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Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

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11-sinf Matematika olimpiada №4

2022-yil 12-oktyabr:

2022-2023 o'quv yilida tuman bosqichida tushgan savollar!

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1. funksiyaning qiymatlar to‘plamini toping.

A) [-2;2]

B) [1;4]

C) [1;3]

D) [-1;3]

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2. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi.

A) a>3, a=0

B) a=3

C) (0;3)

D) 1

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3. y=6sin2x+sin12x funksiyaning hosilasini toping.

A) −24sin7xcos5x

B) 24cos7xcos5x

C) 24sin7xsin5x

D) 24sin5xcos7x

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4. Hisoblang:

A) 2

B) 1.5

C) 0

D) 1

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5. Soddalashtiring:

A) IV

B) I

C) III

D) II

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6. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping.

A) 521

B) 123

C) 216

D) 265

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7. Agar bo‘lsa sin²α ni toping.

A) D

B) C

C) A

D) B

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8. y = x² − 2x + 3 parabolaga y = 3 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing.

A) y = x² − 2x - 3

B) y =-x² + 2x + 3

C) y =-x² + 2x - 3

D) y = -x² − 2x + 3

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9. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 2

B) 6

C) 3

D) 4

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10. bo’lsa, P(−1) ni toping.

A) 105

B) 115

C) 100

D) 120

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11. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping.

A) 23/6

B) 22/3

C) 20/3

D) 25/6

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12. Soddalashtiring:

A) -1

B) −сtg²1°

C) −сtg13°

D) −сtg1°

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13. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 5

B) 7

C) 4

D) 6

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14. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 2

B) 5

C) 4

D) 3

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15. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang)

A) 40°

B) 20°

C) 30°

D) 50°

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16. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta?

A) 106

B) 100

C) 96

D) 89

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17. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping.

A) √3

B) √5 +1

C) √5

D) 2√3

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18. Hisoblang:

A) C

B) D

C) A

D) B

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19. u_nketma-ketlik quyidagicha berilgan: u₁ = 1, u_n+1 = u_n + 8n. U holda, u₅₀ −u₃₀ ni toping.

A) 5320

B) 6320

C) 6230

D) 6320

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20. Nargizada 2 ta olma va 3 ta nok bor. U 5 kun ketma-ket har kuni singliga bittadan meva beradi. Bu ishni necha usul bilan amalga oshirish mumkin?

A) 8

B) 10

C) 6

D) 12

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21. a²b⁵ = 6²⁰ tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud?

A) 10

B) 14

C) 12

D) 8

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22. Tenglamani yeching:

A) 0

B) 10/21

C) ∅

D) 29/462

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23. O‘tkir burchakli uchburchakning ikki tomon uzunliklari ayirmasi 8, bu tomonlarning uchinchi tomondagi proyeksiyalari mos ravishda 8 va 20 ga teng. Berilgan uchburchakka tashqi chizilgan aylana radiusini toping.

A) 85/6

B) 83/6

C) 35/3

D) 37/3

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24. Agar ifodaning qiymatini toping.