hajmini toping. Javobni yozing.
a) O'lchamlari 8, 2, 3
b) O'lchamlari 7, 2, 9
Javob: a) 48; b) 126✔
39. EKUKni toping. Javobni yozing.
a) EKUK(77; 78)
b) EKUK(46; 46)
Javob: a) 6006; b) 46
✔
40. Aylana uzunligini toping (π orqali). Javobni yozing.
a) Radius R = 11
b) Radius R = 14
Javob: a) 22π; b) 28π
✔
41. Guruhlashlar sonini toping. Javobni yozing.
a) C(8; 2)
b) C(8; 3)
Javob: a) 28; b) 56
✔
42. Tenglamalar sistemasini yeching va x + y ni toping. Javobni yozing.
a) { 5x + y = -40; 3x − 4y = -1 }
b) { 3x + 2y = -2; 4x − 5y = -41 }
Javob: a) -12; b) 1
✔
43. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² − 2x − 3
b) y = x² − 4x + 6
Javob: a) -4; b) 2
✔
44. Ifodaning qiymatini toping. Javobni yozing.
a) cos 60° + sin 270°
b) cos 180° + sin 30°
Javob: a) −1/2; b) −1/2
✔
45. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 5, q = -2, n = 3
b) b₁ = 5, q = 2, n = 6
Javob: a) 15; b) 315
✔
Matematika — milliy sertifikat mashq variantlari | 58

8-variant
Y-1 • bitta to'g'ri javob
1. Pifagor teoremasi qanday ifodalanadi?
A) Katetlar kvadratlari ayirmasi gipotenuzaga teng
B) Gipotenuza kvadrati katetlar kvadratlari yig'indisiga teng
C) Gipotenuza katetlar yig'indisiga teng
D) Barcha tomonlar teng
To'g'ri javob: B) Gipotenuza kvadrati katetlar kvadratlari yig'indisiga teng✔
2. Ifodaning qiymatini toping.
log₂8 + log₂16
A) 8
B) 128
C) 7
D) 12
To'g'ri javob: C) 7
✔
3. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 7, d = 2, n = 18
A) 434
B) 414
C) 41
D) 432
To'g'ri javob: D) 432
✔
4. Ifodaning qiymatini toping.
7^6 · 7^4 : 7^2
A) 282475249
B) 5764801
C) 5764808
D) 3909821048582988049
To'g'ri javob: B) 5764801
✔
5. Tengsizlikni yeching: 3x + 1 > 14
A) x < 13/3
B) x > 13/3
C) x > 16/3
D) x > 5
To'g'ri javob: B) x > 13/3
✔
6. x² − 4x − 32 = 0 tenglama ildizlarining ko'paytmasini toping.
A) 32
B) -31
C) -32
D) 4
To'g'ri javob: C) -32
✔
Matematika — milliy sertifikat mashq variantlari | 59

7. f(x₀) qiymatini toping.
f(x) = 3x² + 6x + 4, x₀ = 4
A) -76
B) 79
C) 76
D) 22
To'g'ri javob: C) 76✔
8. Ratsional sonlar to'plami qanday belgilanadi?
A) N
B) Z
C) Q
D) I
To'g'ri javob: C) Q
✔
9. Arifmetik progressiyada a₁ = 3, d = 4. Dastlabki 8 ta had yig'indisini toping.
A) 149
B) 127
C) 130
D) 136
To'g'ri javob: D) 136
✔
10. Tenglamaning katta ildizini toping.
x² − 9x + 14 = 0
A) 8
B) 2
C) 7
D) -7
To'g'ri javob: C) 7
✔
11. Tenglama ildizlari yig'indisini toping.
|x + 3| = 3
A) -6
B) 0
C) 3
D) 6
To'g'ri javob: A) -6
✔
12. A va B nuqtalar orasidagi masofani toping.
A(-1; 3), B(-6; 15)
A) 15
B) 13
C) 17
D) 7
To'g'ri javob: B) 13
✔
Matematika — milliy sertifikat mashq variantlari | 60

13. Ehtimollikni toping.
Qutida 9 ta oq va 2 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 2/11
B) 9/2
C) 9/11
D) 1/11
To'g'ri javob: C) 9/11✔
14. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 2, q = 3, n = 6
A) 725
B) 728
C) 486
D) 730
To'g'ri javob: B) 728
✔
15. Tenglama ildizlari yig'indisini toping.
|x − 5| = 3
A) 3
B) 8
C) -10
D) 10
To'g'ri javob: D) 10
✔
16. A va B nuqtalar orasidagi masofani toping.
A(3; -5), B(-3; 3)
A) 10
B) 2
C) 14
D) 12
To'g'ri javob: A) 10
✔
17. Vektor uzunligini toping.
(-8; 6)
a⃗
A) 2
B) 14
C) 10
D) 11
To'g'ri javob: C) 10
✔
18. Ehtimollikni toping.
Qutida 2 ta oq va 7 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 7/9
B) 2/9
C) 1/9
D) 2/7
To'g'ri javob: B) 2/9
✔
Matematika — milliy sertifikat mashq variantlari | 61

19. Uchburchak yuzini toping.
Asosi 10, unga tushirilgan balandlik 17
A) 85
B) 27
C) 170
D) 86
To'g'ri javob: A) 85✔
20. Tengsizlikning butun yechimlari sonini toping.
x² − 1 < 0
A) 0
B) 1
C) 2
D) 3
To'g'ri javob: B) 1
✔
21. Hisoblang.
√121 + √49
A) 17
B) 18
C) 13
D) 77
To'g'ri javob: B) 18
✔
22. 2x² + x − 7 = 0 tenglamaning diskriminantini toping.
A) 57
B) 61
C) 53
D) -55
To'g'ri javob: A) 57
✔
23. Ko'rsatkichli tenglamani yeching.
3^(x − 1) = 27
A) 5
B) 2
C) 3
D) 4
To'g'ri javob: D) 4
✔
24. Son 3 ga bo'linishi uchun qanday shart bajarilishi kerak?
A) Raqamlari yig'indisi 3 ga bo'linishi kerak
B) Juft bo'lishi kerak
C) Oxirgi raqami 3 bo'lishi kerak
D) Oxirgi ikki raqami 3 ga bo'linishi kerak
To'g'ri javob: A) Raqamlari yig'indisi 3 ga bo'linishi kerak
✔
25. f(x) = 3x² + 3x − 5 funksiyaning x = -3 nuqtadagi hosilasini toping.
A) -13
B) -15
C) 9
D) 13
To'g'ri javob: B) -15
✔
Matematika — milliy sertifikat mashq variantlari | 62

26. Tenglamalar sistemasini yeching: x + y = 4, x − y = 10. x ni toping.
A) 4
B) 7
C) -3
D) 6
To'g'ri javob: B) 7✔
27. Tenglamani yeching.
4(x + 15) = 3x + 53
A) -9
B) 7
C) -7
D) -6
To'g'ri javob: C) -7
✔
28. A va B nuqtalar orasidagi masofani toping.
A(2; 3), B(8; 11)
A) 10
B) 2
C) 12
D) 14
To'g'ri javob: A) 10
✔
29. Kub hajmi formulasi qaysi?
A) V = 3a
B) V = 6a²
C) V = a³
D) V = a²
To'g'ri javob: C) V = a³
✔
30. Ifodaning qiymatini toping.
2^6 · 2^2 : 2^2
A) 1024
B) 256
C) 66
D) 64
To'g'ri javob: D) 64
✔
31. Natural sonlar to'plami qanday belgilanadi?
A) N
B) Z
C) Q
D) R
To'g'ri javob: A) N
✔
32. Uchburchakning ikki burchagi 33° va 82°. Uchinchi burchagini toping.
A) 65°
B) 75°
C) 115°
D) 245°
To'g'ri javob: A) 65°
✔
Matematika — milliy sertifikat mashq variantlari | 63

Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) 5^5 · 5^2 : 5^1 a) 343
2) 7^3 · 7^5 : 7^3 b) 81
3) 2^2 · 2^6 : 2^5 c) 16807
4) 3^4 · 3^3 : 3^3 d) 15625
e) 243
f) 8
A) 1–d, 2–c, 3–f, 4–b
B) 1–c, 2–f, 3–d, 4–b
C) 1–f, 2–b, 3–c, 4–d
D) 1–e, 2–c, 3–f, 4–b
To'g'ri javob: A) 1–d, 2–c, 3–f, 4–b✔
34. Har bir ifodaga uning qiymatini moslang.
1) 4/4 + 7/2 a) 9/2
2) 2/3 + 2/7 b) 20/21
3) 1/7 + 2/9 c) 38/21
4) 8/7 + 6/9 d) 23/63
e) 10/11
f) 9/5
A) 1–a, 2–b, 3–f, 4–c
B) 1–a, 2–b, 3–c, 4–d
C) 1–a, 2–b, 3–d, 4–c
D) 1–a, 2–c, 3–d, 4–b
To'g'ri javob: C) 1–a, 2–b, 3–d, 4–c
✔
35. Har bir ifodaga uning qiymatini moslang.
1) C(9; 2) a) 336
2) C(7; 3) b) 15
3) C(6; 2) c) 360
4) A(8; 4) d) 36
e) 1680
f) 35
A) 1–d, 2–f, 3–e, 4–b
B) 1–d, 2–f, 3–c, 4–e
C) 1–d, 2–f, 3–b, 4–e
D) 1–e, 2–b, 3–f, 4–d
To'g'ri javob: C) 1–d, 2–f, 3–b, 4–e
✔
O • ochiq topshiriq (qisqa javob)
36. Silindr hajmini toping (π orqali). Javobni yozing.
a) Asos radiusi 3, balandligi 4
b) Asos radiusi 6, balandligi 4
Javob: a) 36π; b) 144π
✔
Matematika — milliy sertifikat mashq variantlari | 64

37. Tenglamaning katta ildizini toping. Javobni yozing.
a) x² + x − 6 = 0
b) x² − 8x + 15 = 0
Javob: a) 2; b) 5✔
38. f(x₀) qiymatini toping. Javobni yozing.
a) f(x) = 2x² − 5x + 5, x₀ = -1
b) f(x) = x² + 6x + 1, x₀ = 3
Javob: a) 12; b) 28
✔
39. Ko'rsatkichli tenglamani yeching. Javobni yozing.
a) 2^(x − 2) = 64
b) 2^(x − 4) = 8
Javob: a) 8; b) 7
✔
40. Ko'rsatkichli tenglamani yeching. Javobni yozing.
a) 2^(x − 3) = 4
b) 3^(x − 2) = 81
Javob: a) 5; b) 6
✔
41. Hisoblang. Javobni yozing.
a) √225 + √4
b) √25 + √169
Javob: a) 17; b) 18
✔
42. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 5, q = -2, n = 6
b) b₁ = 3, q = 2, n = 4
Javob: a) -105; b) 45
✔
43. f'(x₀) ni toping. Javobni yozing.
a) f(x) = 4x² + 6x − 3, x₀ = -2
b) f(x) = x³ + 2x² − x + 6, x₀ = -1
Javob: a) -10; b) -2
✔
44. Uchburchak yuzini toping. Javobni yozing.
a) Asosi 14, unga tushirilgan balandlik 15
b) Asosi 2, unga tushirilgan balandlik 3
Javob: a) 105; b) 3
✔
45. f'(x₀) ni toping. Javobni yozing.
a) f(x) = x³ + 4x² − x − 9, x₀ = 0
b) f(x) = x³ + 5x² + 3x − 5, x₀ = 3
Javob: a) -1; b) 60
✔
Matematika — milliy sertifikat mashq variantlari | 65

9-variant
Y-1 • bitta to'g'ri javob
1. EKUBni toping.
EKUB(22; 59)
A) 2
B) 1
C) 37
D) 1298
To'g'ri javob: B) 1✔
2. f'(x₀) ni toping.
f(x) = x³ + 2x² + 7, x₀ = -1
A) 3
B) 8
C) -1
D) -2
To'g'ri javob: C) -1
✔
3. EKUB(10; 18) ni toping.
A) 1
B) 90
C) 2
D) 4
To'g'ri javob: C) 2
✔
4. Guruhlashlar sonini toping.
C(10; 2)
A) 90
B) 45
C) 10
D) 20
To'g'ri javob: B) 45
✔
5. Qirrasi 7 ga teng kubning to'la sirti yuzini toping.
A) 294
B) 196
C) 84
D) 343
To'g'ri javob: A) 294
✔
6. Ehtimollikni toping.
Qutida 3 ta oq va 5 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 5/8
B) 3/8
C) 1/8
D) 3/5
To'g'ri javob: B) 3/8
✔
Matematika — milliy sertifikat mashq variantlari | 66

7. Ifodaning qiymatini toping.
log₅3125 + log₅5
A) 6
B) 5
C) 7
D) 15625
To'g'ri javob: A) 6✔
8. Parabola uchining ordinatasini toping.
y = x² − 2x − 1
A) -1
B) 0
C) -2
D) 1
To'g'ri javob: C) -2
✔
9. Ifodaning qiymatini toping.
log₅125 + log₅5
A) 4
B) 5
C) 625
D) 3
To'g'ri javob: A) 4
✔
10. Aniq integralni hisoblang.
∫₀^2 (8x) dx
A) 18
B) 17
C) 32
D) 16
To'g'ri javob: D) 16
✔
11. Qavariq 9-burchakning ichki burchaklari yig'indisini toping.
A) 1260°
B) 1620°
C) 2520°
D) 1440°
To'g'ri javob: A) 1260°
✔
12. O'rinlashtirishlar sonini toping.
A(6; 4)
A) 360
B) 15
C) 120
D) 1296
To'g'ri javob: A) 360
✔
Matematika — milliy sertifikat mashq variantlari | 67

13. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 5, q = 2, n = 4
A) 75
B) 80
C) 73
D) 40
To'g'ri javob: A) 75✔
14. f(x₀) qiymatini toping.
f(x) = 4x² + 6x − 5, x₀ = -2
A) -1
B) 3
C) -7
D) 1
To'g'ri javob: A) -1
✔
15. Logarifmik tenglamani yeching.
log₂(x − 4) = 2
A) 0
B) 9
C) 4
D) 8
To'g'ri javob: D) 8
✔
16. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 5, q = -2, n = 6
A) -160
B) -100
C) -103
D) -105
To'g'ri javob: D) -105
✔
17. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 3, q = -2, n = 6
A) -61
B) -96
C) -63
D) -60
To'g'ri javob: C) -63
✔
18. sin 30° ning qiymatini toping.
A) √2/2
B) 1/2
C) √3
D) √3/3
To'g'ri javob: B) 1/2
✔
Matematika — milliy sertifikat mashq variantlari | 68

19. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 4, 3, 7
A) 88
B) 14
C) 122
D) 84
To'g'ri javob: D) 84✔
20. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 5, 5, 9
A) 19
B) 225
C) 230
D) 226
To'g'ri javob: B) 225
✔
21. Ifodaning qiymatini toping.
2^5 · 2^5 : 2^2
A) 258
B) 1024
C) 8388608
D) 256
To'g'ri javob: D) 256
✔
22. EKUKni toping.
EKUK(35; 53)
A) 1890
B) 1855
C) 1
D) 3710
To'g'ri javob: B) 1855
✔
23. Uchburchakning ikki burchagi 46° va 20°. Uchinchi burchagini toping.
A) 114°
B) 66°
C) 124°
D) 294°
To'g'ri javob: A) 114°
✔
24. Tengsizlikning butun yechimlari sonini toping.
x² + 7x + 10 < 0
A) 1
B) 2
C) 3
D) 4
To'g'ri javob: B) 2
✔
Matematika — milliy sertifikat mashq variantlari | 69

25. Qirrasi 8 ga teng kubning to'la sirti yuzini toping.
A) 512
B) 96
C) 256
D) 384
To'g'ri javob: D) 384✔
26. Vektorlarning skalyar ko'paytmasini toping.
(-2; 5), (4; 1)
a⃗ b ⃗
A) 3
B) -2
C) -22
D) -3
To'g'ri javob: D) -3
✔
27. Ifodaning qiymatini toping.
3^5 · 3^2 : 3^5
A) 9
B) 12
C) 243
D) 2187
To'g'ri javob: A) 9
✔
28. Parabola uchining ordinatasini toping.
y = x² + 8x + 24
A) 9
B) -4
C) 8
D) 24
To'g'ri javob: C) 8
✔
29. Uchburchak yuzini toping.
Asosi 5, unga tushirilgan balandlik 12
A) 31
B) 30
C) 17
D) 60
To'g'ri javob: B) 30
✔
30. Logarifmik tenglamani yeching.
log₃(x − 7) = 2
A) 9
B) 13
C) 2
D) 16
To'g'ri javob: D) 16
✔
Matematika — milliy sertifikat mashq variantlari | 70

31. Romb diagonallari haqida qaysi fikr to'g'ri?
A) Ular har doim teng
B) Ular parallel
C) Ular o'zaro perpendikulyar va kesishish nuqtasida teng ikkiga bo'linadi
D) Ular kesishmaydi
To'g'ri javob: C) Ular o'zaro perpendikulyar va kesishish nuqtasida teng ikkiga bo'linadi✔
32. Ifodaning qiymatini toping.
log₅5 + log₅5
A) 25
B) 1
C) 2
D) 3
To'g'ri javob: C) 2
✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) 2^4 · 2^6 : 2^5 a) 3125
2) 2^6 · 2^2 : 2^4 b) 78125
3) 7^3 · 7^4 : 7^3 c) 2401
4) 5^2 · 5^4 : 5^1 d) 81
e) 32
f) 16
A) 1–e, 2–a, 3–c, 4–f
B) 1–a, 2–f, 3–e, 4–c
C) 1–e, 2–f, 3–c, 4–a
D) 1–d, 2–f, 3–c, 4–a
To'g'ri javob: C) 1–e, 2–f, 3–c, 4–a
✔
34. Har bir ifodaga uning qiymatini moslang.
1) EKUK(54; 51) a) 1
2) EKUK(84; 8) b) 264
3) EKUK(88; 24) c) 280
4) EKUB(38; 32) d) 2
e) 168
f) 918
A) 1–f, 2–a, 3–b, 4–d
B) 1–f, 2–e, 3–b, 4–d
C) 1–a, 2–e, 3–b, 4–d
D) 1–e, 2–b, 3–f, 4–d
To'g'ri javob: B) 1–f, 2–e, 3–b, 4–d
✔
35. Har bir ifodaga uning qiymatini moslang.
1) C(9; 4) a) 90
2) A(10; 2) b) 120
3) A(8; 2) c) 42
Matematika — milliy sertifikat mashq variantlari | 71

4) A(7; 2) d) 56
e) 126
f) 5
A) 1–e, 2–a, 3–d, 4–c
B) 1–f, 2–a, 3–d, 4–c
C) 1–e, 2–a, 3–d, 4–b
D) 1–a, 2–e, 3–d, 4–c
To'g'ri javob: A) 1–e, 2–a, 3–d, 4–c✔
O • ochiq topshiriq (qisqa javob)
36. Ko'rsatkichli tenglamani yeching. Javobni yozing.
a) 3^(x − 2) = 81
b) 3^(x − 4) = 27
Javob: a) 6; b) 7
✔
37. Vektorlarning skalyar ko'paytmasini toping. Javobni yozing.
a) (3; 4), (4; -1)
a⃗ b ⃗
b) (2; 3), (2; -2)
a⃗ b ⃗
Javob: a) 8; b) -2
✔
38. Ifodaning qiymatini toping. Javobni yozing.
a) cos 0° + cos 180°
b) tg 0° + cos 180°
Javob: a) 0; b) −1
✔
39. EKUBni toping. Javobni yozing.
a) EKUB(47; 42)
b) EKUB(19; 87)
Javob: a) 1; b) 1
✔
40. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 1, q = 3, n = 3
b) b₁ = 3, q = -2, n = 3
Javob: a) 13; b) 9
✔
41. Ehtimollikni toping. Javobni yozing.
a) Qutida 7 ta oq va 3 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 3 ta oq va 3 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 7/10; b) 1/2
✔
42. Hisoblang. Javobni yozing.
a) 7/10 + 9/12
b) 6/5 + 2/2
Javob: a) 29/20; b) 11/5
✔
43. Hisoblang. Javobni yozing.
a) √169 + √196
b) √4 + √225
Javob: a) 27; b) 17
✔
Matematika — milliy sertifikat mashq variantlari | 72

44. O'rinlashtirishlar sonini toping. Javobni yozing.
a) A(8; 2)
b) A(8; 4)
Javob: a) 56; b) 1680✔
45. Uchburchak yuzini toping. Javobni yozing.
a) Asosi 14, unga tushirilgan balandlik 20
b) Asosi 16, unga tushirilgan balandlik 18
Javob: a) 140; b) 144
✔
Matematika — milliy sertifikat mashq variantlari | 73

$10-variant Y-1 • bitta to'g'ri javob 1. x² + 2x − 8 = 0 tenglama ildizlarining ko'paytmasini toping. A) -8 B) 8 C) -2 D) -7 To'g'ri javob: A) -8✔ 2. Aniq integralni hisoblang. ∫₀^2 (2x − 2) dx A) 0 B) 2 C) 3 D) 1 To'g'ri javob: A) 0 ✔ 3. f(x) = 2x − 6 bo'lsa, f(1) ni toping. A) -4 B) -2 C) 0 D) -6 To'g'ri javob: A) -4 ✔ 4. Trapetsiya yuzini toping. Asoslari 4 va 8, balandligi 12 A) 144 B) 84 C) 384 D) 72 To'g'ri javob: D) 72 ✔ 5. Tenglamalar sistemasini yeching va x + y ni toping. { 5x + 4y = 4; 3x − 2y = -24 } A) 2 B) 4 C) -24 D) -10 To'g'ri javob: A) 2 ✔ 6. Tenglama ildizlari yig'indisini toping. x² + 15x + 56 = 0 A) -14 B) -15 C) 15 D) 56 To'g'ri javob: B) -15 ✔ Matematika — milliy sertifikat mashq variantlari | 74$

7. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 2, q = 3, n = 3
A) 26
B) 28
C) 23
D) 18
To'g'ri javob: A) 26✔
8. Parabola uchining ordinatasini toping.
y = x² + 12x + 32
A) 32
B) -3
C) -6
D) -4
To'g'ri javob: D) -4
✔
9. Hisoblang.
√81 + √100
A) 13
B) 90
C) 18
D) 19
To'g'ri javob: D) 19
✔
10. Sinuslar teoremasi qanday ifodalanadi?
A) a / sinA = b / sinB = c / sinC = 2R
B) a + b + c = 2R
C) a² = b² + c² − 2bc·cosA
D) sinA + sinB + sinC = 1
To'g'ri javob: A) a / sinA = b / sinB = c / sinC = 2R
✔
11. Tenglamaning katta ildizini toping.
x² − 14x + 45 = 0
A) 10
B) -9
C) 9
D) 5
To'g'ri javob: C) 9
✔
12. Shar hajmi formulasi qaysi?
A) V = 1/3 · πr²h
B) V = πr²h
C) V = 4/3 · πr³
D) V = 4πr²
To'g'ri javob: C) V = 4/3 · πr³
✔
13. Uchburchakning o'rta chizig'i haqida qaysi fikr to'g'ri?
A) U uchinchi tomondan ikki baravar uzun
B) U uchinchi tomonga teng
C) U uchinchi tomonga perpendikulyar
D) U uchinchi tomonga parallel va uning yarmiga teng
To'g'ri javob: D) U uchinchi tomonga parallel va uning yarmiga teng
✔
Matematika — milliy sertifikat mashq variantlari | 75

14. Uchburchak yuzini toping.
Asosi 12, unga tushirilgan balandlik 5
A) 17
B) 60
C) 31
D) 30
To'g'ri javob: D) 30✔
15. Tenglamani yeching.
2(x + 20) = 3x + 28
A) 13
B) 10
C) 12
D) -12
To'g'ri javob: C) 12
✔
16. Hisoblang.
√100 + √36
A) 15
B) 60
C) 16
D) 11
To'g'ri javob: C) 16
✔
17. Vektorlarning skalyar ko'paytmasi nolga teng bo'lsa, vektorlar qanday joylashgan?
A) Qarama-qarshi yo'nalgan
B) Teng
C) Parallel
D) O'zaro perpendikulyar
To'g'ri javob: D) O'zaro perpendikulyar
✔
18. Arifmetik progressiyaning n-hadi formulasi qaysi?
A) a = a₁ + (n − 1)d
ₙ
B) a = a₁ + nd
ₙ
C) a = a₁ · qⁿ⁻¹
ₙ
D) a = n · d
ₙ
To'g'ri javob: A) aₙ = a₁ + (n − 1)d
✔
19. Silindr hajmini toping (π orqali).
Asos radiusi 3, balandligi 8
A) 24π
B) 144π
C) 72π
D) 48π
To'g'ri javob: C) 72π
✔
Matematika — milliy sertifikat mashq variantlari | 76

20. Parabola uchining ordinatasini toping.
y = x² − 12x + 38
A) 38
B) 2
C) 6
D) 3
To'g'ri javob: B) 2✔
21. Aniq integralni hisoblang.
∫₀^3 (2x) dx
A) 18
B) 6
C) 9
D) 12
To'g'ri javob: C) 9
✔
22. f(x₀) qiymatini toping.
f(x) = 2x² + 3x + 1, x₀ = -1
A) 3
B) 2
C) 0
D) 1
To'g'ri javob: C) 0
✔
23. Ifodani soddalashtiring: 2^3 · 2^4
A) 2^1
B) 2^12
C) 2^7
D) 4^7
To'g'ri javob: C) 2^7
✔
24. Tenglama ildizlari yig'indisini toping.
x² − 6x + 8 = 0
A) -6
B) 8
C) 7
D) 6
To'g'ri javob: D) 6
✔
25. Ifodaning qiymatini toping.
sin 270° + cos 90°
A) 1
B) −3
C) −1
D) −2
To'g'ri javob: C) −1
✔
Matematika — milliy sertifikat mashq variantlari | 77

26. Parabola uchining ordinatasini toping.
y = x² + 8
A) 0
B) 8
C) 10
D) 9
To'g'ri javob: B) 8✔
27. Hisoblang.
√36 + √169
A) 78
B) 18
C) 14
D) 19
To'g'ri javob: D) 19
✔
28. (sin x)' hosilasi nimaga teng?
A) cos x
B) tg x
C) −sin x
D) −cos x
To'g'ri javob: A) cos x
✔
29. Masalani yeching.
Narx 800 so'm. Avval 10% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
A) 800
B) 793
C) 892
D) 792
To'g'ri javob: D) 792
✔
30. Masalani yeching.
Narx 1600 so'm. Avval 25% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
A) 1800
B) 1600
C) 1840
D) 1900
To'g'ri javob: A) 1800
✔
31. Eng kichik tub son qaysi?
A) 3
B) 2
C) 0
D) 1
To'g'ri javob: B) 2
✔
Matematika — milliy sertifikat mashq variantlari | 78

32. Uchburchak yuzini toping.
Asosi 19, unga tushirilgan balandlik 3
A) 57/2
B) 59/2
C) 57
D) 22
To'g'ri javob: A) 57/2✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) 3^4 · 3^2 : 3^3 a) 40353607
2) 7^5 · 7^6 : 7^2 b) 2401
3) 7^4 · 7^3 : 7^4 c) 16807
4) 7^3 · 7^2 : 7^3 d) 49
e) 343
f) 27
A) 1–b, 2–a, 3–e, 4–d
B) 1–f, 2–d, 3–e, 4–a
C) 1–f, 2–a, 3–d, 4–e
D) 1–f, 2–a, 3–e, 4–d
To'g'ri javob: D) 1–f, 2–a, 3–e, 4–d
✔
34. Har bir ifodaga uning qiymatini moslang.
1) 3^4 · 3^6 : 3^4 a) 16
2) 5^6 · 5^2 : 5^5 b) 125
3) 2^2 · 2^6 : 2^4 c) 512
4) 2^3 · 2^6 : 2^4 d) 32
e) 729
f) 3
A) 1–b, 2–d, 3–a, 4–e
B) 1–b, 2–e, 3–a, 4–d
C) 1–e, 2–b, 3–a, 4–d
D) 1–e, 2–c, 3–a, 4–d
To'g'ri javob: C) 1–e, 2–b, 3–a, 4–d
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √64 + √100 a) 13
2) √225 + √144 b) 18
3) √25 + √81 c) 14
4) √196 + √100 d) 24
e) 16
f) 27
Matematika — milliy sertifikat mashq variantlari | 79

A) 1–b, 2–f, 3–c, 4–d
B) 1–b, 2–c, 3–d, 4–f
C) 1–b, 2–f, 3–c, 4–e
D) 1–b, 2–c, 3–f, 4–d
To'g'ri javob: A) 1–b, 2–f, 3–c, 4–d✔
O • ochiq topshiriq (qisqa javob)
36. Ifodaning qiymatini toping. Javobni yozing.
a) tg 0° + cos 90°
b) sin 90° + sin 270°
Javob: a) 0; b) 0
✔
37. A va B nuqtalar orasidagi masofani toping. Javobni yozing.
a) A(-3; 5), B(2; -7)
b) A(5; -2), B(-2; -26)
Javob: a) 13; b) 25
✔
38. Vektor uzunligini toping. Javobni yozing.
a) (6; 8)
a⃗
b) (-12; -5)
a⃗
Javob: a) 10; b) 13
✔
39. O'rinlashtirishlar sonini toping. Javobni yozing.
a) A(8; 4)
b) A(8; 2)
Javob: a) 1680; b) 56
✔
40. EKUBni toping. Javobni yozing.
a) EKUB(32; 52)
b) EKUB(10; 8)
Javob: a) 4; b) 2
✔
41. Guruhlashlar sonini toping. Javobni yozing.
a) C(6; 2)
b) C(8; 2)
Javob: a) 15; b) 28
✔
42. Ehtimollikni toping. Javobni yozing.
a) Qutida 8 ta oq va 6 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 3 ta oq va 4 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 4/7; b) 3/7
✔
43. Tengsizlikning butun yechimlari sonini toping. Javobni yozing.
a) x² + 3x < 0
b) x² − x − 2 < 0
Javob: a) 2; b) 2
✔
44. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x + 4| = 2
b) |x + 7| = 6
Javob: a) -8; b) -14
✔
Matematika — milliy sertifikat mashq variantlari | 80

45. Ifodaning qiymatini toping. Javobni yozing.
a) log₃9 + log₃81
b) log₃81 + log₃3
Javob: a) 6; b) 5✔
Matematika — milliy sertifikat mashq variantlari | 81

11-variant
Y-1 • bitta to'g'ri javob
1. 80 ning 15% ini toping.
A) 12
B) 14
C) 15
D) 10
To'g'ri javob: A) 12✔
2. Trapetsiya yuzini toping.
Asoslari 4 va 9, balandligi 12
A) 78
B) 432
C) 156
D) 90
To'g'ri javob: A) 78
✔
3. Tenglama ildizlari yig'indisini toping.
|x − 2| = 4
A) 5
B) -4
C) 6
D) 4
To'g'ri javob: D) 4
✔
4. 3x² + 8x − 9 = 0 tenglamaning diskriminantini toping.
A) 172
B) 178
C) 168
D) -44
To'g'ri javob: A) 172
✔
5. Ehtimollikni toping.
Qutida 5 ta oq va 7 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 5/7
B) 7/12
C) 1/12
D) 5/12
To'g'ri javob: D) 5/12
✔
6. Parabola uchining ordinatasini toping.
y = x² + 4
A) 5
B) 4
C) 6
D) 0
To'g'ri javob: B) 4
✔
Matematika — milliy sertifikat mashq variantlari | 82

7. Tenglamalar sistemasini yeching: x + y = 5, x − y = 5. x ni toping.
A) 7
B) 0
C) 5
D) 4
To'g'ri javob: C) 5✔
8. f(x) = 1x + 7 bo'lsa, f(3) ni toping.
A) 13
B) 7
C) 9
D) 10
To'g'ri javob: D) 10
✔
9. Tenglama ildizlari yig'indisini toping.
x² + 14x + 48 = 0
A) -13
B) 14
C) 48
D) -14
To'g'ri javob: D) -14
✔
10. Tengsizlikning butun yechimlari sonini toping.
x² + x < 0
A) 2
B) 3
C) 0
D) 1
To'g'ri javob: C) 0
✔
11. Aniq integralni hisoblang.
∫₀^2 (4x − 3) dx
A) 4
B) 5
C) 2
D) 3
To'g'ri javob: C) 2
✔
12. Arifmetik progressiyada a₁ = 12, d = 3. a8 ni toping.
A) 30
B) 33
C) 39
D) 36
To'g'ri javob: B) 33
✔
13. x² − 10x + 24 = 0 tenglama ildizlarining yig'indisini toping.
A) 12
B) 10
C) -10
D) 24
To'g'ri javob: B) 10
✔
Matematika — milliy sertifikat mashq variantlari | 83

14. sin 270° ning qiymatini toping.
A) 0
B) 2
C) −1
D) 1
To'g'ri javob: C) −1✔
15. Tenglama ildizlari yig'indisini toping.
|x − 9| = 3
A) -18
B) 12
C) 3
D) 18
To'g'ri javob: D) 18
✔
16. Arifmetik progressiyada a₁ = 2, d = 4. a9 ni toping.
A) 38
B) 30
C) 42
D) 34
To'g'ri javob: D) 34
✔
17. Ifodaning qiymatini toping.
log₃9 + log₃3
A) 3
B) 27
C) 4
D) 2
To'g'ri javob: A) 3
✔
18. Hisoblang.
√144 + √144
A) 23
B) 24
C) 144
D) 16
To'g'ri javob: B) 24
✔
19. Geometrik progressiyada b₁ = 5, q = 3. b6 ni toping.
A) 405
B) 3645
C) 1215
D) -1215
To'g'ri javob: C) 1215
✔
20. Ehtimollikni toping.
Qutida 8 ta oq va 7 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 1/15
B) 8/7
C) 7/15
D) 8/15
To'g'ri javob: D) 8/15
✔
Matematika — milliy sertifikat mashq variantlari | 84

21. Doira yuzini toping (π orqali).
Radius R = 9
A) 18π
B) 9π
C) 162π
D) 81π
To'g'ri javob: D) 81π✔
22. Tengsizlikning butun yechimlari sonini toping.
x² − 2x − 8 < 0
A) 5
B) 6
C) 4
D) 7
To'g'ri javob: A) 5
✔
23. Masalani yeching.
Narx 900 so'm. Avval 10% ga oshirildi, so'ng 20% ga kamaytirildi. Oxirgi narx necha so'm?
A) 892
B) 810
C) 900
D) 792
To'g'ri javob: D) 792
✔
24. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 3, q = 2, n = 3
A) 12
B) 24
C) 19
D) 21
To'g'ri javob: D) 21
✔
25. Masalani yeching.
Narx 2300 so'm. Avval 20% ga oshirildi, so'ng 20% ga kamaytirildi. Oxirgi narx necha so'm?
A) 2308
B) 2209
C) 2300
D) 2208
To'g'ri javob: D) 2208
✔
26. tgα qanday aniqlanadi?
A) 1 / sinα
B) cosα / sinα
C) sinα / cosα
D) sinα · cosα
To'g'ri javob: C) sinα / cosα
✔
Matematika — milliy sertifikat mashq variantlari | 85

$27. EKUKni toping. EKUK(77; 9) A) 770 B) 1386 C) 693 D) 1 To'g'ri javob: C) 693✔ 28. (eˣ)' hosilasi nimaga teng? A) ln x B) 1/x C) eˣ D) x·eˣ⁻¹ To'g'ri javob: C) eˣ ✔ 29. Tengsizlikning butun yechimlari sonini toping. x² − 11x + 28 < 0 A) 4 B) 1 C) 2 D) 3 To'g'ri javob: C) 2 ✔ 30. Arifmetik progressiyada a₁ = 10, d = 3. a11 ni toping. A) 40 B) 37 C) 43 D) 46 To'g'ri javob: A) 40 ✔ 31. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. a₁ = 11, d = -2, n = 17 A) -21 B) -102 C) -85 D) -87 To'g'ri javob: C) -85 ✔ 32. Tenglamalar sistemasini yeching va x + y ni toping. { 2x + 4y = 26; 3x − 3y = -33 } A) 5 B) 7 C) -11 D) -24 To'g'ri javob: A) 5 ✔ Y-2 • moslashtirish 33. Har bir ifodaga uning qiymatini moslang. 1) 2^3 · 2^4 : 2^5 a) 9 2) 3^3 · 3^4 : 3^5 b) 32 3) 2^5 · 2^4 : 2^4 c) 4 Matematika — milliy sertifikat mashq variantlari | 86$

4) 5^5 · 5^6 : 5^2 d) 64
e) 1953125
f) 81
A) 1–c, 2–e, 3–a, 4–b
B) 1–c, 2–a, 3–b, 4–e
C) 1–c, 2–f, 3–b, 4–e
D) 1–b, 2–e, 3–a, 4–c
To'g'ri javob: B) 1–c, 2–a, 3–b, 4–e✔
34. Har bir ifodaga uning qiymatini moslang.
1) cos 60° + tg 45° a) −2
2) sin 270° + tg 45° b) 2
3) cos 0° + sin 90° c) 0
4) sin 0° + tg 45° d) 3/2
e) 1
f) 1/2
A) 1–d, 2–c, 3–b, 4–f
B) 1–d, 2–f, 3–b, 4–e
C) 1–d, 2–c, 3–b, 4–e
D) 1–d, 2–c, 3–f, 4–e
To'g'ri javob: C) 1–d, 2–c, 3–b, 4–e
✔
35. Har bir ifodaga uning qiymatini moslang.
1) EKUB(51; 11) a) 1800
2) EKUK(11; 48) b) 5214
3) EKUK(79; 66) c) 2310
4) EKUK(42; 55) d) 4350
e) 1
f) 528
A) 1–e, 2–f, 3–b, 4–c
B) 1–a, 2–f, 3–b, 4–c
C) 1–e, 2–b, 3–f, 4–c
D) 1–d, 2–f, 3–b, 4–c
To'g'ri javob: A) 1–e, 2–f, 3–b, 4–c
✔
O • ochiq topshiriq (qisqa javob)
36. Trapetsiya yuzini toping. Javobni yozing.
a) Asoslari 12 va 15, balandligi 3
b) Asoslari 14 va 14, balandligi 8
Javob: a) 81/2; b) 112
✔
37. Tenglamaning katta ildizini toping. Javobni yozing.
a) x² − 3x − 18 = 0
b) x² + 2x − 24 = 0
Javob: a) 6; b) 4
✔
Matematika — milliy sertifikat mashq variantlari | 87

38. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) x² − 9x + 20 = 0
b) x² + 14x + 45 = 0
Javob: a) 9; b) -14✔
39. Logarifmik tenglamani yeching. Javobni yozing.
a) log₁₀(x − 7) = 1
b) log₂(x − 3) = 2
Javob: a) 17; b) 7
✔
40. Tenglamani yeching. Javobni yozing.
a) 2(x + 8) = x + 10
b) 6(x − 8) = x + 12
Javob: a) -6; b) 12
✔
41. Ifodaning qiymatini toping. Javobni yozing.
a) log₅3125 + log₅25
b) log₃81 + log₃27
Javob: a) 7; b) 7
✔
42. Ifodaning qiymatini toping. Javobni yozing.
a) 2^2 · 2^3 : 2^2
b) 3^3 · 3^5 : 3^3
Javob: a) 8; b) 243
✔
43. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² − 2x − 1
b) y = x² + 2x − 1
Javob: a) -2; b) -2
✔
44. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² − 10x + 21
b) y = x² + 10x + 34
Javob: a) -4; b) 9
✔
45. f'(x₀) ni toping. Javobni yozing.
a) f(x) = 3x² + 3x + 1, x₀ = 1
b) f(x) = x³ + x² + 2x − 9, x₀ = 4
Javob: a) 9; b) 58
✔
Matematika — milliy sertifikat mashq variantlari | 88

12-variant
Y-1 • bitta to'g'ri javob
1. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 2, d = 6, n = 9
A) 240
B) 50
C) 225
D) 234
To'g'ri javob: D) 234✔
2. Hisoblang.
6/11 + 7/7
A) 6/11
B) 13/18
C) 120/77
D) 17/11
To'g'ri javob: D) 17/11
✔
3. Tenglamalar sistemasini yeching va x + y ni toping.
{ 5x + 3y = -16; 3x − y = -18 }
A) -8
B) -15
C) 0
D) -2
To'g'ri javob: D) -2
✔
4. Hisoblang.
√121 + √100
A) 110
B) 21
C) 14
D) 20
To'g'ri javob: B) 21
✔
5. Ifodaning qiymatini toping.
log₃243 + log₃27
A) 8
B) 6561
C) 15
D) 9
To'g'ri javob: A) 8
✔
6. Doira yuzi formulasi qaysi?
A) S = πr²
B) S = r²
C) S = 2πr
D) S = πd
To'g'ri javob: A) S = πr²
✔
Matematika — milliy sertifikat mashq variantlari | 89

$7. y = ax² + bx + c funksiya grafigi qanday chiziq? A) Sinusoida B) Parabola C) To'g'ri chiziq D) Giperbola To'g'ri javob: B) Parabola✔ 8. Tenglamalar sistemasini yeching va x + y ni toping. { 5x + 5y = 40; 2x − 5y = -12 } A) 16 B) 10 C) 0 D) 8 To'g'ri javob: D) 8 ✔ 9. 180° necha radianga teng? A) 2π B) π/2 C) π D) 1 To'g'ri javob: C) π ✔ 10. Aniq integralni hisoblang. ∫₀^2 (4x − 2) dx A) 6 B) 5 C) 4 D) 8 To'g'ri javob: C) 4 ✔ 11. Ifodani soddalashtiring: 2^3 · 2^5 A) 2^15 B) 2^2 C) 4^8 D) 2^8 To'g'ri javob: D) 2^8 ✔ 12. Uchburchak yuzi formulasi (asos va balandlik orqali) qaysi? A) S = a + h B) S = a · h C) S = 2a · h D) S = a · h / 2 To'g'ri javob: D) S = a · h / 2 ✔ 13. Tenglamaning katta ildizini toping. x² − 81 = 0 A) 10 B) -9 C) 9 D) 11 To'g'ri javob: C) 9 ✔ Matematika — milliy sertifikat mashq variantlari | 90$ $14. O'rinlashtirishlar sonini toping. A(8; 3) A) 512 B) 56 C) 336 D) 337 To'g'ri javob: C) 336✔ 15. A va B nuqtalar orasidagi masofani toping. A(4; 2), B(10; 10) A) 14 B) 2 C) 12 D) 10 To'g'ri javob: D) 10 ✔ 16. Ifodani soddalashtiring: 4^3 · 4^2 A) 4^1 B) 16^5 C) 4^5 D) 4^6 To'g'ri javob: C) 4^5 ✔ 17. Tenglamalar sistemasini yeching va x + y ni toping. { x + 3y = -19; 3x − 2y = 31 } A) -40 B) 13 C) -3 D) -1 To'g'ri javob: C) -3 ✔ 18. Ehtimollikni toping. Qutida 7 ta oq va 5 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli A) 5/12 B) 7/5 C) 1/12 D) 7/12 To'g'ri javob: D) 7/12 ✔ 19. EKUBni toping. EKUB(84; 70) A) 28 B) 14 C) 154 D) 420 To'g'ri javob: B) 14 ✔ Matematika — milliy sertifikat mashq variantlari | 91$

20. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 1, q = 3, n = 6
A) 365
B) 243
C) 361
D) 364
To'g'ri javob: D) 364✔
21. Ifodaning qiymatini toping.
cos 90° + tg 45°
A) 1
B) −1
C) 2
D) 3
To'g'ri javob: A) 1
✔
22. Tengsizlikning butun yechimlari sonini toping.
x² + 3x − 10 < 0
A) 8
B) 5
C) 6
D) 7
To'g'ri javob: C) 6
✔
23. f(x₀) qiymatini toping.
f(x) = x² − 3x − 2, x₀ = 1
A) -3
B) 4
C) -4
D) -2
To'g'ri javob: C) -4
✔
24. f(x) = 3x − 7 bo'lsa, f(5) ni toping.
A) 6
B) 9
C) 4
D) 8
To'g'ri javob: D) 8
✔
25. Tengsizlikning butun yechimlari sonini toping.
x² + 10x + 24 < 0
A) 0
B) 2
C) 1
D) 3
To'g'ri javob: C) 1
✔
Matematika — milliy sertifikat mashq variantlari | 92

26. EKUBni toping.
EKUB(31; 83)
A) 52
B) 2573
C) 1
D) 2
To'g'ri javob: C) 1✔
27. Tenglamalar sistemasini yeching va x + y ni toping.
{ 5x + 4y = -6; 4x − 4y = -48 }
A) -12
B) 0
C) 2
D) -36
To'g'ri javob: B) 0
✔
28. f'(x₀) ni toping.
f(x) = 3x³ + 2x² + 2x − 3, x₀ = 2
A) 46
B) 45
C) 50
D) 33
To'g'ri javob: A) 46
✔
29. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 4, q = 2, n = 4
A) 58
B) 60
C) 64
D) 32
To'g'ri javob: B) 60
✔
30. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 3, 4, 4
A) 51
B) 11
C) 48
D) 80
To'g'ri javob: C) 48
✔
31. Ifodaning qiymatini toping.
sin 270° + sin 30°
A) −3/2
B) 1/2
C) −1/2
D) −5/2
To'g'ri javob: C) −1/2
✔
Matematika — milliy sertifikat mashq variantlari | 93

32. Ifodaning qiymatini toping.
7^4 · 7^4 : 7^4
A) 13841287201
B) 5764801
C) 2408
D) 2401
To'g'ri javob: D) 2401✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) √49 + √64 a) 21
2) √25 + √49 b) 29
3) √81 + √121 c) 20
4) √121 + √25 d) 15
e) 12
f) 16
A) 1–d, 2–e, 3–c, 4–f
B) 1–b, 2–e, 3–c, 4–f
C) 1–e, 2–d, 3–c, 4–f
D) 1–f, 2–e, 3–c, 4–d
To'g'ri javob: A) 1–d, 2–e, 3–c, 4–f
✔
34. Har bir ifodaga uning qiymatini moslang.
1) EKUK(65; 62) a) 714
2) EKUB(28; 7) b) 405
3) EKUB(25; 90) c) 5
4) EKUK(42; 51) d) 7
e) 4030
f) 1
A) 1–e, 2–a, 3–c, 4–d
B) 1–d, 2–e, 3–c, 4–a
C) 1–e, 2–d, 3–c, 4–a
D) 1–e, 2–d, 3–c, 4–b
To'g'ri javob: C) 1–e, 2–d, 3–c, 4–a
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √100 + √144 a) 17
2) √64 + √16 b) 12
3) √196 + √16 c) 24
4) √81 + √225 d) 18
e) 22
f) 21
Matematika — milliy sertifikat mashq variantlari | 94

$A) 1–b, 2–e, 3–d, 4–c B) 1–a, 2–b, 3–d, 4–c C) 1–e, 2–b, 3–c, 4–d D) 1–e, 2–b, 3–d, 4–c To'g'ri javob: D) 1–e, 2–b, 3–d, 4–c✔ O • ochiq topshiriq (qisqa javob) 36. Parabola uchining ordinatasini toping. Javobni yozing. a) y = x² + 2x + 1 b) y = x² − 12x + 39 Javob: a) 0; b) 3 ✔ 37. f(x₀) qiymatini toping. Javobni yozing. a) f(x) = 4x² + 5x − 3, x₀ = -4 b) f(x) = 4x² + x − 8, x₀ = -1 Javob: a) 41; b) -5 ✔ 38. A va B nuqtalar orasidagi masofani toping. Javobni yozing. a) A(-1; -2), B(-4; 2) b) A(2; 4), B(-5; 28) Javob: a) 5; b) 25 ✔ 39. Ifodaning qiymatini toping. Javobni yozing. a) 3^2 · 3^6 : 3^2 b) 5^3 · 5^3 : 5^5 Javob: a) 729; b) 5 ✔ 40. EKUBni toping. Javobni yozing. a) EKUB(35; 72) b) EKUB(90; 68) Javob: a) 1; b) 2 ✔ 41. Tenglamalar sistemasini yeching va x + y ni toping. Javobni yozing. a) { x + 4y = 17; 2x − 5y = -44 } b) { 4x + 5y = 40; 3x − y = 11 } Javob: a) -1; b) 9 ✔ 42. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing. a) a₁ = -5, d = -3, n = 17 b) a₁ = -5, d = -3, n = 19 Javob: a) -493; b) -608 ✔ 43. Tenglamani yeching. Javobni yozing. a) 3(x − 2) = x − 24 b) 3(x + 0) = 2x − 3 Javob: a) -9; b) -3 ✔ 44. Uchburchak yuzini toping. Javobni yozing. a) Asosi 15, unga tushirilgan balandlik 15 b) Asosi 15, unga tushirilgan balandlik 20 Javob: a) 225/2; b) 150 ✔ Matematika — milliy sertifikat mashq variantlari | 95$

45. Tenglamani yeching. Javobni yozing.
a) 7(x + 18) = 2x + 181
b) 4(x + 8) = 3x + 44
Javob: a) 11; b) 12✔
Matematika — milliy sertifikat mashq variantlari | 96

13-variant
Y-1 • bitta to'g'ri javob
1. Tenglamaning katta ildizini toping.
x² − 11x + 18 = 0
A) 9
B) 2
C) 10
D) -9
To'g'ri javob: A) 9✔
2. Logarifmik tenglamani yeching.
log₅(x − 8) = 2
A) 33
B) 18
C) 25
D) 17
To'g'ri javob: A) 33
✔
3. Qirrasi 5 ga teng kubning hajmini toping.
A) 25
B) 125
C) 150
D) 60
To'g'ri javob: B) 125
✔
4. tg 60° ning qiymatini toping.
A) √3
B) 1
C) 2
D) √3/3
To'g'ri javob: A) √3
✔
5. √100 ni hisoblang.
A) 9
B) 50
C) 10
D) 11
To'g'ri javob: C) 10
✔
6. Aniq integralni hisoblang.
∫₀^2 (8x + 4) dx
A) 24
B) 26
C) 20
D) 48
To'g'ri javob: A) 24
✔
Matematika — milliy sertifikat mashq variantlari | 97

7. Qirrasi 9 ga teng kubning hajmini toping.
A) 729
B) 81
C) 486
D) 108
To'g'ri javob: A) 729✔
8. O'yin soqqasi bir marta tashlanganda 2 dan katta son tushish ehtimolini toping.
A) 1/6
B) 5/6
C) 1/3
D) 2/3
To'g'ri javob: D) 2/3
✔
9. Ifodani soddalashtiring: 2^2 · 2^5
A) 4^7
B) 2^10
C) 2^7
D) 2^3
To'g'ri javob: C) 2^7
✔
10. f(x) = 3x − 7 bo'lsa, f(-4) ni toping.
A) -20
B) -19
C) -17
D) -15
To'g'ri javob: B) -19
✔
11. Doira yuzini toping (π orqali).
Radius R = 11
A) 11π
B) 121π
C) 22π
D) 242π
To'g'ri javob: B) 121π
✔
12. Ko'rsatkichli tenglamani yeching.
3^(x − 3) = 81
A) 7
B) 1
C) 4
D) 8
To'g'ri javob: A) 7
✔
13. Parabola uchining ordinatasini toping.
y = x² + 8x + 18
A) 2
B) 3
C) -4
D) 18
To'g'ri javob: A) 2
✔
Matematika — milliy sertifikat mashq variantlari | 98

14. Doira yuzini toping (π orqali).
Radius R = 10
A) 100π
B) 10π
C) 200π
D) 20π
To'g'ri javob: A) 100π✔
15. Tenglamaning katta ildizini toping.
x² − 7x + 6 = 0
A) 6
B) 7
C) 1
D) -6
To'g'ri javob: A) 6
✔
16. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 6, d = -1, n = 7
A) 20
B) 21
C) 0
D) 14
To'g'ri javob: B) 21
✔
17. f'(x₀) ni toping.
f(x) = 2x³ + 3x² + x + 3, x₀ = -3
A) -27
B) 43
C) 36
D) 37
To'g'ri javob: D) 37
✔
18. Radiusi 12 ga teng doiraning yuzini toping.
A) 12π
B) 288π
C) 144π
D) 24π
To'g'ri javob: C) 144π
✔
19. Silindr hajmini toping (π orqali).
Asos radiusi 6, balandligi 9
A) 54π
B) 108π
C) 324π
D) 648π
To'g'ri javob: C) 324π
✔
Matematika — milliy sertifikat mashq variantlari | 99

20. f(x) = 4x − 9 bo'lsa, f(1) ni toping.
A) -8
B) -5
C) -6
D) -2
To'g'ri javob: B) -5✔
21. Parabola uchining ordinatasini toping.
y = x² − 12x + 31
A) 6
B) 31
C) -5
D) -4
To'g'ri javob: C) -5
✔
22. Tenglamaning katta ildizini toping.
x² − 5x + 6 = 0
A) 4
B) -3
C) 2
D) 3
To'g'ri javob: D) 3
✔
23. x² + 6x + 5 = 0 tenglama ildizlarining yig'indisini toping.
A) 5
B) 6
C) -4
D) -6
To'g'ri javob: D) -6
✔
24. Tenglamani yeching.
3(x − 20) = x − 46
A) 8
B) 7
C) -7
D) 5
To'g'ri javob: B) 7
✔
25. Masalani yeching.
Narx 1800 so'm. Avval 10% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
A) 1782
B) 1882
C) 1800
D) 1783
To'g'ri javob: A) 1782
✔
Matematika — milliy sertifikat mashq variantlari | 100

26. Uchburchak yuzini toping.
Asosi 14, unga tushirilgan balandlik 19
A) 133
B) 33
C) 134
D) 266
To'g'ri javob: A) 133✔
27. Trapetsiya yuzini toping.
Asoslari 3 va 8, balandligi 6
A) 39
B) 66
C) 144
D) 33
To'g'ri javob: D) 33
✔
28. EKUKni toping.
EKUK(71; 42)
A) 1
B) 5964
C) 3053
D) 2982
To'g'ri javob: D) 2982
✔
29. EKUBni toping.
EKUB(41; 43)
A) 1763
B) 1
C) 3
D) 2
To'g'ri javob: B) 1
✔
30. Trapetsiya yuzini toping.
Asoslari 15 va 14, balandligi 9
A) 279/2
B) 261
C) 1890
D) 261/2
To'g'ri javob: D) 261/2
✔
31. √289 ni hisoblang.
A) 18
B) 144
C) 16
D) 17
To'g'ri javob: D) 17
✔
Matematika — milliy sertifikat mashq variantlari | 101

32. lg 10000 ni hisoblang.
A) 4
B) 1000
C) 3
D) 5
To'g'ri javob: A) 4✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) log₃27 + log₃9 a) 7
2) log₂8 + log₂8 b) 5
3) log₃243 + log₃27 c) 8
4) log₅125 + log₅5 d) 6
e) 4
f) 9
A) 1–b, 2–d, 3–c, 4–e
B) 1–c, 2–d, 3–b, 4–e
C) 1–a, 2–d, 3–c, 4–e
D) 1–b, 2–d, 3–c, 4–f
To'g'ri javob: A) 1–b, 2–d, 3–c, 4–e
✔
34. Har bir ifodaga uning qiymatini moslang.
1) √9 + √64 a) 18
2) √144 + √144 b) 25
3) √36 + √100 c) 24
4) √64 + √100 d) 11
e) 16
f) 17
A) 1–a, 2–e, 3–d, 4–c
B) 1–d, 2–c, 3–b, 4–a
C) 1–d, 2–c, 3–e, 4–a
D) 1–d, 2–e, 3–c, 4–a
To'g'ri javob: C) 1–d, 2–c, 3–e, 4–a
✔
35. Har bir ifodaga uning qiymatini moslang.
1) cos 0° + cos 90° a) 3/2
2) cos 0° + sin 30° b) −1/2
3) tg 45° + sin 90° c) 1/2
4) cos 90° + sin 270° d) 1
e) 2
f) −1
Matematika — milliy sertifikat mashq variantlari | 102

A) 1–e, 2–a, 3–d, 4–f
B) 1–f, 2–a, 3–e, 4–d
C) 1–d, 2–a, 3–e, 4–f
D) 1–d, 2–f, 3–e, 4–a
To'g'ri javob: C) 1–d, 2–a, 3–e, 4–f✔
O • ochiq topshiriq (qisqa javob)
36. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 5, q = 2, n = 3
b) b₁ = 5, q = -2, n = 6
Javob: a) 35; b) -105
✔
37. Silindr hajmini toping (π orqali). Javobni yozing.
a) Asos radiusi 2, balandligi 2
b) Asos radiusi 5, balandligi 9
Javob: a) 8π; b) 225π
✔
38. Aniq integralni hisoblang. Javobni yozing.
a) ∫₀^2 (4x + 6) dx
b) ∫₀^1 (8x + 4) dx
Javob: a) 20; b) 8
✔
39. Ehtimollikni toping. Javobni yozing.
a) Qutida 7 ta oq va 5 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 2 ta oq va 8 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 7/12; b) 1/5
✔
40. Ehtimollikni toping. Javobni yozing.
a) Qutida 2 ta oq va 6 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 3 ta oq va 9 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 1/4; b) 1/4
✔
41. Ifodaning qiymatini toping. Javobni yozing.
a) 5^5 · 5^5 : 5^5
b) 3^2 · 3^4 : 3^1
Javob: a) 3125; b) 243
✔
42. Tenglamaning katta ildizini toping. Javobni yozing.
a) x² + 6x − 27 = 0
b) x² + 5x − 14 = 0
Javob: a) 3; b) 2
✔
43. A va B nuqtalar orasidagi masofani toping. Javobni yozing.
a) A(-2; -2), B(6; 13)
b) A(-1; 4), B(6; 28)
Javob: a) 17; b) 25
✔
44. Logarifmik tenglamani yeching. Javobni yozing.
a) log₃(x − 1) = 4
b) log₅(x − 8) = 1
Javob: a) 82; b) 13
✔
Matematika — milliy sertifikat mashq variantlari | 103

45. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² + 6x
b) y = x² + 8x + 25
Javob: a) -9; b) 9✔
Matematika — milliy sertifikat mashq variantlari | 104

14-variant
Y-1 • bitta to'g'ri javob
1. 4x² + 4x + 5 = 0 tenglamaning diskriminantini toping.
A) -64
B) -56
C) 96
D) -68
To'g'ri javob: A) -64✔
2. Vektorlarning skalyar ko'paytmasini toping.
(6; 6), (-5; 6)
a⃗ b ⃗
A) 66
B) 6
C) -6
D) 7
To'g'ri javob: B) 6
✔
3. Ehtimollikni toping.
Qutida 6 ta oq va 5 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 6/5
B) 5/11
C) 6/11
D) 1/11
To'g'ri javob: C) 6/11
✔
4. EKUBni toping.
EKUB(44; 38)
A) 6
B) 836
C) 2
D) 4
To'g'ri javob: C) 2
✔
5. Geometrik progressiyada b₁ = 3, q = 3. b4 ni toping.
A) -81
B) 81
C) 27
D) 243
To'g'ri javob: B) 81
✔
6. A va B nuqtalar orasidagi masofani toping.
A(-4; 1), B(-11; -23)
A) 31
B) 25
C) 17
D) 27
To'g'ri javob: B) 25
✔
Matematika — milliy sertifikat mashq variantlari | 105

7. Tenglamalar sistemasini yeching va x + y ni toping.
{ 4x + 2y = -16; 2x − y = 0 }
A) 2
B) -4
C) -6
D) 8
To'g'ri javob: C) -6✔
8. Butun sonlar to'plami qanday belgilanadi?
A) Q
B) R
C) Z
D) N
To'g'ri javob: C) Z
✔
9. Ehtimollikni toping.
Qutida 4 ta oq va 6 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 1/10
B) 3/5
C) 2/5
D) 2/3
To'g'ri javob: C) 2/5
✔
10. To'g'ri burchakli uchburchakning katetlari 5 va 12. Gipotenuzasini toping.
A) 17
B) 14
C) 11
D) 13
To'g'ri javob: D) 13
✔
11. Tenglama ildizlari yig'indisini toping.
|x − 3| = 7
A) -6
B) 6
C) 10
D) 7
To'g'ri javob: B) 6
✔
12. a³ + b³ ifoda nimaga teng?
A) (a + b)³
B) a³ + 3ab + b³
C) (a + b)(a² + ab + b²)
D) (a + b)(a² − ab + b²)
To'g'ri javob: D) (a + b)(a² − ab + b²)
✔
13. Hisoblang.
7/9 + 8/7
A) 15/16
B) 122/63
C) 8/9
D) 121/63
To'g'ri javob: D) 121/63
✔
Matematika — milliy sertifikat mashq variantlari | 106

14. Masalani yeching.
Narx 4000 so'm. Avval 30% ga oshirildi, so'ng 20% ga kamaytirildi. Oxirgi narx necha so'm?
A) 4400
B) 4000
C) 4260
D) 4160
To'g'ri javob: D) 4160✔
15. Hisoblang.
√100 + √144
A) 15
B) 22
C) 21
D) 120
To'g'ri javob: B) 22
✔
16. Parabola uchining ordinatasini toping.
y = x² − 4x − 1
A) 2
B) -1
C) -5
D) -4
To'g'ri javob: C) -5
✔
17. Tenglamalar sistemasini yeching va x + y ni toping.
{ 5x + 3y = 46; 4x − 2y = 28 }
A) 6
B) 10
C) 16
D) 12
To'g'ri javob: B) 10
✔
18. Silindr hajmini toping (π orqali).
Asos radiusi 2, balandligi 8
A) 16π
B) 64π
C) 33π
D) 32π
To'g'ri javob: D) 32π
✔
19. A va B nuqtalar orasidagi masofani toping.
A(-1; 2), B(-8; 26)
A) 31
B) 25
C) 17
D) 27
To'g'ri javob: B) 25
✔
Matematika — milliy sertifikat mashq variantlari | 107

20. √441 ni hisoblang.
A) 22
B) 21
C) 20
D) 220
To'g'ri javob: B) 21✔
21. Aniq integralni hisoblang.
∫₀^3 (6x − 2) dx
A) 24
B) 16
C) 21
D) 42
To'g'ri javob: C) 21
✔
22. Trapetsiya yuzini toping.
Asoslari 5 va 5, balandligi 3
A) 18
B) 15
C) 75
D) 30
To'g'ri javob: B) 15
✔
23. Trapetsiya yuzini toping.
Asoslari 7 va 10, balandligi 11
A) 187/2
B) 209/2
C) 770
D) 187
To'g'ri javob: A) 187/2
✔
24. Logarifmik tenglamani yeching.
log₂(x − 5) = 4
A) 21
B) 13
C) 11
D) 16
To'g'ri javob: A) 21
✔
25. A va B nuqtalar orasidagi masofani toping.
A(0; -2), B(-9; -14)
A) 3
B) 17
C) 15
D) 21
To'g'ri javob: C) 15
✔
Matematika — milliy sertifikat mashq variantlari | 108

26. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -7, d = -1, n = 16
A) -248
B) -233
C) -22
D) -232
To'g'ri javob: D) -232✔
27. Trapetsiya yuzini toping.
Asoslari 15 va 6, balandligi 7
A) 630
B) 147/2
C) 147
D) 161/2
To'g'ri javob: B) 147/2
✔
28. Uchburchak yuzini toping.
Asosi 16, unga tushirilgan balandlik 17
A) 33
B) 272
C) 137
D) 136
To'g'ri javob: D) 136
✔
29. Logarifmik tenglamani yeching.
log₁₀(x − 1) = 1
A) 12
B) 11
C) 9
D) 10
To'g'ri javob: B) 11
✔
30. f(x₀) qiymatini toping.
f(x) = x² + 2x + 5, x₀ = -3
A) -8
B) 9
C) 8
D) 4
To'g'ri javob: C) 8
✔
31. Tengsizlikning butun yechimlari sonini toping.
x² − 3x − 10 < 0
A) 7
B) 6
C) 5
D) 8
To'g'ri javob: B) 6
✔
Matematika — milliy sertifikat mashq variantlari | 109

32. Ehtimollikni toping.
Qutida 2 ta oq va 5 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 1/7
B) 5/7
C) 2/5
D) 2/7
To'g'ri javob: D) 2/7✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) A(7; 3) a) 35
2) A(5; 3) b) 1680
3) A(8; 4) c) 70
4) C(8; 4) d) 210
e) 28
f) 60
A) 1–d, 2–f, 3–b, 4–c
B) 1–a, 2–f, 3–b, 4–c
C) 1–d, 2–e, 3–b, 4–c
D) 1–f, 2–c, 3–d, 4–b
To'g'ri javob: A) 1–d, 2–f, 3–b, 4–c
✔
34. Har bir ifodaga uning qiymatini moslang.
1) EKUB(58; 44) a) 1
2) EKUK(22; 74) b) 870
3) EKUK(13; 28) c) 7
4) EKUB(14; 63) d) 2
e) 814
f) 364
A) 1–d, 2–e, 3–c, 4–f
B) 1–d, 2–e, 3–f, 4–c
C) 1–a, 2–e, 3–f, 4–c
D) 1–d, 2–e, 3–b, 4–c
To'g'ri javob: B) 1–d, 2–e, 3–f, 4–c
✔
35. Har bir ifodaga uning qiymatini moslang.
1) EKUK(43; 53) a) 1110
2) EKUK(37; 30) b) 30
3) EKUB(33; 79) c) 2
4) EKUK(30; 6) d) 2225
e) 1
f) 2279
Matematika — milliy sertifikat mashq variantlari | 110

$A) 1–f, 2–a, 3–e, 4–d B) 1–f, 2–a, 3–e, 4–b C) 1–d, 2–a, 3–e, 4–b D) 1–f, 2–a, 3–b, 4–e To'g'ri javob: B) 1–f, 2–a, 3–e, 4–b✔ O • ochiq topshiriq (qisqa javob) 36. Ifodaning qiymatini toping. Javobni yozing. a) 3^4 · 3^5 : 3^3 b) 5^6 · 5^6 : 5^3 Javob: a) 729; b) 1953125 ✔ 37. Tenglamaning katta ildizini toping. Javobni yozing. a) x² − 16 = 0 b) x² − 16x + 63 = 0 Javob: a) 4; b) 9 ✔ 38. f'(x₀) ni toping. Javobni yozing. a) f(x) = x³ + x² − 2x + 3, x₀ = 4 b) f(x) = x² − x + 7, x₀ = 3 Javob: a) 54; b) 5 ✔ 39. Hisoblang. Javobni yozing. a) 3/2 + 5/4 b) 1/3 + 4/9 Javob: a) 11/4; b) 7/9 ✔ 40. f(x₀) qiymatini toping. Javobni yozing. a) f(x) = x² − 4x + 8, x₀ = -1 b) f(x) = −x² − 2x − 7, x₀ = -4 Javob: a) 13; b) -15 ✔ 41. Tenglamalar sistemasini yeching va x + y ni toping. Javobni yozing. a) { 2x + 2y = 8; 2x − y = -10 } b) { 4x + y = -4; 3x − 2y = -3 } Javob: a) 4; b) -1 ✔ 42. Uchburchak yuzini toping. Javobni yozing. a) Asosi 16, unga tushirilgan balandlik 11 b) Asosi 19, unga tushirilgan balandlik 4 Javob: a) 88; b) 38 ✔ 43. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing. a) b₁ = 3, q = 3, n = 5 b) b₁ = 4, q = -2, n = 6 Javob: a) 363; b) -84 ✔ 44. Logarifmik tenglamani yeching. Javobni yozing. a) log₅(x − 6) = 2 b) log₅(x − 1) = 2 Javob: a) 31; b) 26 ✔ Matematika — milliy sertifikat mashq variantlari | 111$

45. Ifodaning qiymatini toping. Javobni yozing.
a) tg 0° + sin 0°
b) cos 180° + cos 90°
Javob: a) 0; b) −1✔
Matematika — milliy sertifikat mashq variantlari | 112

15-variant
Y-1 • bitta to'g'ri javob
1. 7! ni hisoblang.
A) 720
B) 49
C) 5040
D) 5047
To'g'ri javob: C) 5040✔
2. Logarifmik tenglamani yeching.
log₃(x − 4) = 4
A) 16
B) 85
C) 77
D) 81
To'g'ri javob: B) 85
✔
3. Aniq integralni hisoblang.
∫₀^2 (4x − 1) dx
A) 7
B) 12
C) 8
D) 6
To'g'ri javob: D) 6
✔
4. Hisoblang.
9/9 + 7/11
A) 18/11
B) 4/5
C) 163/99
D) 7/11
To'g'ri javob: A) 18/11
✔
5. Ifodaning qiymatini toping.
log₅125 + log₅25
A) 7
B) 5
C) 3125
D) 6
To'g'ri javob: B) 5
✔
6. Ehtimollikni toping.
Qutida 2 ta oq va 3 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 3/5
B) 2/5
C) 1/5
D) 2/3
To'g'ri javob: B) 2/5
✔
Matematika — milliy sertifikat mashq variantlari | 113

7. Uchburchakning asosi 4, unga tushirilgan balandligi 20. Uchburchak yuzini toping.
A) 44
B) 40
C) 80
D) 24
To'g'ri javob: B) 40✔
8. Tenglamalar sistemasini yeching va x + y ni toping.
{ 4x + 4y = 36; 5x − y = 27 }
A) 18
B) 9
C) 3
D) 11
To'g'ri javob: B) 9
✔
9. f(x₀) qiymatini toping.
f(x) = −2x² − x + 6, x₀ = -3
A) -11
B) -9
C) 11
D) 9
To'g'ri javob: B) -9
✔
10. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -6, d = -1, n = 13
A) -169
B) -18
C) -156
D) -157
To'g'ri javob: C) -156
✔
11. Doira yuzini toping (π orqali).
Radius R = 3
A) 3π
B) 9π
C) 6π
D) 18π
To'g'ri javob: B) 9π
✔
12. √256 ni hisoblang.
A) 16
B) 17
C) 15
D) 128
To'g'ri javob: A) 16
✔
Matematika — milliy sertifikat mashq variantlari | 114

13. Ehtimollikni toping.
Qutida 8 ta oq va 9 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 8/17
B) 9/17
C) 1/17
D) 8/9
To'g'ri javob: A) 8/17✔
14. Tenglamaning katta ildizini toping.
x² + 10x + 16 = 0
A) -1
B) -2
C) -8
D) 2
To'g'ri javob: B) -2
✔
15. 400 ning 75% ini toping.
A) 205
B) 370
C) 300
D) 317
To'g'ri javob: C) 300
✔
16. Ifodaning qiymatini toping.
2^4 · 2^4 : 2^5
A) 8
B) 10
C) 256
D) 2048
To'g'ri javob: A) 8
✔
17. Vektorlarning skalyar ko'paytmasini toping.
(-4; 0), (-3; 6)
a⃗ b ⃗
A) 13
B) -12
C) -24
D) 12
To'g'ri javob: D) 12
✔
18. Tenglamani yeching.
6(x + 4) = 3x + 36
A) -4
B) 4
C) 5
D) 2
To'g'ri javob: B) 4
✔
Matematika — milliy sertifikat mashq variantlari | 115

19. Vektor uzunligini toping.
(6; -8)a⃗
A) 11
B) 14
C) 10
D) 2
To'g'ri javob: C) 10
✔
20. O'rinlashtirishlar sonini toping.
A(9; 3)
A) 504
B) 84
C) 729
D) 72
To'g'ri javob: A) 504
✔
21. O'rinlashtirishlar sonini toping.
A(10; 3)
A) 120
B) 1000
C) 90
D) 720
To'g'ri javob: D) 720
✔
22. Masalani yeching.
Narx 3000 so'm. Avval 15% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
A) 3150
B) 3205
C) 3105
D) 3000
To'g'ri javob: C) 3105
✔
23. Parabola uchining ordinatasini toping.
y = x² + 6x + 6
A) -3
B) -2
C) -1
D) 6
To'g'ri javob: A) -3
✔
24. To'g'ri burchakli uchburchakning gipotenuzasi 15, bir kateti 9. Ikkinchi katetini toping.
A) 10
B) 6
C) 12
D) 13
To'g'ri javob: C) 12
✔
Matematika — milliy sertifikat mashq variantlari | 116

25. Tenglamani yeching.
7(x − 4) = 2x − 8
A) 2
B) 5
C) -4
D) 4
To'g'ri javob: D) 4✔
26. Tenglama ildizlari yig'indisini toping.
x² − 3x − 54 = 0
A) 4
B) -3
C) -54
D) 3
To'g'ri javob: D) 3
✔
27. Hisoblang.
√81 + √64
A) 17
B) 72
C) 12
D) 16
To'g'ri javob: A) 17
✔
28. Ifodaning qiymatini toping.
log₅3125 + log₅25
A) 10
B) 78125
C) 7
D) 8
To'g'ri javob: C) 7
✔
29. Arifmetik progressiyada a₁ = 12, d = 8. a24 ni toping.
A) 212
B) 188
C) 196
D) 204
To'g'ri javob: C) 196
✔
30. Silindr hajmini toping (π orqali).
Asos radiusi 6, balandligi 10
A) 720π
B) 60π
C) 120π
D) 360π
To'g'ri javob: D) 360π
✔
Matematika — milliy sertifikat mashq variantlari | 117

31. Logarifmik tenglamani yeching.
log₂(x − 7) = 2
A) 11
B) -3
C) 4
D) 12
To'g'ri javob: A) 11✔
32. cos 90° ning qiymatini toping.
A) −1
B) 1
C) 0
D) √3/2
To'g'ri javob: C) 0
✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) cos 0° + cos 60° a) 0
2) cos 0° + tg 45° b) 1/2
3) sin 0° + sin 30° c) 3/2
4) cos 0° + sin 0° d) 1
e) 2
f) −1/2
A) 1–a, 2–e, 3–b, 4–d
B) 1–e, 2–b, 3–c, 4–d
C) 1–c, 2–e, 3–b, 4–d
D) 1–c, 2–e, 3–a, 4–d
To'g'ri javob: C) 1–c, 2–e, 3–b, 4–d
✔
34. Har bir ifodaga uning qiymatini moslang.
1) 2^5 · 2^6 : 2^2 a) 16807
2) 2^3 · 2^5 : 2^2 b) 512
3) 7^2 · 7^4 : 7^1 c) 78125
4) 5^6 · 5^2 : 5^1 d) 64
e) 1953125
f) 729
A) 1–f, 2–d, 3–a, 4–c
B) 1–b, 2–d, 3–a, 4–c
C) 1–e, 2–d, 3–a, 4–c
D) 1–b, 2–a, 3–d, 4–c
To'g'ri javob: B) 1–b, 2–d, 3–a, 4–c
✔
35. Har bir ifodaga uning qiymatini moslang.
1) sin 90° + sin 30° a) 1
2) sin 90° + tg 0° b) −1/2
3) tg 45° + cos 180° c) 0
Matematika — milliy sertifikat mashq variantlari | 118

4) tg 0° + sin 270° d) 2
e) 3/2
f) −1
A) 1–e, 2–a, 3–c, 4–f
B) 1–e, 2–a, 3–d, 4–f
C) 1–c, 2–a, 3–e, 4–f
D) 1–e, 2–a, 3–b, 4–f
To'g'ri javob: A) 1–e, 2–a, 3–c, 4–f✔
O • ochiq topshiriq (qisqa javob)
36. Tenglamani yeching. Javobni yozing.
a) 3(x − 6) = 2x − 6
b) 2(x + 6) = x + 5
Javob: a) 12; b) -7
✔
37. Vektorlarning skalyar ko'paytmasini toping. Javobni yozing.
a) (0; 6), (6; 2)
a⃗ b ⃗
b) (2; -3), (4; -1)
a⃗ b ⃗
Javob: a) 12; b) 11
✔
38. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² − 4x + 5
b) y = x² − 6x + 7
Javob: a) 1; b) -2
✔
39. O'rinlashtirishlar sonini toping. Javobni yozing.
a) A(5; 4)
b) A(9; 2)
Javob: a) 120; b) 72
✔
40. Tengsizlikning butun yechimlari sonini toping. Javobni yozing.
a) x² − 5x − 14 < 0
b) x² − 4x + 3 < 0
Javob: a) 8; b) 1
✔
41. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) x² − 2x − 24 = 0
b) x² + 2x − 24 = 0
Javob: a) 2; b) -2
✔
42. f'(x₀) ni toping. Javobni yozing.
a) f(x) = x³ + 2x² − 2x − 3, x₀ = -3
b) f(x) = x³ + 2x² − 6x − 6, x₀ = 4
Javob: a) 13; b) 58
✔
43. Hisoblang. Javobni yozing.
a) √9 + √196
b) √9 + √36
Javob: a) 17; b) 9
✔
Matematika — milliy sertifikat mashq variantlari | 119

44. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) x² + 4x + 3 = 0
b) x² − 3x − 4 = 0
Javob: a) -4; b) 3✔
45. Trapetsiya yuzini toping. Javobni yozing.
a) Asoslari 11 va 14, balandligi 10
b) Asoslari 14 va 13, balandligi 11
Javob: a) 125; b) 297/2
✔
Matematika — milliy sertifikat mashq variantlari | 120

16-variant
Y-1 • bitta to'g'ri javob
1. EKUBni toping.
EKUB(26; 6)
A) 78
B) 4
C) 2
D) 20
To'g'ri javob: C) 2✔
2. Aylana uzunligini toping (π orqali).
Radius R = 13
A) 169π
B) 52π
C) 26π
D) 13π
To'g'ri javob: C) 26π
✔
3. Logarifmik tenglamani yeching.
log₂(x − 3) = 3
A) 8
B) 9
C) 11
D) 5
To'g'ri javob: C) 11
✔
4. EKUBni toping.
EKUB(33; 43)
A) 1
B) 10
C) 1419
D) 2
To'g'ri javob: A) 1
✔
5. Hisoblang.
√4 + √225
A) 16
B) 15
C) 30
D) 17
To'g'ri javob: D) 17
✔
6. Hisoblang.
8/11 + 7/9
A) 50/33
B) 56/99
C) 149/99
D) 3/4
To'g'ri javob: C) 149/99
✔
Matematika — milliy sertifikat mashq variantlari | 121

7. Parabola uchining ordinatasini toping.
y = x² − 10x + 19
A) 19
B) 5
C) -5
D) -6
To'g'ri javob: D) -6✔
8. Ko'rsatkichli tenglamani yeching.
2^(x − 1) = 4
A) 2
B) 1
C) 4
D) 3
To'g'ri javob: D) 3
✔
9. Ehtimollikni toping.
Qutida 3 ta oq va 7 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 3/10
B) 1/10
C) 7/10
D) 3/7
To'g'ri javob: A) 3/10
✔
10. f(x₀) qiymatini toping.
f(x) = 2x² − 2x + 5, x₀ = -2
A) 19
B) -1
C) -17
D) 17
To'g'ri javob: D) 17
✔
11. Masalani yeching.
Narx 400 so'm. Avval 50% ga oshirildi, so'ng 25% ga kamaytirildi. Oxirgi narx necha so'm?
A) 400
B) 450
C) 500
D) 550
To'g'ri javob: B) 450
✔
12. Parabola uchining ordinatasini toping.
y = x² + 10x + 29
A) 4
B) -5
C) 29
D) 5
To'g'ri javob: A) 4
✔
Matematika — milliy sertifikat mashq variantlari | 122

13. Uchburchak yuzini toping.
Asosi 15, unga tushirilgan balandlik 4
A) 19
B) 31
C) 60
D) 30
To'g'ri javob: D) 30✔
14. cos 30° ning qiymatini toping.
A) √3/2
B) √3
C) 2
D) 0
To'g'ri javob: A) √3/2
✔
15. sin 0° ning qiymatini toping.
A) √2/2
B) 0
C) 1/2
D) −1
To'g'ri javob: B) 0
✔
16. Quyidagilardan qaysi biri irratsional son?
A) 3/4
B) √2
C) −7
D) 0,5
To'g'ri javob: B) √2
✔
17. Hisoblang.
3/11 + 4/10
A) 15/22
B) 1/3
C) 37/55
D) 6/55
To'g'ri javob: C) 37/55
✔
18. Uchburchak yuzini toping.
Asosi 7, unga tushirilgan balandlik 3
A) 10
B) 21/2
C) 23/2
D) 21
To'g'ri javob: B) 21/2
✔
19. To'g'ri burchakli uchburchakning katetlari 9 va 12. Gipotenuzasini toping.
A) 21
B) 15
C) 16
D) 13
To'g'ri javob: B) 15
✔
Matematika — milliy sertifikat mashq variantlari | 123

20. Markazi (a; b), radiusi R bo'lgan aylana tenglamasi qaysi?
A) x² + y² = a + b
B) (x + a)² + (y + b)² = R
C) (x − a) + (y − b) = R
D) (x − a)² + (y − b)² = R²
To'g'ri javob: D) (x − a)² + (y − b)² = R²✔
21. Ko'rsatkichli tenglamani yeching.
3^(x − 3) = 9
A) 6
B) -1
C) 5
D) 2
To'g'ri javob: C) 5
✔
22. f(x) = 3x + 2 bo'lsa, f(-4) ni toping.
A) -10
B) -14
C) -11
D) -13
To'g'ri javob: A) -10
✔
23. Ifodaning qiymatini toping.
3^5 · 3^6 : 3^1
A) 59052
B) 177147
C) 68630377364883
D) 59049
To'g'ri javob: D) 59049
✔
24. Trapetsiya yuzini toping.
Asoslari 2 va 15, balandligi 6
A) 102
B) 57
C) 51
D) 180
To'g'ri javob: C) 51
✔
25. Tenglamalar sistemasini yeching: x + y = 11, x − y = 7. x ni toping.
A) 9
B) 11
C) 2
D) 8
To'g'ri javob: A) 9
✔
26. Parabola uchining ordinatasini toping.
y = x² − 12x + 44
A) 8
B) 9
C) 44
D) 6
To'g'ri javob: A) 8
✔
Matematika — milliy sertifikat mashq variantlari | 124

27. To'g'ri burchakli uchburchakning katetlari 7 va 24. Gipotenuzasini toping.
A) 25
B) 31
C) 23
D) 26
To'g'ri javob: A) 25✔
28. Uchburchak yuzini toping.
Asosi 12, unga tushirilgan balandlik 13
A) 78
B) 79
C) 156
D) 25
To'g'ri javob: A) 78
✔
29. Diskriminant manfiy bo'lsa, kvadrat tenglama haqiqiy sonlar to'plamida nechta ildizga ega?
A) Cheksiz ko'p ildizga
B) Bitta ildizga
C) Ikkita ildizga
D) Ildizga ega emas
To'g'ri javob: D) Ildizga ega emas
✔
30. Logarifmik tenglamani yeching.
log₁₀(x − 2) = 3
A) 32
B) 998
C) 1000
D) 1002
To'g'ri javob: D) 1002
✔
31. Logarifmik tenglamani yeching.
log₃(x − 8) = 1
A) 12
B) 11
C) 3
D) -5
To'g'ri javob: B) 11
✔
32. EKUKni toping.
EKUK(16; 84)
A) 336
B) 4
C) 352
D) 1344
To'g'ri javob: A) 336
✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) C(9; 3) a) 42
2) A(7; 2) b) 210
3) C(6; 4) c) 84
Matematika — milliy sertifikat mashq variantlari | 125

4) A(10; 2) d) 15
e) 504
f) 90
A) 1–c, 2–a, 3–e, 4–f
B) 1–d, 2–c, 3–f, 4–a
C) 1–c, 2–a, 3–d, 4–f
D) 1–f, 2–a, 3–c, 4–d
To'g'ri javob: C) 1–c, 2–a, 3–d, 4–f✔
34. Har bir ifodaga uning qiymatini moslang.
1) 9/2 + 7/3 a) 17/7
2) 3/11 + 1/4 b) 47/20
3) 7/5 + 9/9 c) 23/44
4) 8/5 + 3/4 d) 54/55
e) 12/5
f) 41/6
A) 1–d, 2–c, 3–e, 4–b
B) 1–f, 2–c, 3–e, 4–b
C) 1–f, 2–c, 3–e, 4–a
D) 1–b, 2–e, 3–f, 4–c
To'g'ri javob: B) 1–f, 2–c, 3–e, 4–b
✔
35. Har bir ifodaga uning qiymatini moslang.
1) 3^3 · 3^5 : 3^2 a) 729
2) 7^2 · 7^4 : 7^5 b) 7
3) 2^5 · 2^2 : 2^1 c) 64
4) 5^6 · 5^6 : 5^2 d) 117649
e) 2187
f) 9765625
A) 1–b, 2–a, 3–c, 4–f
B) 1–a, 2–c, 3–b, 4–f
C) 1–a, 2–b, 3–f, 4–c
D) 1–a, 2–b, 3–c, 4–f
To'g'ri javob: D) 1–a, 2–b, 3–c, 4–f
✔
O • ochiq topshiriq (qisqa javob)
36. Logarifmik tenglamani yeching. Javobni yozing.
a) log₃(x − 9) = 2
b) log₂(x − 2) = 1
Javob: a) 18; b) 4
✔
37. To'g'ri burchakli parallelepiped hajmini toping. Javobni yozing.
a) O'lchamlari 8, 8, 3
b) O'lchamlari 9, 6, 4
Javob: a) 192; b) 216
✔
Matematika — milliy sertifikat mashq variantlari | 126

38. Logarifmik tenglamani yeching. Javobni yozing.
a) log₅(x − 2) = 1
b) log₁₀(x − 9) = 3
Javob: a) 7; b) 1009✔
39. Tenglamaning katta ildizini toping. Javobni yozing.
a) x² + 11x + 30 = 0
b) x² + x − 30 = 0
Javob: a) -5; b) 5
✔
40. Vektorlarning skalyar ko'paytmasini toping. Javobni yozing.
a) (3; -3), (6; 1)
a⃗ b ⃗
b) (-2; -4), (-1; 2)
a⃗ b ⃗
Javob: a) 15; b) -6
✔
41. Ehtimollikni toping. Javobni yozing.
a) Qutida 4 ta oq va 6 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 8 ta oq va 6 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 2/5; b) 4/7
✔
42. Vektor uzunligini toping. Javobni yozing.
a) (-9; 12)
a⃗
b) (-9; -12)
a⃗
Javob: a) 15; b) 15
✔
43. A va B nuqtalar orasidagi masofani toping. Javobni yozing.
a) A(-1; -1), B(8; 11)
b) A(2; -4), B(-7; 8)
Javob: a) 15; b) 15
✔
44. Aylana uzunligini toping (π orqali). Javobni yozing.
a) Radius R = 13
b) Radius R = 2
Javob: a) 26π; b) 4π
✔
45. A va B nuqtalar orasidagi masofani toping. Javobni yozing.
a) A(-3; -5), B(-12; -17)
b) A(-4; -5), B(5; 7)
Javob: a) 15; b) 15
✔
Matematika — milliy sertifikat mashq variantlari | 127

17-variant
Y-1 • bitta to'g'ri javob
1. Trapetsiya yuzini toping.
Asoslari 2 va 9, balandligi 7
A) 77
B) 126
C) 77/2
D) 91/2
To'g'ri javob: C) 77/2✔
2. Silindr hajmini toping (π orqali).
Asos radiusi 1, balandligi 6
A) 7π
B) 12π
C) 8π
D) 6π
To'g'ri javob: D) 6π
✔
3. Tenglamalar sistemasini yeching va x + y ni toping.
{ x + 5y = -31; 5x − 5y = 55 }
A) -1
B) -3
C) -28
D) 11
To'g'ri javob: B) -3
✔
4. f'(x₀) ni toping.
f(x) = 2x³ + 2x² − x − 4, x₀ = 3
A) 65
B) 64
C) 66
D) 69
To'g'ri javob: A) 65
✔
5. Tenglamani yeching.
4(x − 6) = 3x − 18
A) 7
B) -6
C) 4
D) 6
To'g'ri javob: D) 6
✔
6. f(x₀) qiymatini toping.
f(x) = −3x² − 2x + 4, x₀ = 1
A) -1
B) 1
C) 0
D) -4
To'g'ri javob: A) -1
✔
Matematika — milliy sertifikat mashq variantlari | 128

7. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -6, d = 5, n = 6
A) 44
B) 33
C) 39
D) 19
To'g'ri javob: C) 39✔
8. 1200 ning 10% ini toping.
A) 120
B) 81
C) 141
D) 130
To'g'ri javob: A) 120
✔
9. Ifodaning qiymatini toping.
log₃243 + log₃9
A) 7
B) 10
C) 2187
D) 8
To'g'ri javob: A) 7
✔
10. Tenglamani yeching.
6(x + 18) = 2x + 76
A) -7
B) -8
C) 8
D) -10
To'g'ri javob: B) -8
✔
11. Geometrik progressiyada b₁ = 1, q = 2. b7 ni toping.
A) -64
B) 32
C) 64
D) 128
To'g'ri javob: C) 64
✔
12. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 8, d = 5, n = 10
A) 305
B) 53
C) 295
D) 310
To'g'ri javob: A) 305
✔
13. Aniq integral geometrik jihatdan nimani bildiradi?
A) Egri chiziqli trapetsiya yuzini
B) Funksiya nollarini
C) Urinmaning qiyaligini
D) Funksiyaning o'sish tezligini
To'g'ri javob: A) Egri chiziqli trapetsiya yuzini
✔
Matematika — milliy sertifikat mashq variantlari | 129

$14. √225 ni hisoblang. A) 15 B) 112 C) 16 D) 14 To'g'ri javob: A) 15✔ 15. Hisoblang. 1/3 + 9/9 A) 37/27 B) 4/3 C) 1/3 D) 5/6 To'g'ri javob: B) 4/3 ✔ 16. Tenglamalar sistemasini yeching va x + y ni toping. { x + y = 1; 3x − 4y = -4 } A) 0 B) 3 C) -1 D) 1 To'g'ri javob: D) 1 ✔ 17. Aniq integralni hisoblang. ∫₀^1 (6x − 4) dx A) -1 B) 0 C) 2 D) -2 To'g'ri javob: A) -1 ✔ 18. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. b₁ = 4, q = -2, n = 6 A) -128 B) -80 C) -84 D) -82 To'g'ri javob: C) -84 ✔ 19. Hisoblang. √144 + √4 A) 14 B) 13 C) 24 D) 12 To'g'ri javob: A) 14 ✔ Matematika — milliy sertifikat mashq variantlari | 130$

20. Aniq integralni hisoblang.
∫₀^3 (4x − 2) dx
A) 15
B) 24
C) 12
D) 10
To'g'ri javob: C) 12✔
21. f'(x₀) ni toping.
f(x) = 3x³ + 2x² + x + 5, x₀ = -2
A) -13
B) 29
C) 33
D) 28
To'g'ri javob: B) 29
✔
22. Geometrik progressiyada b₁ = 2, q = -2. b4 ni toping.
A) 8
B) 32
C) -16
D) 16
To'g'ri javob: C) -16
✔
23. EKUK(24; 6) ni toping.
A) 6
B) 24
C) 144
D) 48
To'g'ri javob: B) 24
✔
24. EKUB(12; 10) ni toping.
A) 1
B) 2
C) 60
D) 4
To'g'ri javob: B) 2
✔
25. Hisoblang.
√196 + √16
A) 14
B) 56
C) 18
D) 17
To'g'ri javob: C) 18
✔
26. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 1, q = 3, n = 4
A) 41
B) 37
C) 40
D) 27
To'g'ri javob: C) 40
✔
Matematika — milliy sertifikat mashq variantlari | 131

27. Hisoblang.
8/7 + 4/5
A) 68/35
B) 1
C) 32/35
D) 69/35
To'g'ri javob: A) 68/35✔
28. Masalani yeching.
Mahsulot narxi 3800 so'm edi. Narx 10% ga oshirildi. Yangi narx necha so'm?
A) 380
B) 3810
C) 4180
D) 3420
To'g'ri javob: C) 4180
✔
29. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -7, d = -3, n = 16
A) -475
B) -472
C) -488
D) -52
To'g'ri javob: B) -472
✔
30. Arifmetik progressiya dastlabki n ta hadi yig'indisi formulasi qaysi?
A) S = (a₁ − a ) · n
ₙ ₙ
B) S = (a₁ + a ) · n / 2
ₙ ₙ
C) S = a₁ · n
ₙ
D) S = a / n
ₙ ₙ
To'g'ri javob: B) Sₙ = (a₁ + aₙ) · n / 2
✔
31. Aniq integralni hisoblang.
∫₀^2 (8x + 2) dx
A) 22
B) 40
C) 18
D) 20
To'g'ri javob: D) 20
✔
32. Hisoblang.
√16 + √4
A) 5
B) 8
C) 4
D) 6
To'g'ri javob: D) 6
✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) √49 + √196 a) 21
2) √9 + √4 b) 5
Matematika — milliy sertifikat mashq variantlari | 132

3) √196 + √81 c) 14
4) √121 + √9 d) 17
e) 23
f) 20
A) 1–c, 2–e, 3–b, 4–a
B) 1–b, 2–c, 3–a, 4–e
C) 1–a, 2–b, 3–e, 4–d
D) 1–a, 2–b, 3–e, 4–c
To'g'ri javob: D) 1–a, 2–b, 3–e, 4–c✔
34. Har bir ifodaga uning qiymatini moslang.
1) log₃243 + log₃27 a) 3
2) log₂16 + log₂2 b) 5
3) log₅5 + log₅5 c) 7
4) log₃9 + log₃3 d) 6
e) 8
f) 2
A) 1–e, 2–b, 3–a, 4–f
B) 1–e, 2–b, 3–f, 4–a
C) 1–e, 2–c, 3–f, 4–a
D) 1–f, 2–e, 3–b, 4–a
To'g'ri javob: B) 1–e, 2–b, 3–f, 4–a
✔
35. Har bir ifodaga uning qiymatini moslang.
1) Radius R = 12 a) 16π
2) Radius R = 5 b) 24π
3) Radius R = 9 c) 81π
4) Radius R = 8 d) 49π
e) 25π
f) 6π
A) 1–b, 2–c, 3–e, 4–a
B) 1–b, 2–f, 3–c, 4–a
C) 1–b, 2–e, 3–c, 4–a
D) 1–b, 2–e, 3–a, 4–c
To'g'ri javob: C) 1–b, 2–e, 3–c, 4–a
✔
O • ochiq topshiriq (qisqa javob)
36. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) a₁ = 4, d = 0, n = 18
b) a₁ = 0, d = 4, n = 9
Javob: a) 72; b) 144
✔
37. Ifodaning qiymatini toping. Javobni yozing.
a) cos 0° + sin 0°
b) cos 180° + cos 60°
Javob: a) 1; b) −1/2
✔
Matematika — milliy sertifikat mashq variantlari | 133

38. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x − 7| = 7
b) |x − 5| = 9
Javob: a) 14; b) 10✔
39. Ehtimollikni toping. Javobni yozing.
a) Qutida 5 ta oq va 7 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 9 ta oq va 2 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 5/12; b) 9/11
✔
40. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² + 8x + 8
b) y = x² − 2
Javob: a) -8; b) -2
✔
41. Hisoblang. Javobni yozing.
a) 1/11 + 2/8
b) 4/6 + 4/12
Javob: a) 15/44; b) 1
✔
42. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) b₁ = 1, q = 2, n = 5
b) b₁ = 2, q = -2, n = 5
Javob: a) 31; b) 22
✔
43. Ifodaning qiymatini toping. Javobni yozing.
a) cos 180° + cos 0°
b) sin 30° + tg 0°
Javob: a) 0; b) 1/2
✔
44. Trapetsiya yuzini toping. Javobni yozing.
a) Asoslari 13 va 3, balandligi 12
b) Asoslari 15 va 4, balandligi 7
Javob: a) 96; b) 133/2
✔
45. Ifodaning qiymatini toping. Javobni yozing.
a) tg 45° + sin 30°
b) tg 0° + cos 90°
Javob: a) 3/2; b) 0
✔
Matematika — milliy sertifikat mashq variantlari | 134

18-variant
Y-1 • bitta to'g'ri javob
1. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 6, d = 0, n = 15
A) 90
B) 91
C) 6
D) 75
To'g'ri javob: A) 90✔
2. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 3, 2, 8
A) 92
B) 48
C) 51
D) 13
To'g'ri javob: B) 48
✔
3. Ifodaning qiymatini toping.
7^2 · 7^6 : 7^5
A) 343
B) 823543
C) 350
D) 5764801
To'g'ri javob: A) 343
✔
4. f'(x₀) ni toping.
f(x) = 2x³ + 3x² + 3x + 9, x₀ = -1
A) 2
B) 7
C) 9
D) 3
To'g'ri javob: D) 3
✔
5. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -8, d = -2, n = 18
A) -450
B) -42
C) -468
D) -452
To'g'ri javob: A) -450
✔
6. f'(x₀) ni toping.
f(x) = x³ + 2x² + 2x, x₀ = -3
A) 16
B) 21
C) -15
D) 17
To'g'ri javob: D) 17
✔
Matematika — milliy sertifikat mashq variantlari | 135

7. Ehtimollikni toping.
Qutida 2 ta oq va 2 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 1/4
B) 3/2
C) 1
D) 1/2
To'g'ri javob: D) 1/2✔
8. Ifodaning qiymatini toping.
tg 45° + cos 90°
A) −1
B) 0
C) 1
D) 2
To'g'ri javob: C) 1
✔
9. EKUBni toping.
EKUB(83; 73)
A) 10
B) 1
C) 6059
D) 2
To'g'ri javob: B) 1
✔
10. Diskriminant nolga teng bo'lsa, kvadrat tenglama nechta ildizga ega?
A) Uchta ildizga
B) Ildizga ega emas
C) Bitta (ikki karrali) ildizga
D) Ikkita turli ildizga
To'g'ri javob: C) Bitta (ikki karrali) ildizga
✔
11. Tenglama ildizlari yig'indisini toping.
x² − 7x − 8 = 0
A) 7
B) -7
C) 8
D) -8
To'g'ri javob: A) 7
✔
12. C(6;2) — 6 ta elementdan 2 tadan guruhlashlar sonini toping.
A) 21
B) 12
C) 15
D) 30
To'g'ri javob: C) 15
✔
Matematika — milliy sertifikat mashq variantlari | 136

13. EKUBni toping.
EKUB(11; 37)
A) 407
B) 2
C) 26
D) 1
To'g'ri javob: D) 1✔
14. Logarifmik tenglamani yeching.
log₅(x − 2) = 3
A) 123
B) 125
C) 17
D) 127
To'g'ri javob: D) 127
✔
15. 240 ning 15% ini toping.
A) 36
B) 44
C) 38
D) 47
To'g'ri javob: A) 36
✔
16. EKUK(32; 24) ni toping.
A) 128
B) 8
C) 768
D) 96
To'g'ri javob: D) 96
✔
17. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 4, d = -1, n = 8
A) 3
B) -4
C) 4
D) -3
To'g'ri javob: C) 4
✔
18. x² − 13x + 40 = 0 tenglama ildizlarining yig'indisini toping.
A) 15
B) 13
C) -13
D) 40
To'g'ri javob: B) 13
✔
19. Ifodaning qiymatini toping.
log₅125 + log₅125
A) 15625
B) 9
C) 7
D) 6
To'g'ri javob: D) 6
✔
Matematika — milliy sertifikat mashq variantlari | 137

20. Parabola uchining ordinatasini toping.
y = x² − 2x + 5
A) 5
B) 6
C) 4
D) 1
To'g'ri javob: C) 4✔
21. x² − 3x − 18 = 0 tenglama ildizlarining yig'indisini toping.
A) 3
B) -18
C) -3
D) 5
To'g'ri javob: A) 3
✔
22. Vektorlarning skalyar ko'paytmasini toping.
(-1; -6), (5; 5)
a⃗ b ⃗
A) -35
B) -34
C) 25
D) 35
To'g'ri javob: A) -35
✔
23. Hisoblang.
6/5 + 2/10
A) 71/50
B) 6/25
C) 7/5
D) 8/15
To'g'ri javob: C) 7/5
✔
24. Trapetsiya yuzini toping.
Asoslari 2 va 14, balandligi 7
A) 196
B) 63
C) 112
D) 56
To'g'ri javob: D) 56
✔
25. Aylana uzunligini toping (π orqali).
Radius R = 14
A) 14π
B) 28π
C) 196π
D) 56π
To'g'ri javob: B) 28π
✔
Matematika — milliy sertifikat mashq variantlari | 138

26. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 5, q = -2, n = 3
A) 20
B) 16
C) 15
D) 17
To'g'ri javob: C) 15✔
27. 1 soni tub sonmi?
A) Yo'q, 1 na tub, na murakkab son
B) Ha, murakkab son
C) Ha, eng kichik tub son
D) Faqat ba'zi hollarda
To'g'ri javob: A) Yo'q, 1 na tub, na murakkab son
✔
28. Aylana uzunligini toping (π orqali).
Radius R = 8
A) 32π
B) 16π
C) 64π
D) 8π
To'g'ri javob: B) 16π
✔
29. Tenglama ildizlari yig'indisini toping.
|x − 3| = 4
A) 4
B) 7
C) -6
D) 6
To'g'ri javob: D) 6
✔
30. Aniq integralni hisoblang.
∫₀^1 (4x − 1) dx
A) 1
B) 2
C) 4
D) 3
To'g'ri javob: A) 1
✔
31. Arifmetik progressiyada a₁ = -7, d = 6. a18 ni toping.
A) 95
B) 89
C) 107
D) 101
To'g'ri javob: A) 95
✔
32. 4! ni hisoblang.
A) 16
B) 6
C) 28
D) 24
To'g'ri javob: D) 24
✔
Matematika — milliy sertifikat mashq variantlari | 139

Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) log₂32 + log₂16 a) 5
2) log₃3 + log₃3 b) 2
3) log₂16 + log₂8 c) 9
4) log₅625 + log₅25 d) 7
e) 6
f) 3
A) 1–c, 2–b, 3–d, 4–e
B) 1–e, 2–c, 3–d, 4–b
C) 1–c, 2–d, 3–b, 4–e
D) 1–c, 2–a, 3–d, 4–e
To'g'ri javob: A) 1–c, 2–b, 3–d, 4–e✔
34. Har bir ifodaga uning qiymatini moslang.
1) √4 + √36 a) 18
2) √169 + √64 b) 15
3) √100 + √25 c) 21
4) √16 + √4 d) 8
e) 13
f) 6
A) 1–c, 2–b, 3–d, 4–f
B) 1–d, 2–c, 3–b, 4–f
C) 1–d, 2–e, 3–b, 4–f
D) 1–c, 2–b, 3–f, 4–d
To'g'ri javob: B) 1–d, 2–c, 3–b, 4–f
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √49 + √16 a) 20
2) √196 + √100 b) 17
3) √36 + √196 c) 11
4) √49 + √100 d) 10
e) 24
f) 18
A) 1–b, 2–a, 3–c, 4–e
B) 1–c, 2–e, 3–a, 4–b
C) 1–c, 2–e, 3–d, 4–b
D) 1–b, 2–e, 3–a, 4–c
To'g'ri javob: B) 1–c, 2–e, 3–a, 4–b
✔
O • ochiq topshiriq (qisqa javob)
36. Aniq integralni hisoblang. Javobni yozing.
a) ∫₀^3 (6x − 1) dx
b) ∫₀^3 (4x) dx
Javob: a) 24; b) 18
✔
Matematika — milliy sertifikat mashq variantlari | 140

37. Uchburchak yuzini toping. Javobni yozing.
a) Asosi 2, unga tushirilgan balandlik 7
b) Asosi 7, unga tushirilgan balandlik 19
Javob: a) 7; b) 133/2✔
38. EKUKni toping. Javobni yozing.
a) EKUK(78; 41)
b) EKUK(82; 23)
Javob: a) 3198; b) 1886
✔
39. Ko'rsatkichli tenglamani yeching. Javobni yozing.
a) 3^(x − 1) = 27
b) 5^(x − 4) = 125
Javob: a) 4; b) 7
✔
40. Doira yuzini toping (π orqali). Javobni yozing.
a) Radius R = 15
b) Radius R = 10
Javob: a) 225π; b) 100π
✔
41. Tenglamani yeching. Javobni yozing.
a) 6(x − 18) = 3x − 93
b) 7(x + 5) = 2x − 5
Javob: a) 5; b) -8
✔
42. EKUBni toping. Javobni yozing.
a) EKUB(46; 26)
b) EKUB(28; 23)
Javob: a) 2; b) 1
✔
43. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² + 8x + 19
b) y = x² − 10x + 29
Javob: a) 3; b) 4
✔
44. A va B nuqtalar orasidagi masofani toping. Javobni yozing.
a) A(-1; 3), B(-10; 15)
b) A(3; 2), B(-6; -10)
Javob: a) 15; b) 15
✔
45. EKUKni toping. Javobni yozing.
a) EKUK(90; 21)
b) EKUK(32; 16)
Javob: a) 630; b) 32
✔
Matematika — milliy sertifikat mashq variantlari | 141

19-variant
Y-1 • bitta to'g'ri javob
1. EKUK(15; 25) ni toping.
A) 375
B) 90
C) 5
D) 75
To'g'ri javob: D) 75✔
2. Doira yuzini toping (π orqali).
Radius R = 15
A) 225π
B) 15π
C) 30π
D) 450π
To'g'ri javob: A) 225π
✔
3. f(x₀) qiymatini toping.
f(x) = −2x² − 5x − 9, x₀ = 3
A) 42
B) -20
C) -42
D) -44
To'g'ri javob: C) -42
✔
4. Hosila geometrik jihatdan nimani bildiradi?
A) Funksiyaning nollarini
B) Grafik ostidagi yuzani
C) Funksiya grafigiga o'tkazilgan urinmaning burchak koeffitsientini
D) Funksiyaning eng katta qiymatini
To'g'ri javob: C) Funksiya grafigiga o'tkazilgan urinmaning burchak koeffitsientini
✔
5. Radiusi 9 ga teng doiraning yuzini toping.
A) 9π
B) 81π
C) 162π
D) 18π
To'g'ri javob: B) 81π
✔
6. Aniq integralni hisoblang.
∫₀^2 (2x + 2) dx
A) 10
B) 16
C) 8
D) 6
To'g'ri javob: C) 8
✔
Matematika — milliy sertifikat mashq variantlari | 142

7. Guruhlashlar sonini toping.
C(6; 4)
A) 24
B) 20
C) 15
D) 360
To'g'ri javob: C) 15✔
8. Hisoblang.
1/10 + 6/5
A) 33/25
B) 3/25
C) 7/15
D) 13/10
To'g'ri javob: D) 13/10
✔
9. Ifodaning qiymatini toping.
2^2 · 2^3 : 2^5
A) 2
B) 1
C) 32
D) 3
To'g'ri javob: B) 1
✔
10. Tenglama ildizlari yig'indisini toping.
|x − 6| = 6
A) 12
B) 6
C) -12
D) 13
To'g'ri javob: A) 12
✔
11. Ko'rsatkichli tenglamani yeching.
2^(x − 1) = 8
A) 5
B) 3
C) 4
D) 2
To'g'ri javob: C) 4
✔
12. Radiusi 5 ga teng doiraning yuzini toping.
A) 5π
B) 50π
C) 10π
D) 25π
To'g'ri javob: D) 25π
✔
Matematika — milliy sertifikat mashq variantlari | 143

$13. O'rinlashtirishlar sonini toping. A(8; 4) A) 4096 B) 1680 C) 336 D) 70 To'g'ri javob: B) 1680✔ 14. Tenglamalar sistemasini yeching va x + y ni toping. { 2x + y = -13; 3x − 5y = -13 } A) 6 B) -5 C) -7 D) -6 To'g'ri javob: C) -7 ✔ 15. f'(x₀) ni toping. f(x) = 4x² − 3x − 4, x₀ = 1 A) 13 B) 5 C) 4 D) -3 To'g'ri javob: B) 5 ✔ 16. Ehtimollikni toping. Qutida 2 ta oq va 9 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli A) 9/11 B) 2/9 C) 1/11 D) 2/11 To'g'ri javob: D) 2/11 ✔ 17. Ko'rsatkichli tenglamani yeching. 5^(x − 2) = 625 A) 2 B) 7 C) 4 D) 6 To'g'ri javob: D) 6 ✔ 18. Tenglama ildizlari yig'indisini toping. |x − 2| = 9 A) 11 B) 9 C) 4 D) -4 To'g'ri javob: C) 4 ✔ Matematika — milliy sertifikat mashq variantlari | 144$

19. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 1, q = 2, n = 4
A) 15
B) 8
C) 16
D) 13
To'g'ri javob: A) 15✔
20. C(4;2) — 4 ta elementdan 2 tadan guruhlashlar sonini toping.
A) 8
B) 10
C) 6
D) 12
To'g'ri javob: C) 6
✔
21. Tenglamani yeching: 3x − 4 = 29
A) 13
B) 10
C) 14
D) 11
To'g'ri javob: D) 11
✔
22. Ikki nuqta orasidagi masofa formulasi qaysi?
A) d = (x₂ + x₁)/2
B) d = √((x₂ − x₁)² + (y₂ − y₁)²)
C) d = x₂ · x₁ + y₂ · y₁
D) d = (x₂ − x₁) + (y₂ − y₁)
To'g'ri javob: B) d = √((x₂ − x₁)² + (y₂ − y₁)²)
✔
23. Parabola uchining ordinatasini toping.
y = x² + 4x
A) 0
B) -2
C) -3
D) -4
To'g'ri javob: D) -4
✔
24. Ifodaning qiymatini toping.
tg 0° + sin 90°
A) −1
B) 1
C) 2
D) 3
To'g'ri javob: B) 1
✔
25. Trapetsiya yuzini toping.
Asoslari 10 va 12, balandligi 10
A) 120
B) 220
C) 110
D) 1200
To'g'ri javob: C) 110
✔
Matematika — milliy sertifikat mashq variantlari | 145

26. Uchburchak yuzini toping.
Asosi 3, unga tushirilgan balandlik 17
A) 51/2
B) 51
C) 53/2
D) 20
To'g'ri javob: A) 51/2✔
27. Tenglamaning katta ildizini toping.
x² + 5x − 14 = 0
A) 3
B) 2
C) -7
D) -2
To'g'ri javob: B) 2
✔
28. Trapetsiya yuzi formulasi qaysi?
A) S = (a − b) · h
B) S = (a + b) · h / 2
C) S = a · b · h
D) S = a · h
To'g'ri javob: B) S = (a + b) · h / 2
✔
29. To'g'ri burchakli uchburchakning katetlari 3 va 4. Gipotenuzasini toping.
A) 3
B) 5
C) 7
D) 6
To'g'ri javob: B) 5
✔
30. Tenglama ildizlari yig'indisini toping.
|x + 1| = 6
A) 2
B) -2
C) 5
D) 6
To'g'ri javob: B) -2
✔
31. f'(x₀) ni toping.
f(x) = 3x³ + 4x² + 4x − 2, x₀ = 0
A) -2
B) 12
C) 3
D) 4
To'g'ri javob: D) 4
✔
Matematika — milliy sertifikat mashq variantlari | 146

32. Ko'rsatkichli tenglamani yeching.
3^(x − 3) = 27
A) 0
B) 7
C) 6
D) 3
To'g'ri javob: C) 6✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) C(8; 3) a) 56
2) C(10; 4) b) 1680
3) A(8; 4) c) 42
4) A(5; 3) d) 20
e) 60
f) 210
A) 1–a, 2–f, 3–b, 4–e
B) 1–a, 2–e, 3–b, 4–f
C) 1–a, 2–e, 3–f, 4–b
D) 1–e, 2–f, 3–a, 4–b
To'g'ri javob: A) 1–a, 2–f, 3–b, 4–e
✔
34. Har bir ifodaga uning qiymatini moslang.
1) √16 + √4 a) 6
2) √81 + √64 b) 22
3) √36 + √9 c) 17
4) √81 + √25 d) 19
e) 9
f) 14
A) 1–a, 2–c, 3–e, 4–f
B) 1–d, 2–c, 3–e, 4–f
C) 1–c, 2–a, 3–e, 4–f
D) 1–a, 2–f, 3–e, 4–c
To'g'ri javob: A) 1–a, 2–c, 3–e, 4–f
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √49 + √225 a) 20
2) √64 + √25 b) 22
3) √36 + √196 c) 11
4) √9 + √64 d) 23
e) 13
f) 14
Matematika — milliy sertifikat mashq variantlari | 147

A) 1–b, 2–c, 3–a, 4–e
B) 1–e, 2–b, 3–a, 4–c
C) 1–b, 2–e, 3–a, 4–c
D) 1–b, 2–e, 3–a, 4–f
To'g'ri javob: C) 1–b, 2–e, 3–a, 4–c✔
O • ochiq topshiriq (qisqa javob)
36. Uchburchak yuzini toping. Javobni yozing.
a) Asosi 19, unga tushirilgan balandlik 18
b) Asosi 20, unga tushirilgan balandlik 18
Javob: a) 171; b) 180
✔
37. Tenglamani yeching. Javobni yozing.
a) 7(x + 3) = 2x + 16
b) 6(x + 5) = 2x + 10
Javob: a) -1; b) -5
✔
38. Logarifmik tenglamani yeching. Javobni yozing.
a) log₅(x − 1) = 2
b) log₃(x − 4) = 2
Javob: a) 26; b) 13
✔
39. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) a₁ = -2, d = -4, n = 9
b) a₁ = -9, d = 3, n = 15
Javob: a) -162; b) 180
✔
40. Aniq integralni hisoblang. Javobni yozing.
a) ∫₀^1 (8x − 4) dx
b) ∫₀^2 (6x + 4) dx
Javob: a) 0; b) 20
✔
41. Uchburchak yuzini toping. Javobni yozing.
a) Asosi 10, unga tushirilgan balandlik 14
b) Asosi 18, unga tushirilgan balandlik 15
Javob: a) 70; b) 135
✔
42. f'(x₀) ni toping. Javobni yozing.
a) f(x) = x³ + x² − 5x + 1, x₀ = -2
b) f(x) = 2x³ + x² + x + 6, x₀ = -3
Javob: a) 3; b) 49
✔
43. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x − 6| = 9
b) |x − 3| = 3
Javob: a) 12; b) 6
✔
44. f(x₀) qiymatini toping. Javobni yozing.
a) f(x) = −2x² + 2x − 9, x₀ = 4
b) f(x) = −4x² − 6x − 3, x₀ = -3
Javob: a) -33; b) -21
✔
Matematika — milliy sertifikat mashq variantlari | 148

45. Ehtimollikni toping. Javobni yozing.
a) Qutida 2 ta oq va 2 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
b) Qutida 6 ta oq va 8 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
Javob: a) 1/2; b) 3/7✔
Matematika — milliy sertifikat mashq variantlari | 149

20-variant
Y-1 • bitta to'g'ri javob
1. Parabola uchining ordinatasini toping.
y = x² + 4x + 10
A) 10
B) 7
C) -2
D) 6
To'g'ri javob: D) 6✔
2. (2^4)^2 ni hisoblang.
A) 32
B) 64
C) 256
D) 257
To'g'ri javob: C) 256
✔
3. (4^2)^3 ni hisoblang.
A) 1024
B) 4097
C) 48
D) 4096
To'g'ri javob: D) 4096
✔
4. Hisoblang.
7/4 + 3/2
A) 27/8
B) 13/4
C) 21/8
D) 5/3
To'g'ri javob: B) 13/4
✔
5. f(x) = 1x − 7 bo'lsa, f(-1) ni toping.
A) -7
B) -8
C) -11
D) -5
To'g'ri javob: B) -8
✔
6. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 3, q = 3, n = 5
A) 360
B) 363
C) 366
D) 243
To'g'ri javob: B) 363
✔
Matematika — milliy sertifikat mashq variantlari | 150

7. Logarifmik tenglamani yeching.
log₅(x − 5) = 1
A) 0
B) 11
C) 5
D) 10
To'g'ri javob: D) 10✔
8. logₐ(xy) nimaga teng?
A) logₐx · logₐy
B) logₐx − logₐy
C) logₐx / logₐy
D) logₐx + logₐy
To'g'ri javob: D) logₐx + logₐy
✔
9. Ifodaning qiymatini toping.
sin 30° + cos 0°
A) 3/2
B) 1/2
C) −1/2
D) 5/2
To'g'ri javob: A) 3/2
✔
10. O'rinlashtirishlar sonini toping.
A(5; 2)
A) 5
B) 20
C) 10
D) 25
To'g'ri javob: B) 20
✔
11. Masalani yeching.
Mahsulot narxi 2300 so'm edi. Narx 30% ga oshirildi. Yangi narx necha so'm?
A) 1610
B) 2330
C) 2990
D) 690
To'g'ri javob: C) 2990
✔
12. Ifodaning qiymatini toping.
2^2 · 2^4 : 2^4
A) 16
B) 4
C) 64
D) 6
To'g'ri javob: B) 4
✔
Matematika — milliy sertifikat mashq variantlari | 151

13. x² + 7x = 0 tenglama ildizlarining ko'paytmasini toping.
A) 0
B) 1
C) 3
D) -7
To'g'ri javob: A) 0✔
14. x² + 8x + 7 = 0 tenglama ildizlarining yig'indisini toping.
A) 7
B) -6
C) -8
D) 8
To'g'ri javob: C) -8
✔
15. f(x₀) qiymatini toping.
f(x) = x² + 4x − 7, x₀ = 3
A) 14
B) -14
C) 15
D) 0
To'g'ri javob: A) 14
✔
16. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -2, d = 0, n = 7
A) -2
B) -14
C) -13
D) -21
To'g'ri javob: B) -14
✔
17. Masalani yeching.
Narx 3800 so'm. Avval 50% ga oshirildi, so'ng 25% ga kamaytirildi. Oxirgi narx necha so'm?
A) 4750
B) 4375
C) 4275
D) 3800
To'g'ri javob: C) 4275
✔
18. f(x₀) qiymatini toping.
f(x) = x² + x − 7, x₀ = 4
A) -2
B) 13
C) -13
D) 14
To'g'ri javob: B) 13
✔
Matematika — milliy sertifikat mashq variantlari | 152

$19. Ehtimollikni toping. Qutida 9 ta oq va 3 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli A) 3 B) 1/4 C) 3/4 D) 1/12 To'g'ri javob: C) 3/4✔ 20. Tenglamalar sistemasini yeching va x + y ni toping. { 3x + 4y = 5; x − 3y = 6 } A) 3 B) 2 C) -3 D) 4 To'g'ri javob: B) 2 ✔ 21. Ko'rsatkichli tenglamani yeching. 5^(x − 2) = 125 A) 5 B) 6 C) 3 D) 1 To'g'ri javob: A) 5 ✔ 22. Arifmetik progressiyada a₁ = -10, d = -5. a28 ni toping. A) -140 B) -150 C) -155 D) -145 To'g'ri javob: D) -145 ✔ 23. Masalani yeching. Mahsulot narxi 2900 so'm edi. Narx 40% ga oshirildi. Yangi narx necha so'm? A) 1740 B) 4060 C) 2940 D) 1160 To'g'ri javob: B) 4060 ✔ 24. 5! ni hisoblang. A) 24 B) 120 C) 125 D) 25 To'g'ri javob: B) 120 ✔ 25. log₃3 ni hisoblang. A) 1 B) 2 C) 4 D) 3 To'g'ri javob: A) 1 ✔ Matematika — milliy sertifikat mashq variantlari | 153$

26. Qavariq 8-burchakning ichki burchaklari yig'indisini toping.
A) 2160°
B) 1080°
C) 1260°
D) 1440°
To'g'ri javob: B) 1080°✔
27. Logarifmik tenglamani yeching.
log₅(x − 9) = 3
A) 116
B) 24
C) 134
D) 125
To'g'ri javob: C) 134
✔
28. Tenglama ildizlari yig'indisini toping.
|x + 9| = 7
A) 18
B) 7
C) -2
D) -18
To'g'ri javob: D) -18
✔
29. Vektorlarning skalyar ko'paytmasini toping.
(-5; 3), (-6; 2)
a⃗ b ⃗
A) 8
B) -36
C) 36
D) 37
To'g'ri javob: C) 36
✔
30. To'g'ri burchakli parallelepiped hajmini toping.
O'lchamlari 7, 8, 2
A) 172
B) 17
C) 119
D) 112
To'g'ri javob: D) 112
✔
31. Ifodaning qiymatini toping.
tg 0° + cos 180°
A) 0
B) −1
C) 1
D) −3
To'g'ri javob: B) −1
✔
Matematika — milliy sertifikat mashq variantlari | 154

32. Ifodani soddalashtiring: 2^5 · 2^2
A) 2^10
B) 2^3
C) 2^7
D) 4^7
To'g'ri javob: C) 2^7✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) 2/8 + 8/5 a) 37/20
2) 1/11 + 5/11 b) 41/11
3) 8/6 + 1/8 c) 6/11
4) 9/7 + 8/7 d) 17/7
e) 13/7
f) 35/24
A) 1–e, 2–c, 3–f, 4–d
B) 1–d, 2–a, 3–c, 4–f
C) 1–d, 2–f, 3–a, 4–c
D) 1–a, 2–c, 3–f, 4–d
To'g'ri javob: D) 1–a, 2–c, 3–f, 4–d
✔
34. Har bir ifodaga uning qiymatini moslang.
1) 3/8 + 2/2 a) 57/28
2) 6/3 + 4/10 b) 21/4
3) 1/10 + 5/5 c) 11/10
4) 9/7 + 3/4 d) 11/8
e) 12/5
f) 10/3
A) 1–f, 2–e, 3–c, 4–a
B) 1–d, 2–a, 3–c, 4–e
C) 1–d, 2–e, 3–c, 4–a
D) 1–d, 2–f, 3–c, 4–a
To'g'ri javob: C) 1–d, 2–e, 3–c, 4–a
✔
35. Har bir ifodaga uning qiymatini moslang.
1) √36 + √121 a) 9
2) √4 + √100 b) 12
3) √169 + √9 c) 14
4) √25 + √16 d) 18
e) 17
f) 16
Matematika — milliy sertifikat mashq variantlari | 155

A) 1–e, 2–b, 3–f, 4–a
B) 1–e, 2–a, 3–f, 4–b
C) 1–f, 2–a, 3–e, 4–b
D) 1–e, 2–c, 3–f, 4–a
To'g'ri javob: A) 1–e, 2–b, 3–f, 4–a✔
O • ochiq topshiriq (qisqa javob)
36. Ifodaning qiymatini toping. Javobni yozing.
a) cos 90° + sin 270°
b) cos 0° + sin 90°
Javob: a) −1; b) 2
✔
37. Ifodaning qiymatini toping. Javobni yozing.
a) log₅125 + log₅125
b) log₅625 + log₅125
Javob: a) 6; b) 7
✔
38. Ifodaning qiymatini toping. Javobni yozing.
a) log₂4 + log₂16
b) log₃243 + log₃9
Javob: a) 6; b) 7
✔
39. Masalani yeching. Javobni yozing.
a) Narx 900 so'm. Avval 30% ga oshirildi, so'ng 20% ga kamaytirildi. Oxirgi narx necha so'm?
b) Narx 1900 so'm. Avval 20% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
Javob: a) 936; b) 2052
✔
40. Logarifmik tenglamani yeching. Javobni yozing.
a) log₅(x − 3) = 2
b) log₂(x − 3) = 2
Javob: a) 28; b) 7
✔
41. Ifodaning qiymatini toping. Javobni yozing.
a) cos 60° + cos 0°
b) sin 30° + cos 0°
Javob: a) 3/2; b) 3/2
✔
42. f(x₀) qiymatini toping. Javobni yozing.
a) f(x) = x² + x − 8, x₀ = -3
b) f(x) = 2x², x₀ = 4
Javob: a) -2; b) 32
✔
43. f'(x₀) ni toping. Javobni yozing.
a) f(x) = 3x³ + 5x² − x + 8, x₀ = 4
b) f(x) = 3x² + 9, x₀ = 4
Javob: a) 183; b) 24
✔
44. Ifodaning qiymatini toping. Javobni yozing.
a) log₅25 + log₅5
b) log₂8 + log₂4
Javob: a) 3; b) 5
✔
Matematika — milliy sertifikat mashq variantlari | 156

45. Ifodaning qiymatini toping. Javobni yozing.
a) tg 45° + cos 180°
b) sin 30° + cos 0°
Javob: a) 0; b) 3/2✔
Matematika — milliy sertifikat mashq variantlari | 157

21-variant
Y-1 • bitta to'g'ri javob
1. Ehtimollikni toping.
Qutida 4 ta oq va 5 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 1/9
B) 5/9
C) 4/9
D) 4/5
To'g'ri javob: C) 4/9✔
2. Guruhlashlar sonini toping.
C(7; 4)
A) 35
B) 36
C) 28
D) 840
To'g'ri javob: A) 35
✔
3. Vektorlarning skalyar ko'paytmasini toping.
(-3; -4), (4; 0)
a⃗ b ⃗
A) -11
B) 12
C) -12
D) 16
To'g'ri javob: C) -12
✔
4. Guruhlashlar sonini toping.
C(8; 4)
A) 1680
B) 32
C) 56
D) 70
To'g'ri javob: D) 70
✔
5. Aylana uzunligini toping (π orqali).
Radius R = 3
A) 3π
B) 12π
C) 9π
D) 6π
To'g'ri javob: D) 6π
✔
6. EKUK(20; 14) ni toping.
A) 160
B) 280
C) 2
D) 140
To'g'ri javob: D) 140
✔
Matematika — milliy sertifikat mashq variantlari | 158

7. x² + 7x + 6 = 0 tenglama ildizlarining ko'paytmasini toping.
A) -7
B) 7
C) 6
D) -6
To'g'ri javob: C) 6✔
8. f'(x₀) ni toping.
f(x) = 2x³ + x² + 3x − 8, x₀ = 1
A) 13
B) 11
C) 10
D) -2
To'g'ri javob: B) 11
✔
9. f'(x₀) ni toping.
f(x) = 2x³ + x² + 3x − 7, x₀ = -2
A) 25
B) 22
C) 23
D) -25
To'g'ri javob: C) 23
✔
10. Uchburchak yuzini toping.
Asosi 14, unga tushirilgan balandlik 20
A) 280
B) 140
C) 34
D) 141
To'g'ri javob: B) 140
✔
11. Vektorlarning skalyar ko'paytmasini toping.
(-4; 5), (-6; -5)
a⃗ b ⃗
A) 50
B) 1
C) -1
D) 0
To'g'ri javob: C) -1
✔
12. Ko'rsatkichli tenglamani yeching.
5^(x − 2) = 25
A) 2
B) 0
C) 5
D) 4
To'g'ri javob: D) 4
✔
Matematika — milliy sertifikat mashq variantlari | 159

13. f(x₀) qiymatini toping.
f(x) = x² + x − 7, x₀ = 0
A) 7
B) -6
C) -7
D) -5
To'g'ri javob: C) -7✔
14. f(x₀) qiymatini toping.
f(x) = −4x² + 5, x₀ = -4
A) 59
B) 21
C) -63
D) -59
To'g'ri javob: D) -59
✔
15. Tenglamaning katta ildizini toping.
x² + 2x = 0
A) 2
B) 1
C) 0
D) -2
To'g'ri javob: C) 0
✔
16. Ehtimollikni toping.
Qutida 2 ta oq va 4 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 1/3
B) 2/3
C) 1/2
D) 1/6
To'g'ri javob: A) 1/3
✔
17. Vektorlarning skalyar ko'paytmasini toping.
(-4; 1), (2; -4)
a⃗ b ⃗
A) -12
B) 12
C) 14
D) -11
To'g'ri javob: A) -12
✔
18. (xⁿ)' hosilasi nimaga teng?
A) xⁿ⁺¹ / (n + 1)
B) n · xⁿ⁻¹
C) xⁿ⁻¹
D) n · xⁿ
To'g'ri javob: B) n · xⁿ⁻¹
✔
Matematika — milliy sertifikat mashq variantlari | 160

19. Parabola uchining ordinatasini toping.
y = x² − 8x + 18
A) 2
B) 4
C) 18
D) 3
To'g'ri javob: A) 2✔
20. Arifmetik progressiyada a₁ = 3, d = -4. a20 ni toping.
A) -77
B) -81
C) -73
D) -69
To'g'ri javob: C) -73
✔
21. Uchburchakning ikki burchagi 71° va 42°. Uchinchi burchagini toping.
A) 77°
B) 113°
C) 67°
D) 247°
To'g'ri javob: C) 67°
✔
22. Uchburchak yuzini toping.
Asosi 8, unga tushirilgan balandlik 10
A) 80
B) 40
C) 41
D) 18
To'g'ri javob: B) 40
✔
23. Logarifmik tenglamani yeching.
log₂(x − 7) = 3
A) 1
B) 13
C) 8
D) 15
To'g'ri javob: D) 15
✔
24. Vektor uzunligini toping.
(12; -5)
a⃗
A) 7
B) 17
C) 14
D) 13
To'g'ri javob: D) 13
✔
Matematika — milliy sertifikat mashq variantlari | 161

25. Ko'rsatkichli tenglamani yeching.
5^(x − 4) = 625
A) 0
B) 8
C) 9
D) 4
To'g'ri javob: B) 8✔
26. A va B nuqtalar orasidagi masofani toping.
A(-1; -1), B(8; 11)
A) 17
B) 21
C) 3
D) 15
To'g'ri javob: D) 15
✔
27. Guruhlashlar soni C ᵏ qanday hisoblanadi?
ₙ
A) n! / (k!(n − k)!)
B) n · k
C) k!
D) n! / (n − k)!
To'g'ri javob: A) n! / (k!(n − k)!)
✔
28. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 1, q = 3, n = 5
A) 81
B) 122
C) 118
D) 121
To'g'ri javob: D) 121
✔
29. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = 0, d = 4, n = 9
A) 135
B) 144
C) 32
D) 148
To'g'ri javob: B) 144
✔
30. To'rtburchak ichki burchaklarining yig'indisi necha gradus?
A) 270°
B) 180°
C) 540°
D) 360°
To'g'ri javob: D) 360°
✔
31. (4^4)^2 ni hisoblang.
A) 65536
B) 65537
C) 512
D) 4096
To'g'ri javob: A) 65536
✔
Matematika — milliy sertifikat mashq variantlari | 162

32. f(x₀) qiymatini toping.
f(x) = 3x² + 6x + 9, x₀ = 3
A) 24
B) 54
C) 57
D) -54
To'g'ri javob: B) 54✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) 9/8 + 4/7 a) 5
2) 3/4 + 6/2 b) 3/2
3) 2/10 + 7/2 c) 95/56
4) 3/5 + 4/5 d) 7/5
e) 37/10
f) 15/4
A) 1–f, 2–d, 3–e, 4–c
B) 1–e, 2–f, 3–c, 4–d
C) 1–a, 2–f, 3–e, 4–d
D) 1–c, 2–f, 3–e, 4–d
To'g'ri javob: D) 1–c, 2–f, 3–e, 4–d
✔
34. Har bir ifodaga uning qiymatini moslang.
1) EKUK(34; 90) a) 3776
2) EKUK(53; 83) b) 4686
3) EKUB(64; 33) c) 1530
4) EKUB(77; 55) d) 1
e) 11
f) 4399
A) 1–b, 2–f, 3–d, 4–e
B) 1–c, 2–f, 3–d, 4–e
C) 1–f, 2–c, 3–e, 4–d
D) 1–c, 2–b, 3–d, 4–e
To'g'ri javob: B) 1–c, 2–f, 3–d, 4–e
✔
35. Har bir ifodaga uning qiymatini moslang.
1) EKUK(63; 49) a) 8010
2) EKUK(29; 71) b) 3290
3) EKUK(89; 90) c) 1
4) EKUK(70; 47) d) 2059
e) 682
f) 441
Matematika — milliy sertifikat mashq variantlari | 163

A) 1–f, 2–d, 3–a, 4–b
B) 1–f, 2–b, 3–a, 4–d
C) 1–a, 2–d, 3–f, 4–b
D) 1–f, 2–d, 3–b, 4–a
To'g'ri javob: A) 1–f, 2–d, 3–a, 4–b✔
O • ochiq topshiriq (qisqa javob)
36. Aniq integralni hisoblang. Javobni yozing.
a) ∫₀^1 (8x − 3) dx
b) ∫₀^1 (4x + 6) dx
Javob: a) 1; b) 8
✔
37. Vektorlarning skalyar ko'paytmasini toping. Javobni yozing.
a) (-3; -3), (5; -5)
a⃗ b ⃗
b) (3; 0), (3; -3)
a⃗ b ⃗
Javob: a) 0; b) 9
✔
38. Ko'rsatkichli tenglamani yeching. Javobni yozing.
a) 3^(x − 3) = 81
b) 5^(x − 2) = 625
Javob: a) 7; b) 6
✔
39. Logarifmik tenglamani yeching. Javobni yozing.
a) log₂(x − 1) = 2
b) log₃(x − 6) = 1
Javob: a) 5; b) 9
✔
40. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) a₁ = 8, d = 2, n = 6
b) a₁ = -8, d = 0, n = 5
Javob: a) 78; b) -40
✔
41. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping. Javobni yozing.
a) a₁ = -2, d = 2, n = 5
b) a₁ = 11, d = 6, n = 6
Javob: a) 10; b) 156
✔
42. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² + 10x + 30
b) y = x² − 8x + 7
Javob: a) 5; b) -9
✔
43. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x + 8| = 8
b) |x − 0| = 4
Javob: a) -16; b) 0
✔
44. Aniq integralni hisoblang. Javobni yozing.
a) ∫₀^3 (2x + 2) dx
b) ∫₀^1 (6x + 1) dx
Javob: a) 15; b) 4
✔
Matematika — milliy sertifikat mashq variantlari | 164

45. Tenglamani yeching. Javobni yozing.
a) 4(x − 1) = x − 31
b) 3(x + 1) = x + 19
Javob: a) -9; b) 8✔
Matematika — milliy sertifikat mashq variantlari | 165

22-variant
Y-1 • bitta to'g'ri javob
1. f(x₀) qiymatini toping.
f(x) = −4x² − 6x + 7, x₀ = 3
A) -11
B) -51
C) 47
D) -47
To'g'ri javob: D) -47✔
2. C(9;2) — 9 ta elementdan 2 tadan guruhlashlar sonini toping.
A) 36
B) 45
C) 18
D) 72
To'g'ri javob: A) 36
✔
3. Uchburchakning ikki burchagi 49° va 30°. Uchinchi burchagini toping.
A) 281°
B) 111°
C) 101°
D) 79°
To'g'ri javob: C) 101°
✔
4. Arifmetik progressiyada a₁ = 5, d = 4. Dastlabki 5 ta had yig'indisini toping.
A) 68
B) 67
C) 70
D) 65
To'g'ri javob: D) 65
✔
5. Tenglamani yeching.
3(x − 16) = 2x − 52
A) -6
B) 4
C) -4
D) -3
To'g'ri javob: C) -4
✔
6. A va B nuqtalar orasidagi masofani toping.
A(5; 2), B(8; -2)
A) 6
B) 7
C) 1
D) 5
To'g'ri javob: D) 5
✔
Matematika — milliy sertifikat mashq variantlari | 166

7. Ifodaning qiymatini toping.
sin 270° + sin 90°
A) 0
B) −2
C) 1
D) −1
To'g'ri javob: A) 0✔
8. Silindr hajmini toping (π orqali).
Asos radiusi 2, balandligi 6
A) 24π
B) 12π
C) 48π
D) 25π
To'g'ri javob: A) 24π
✔
9. Chiziqli funksiya y = kx + b grafigi qanday chiziq?
A) Giperbola
B) Aylana
C) To'g'ri chiziq
D) Parabola
To'g'ri javob: C) To'g'ri chiziq
✔
10. Masalani yeching.
Narx 2400 so'm. Avval 10% ga oshirildi, so'ng 10% ga kamaytirildi. Oxirgi narx necha so'm?
A) 2377
B) 2476
C) 2376
D) 2400
To'g'ri javob: C) 2376
✔
11. Ko'rsatkichli tenglamani yeching.
5^(x − 3) = 25
A) 5
B) 6
C) -1
D) 2
To'g'ri javob: A) 5
✔
12. Tenglama ildizlari yig'indisini toping.
|x + 7| = 7
A) 14
B) 7
C) -14
D) 0
To'g'ri javob: C) -14
✔
Matematika — milliy sertifikat mashq variantlari | 167

$13. A va B nuqtalar orasidagi masofani toping. A(-3; 4), B(2; 16) A) 17 B) 13 C) 15 D) 7 To'g'ri javob: B) 13✔ 14. Aniq integralni hisoblang. ∫₀^3 (2x + 1) dx A) 12 B) 24 C) 7 D) 15 To'g'ri javob: A) 12 ✔ 15. To'g'ri burchakli parallelepiped hajmini toping. O'lchamlari 2, 9, 8 A) 144 B) 212 C) 146 D) 19 To'g'ri javob: A) 144 ✔ 16. Tenglamalar sistemasini yeching va x + y ni toping. { 2x + 5y = -14; 4x − 4y = 56 } A) -48 B) 2 C) 4 D) 14 To'g'ri javob: B) 2 ✔ 17. Ko'rsatkichli tenglamani yeching. 5^(x − 1) = 125 A) 5 B) 4 C) 2 D) 3 To'g'ri javob: B) 4 ✔ 18. Tengsizlikning butun yechimlari sonini toping. x² − 36 < 0 A) 11 B) 10 C) 13 D) 12 To'g'ri javob: A) 11 ✔ Matematika — milliy sertifikat mashq variantlari | 168$

19. Aniq integralni hisoblang.
∫₀^2 (6x − 2) dx
A) 9
B) 10
C) 8
D) 16
To'g'ri javob: C) 8✔
20. Hisoblang.
6/3 + 2/3
A) 4/3
B) 25/9
C) 8/3
D) 11/3
To'g'ri javob: C) 8/3
✔
21. Ifodaning qiymatini toping.
log₂16 + log₂8
A) 8
B) 12
C) 128
D) 7
To'g'ri javob: D) 7
✔
22. EKUBni toping.
EKUB(18; 33)
A) 198
B) 6
C) 3
D) 15
To'g'ri javob: C) 3
✔
23. Guruhlashlar sonini toping.
C(10; 3)
A) 45
B) 30
C) 720
D) 120
To'g'ri javob: D) 120
✔
24. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -1, d = 0, n = 14
A) -14
B) -28
C) -13
D) -1
To'g'ri javob: A) -14
✔
Matematika — milliy sertifikat mashq variantlari | 169

25. y = k/x funksiya grafigi qanday chiziq?
A) Giperbola
B) Aylana
C) To'g'ri chiziq
D) Parabola
To'g'ri javob: A) Giperbola✔
26. Viyet teoremasiga ko'ra x² + px + q = 0 tenglama ildizlari yig'indisi nimaga teng?
A) q
B) −q
C) −p
D) p
To'g'ri javob: C) −p
✔
27. Hisoblang.
9/5 + 2/11
A) 18/55
B) 2
C) 11/16
D) 109/55
To'g'ri javob: D) 109/55
✔
28. Tenglamalar sistemasini yeching va x + y ni toping.
{ x + 4y = 34; 4x − 4y = -24 }
A) 16
B) 12
C) 10
D) -6
To'g'ri javob: C) 10
✔
29. Logarifmik tenglamani yeching.
log₁₀(x − 7) = 3
A) 993
B) 1000
C) 37
D) 1007
To'g'ri javob: D) 1007
✔
30. Ehtimollikni toping.
Qutida 9 ta oq va 8 ta qora shar bor. Tasodifan olingan shar oq bo'lishi ehtimoli
A) 8/17
B) 9/8
C) 1/17
D) 9/17
To'g'ri javob: D) 9/17
✔
Matematika — milliy sertifikat mashq variantlari | 170

31. Hisoblang.
√36 + √144
A) 18
B) 72
C) 17
D) 13
To'g'ri javob: A) 18✔
32. Tenglama ildizlari yig'indisini toping.
x² − x = 0
A) 1
B) 2
C) -1
D) 0
To'g'ri javob: A) 1
✔
Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) C(7; 4) a) 21
2) C(7; 2) b) 84
3) C(9; 3) c) 60
4) A(8; 4) d) 1680
e) 42
f) 35
A) 1–f, 2–d, 3–b, 4–a
B) 1–b, 2–a, 3–f, 4–d
C) 1–f, 2–a, 3–b, 4–d
D) 1–f, 2–c, 3–b, 4–d
To'g'ri javob: C) 1–f, 2–a, 3–b, 4–d
✔
34. Har bir ifodaga uning qiymatini moslang.
1) Radius R = 12 a) 18π
2) Radius R = 15 b) 16π
3) Radius R = 9 c) 30π
4) Radius R = 6 d) 12π
e) 169π
f) 144π
A) 1–a, 2–c, 3–f, 4–d
B) 1–f, 2–c, 3–a, 4–b
C) 1–f, 2–c, 3–a, 4–d
D) 1–c, 2–a, 3–d, 4–f
To'g'ri javob: C) 1–f, 2–c, 3–a, 4–d
✔
35. Har bir ifodaga uning qiymatini moslang.
1) EKUB(38; 12) a) 2
2) EKUB(63; 14) b) 459
3) EKUK(51; 27) c) 1
Matematika — milliy sertifikat mashq variantlari | 171

$4) EKUK(83; 20) d) 1660 e) 336 f) 7 A) 1–b, 2–f, 3–a, 4–d B) 1–a, 2–f, 3–b, 4–c C) 1–a, 2–f, 3–b, 4–d D) 1–d, 2–b, 3–a, 4–f To'g'ri javob: C) 1–a, 2–f, 3–b, 4–d✔ O • ochiq topshiriq (qisqa javob) 36. Guruhlashlar sonini toping. Javobni yozing. a) C(5; 3) b) C(10; 2) Javob: a) 10; b) 45 ✔ 37. f(x₀) qiymatini toping. Javobni yozing. a) f(x) = 2x² − 5x − 1, x₀ = -1 b) f(x) = 4x² + x + 8, x₀ = 2 Javob: a) 6; b) 26 ✔ 38. Aylana uzunligini toping (π orqali). Javobni yozing. a) Radius R = 5 b) Radius R = 12 Javob: a) 10π; b) 24π ✔ 39. Tengsizlikning butun yechimlari sonini toping. Javobni yozing. a) x² + 8x + 12 < 0 b) x² − 6x + 5 < 0 Javob: a) 3; b) 3 ✔ 40. Tenglamalar sistemasini yeching va x + y ni toping. Javobni yozing. a) { x + 2y = -10; 3x − y = -2 } b) { x + 5y = -14; 4x − 3y = 13 } Javob: a) -6; b) -2 ✔ 41. Tenglama ildizlari yig'indisini toping. Javobni yozing. a) x² + 3x − 28 = 0 b) x² + 6x − 16 = 0 Javob: a) -3; b) -6 ✔ 42. Ko'rsatkichli tenglamani yeching. Javobni yozing. a) 5^(x − 2) = 125 b) 2^(x − 4) = 8 Javob: a) 5; b) 7 ✔ 43. EKUBni toping. Javobni yozing. a) EKUB(44; 60) b) EKUB(19; 42) Javob: a) 4; b) 1 ✔ Matematika — milliy sertifikat mashq variantlari | 172$

44. Ifodaning qiymatini toping. Javobni yozing.
a) 3^3 · 3^2 : 3^2
b) 7^5 · 7^4 : 7^2
Javob: a) 27; b) 823543✔
45. Hisoblang. Javobni yozing.
a) 8/5 + 9/10
b) 4/3 + 5/5
Javob: a) 5/2; b) 7/3
✔
Matematika — milliy sertifikat mashq variantlari | 173

23-variant
Y-1 • bitta to'g'ri javob
1. Aniq integralni hisoblang.
∫₀^2 (8x − 1) dx
A) 28
B) 14
C) 16
D) 15
To'g'ri javob: B) 14✔
2. Hisoblang.
√144 + √49
A) 18
B) 84
C) 13
D) 19
To'g'ri javob: D) 19
✔
3. Aniq integralni hisoblang.
∫₀^3 (8x + 3) dx
A) 45
B) 27
C) 48
D) 90
To'g'ri javob: A) 45
✔
4. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 4, q = -2, n = 3
A) 12
B) 16
C) 14
D) 13
To'g'ri javob: A) 12
✔
5. Tengsizlikning butun yechimlari sonini toping.
x² − 6x − 16 < 0
A) 9
B) 8
C) 11
D) 10
To'g'ri javob: A) 9
✔
6. Arifmetik progressiyada a₁ = -2, d = 9. a12 ni toping.
A) 97
B) 115
C) 88
D) 106
To'g'ri javob: A) 97
✔
Matematika — milliy sertifikat mashq variantlari | 174

7. Hisoblang.
√169 + √100
A) 16
B) 130
C) 23
D) 22
To'g'ri javob: C) 23✔
8. y = ax² parabolaning shoxlari a > 0 bo'lganda qayoqqa yo'nalgan?
A) Chapga
B) O'ngga
C) Yuqoriga
D) Pastga
To'g'ri javob: C) Yuqoriga
✔
9. Guruhlashlar sonini toping.
C(10; 4)
A) 120
B) 5040
C) 40
D) 210
To'g'ri javob: D) 210
✔
10. Tenglamaning katta ildizini toping.
x² − 5x + 4 = 0
A) 4
B) -4
C) 5
D) 1
To'g'ri javob: A) 4
✔
11. f(x) = 3x² − 5x + 3 funksiyaning x = 4 nuqtadagi hosilasini toping.
A) 21
B) 31
C) 19
D) 1
To'g'ri javob: C) 19
✔
12. Parabola uchining ordinatasini toping.
y = x² − 2x + 10
A) 10
B) 11
C) 9
D) 1
To'g'ri javob: C) 9
✔
Matematika — milliy sertifikat mashq variantlari | 175

13. A va B nuqtalar orasidagi masofani toping.
A(-5; -4), B(-11; 4)
A) 12
B) 10
C) 2
D) 14
To'g'ri javob: B) 10✔
14. Geometrik progressiyada b₁ = 4, q = -2. b4 ni toping.
A) 16
B) -32
C) 32
D) 64
To'g'ri javob: B) -32
✔
15. Hisoblang.
2/8 + 8/11
A) 87/88
B) 2/11
C) 10/19
D) 43/44
To'g'ri javob: D) 43/44
✔
16. Uchburchak yuzini toping.
Asosi 20, unga tushirilgan balandlik 16
A) 160
B) 161
C) 320
D) 36
To'g'ri javob: A) 160
✔
17. Asosiy trigonometrik ayniyat qaysi?
A) tgα · sinα = 1
B) sinα + cosα = 1
C) sin²α − cos²α = 1
D) sin²α + cos²α = 1
To'g'ri javob: D) sin²α + cos²α = 1
✔
18. Arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.
a₁ = -10, d = -3, n = 5
A) -22
B) -83
C) -80
D) -85
To'g'ri javob: C) -80
✔
Matematika — milliy sertifikat mashq variantlari | 176

19. Vektorlarning skalyar ko'paytmasini toping.
(6; 0), (-1; -1)a⃗ b ⃗
A) 6
B) -6
C) -5
D) -4
To'g'ri javob: B) -6
✔
20. Hisoblang: 4/3 + 5/2
A) 10/3
B) 9/5
C) 7/6
D) 23/6
To'g'ri javob: D) 23/6
✔
21. To'g'ri burchakli uchburchakning katetlari 8 va 15. Gipotenuzasini toping.
A) 18
B) 17
C) 15
D) 23
To'g'ri javob: B) 17
✔
22. Aylana uzunligini toping (π orqali).
Radius R = 6
A) 6π
B) 36π
C) 24π
D) 12π
To'g'ri javob: D) 12π
✔
23. Ifodani soddalashtiring: 4^3 · 4^4
A) 4^7
B) 4^1
C) 16^7
D) 4^12
To'g'ri javob: A) 4^7
✔
24. Geometrik progressiyaning dastlabki n ta hadi yig'indisini toping.
b₁ = 5, q = -2, n = 5
A) 57
B) 55
C) 60
D) 80
To'g'ri javob: B) 55
✔
25. A va B nuqtalar orasidagi masofani toping.
A(-1; 3), B(2; 7)
A) 7
B) 6
C) 5
D) 1
To'g'ri javob: C) 5
✔
Matematika — milliy sertifikat mashq variantlari | 177

26. Geometrik progressiyada b₁ = 5, q = 3. b5 ni toping.
A) -405
B) 135
C) 1215
D) 405
To'g'ri javob: D) 405✔
27. f'(x₀) ni toping.
f(x) = 5x² + 4x − 5, x₀ = -2
A) 7
B) -17
C) -16
D) -6
To'g'ri javob: C) -16
✔
28. x² + 3x + 2 = 0 tenglama ildizlarining yig'indisini toping.
A) -1
B) 2
C) -3
D) 3
To'g'ri javob: C) -3
✔
29. Hisoblang.
5/7 + 7/11
A) 2/3
B) 5/11
C) 15/11
D) 104/77
To'g'ri javob: D) 104/77
✔
30. Ifodaning qiymatini toping.
tg 0° + tg 45°
A) 2
B) 3
C) 1
D) −1
To'g'ri javob: C) 1
✔
31. To'g'ri burchakli uchburchakning gipotenuzasi 10, bir kateti 6. Ikkinchi katetini toping.
A) 4
B) 6
C) 8
D) 9
To'g'ri javob: C) 8
✔
32. Uchburchak yuzini toping.
Asosi 16, unga tushirilgan balandlik 16
A) 128
B) 256
C) 32
D) 129
To'g'ri javob: A) 128
✔
Matematika — milliy sertifikat mashq variantlari | 178

Y-2 • moslashtirish
33. Har bir ifodaga uning qiymatini moslang.
1) Radius R = 4 a) 4π
2) Radius R = 3 b) 9π
3) Radius R = 11 c) 14π
4) Radius R = 2 d) 8π
e) 100π
f) 121π
A) 1–d, 2–e, 3–f, 4–a
B) 1–b, 2–a, 3–f, 4–d
C) 1–d, 2–b, 3–f, 4–a
D) 1–d, 2–c, 3–f, 4–a
To'g'ri javob: C) 1–d, 2–b, 3–f, 4–a✔
34. Har bir ifodaga uning qiymatini moslang.
1) 2^4 · 2^6 : 2^4 a) 2401
2) 2^6 · 2^2 : 2^5 b) 64
3) 5^4 · 5^6 : 5^3 c) 1
4) 7^2 · 7^5 : 7^1 d) 78125
e) 117649
f) 8
A) 1–e, 2–f, 3–d, 4–b
B) 1–b, 2–f, 3–d, 4–e
C) 1–a, 2–f, 3–d, 4–e
D) 1–b, 2–c, 3–d, 4–e
To'g'ri javob: B) 1–b, 2–f, 3–d, 4–e
✔
35. Har bir ifodaga uning qiymatini moslang.
1) 2/2 + 5/12 a) 16/21
2) 4/6 + 8/12 b) 7/6
3) 6/9 + 4/8 c) 17/12
4) 8/11 + 9/2 d) 4/3
e) 115/22
f) 5/18
A) 1–c, 2–d, 3–a, 4–e
B) 1–c, 2–b, 3–d, 4–e
C) 1–c, 2–d, 3–b, 4–e
D) 1–c, 2–e, 3–b, 4–d
To'g'ri javob: C) 1–c, 2–d, 3–b, 4–e
✔
O • ochiq topshiriq (qisqa javob)
36. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) |x − 4| = 4
b) |x − 7| = 7
Javob: a) 8; b) 14
✔
Matematika — milliy sertifikat mashq variantlari | 179

37. Silindr hajmini toping (π orqali). Javobni yozing.
a) Asos radiusi 2, balandligi 10
b) Asos radiusi 6, balandligi 7
Javob: a) 40π; b) 252π✔
38. f(x₀) qiymatini toping. Javobni yozing.
a) f(x) = −4x² + 5x + 9, x₀ = 1
b) f(x) = −3x² − 4x + 1, x₀ = -2
Javob: a) 10; b) -3
✔
39. Hisoblang. Javobni yozing.
a) 5/2 + 2/9
b) 8/2 + 7/8
Javob: a) 49/18; b) 39/8
✔
40. Parabola uchining ordinatasini toping. Javobni yozing.
a) y = x² + 4x − 4
b) y = x² + 8x + 14
Javob: a) -8; b) -2
✔
41. A va B nuqtalar orasidagi masofani toping. Javobni yozing.
a) A(3; -5), B(9; 3)
b) A(1; 3), B(7; -5)
Javob: a) 10; b) 10
✔
42. Ifodaning qiymatini toping. Javobni yozing.
a) cos 90° + cos 0°
b) cos 0° + sin 0°
Javob: a) 1; b) 1
✔
43. Tenglama ildizlari yig'indisini toping. Javobni yozing.
a) x² + 13x + 36 = 0
b) x² − 10x + 21 = 0
Javob: a) -13; b) 10
✔
44. Ifodaning qiymatini toping. Javobni yozing.
a) 2^4 · 2^2 : 2^3
b) 5^4 · 5^6 : 5^3
Javob: a) 8; b) 78125
✔
45. Masalani yeching. Javobni yozing.
a) Mahsulot narxi 600 so'm edi. Narx 50% ga oshirildi. Yangi narx necha so'm?
b) Mahsulot narxi 2100 so'm edi. Narx 15% ga oshirildi. Yangi narx necha so'm?
Javob: a) 900; b) 2415
✔
Matematika — milliy sertifikat mashq variantlari | 180

Javoblar kaliti
Har bir variant bo'yicha: topshiriq raqami va to'g'ri javob.
1-variant
1- B 2- A 3- C 4- D 5- B 6- C 7- B 8- D 9- D 10- C
11- D 12- C 13- B 14- A 15- B 16- A 17- A 18- D 19- C 20- C
21- C 22- D 23- D 24- A 25- B 26- D 27- B 28- C 29- A 30- B
31- A 32- B 33- D 34- D 35- D
36. a) 6; b) 7
37. a) 99/2; b) 105
38. a) 0; b) -30
39. a) 30; b) 120
40. a) -5; b) 8
41. a) 4; b) 65
42. a) 1; b) 1
43. a) 3; b) 7
44. a) -11; b) 0
45. a) 0; b) 1
2-variant
1- D 2- D 3- A 4- A 5- D 6- A 7- D 8- B 9- D 10- C
11- D 12- C 13- A 14- B 15- A 16- A 17- A 18- D 19- C 20- D
21- D 22- D 23- A 24- B 25- A 26- C 27- D 28- B 29- C 30- C
31- C 32- C 33- C 34- A 35- A
36. a) -10; b) -9
37. a) 93; b) 60
38. a) -38; b) 23
39. a) 2; b) 2
40. a) -18; b) 6
41. a) 9; b) 12
42. a) -4; b) 4
43. a) 10; b) 15
44. a) -3; b) -6
45. a) 7; b) 6
3-variant
1- D 2- D 3- B 4- A 5- B 6- A 7- C 8- B 9- C 10- A
11- B 12- B 13- C 14- A 15- A 16- A 17- C 18- B 19- D 20- C
21- D 22- A 23- C 24- B 25- B 26- D 27- D 28- A 29- A 30- D
31- C 32- C 33- B 34- D 35- C
36. a) 6/13; b) 5/8
37. a) 13; b) 13
38. a) 4; b) 1
39. a) 33; b) 35
40. a) 90; b) 1008
41. a) -63; b) 93
42. a) -9; b) 3
43. a) -12; b) 37
44. a) 77; b) 25
45. a) 1/3; b) 6/13
Matematika — milliy sertifikat mashq variantlari | 181

4-variant
1- C 2- C 3- C 4- D 5- B 6- B 7- B 8- D 9- D 10- D
11- B 12- D 13- A 14- A 15- B 16- A 17- A 18- A 19- C 20- A
21- D 22- A 23- C 24- C 25- B 26- C 27- C 28- C 29- A 30- B
31- A 32- A 33- C 34- C 35- B
36. a) 12; b) -12
37. a) -4; b) 7
38. a) 25; b) 18
39. a) 2; b) 1
40. a) 2250; b) 4320
41. a) 7/2; b) 67/28
42. a) 2415; b) 396
43. a) 3380; b) 1344
44. a) 3255; b) 1200
45. a) 8; b) -7
5-variant
1- A 2- A 3- C 4- C 5- C 6- A 7- B 8- D 9- B 10- B
11- C 12- B 13- A 14- C 15- B 16- C 17- A 18- C 19- B 20- A
21- B 22- A 23- A 24- B 25- C 26- B 27- B 28- D 29- C 30- A
31- C 32- C 33- A 34- B 35- D
36. a) 5; b) 6
37. a) 242; b) -63
38. a) 125; b) 8
39. a) -6; b) 11
40. a) 6; b) -10
41. a) 160; b) 1820
42. a) -12; b) -16
43. a) 198; b) 408
44. a) 8; b) 18
45. a) -7; b) 8
6-variant
1- B 2- C 3- B 4- A 5- C 6- D 7- B 8- D 9- A 10- A
11- C 12- C 13- B 14- A 15- A 16- D 17- B 18- A 19- A 20- A
21- C 22- D 23- B 24- A 25- C 26- B 27- C 28- C 29- B 30- D
31- B 32- A 33- B 34- A 35- C
36. a) 112; b) 315
37. a) 9; b) 1
38. a) 84; b) 85
39. a) 0; b) -10
40. a) 5; b) 7
41. a) 3; b) 4
42. a) 200; b) 108
43. a) 36; b) 50
44. a) -153; b) 220
45. a) 4; b) 2
7-variant
1- D 2- C 3- C 4- D 5- B 6- D 7- B 8- D 9- B 10- B
11- B 12- A 13- D 14- A 15- A 16- C 17- A 18- D 19- B 20- D
Matematika — milliy sertifikat mashq variantlari | 182

21- B 22- A 23- A 24- A 25- C 26- C 27- A 28- C 29- C 30- D
31- B 32- B 33- A 34- A 35- B
36. a) 24π; b) 30π
37. a) -5; b) -6
38. a) 48; b) 126
39. a) 6006; b) 46
40. a) 22π; b) 28π
41. a) 28; b) 56
42. a) -12; b) 1
43. a) -4; b) 2
44. a) −1/2; b) −1/2
45. a) 15; b) 315
8-variant
1- B 2- C 3- D 4- B 5- B 6- C 7- C 8- C 9- D 10- C
11- A 12- B 13- C 14- B 15- D 16- A 17- C 18- B 19- A 20- B
21- B 22- A 23- D 24- A 25- B 26- B 27- C 28- A 29- C 30- D
31- A 32- A 33- A 34- C 35- C
36. a) 36π; b) 144π
37. a) 2; b) 5
38. a) 12; b) 28
39. a) 8; b) 7
40. a) 5; b) 6
41. a) 17; b) 18
42. a) -105; b) 45
43. a) -10; b) -2
44. a) 105; b) 3
45. a) -1; b) 60
9-variant
1- B 2- C 3- C 4- B 5- A 6- B 7- A 8- C 9- A 10- D
11- A 12- A 13- A 14- A 15- D 16- D 17- C 18- B 19- D 20- B
21- D 22- B 23- A 24- B 25- D 26- D 27- A 28- C 29- B 30- D
31- C 32- C 33- C 34- B 35- A
36. a) 6; b) 7
37. a) 8; b) -2
38. a) 0; b) −1
39. a) 1; b) 1
40. a) 13; b) 9
41. a) 7/10; b) 1/2
42. a) 29/20; b) 11/5
43. a) 27; b) 17
44. a) 56; b) 1680
45. a) 140; b) 144
10-variant
1- A 2- A 3- A 4- D 5- A 6- B 7- A 8- D 9- D 10- A
11- C 12- C 13- D 14- D 15- C 16- C 17- D 18- A 19- C 20- B
21- C 22- C 23- C 24- D 25- C 26- B 27- D 28- A 29- D 30- A
31- B 32- A 33- D 34- C 35- A
36. a) 0; b) 0
Matematika — milliy sertifikat mashq variantlari | 183

37. a) 13; b) 25
38. a) 10; b) 13
39. a) 1680; b) 56
40. a) 4; b) 2
41. a) 15; b) 28
42. a) 4/7; b) 3/7
43. a) 2; b) 2
44. a) -8; b) -14
45. a) 6; b) 5
11-variant
1- A 2- A 3- D 4- A 5- D 6- B 7- C 8- D 9- D 10- C
11- C 12- B 13- B 14- C 15- D 16- D 17- A 18- B 19- C 20- D
21- D 22- A 23- D 24- D 25- D 26- C 27- C 28- C 29- C 30- A
31- C 32- A 33- B 34- C 35- A
36. a) 81/2; b) 112
37. a) 6; b) 4
38. a) 9; b) -14
39. a) 17; b) 7
40. a) -6; b) 12
41. a) 7; b) 7
42. a) 8; b) 243
43. a) -2; b) -2
44. a) -4; b) 9
45. a) 9; b) 58
12-variant
1- D 2- D 3- D 4- B 5- A 6- A 7- B 8- D 9- C 10- C
11- D 12- D 13- C 14- C 15- D 16- C 17- C 18- D 19- B 20- D
21- A 22- C 23- C 24- D 25- C 26- C 27- B 28- A 29- B 30- C
31- C 32- D 33- A 34- C 35- D
36. a) 0; b) 3
37. a) 41; b) -5
38. a) 5; b) 25
39. a) 729; b) 5
40. a) 1; b) 2
41. a) -1; b) 9
42. a) -493; b) -608
43. a) -9; b) -3
44. a) 225/2; b) 150
45. a) 11; b) 12
13-variant
1- A 2- A 3- B 4- A 5- C 6- A 7- A 8- D 9- C 10- B
11- B 12- A 13- A 14- A 15- A 16- B 17- D 18- C 19- C 20- B
21- C 22- D 23- D 24- B 25- A 26- A 27- D 28- D 29- B 30- D
31- D 32- A 33- A 34- C 35- C
36. a) 35; b) -105
37. a) 8π; b) 225π
38. a) 20; b) 8
39. a) 7/12; b) 1/5
40. a) 1/4; b) 1/4
Matematika — milliy sertifikat mashq variantlari | 184

41. a) 3125; b) 243
42. a) 3; b) 2
43. a) 17; b) 25
44. a) 82; b) 13
45. a) -9; b) 9
14-variant
1- A 2- B 3- C 4- C 5- B 6- B 7- C 8- C 9- C 10- D
11- B 12- D 13- D 14- D 15- B 16- C 17- B 18- D 19- B 20- B
21- C 22- B 23- A 24- A 25- C 26- D 27- B 28- D 29- B 30- C
31- B 32- D 33- A 34- B 35- B
36. a) 729; b) 1953125
37. a) 4; b) 9
38. a) 54; b) 5
39. a) 11/4; b) 7/9
40. a) 13; b) -15
41. a) 4; b) -1
42. a) 88; b) 38
43. a) 363; b) -84
44. a) 31; b) 26
45. a) 0; b) −1
15-variant
1- C 2- B 3- D 4- A 5- B 6- B 7- B 8- B 9- B 10- C
11- B 12- A 13- A 14- B 15- C 16- A 17- D 18- B 19- C 20- A
21- D 22- C 23- A 24- C 25- D 26- D 27- A 28- C 29- C 30- D
31- A 32- C 33- C 34- B 35- A
36. a) 12; b) -7
37. a) 12; b) 11
38. a) 1; b) -2
39. a) 120; b) 72
40. a) 8; b) 1
41. a) 2; b) -2
42. a) 13; b) 58
43. a) 17; b) 9
44. a) -4; b) 3
45. a) 125; b) 297/2
16-variant
1- C 2- C 3- C 4- A 5- D 6- C 7- D 8- D 9- A 10- D
11- B 12- A 13- D 14- A 15- B 16- B 17- C 18- B 19- B 20- D
21- C 22- A 23- D 24- C 25- A 26- A 27- A 28- A 29- D 30- D
31- B 32- A 33- C 34- B 35- D
36. a) 18; b) 4
37. a) 192; b) 216
38. a) 7; b) 1009
39. a) -5; b) 5
40. a) 15; b) -6
41. a) 2/5; b) 4/7
42. a) 15; b) 15
43. a) 15; b) 15
44. a) 26π; b) 4π
Matematika — milliy sertifikat mashq variantlari | 185

45. a) 15; b) 15
17-variant
1- C 2- D 3- B 4- A 5- D 6- A 7- C 8- A 9- A 10- B
11- C 12- A 13- A 14- A 15- B 16- D 17- A 18- C 19- A 20- C
21- B 22- C 23- B 24- B 25- C 26- C 27- A 28- C 29- B 30- B
31- D 32- D 33- D 34- B 35- C
36. a) 72; b) 144
37. a) 1; b) −1/2
38. a) 14; b) 10
39. a) 5/12; b) 9/11
40. a) -8; b) -2
41. a) 15/44; b) 1
42. a) 31; b) 22
43. a) 0; b) 1/2
44. a) 96; b) 133/2
45. a) 3/2; b) 0
18-variant
1- A 2- B 3- A 4- D 5- A 6- D 7- D 8- C 9- B 10- C
11- A 12- C 13- D 14- D 15- A 16- D 17- C 18- B 19- D 20- C
21- A 22- A 23- C 24- D 25- B 26- C 27- A 28- B 29- D 30- A
31- A 32- D 33- A 34- B 35- B
36. a) 24; b) 18
37. a) 7; b) 133/2
38. a) 3198; b) 1886
39. a) 4; b) 7
40. a) 225π; b) 100π
41. a) 5; b) -8
42. a) 2; b) 1
43. a) 3; b) 4
44. a) 15; b) 15
45. a) 630; b) 32
19-variant
1- D 2- A 3- C 4- C 5- B 6- C 7- C 8- D 9- B 10- A
11- C 12- D 13- B 14- C 15- B 16- D 17- D 18- C 19- A 20- C
21- D 22- B 23- D 24- B 25- C 26- A 27- B 28- B 29- B 30- B
31- D 32- C 33- A 34- A 35- C
36. a) 171; b) 180
37. a) -1; b) -5
38. a) 26; b) 13
39. a) -162; b) 180
40. a) 0; b) 20
41. a) 70; b) 135
42. a) 3; b) 49
43. a) 12; b) 6
44. a) -33; b) -21
45. a) 1/2; b) 3/7
Matematika — milliy sertifikat mashq variantlari | 186

20-variant
1- D 2- C 3- D 4- B 5- B 6- B 7- D 8- D 9- A 10- B
11- C 12- B 13- A 14- C 15- A 16- B 17- C 18- B 19- C 20- B
21- A 22- D 23- B 24- B 25- A 26- B 27- C 28- D 29- C 30- D
31- B 32- C 33- D 34- C 35- A
36. a) −1; b) 2
37. a) 6; b) 7
38. a) 6; b) 7
39. a) 936; b) 2052
40. a) 28; b) 7
41. a) 3/2; b) 3/2
42. a) -2; b) 32
43. a) 183; b) 24
44. a) 3; b) 5
45. a) 0; b) 3/2
21-variant
1- C 2- A 3- C 4- D 5- D 6- D 7- C 8- B 9- C 10- B
11- C 12- D 13- C 14- D 15- C 16- A 17- A 18- B 19- A 20- C
21- C 22- B 23- D 24- D 25- B 26- D 27- A 28- D 29- B 30- D
31- A 32- B 33- D 34- B 35- A
36. a) 1; b) 8
37. a) 0; b) 9
38. a) 7; b) 6
39. a) 5; b) 9
40. a) 78; b) -40
41. a) 10; b) 156
42. a) 5; b) -9
43. a) -16; b) 0
44. a) 15; b) 4
45. a) -9; b) 8
22-variant
1- D 2- A 3- C 4- D 5- C 6- D 7- A 8- A 9- C 10- C
11- A 12- C 13- B 14- A 15- A 16- B 17- B 18- A 19- C 20- C
21- D 22- C 23- D 24- A 25- A 26- C 27- D 28- C 29- D 30- D
31- A 32- A 33- C 34- C 35- C
36. a) 10; b) 45
37. a) 6; b) 26
38. a) 10π; b) 24π
39. a) 3; b) 3
40. a) -6; b) -2
41. a) -3; b) -6
42. a) 5; b) 7
43. a) 4; b) 1
44. a) 27; b) 823543
45. a) 5/2; b) 7/3
23-variant
1- B 2- D 3- A 4- A 5- A 6- A 7- C 8- C 9- D 10- A
11- C 12- C 13- B 14- B 15- D 16- A 17- D 18- C 19- B 20- D
Matematika — milliy sertifikat mashq variantlari | 187

21- B 22- D 23- A 24- B 25- C 26- D 27- C 28- C 29- D 30- C
31- C 32- A 33- C 34- B 35- C
36. a) 8; b) 14
37. a) 40π; b) 252π
38. a) 10; b) -3
39. a) 49/18; b) 39/8
40. a) -8; b) -2
41. a) 10; b) 10
42. a) 1; b) 1
43. a) -13; b) 10
44. a) 8; b) 78125
45. a) 900; b) 2415
Matematika — milliy sertifikat mashq variantlari | 188

MATEMATIKA

Milliy sertifikat imtihoniga tayyorgarlik: variantlar to'plami (2025–2026)

23 ta variant • 1035 ta topshiriq • javoblari bilan

Mashq to'plami • 2025–2026 o'quv yili

Imtihon tuzilishi va yo'riqnoma

• Imtihon Bilimni baholash agentligi tomonidan an'anaviy (qog'oz) shaklda o'tkaziladi: 45 ta topshiriq, 150 daqiqa. Har bir variant xuddi shu tuzilishda: 32 ta Y-1, 3 ta Y-2 va 10 ta ochiq (a/b) topshiriq.

• Ballar: Y-1 — 1,3 yoki 2,2; Y-2 — 2,2; ochiq topshiriq — a) 1,5 + b) 1,7 = 3,2 ball. Yakuniy natija Rash modeli bo'yicha hisoblanadi; sertifikat uchun kamida 46 ball kerak (C), 70 dan yuqori — A+.

• Noto'g'ri javob uchun ball ayirilmaydi — barcha topshiriqlarga javob bering. Ochiq topshiriqlarda kasr javobni qisqarmas kasr ko'rinishida, π li javoblarni π orqali yozing.

• Har bir topshiriq ostida to'g'ri javob yashil rangda berilgan; hujjat oxirida har bir variant uchun javoblar kaliti bor. Tavsiya: variantni 150 daqiqa ichida javoblarga qaramasdan yeching, so'ng kalit bilan tekshiring.

• Muhim: rasmiy imtihon savollari ochiq e'lon qilinmaydi. Bu to'plam rasmiy spetsifikatsiya (topshiriq turlari va mazmun sohalari) asosida tuzilgan mashq variantlaridir. Barcha hisoblash javoblari dastur yordamida tekshirilgan. Imtihon tartibidagi o'zgarishlarni uzbmb.uz da kuzatib boring.

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Matematika. Milliy sertifikat imtihoniga tayyorgarlik: variantlar to‘plami (2025–2026)

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