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Matematika olimpiada Viloyat 2021-2022 o'quv yili

11-sinf Matematika olimpiada №3

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Avgust 19, 2024

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11-sinf Matematika olimpiada №3

2021-2022 o'quv yilida viloyat bosqichida tushgan savollar

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1. Sonlarni kamayish tartibida joylashtiring:

A) c>a>b

B) b>c>a

C) c>b>a

D) a>b>c

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2. ifodani soddalshtiring

A) cosα

B) 2cosα

C) 2sinα

D) 1

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3. АВCDE beshburchak berilgan, М, N, Р va Q nuqtalar —АВ, ВС, CD va DE tomonlarning o‘rtalari. Agar U va V — МP? va NQ ning o‘rtasi bo‘lsa, АЕ: UV nisbatni toping.

A) 5

B) 4

C) 6

D) 3

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4. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping.

A) 30°

B) 60°

C) 90°

D) 120°

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5. Soddalashtiring:

A) II

B) III

C) I

D) IV

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6. Hisoblang:

A) 85/104

B) 172/249

C) 95/243

D) 81/109

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7. To‘g‘ri burchakli uchburchak o‘tkir burchaklari yarimlarining tangenslari ko‘paytmasi 1/6 ga teng bo‘lsa, uchburchak o‘tkir burchaklarining kosinuslari yig‘indisini toping.

A) 4/3

B) √6/2

C) 1.4

D) √5/2

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8. Berilgan natural son 400 dan katta va 500 dan kichik. Uning raqamlari yig‘indisi 9 va u berilgan sonning raqamlari teskari tartibda yozilgan sonning 47/36 qismiga teng. Berilgan sonni toping.

A) 443

B) 423

C) 444

D) 433

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9. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47)

A) 14

B) 12

C) 16

D) 15

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10. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 10

B) 21

C) 19

D) 11

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11. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping.

A) √5

B) 4

C) 1

D) 2

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12. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 2² + 4 ∙ 2³+. … + 100 ∙ 2⁹⁹

A) D

B) B

C) C

D) A

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13. Soddalashtiring:

A) 3cos2x

B) cosx

C) 3cosx

D) 3sin2x

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14. Agar ?(?) = ?²⁰²¹ + 3?²⁰²⁰ + 3?²⁰¹⁹ − ?²⁰¹⁸ + 1 bo‘lsa, ni toping.

A) 3

B) 0

C) 2

D) 1

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15. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping.

A) A

B) D

C) C

D) B

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16. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -5

B) -6

C) -7

D) -11

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17. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 12

C) 10

D) 8

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18. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 20

C) 61/20

D) 20.2

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19. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping.

A) 7 sm

B) 14 sm

C) 12 sm

D) 18 sm

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20. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping.

A) 4

B) 3

C) 2

D) 1

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21. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)⁵ − 4(2? + 6)⁴, bunda |? + 3| ≤ 2.

A) -2¹¹

B) -4⁴

C) -4⁵

D) -2⁹

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22. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping.

A) 0.8

B) 0.6

C) 0.5

D) 0.2

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23. Soddalashtiring: