9-sinf 1-variant

11-sinf

2-variant

3 3

1. Soddalashtiring: +

a − a² −6 a + a² −6

A) 1,5a B) 3a C) 2,5a D) 2a E) a 2. Agar x² + 4xy + y² = 15 + 3xy, x + y =4 bo’lsa, xy=?

A) 0 B) 1 C) 2 D) 3 E)–1

3x +1

3. 
   > 1 tenglama nechta butun yechimga ega?
   

9− x

A) 2 B) 3 C) 4 D) 6 E) 7

3. 
   Tengsizlikni yeching: |x² – 6| < 1 .
   

A) (− 7; 7) B) (− 7;− 5) ∪ ( 5; 7) C) (− 7;−1) ∪ (1; 7)

D) (1; 3) E) (− 3;−1)

3. 
   tg α = 1/2, tg β = 2/3, tg γ = 9/10, α, β, γ - o'tkir burchaklar bo'lsa, γ ni α va β orqali ifodalang.
   

A) γ = β - α B) γ = α - β C) γ = α + β D) γ = 2α - β E) γ = 2β -α 6. Agar a² + 9/a² = 22 bo’lsa, a – 3/a ni hisoblang.

A) 3 B) –3 C) ± 4 D) 1 E) 0

₂

7. f (x) = ^⎧⎨^{2x +1 , | x | < 3} bo'lsa, f(x² +7) ni hisoblang.

⎩5x -1 , | x | ≥ 3

A) 5x² – 34 B) 2x² – 8 C) 5x² + 36 D) 5x² + 34 E) 2(x² +7)²+ 1

8. 
   Agar f(x+1) = 3 - 2x va f( ϕ(x))= 6x-3 bo'lsa, ϕ(x) ni toping.
   

A) 4 – 3x B) 3x – 4 C) 4x + 3 D) 4x – 3 E) 6x – 8

8. 
   Hisoblang: 1− 3ctg40⁰ +
   

A) sin20⁰ B) 1/2 C) 0 D) 3/2 E) cos28⁰

8. 
   Hisoblang: lg tg22⁰ + lg tg68⁰ + lg sin90⁰
   

A) 0,5 B) 1 C) 0 D) 0,6 E) –1

8. 
   Hisoblang:
   

A) 1 B) 2 C) 3 D) 4 E) 5

8. 
   y = x² funksiyaning grafigi a(−3;2) vektorga parallel ko‘chirilgan bo’lsa, uning tenglamasini aniqlang.
   

A) y = x²+6x+4 B) y=x²+5 C) y=x² –1 D) y=x²+9 E) y=x²+4x–9

13. 
    Funksiyaning qiymatlar sohasini toping: y = x − x² .
    

A) [0; 1] B) [1/2; 1] C) [0; 1/2] D) [0; 2] E) [1; 2]

1− x 1 1

13. 
    Agar f (x) = bo’lsa, f ( )+ ni toping.
    

1+ x x f (x)

4x 4x x² +1 2x(x² +1) 2(x² +1)

A) ₂ B) ₂ C) ₂ D) ₂ E) ₂

1− x x −1 x −1 x −1 1− x

13. 
    (-∞; 2] oraliqda y = x² – 4x + 7 funksiyaga teskari funksiyani toping.
    

A) 2 ± x −3 B) 2 - x −3 C) 2 + x −3 D) 2 + 3− x

E) 2 ± 3− x

13. 
    Funksiyaning qiymatlar sohasini toping: y
    

A) [ ;3] B) (0; 3] C) [0;3] D) (-∞; 3] E) [ −

17. 
    Tenglamani yeching: 9^x + 6^x = 2 ⋅ 4^x
    

A) 1 B) 0 C) 0; 1 D) E) –1

x²−3x−10 x²−3x−10

⎛ π⎞ ⎛ π⎞

17. 
    ⎜cos ⎟ < ⎜sin ⎟ tengsizlikni eng katta butun yechi-
    

⎝ 6 ⎠ ⎝ 6 ⎠

mini toping

A) –2 B) 1 C) 3 D) 4 E) 5 19. Funksiyaning aniqlanish sohasini toping:

f (x) = log₃ (81⁻³ −3^x2+3 ).

A) (-∞; 3)U (-2; ∞) B) (-∞; -1)U (3; ∞) C) (1; 3) D) (-3; 1) E) (0; ∞)

20. 
    Hisoblang:
    

A) 16 B) 25 C) 36 D) 32 E) 24

20. 
    log₃₀8 ni lg5 = a, lg3 = b orqali ifodalang.
    

3−3a 3(1− b) 3(a −b) b−1 a +1

1. 
   B) C) D) E)
   

1+ b 1+a a +b a +1 1−b

20. 
    Ifodani soddalashtiring: 5 ^log5a − a ^{loga 5} ( a > 1)
    

A) a B) –a² C) 5a D) 1 E) 0

20. 
    Tengsizlikni yeching:
    
    1. 
       (1/2;1) B) (-∞; 1/2) C) (-∞; 0) D) (-∞; -1) U (-1; 0) E) (-∞; -1) U (-1; 1/2)
       
21. 
    tg α =2 bo’lsa, ni hisoblang.
    

A) 3/4 B) 4/5 C) 6/7 D) 7/8 E) 8/9

20. 
    2sin6x(cos⁴3x – sin⁴3x)=sin kx tenglik doim bajariladigan k ning qiymatini toping.
    

A) 12 B) 24 C) 6 D) 18 E) 4

20. 
    Hisoblang: arcsin +arccos .
    

A) 3π /4 B) π /2 C) π /6 D) π /2 E) E) π /3

3x 3x ^{2 0 0}

20. 
    1−sin5x = (cos −sin ) tenglamaning [360 ; 450 ] oraliqdagi
    

2 2

ildizlari yig'indisini toping.

A) 495⁰ B) 1575⁰ C) 1170⁰ D) 1255⁰ E) 975⁰

20. 
    log_{sin x} cosx =1 tenglamani yeching.
    

A) π /4 B) π /4 + π n, n ∈ Z C) – π /4 + π n , n ∈ Z D) π /4 + 2π n , n ∈ Z E) – π /4 + 2π n , n ∈ Z

20. 
    Tengsizlikni yeching: .
    

A) [0; π /3] U [ 5π /3; 2π] B) [0; π /2] C) [ 5π /3; 2π] D) [π /3; π /2] U [ 3π /2; 5π /3] E) [π /3; π /2]

20. 
    6sin x + 3sin2x = 0 tenglamaning [π; 2π] oraliqdagi ildizlari yig'indisini toping.
    

A) π B) 3π C) 11π / 6 D) 17π /4 E) 9π / 2

1 ²

20. 
    Funksiyaning eng katta qiymatini toping: y = _{cos x} + lne .
    

2

A) 2,5 B) 3 C) 1 + e² D) 4 E) aniqlash mumkin emas

20. 
    k ning qanday qiymatlarida: f(x)=1–cos2x–kcos2x funksiya o'zgarmas bo'ladi?
    

A) 2 B) –2 C) 1,5 D) –1,5 E) –1

20. 
    Funksiyaning eng kichik qiymatini toping: y = ( 3cos3x +sin3x)⁷ .
    

A) –14 B) –21 C) –64 D) –128 E) –3⁷

20. 
    sin x + cosx =1 tenglamaning [-3π; π ] oraliqdagi ildizlari yig'indisini toping.
    

A) – 3π B) – 2π C) – π D) 3π /2 E) 3π

20. 
    Tenglama nechta ildizga ega |x – 4| + |x – 1| + |x + 2| = 0?
    

A) ildizi yo'q B) 2 C) 3 D) 1 E) cheksiz ko'p

20. 
    Tenglamani yeching: log₂(3^2x – 26 ⋅ 3^x) = x
    

A) 9 B) 6 C) 4 D) 3 E) 2

20. 
    Tengsizlikni yeching: log ₂ (x+ 2) ≤1
    

x

A) (-∞; -1] U [2; ∞) B) (-∞; -1) U [2; ∞)

C)(-2; -1) U (-1; 0) U (0; 1) U [2; ∞)

D) (-1; 2] E) (-∞; -1) U [-1; ∞)

20. 
    Tenglamani yeching: 2^x-4 +2^x-2 +2^x-1 = 6,5 + 3,25 + 1,625 + …
    

A) 4 B) 2 C)1 D) 0 E) aniqlash mumkin emas

20. 
    Tenglamani yeching: 5^{x –3} – 5^{x –4} – 16 ⋅ 5^{x –5} = 2^{x –3}
    

A) 2 B) 3 C) 4,5 D) 5 E)6

20. 
    2^x2 ⋅3^x = 6 tenglamani yechimlaridan biri 1. Ikkinchisini toping.
    

A) – log₂6 B) log₂3 C) log₃6 D) 3 E) − 3

20. 
    To’g’riburchakli uchburchakning gipotenuzasiga o‘tkazilgan balandlik va katetlarning gipotenuzadagi proyeksiyalari ayirmasi 6 ga teng. Gipotenuza uzunligini toping.
    

A) 6 5 B) 10 3 C) 2 10 D) 3 10 E) 10

20. 
    ABC to’g’riburchakli uchburchakning gipotenuzasiga CD balandlik o‘tkazilgan. Agar ∠ B = 60⁰ va BD = 2 bo‘lsa, gipotenuza uzunligini toping.
    

A) 8 B) 9 C) 6 D) 7 E) 10

20. 
    Gipotenuzasi 10 ga, katetlaridan biri 8 ga teng bo‘lgan to’g’riburchakli uchburchakning kichik burchagining bissektrisasini toping.
    
    1. 
       B) C) D) E)
       
21. 
    Katetining uzunligi 2 ga teng tengyonli to’g’riburchakli uchburchakning medianalari kesishgan nuqtasi bilan bissektrisalar kesishgan nuqtasi orasidagi masafoni toping.
    

A) B) C) D) E)

45. Quyidagi uchta sonlardan qaysinisi o’tkir burchakli uchburchakning tomonlari bo‘la oladi ?

A) 2; 3; 4 B) 4; 5; 7 C) 5; 6; 7 D) 8; 15;17 E) 5; 7; 13

11-sinf

3-variant

1. 
   Parallelogramning diagonallari yig‘indisi 8 ga teng. Tomonlari kvadratlarining yig‘indisini eng kichik qiymatini toping.
   

A) 32 B) 30 C) 64 D) 48 E) 34

2. 
   Parallelogramning perimetri 14. Uning diagonallari parallelogramni to‘rtta uchburchakka ajratadi. Ikki qo‘shni uchburchak perimetrlarining ayirmasi 2 ga teng. Parallelogramm katta tomonini uznunligini toping.
   

A) 10 B) 12 C) 8 D) 10,5 E) 8,5

3. 
   Trapetsiyaning asoslari 28 va 12 ga teng. Diagonallari o‘rtalari orasidagi masofani toping.
   

A) 8 B) 10 C) 6 D) 9 E) 7

4. 
   ABCD trapetsiyaning o‘rta chizig‘i uni o‘rta chziqlari 13 va 17 ga teng bo‘lgan ikkitra trapetsiyaga ajratadi. ABCD trapetsiyaning katta asosini toping.
   

A) 19 B) 21 C) 18 D) 30 E) 23

5. 
   Qavariq n burchakli ko‘pburchakning diagonallari soni 25 tadan kam emas, 30 tadan ortiq emas. Ko‘pburchak tomonlari sonini toping.
   

A) 7 B) 8 C) 9 D) 10 E) 11

6. 
   Radiusi 2 ga teng bo‘lgan ikki doiraning umumiy vatari uzunligi 2 ga teng. Ikki doira umumiy qismining yuzini toping.
   
   1. 
      π -1 B) π /2 –1 C) π - 2 D) (π -1) /2 E) (π -3)/2
      
7. 
   Teng yonli trapetsiyaga ichki chizilgan doiraning markazi yuqori asosining uchidan 3 , pastki asosining uchidan 4 birlik masofada yotadi.
   

Trapetsiyaga ichki chizilgan doiraning yuzini toping.

1. 
   2,86 π B) 4,86 π C) 3,24 π D) 6,76 π E) 5,76 π
   
1. 
   C (-6; 4; 3) nuqtadan o‘tkazilgan a (-3; 2; -4) va b (4; 3; -2) vektorlar teng yonli uchburchakning yon tomonlaridir. Uchburchak C uchidan asosiga o‘tkazilgan balandlik asosining koordinatalari yig‘indisini toping.
   

A) –1 B) 1 C) –2,5 D) 2,5 E) 3

9. 
   Uchburchak yuzi 72 ga teng. Uning tekislikka ortogonal proyeksiyasi kavadratdan iborat. To‘g‘ri to‘rtburchakning tekisligi proyeksiya tekisligi bilan 60⁰ li burchak tashkil etadi. Kvadrat perimetrini toping.
   

A) 32 B) 26 C) 30 D) 28 E) 24

10. 
    Agar prizmaning barcha qirralari soni 60 ga teng bo‘lsa, u holda yoqlarining soni nechta?
    

A ) 20 B) 21 C) 22 D) 24 E) 25

11. 
    Qirrasining uzunligi a ga teng oktaedrning to‘la sirtining yuzini toping.
    
    1. 
       2a² 3 B) a² 3 C) a D) ² 4a² 3 E) a ²
       
12. 
    Qirralarining uzunligi a ga teng bo‘lgan kub yuqori asosining markazi pastki asosining tomonlari o‘rtalari bilan birlashtirilgan. Pastki asoslarining o’rtalari ham o’zaro birlashtirilgan. Hosil bo‘lgan piramida to‘la sirtini toping.
    

2a2 2 2 22

A) B) 3a C) 1,5a D) 2a E) a

3 3

13. 
    Asosi muntazam oltiburchakdan iborat prizmaning yon yoqlari kvadratdan iborat. Agar asosining tomoni 2 5 ga teng bo‘lsa, prizmaning katta diagonali uzunligini toping.
    

A) 4 5 B) 10 C) 3 5 D) 12 E) 11

14. 
    y = x² + 4(a – 2)x + 5 parabolaning uchi x + a = 0 to‘g‘ri chiziqda yotsa, a ning qiymatini toping.
    

A) 4 B) 8 C) –4 D) –2 E) 1

15. 
    Funksiyaning qiymatlar sohasini toping: f(x) = |x - 1| + |x - 3|.
    

A) [0; +∞) B [1; +∞) C) [2; +∞) D) [3; +∞) E) [4; +∞)

4

16. 
    y = −3 funksiyaga teskari funksiyani toping.
    

2− x

1. 
   y = 4 −2 B) y ₌ ⁴ ₋2 C) y = ⁴ + 2
   

2− x 3− x x + 3

4 4

D) y = + 3 E) y = − + 2 x − 2 x +3

2

17. 
    Agar x uchun 2^3x ⋅ 7^x-2 = 4^x+1 bo‘lsa, ^{x −1} ning qiymatini hisoblang.
    

x + 2

A) 2/3 B) 0,75 C) 0,6 D) 0 E) 2,5

18. 
    2^x⋅ x² – 2 ⋅ x² + 2 – 2^x = 0 tenglamaning ildizlari ko‘paytmasini toping.
    

A) 1 B) –1 C) 2 D) –2 E) –5,5

19. 
    Tenglamaning ildizlari yig’indisini toping: 9 ⋅ 16^x – 7 ⋅ 12^x – 16 ⋅ 9^x = 0.
    

A) 2 B) –2 C) 3 D) –1 E) 1

20. 
    Tenglamaning ildizlari ko‘paytmasini toping:
    

( 3+ 2 2)^x +( 3−2 2)^x = 6 .

A) 2 B) 4 C) –4 D) –2 E) 16

21. 
    Sistema ildizlarini ifodalovchi nuqtalar orasidagi masofani toping:
    

⎧⎪x

⎨

⎪⎩y

7 B) 4 C) 10 D) 2 2 E) 9 22. а ni b orqali iodalang: 5^a = 3, 75^b = 81.

2b b 3b 2b b

A) B) C) D) E)

4 − b 4 + b b − 4 4+b 4 − b

23. 3^-x = 4 + x – x² tenglamani nechta yechimi bor?

A) ∅ B) 1 C) 2 D) 3 E) 4 24. 2^x = x³ tenglama nechta haqiqiy ildizga ega?

A) 2 B) 1 C) 3 D) ∅ E) aniqlab bo’lmaydi

^x 7 ^−x

25. 
    Tengsizlikni eng katta butun yechimini toping: 2⋅3 + _x < 61⋅3
    

3

A) 2 B) –2 C) 1 D) 4 E) 0

25. 
    Funksiyaning aniqlanish sohasini toping: y = log₃(x(x – 3)) – log₃x . A) (-∞; 0) B) (-∞; -1) C) (-∞; -2) D) (1; +∞ ) E)(2; +∞ )
    
26. 
    Hisoblang:
    

A) 4 B) 16 C) 7 D) 32 E) 8

3

⎛ ⎞

25. 
    Hisoblang: ⎜⎜ log6 27+ 2log6 2 ⎟⎟ .
    

^⎜⎜ log₆ ³ 0,25 +log₆ ^{1 ⎟}⎟

⎝ 3 ⎠

A) –27 B) 27 C) –8 D) 8log 27₆ E) 16

25. 
    log₄39,2 ni а va b orqali ifodalang : log₇2 = a, log₂10 = b.
    

1 2 b 1 3 b 1 3 b 1 2 b 1 2 b

A) + − B) + − C) − + D) − + E) − + a 3 2 a 2 2 a 2 2 a 3 2 a 3 3

log ₃² x log ₃ x

30. 
    3 +x =162 tenglamaning ildizlari ko‘paytmasini toping.
    

A) 9 B) 3 C) 1 D) 1/3 E) 2/4

30. 
    12^log12(x+3) >2x−5 tenglamaning eng kichik butun yechimini toping..
    

A) –1 B) –2 C) –3 D) 2 E) –2,5

30. 
    Hisoblang: cos⁸165⁰ – cos⁸165⁰ .
    

A) B) C) D) E)

30. 
    Hisoblang: tg (arctg 2 – arcos
    

A) 19/22 B) 1/2 C) 2/13 D) 0 E) 18/22 34. Hisoblang: sin (2 arctg 3) – cos (2 arctg 2).

A) 1,2 B) 1,4 C) –0,8 D) 0,8 E) 1,6 cos2x

35. 
    = 0 tenglamaning [0; 4π ] kesmada nechta ildizi bor?
    

+sin x

A) 8 B) 6 C) 4 D) 2 E) 12

35. 
    Tenglamani yeching: log_{sin x} cos x = 1.
    

A) π / 4 B) π / 4 + π n, n ∈ Z C) - π / 4 + π n, n ∈ Z D) π / 4 + 2π n, n ∈ Z E) - π / 4 + 2π n, n ∈ Z

35. 
    Tengsizlikni [0; π ] oraliqdagi barcha yechimlarini aniqlang:
    

ln(cos⁴ x−sin⁴ x)

(π−e) ≥1.

A) [0; π /2] U [8π /2; 2π ] B) [0; π /2] U [3π /2; 2π ]

C) [0; π /4] U [3π /4;2π ] D) [π /4; π /2] U [3π /2; 2π ] E) [0; π /4] U [3π /2; π ]

⎧⎪x³ + 2x²y + xy² − x − y = 2

35. 
    Agar ^⎨ 3 2 2 bo’lsa, x + y ni toping.
    

⎪_⎩x − 2xy + x y + x + y = 6

A) 1 B) 2 C) –1 D) –2 E) 3

35. 
    Agar 5 ≤ x ≤ y ≤ z ≤ z ≤ t ≤ 320 bo’lsa, x/y + z/t ifodaning eng kichik qiymatini toping.
    

A) 0,25 B) 0,5 C) 1,6 D) 0,6 E) aniqlab bo’lmaydi

35. 
    Tengsizlikni yeching: x² – 7x + 12 < |x – 4|.
    

A) (2; 4) B) ∅ C) (3; 4) D) (2; 3) E) (-∞; 3) U (4; +∞)

x

35. 
    Agar x +3− x +14 + x +3+ x +14 = 4 bo’lsa, ni x +1
    

hisoblang.

A) 2/3 B) – 2/3 C) 3 D) 3/2 E) – 3/2

2| x |

35. 
    | x | −2 < tengsizlikni nechta butun yechimi bor? x
    

A) 6 B) 5 C) 3 D) 4 E) 7

35. 
    O‘suvchi geometrik progressiyaning dastlabki uchta hadining yig‘indisi 24 ga teng. Shu progressiyaning ikkinchi hadini toping.
    

A) 8 B) aniqlab bo’lmaydi C) 10 D) 6 E) 7

35. 
    Hisoblang: 100² – 97² +96²– 93² + 92² – 89² + … + 4² – 1² . A) 7575 B) 5055 C) 6675 D) 6775 E) 7475 45. Tenglamani yeching: 1 – 3x + 9x² – … – (3x)⁹ = 0.
    

A) ± 1/3 B) 1/3 C) – 1/3 D) 1/5 E) 3/4

11-sinf

4-variant

1. 
   Bir hil raqamlardan iborat ikki honali sonlar yig‘indisini toping. A) 495 B) 505 C) 491 D) 550 E)521
   
2. 
   1; 3;7;15; 31;…;2ⁿ –1 ketma-ketlikning dastlabki n ta hadining yig‘indisini toping.
   

A) 4ⁿ + 3n B) 2(2ⁿ – 1) – n C) 2ⁿ + n + 1 D) 2²ⁿ + 4n E) aniqlab bo’lmaydi a

3. 
   a ning qanday qiymatida 2a + a 2a + a + +... cheksiz kamayuvchi
   

2

geometrik progressiyaning yig‘indisi 8 ga teng bo‘ladi?

3 C)1 D) 3 E) 3

⎪ 2

⎪ π

_⎪α+β= ₄

⎩

A) π /3 B) –17 C) – π /6 + π k, k ∈ Z D) 17 E) to’g’ri javob yo’q

6. α, β, γ o‘tkir burchaklar bo‘lib, tg α = 1/2, tg β = 1/5, tg γ = 7/9 bo‘lsa, γ ni α va β lar orqali ifodalang.

A) γ = α + β B) γ = 2α + β C) γ = α + 2β D) γ = α - β E) γ = 2(α + β) 7. Hisoblang: cos 36⁰ ⋅ cos 72⁰ .

A) 1 /2 B) 1/8 C) 1 /4 D) 1/12 E) 3 /4

8. 
   Soddalashtiring: sin⁶x + cos⁶x +(3 /4) sin²2α
   

A) 1 B) –1 C) sin²α D) cos²α E) to’g’ri javob yo’q x ³ x ³ x x

8. 
   sin cos −sin cos ifodaning eng katta qiymatini toping.