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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. Tenglamani yeching:

A) (1;-2)

B) (1;-2)

C) (-2;1)

D) (2;1)

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2. Tenglamani yeching:

A) πk; −arcctg4+πk; k∈Z

B) π −arcctg4+πk; k∈Z

C) πk; π−arcctg4+πk; k∈Z

D) arccos0,8+2πk; k∈Z

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3. Hisoblang:

A) 1

B) 2

C) 1.5

D) 0

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4. Soddalashtiring:

A) 2

B) 2sinα

C) 1

D) cosα

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

A) 15

B) 12

C) 16

D) 14

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7. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 20

C) 61/20

D) 20.2

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

A) 90°

B) 30°

C) 60°

D) 120°

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

A) 1

B) 2

C) 3

D) 4

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

A) 0.6

B) 0.2

C) 0.8

D) 0.5

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

A) 2

B) 4

C) √5

D) 1

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

A) -4⁵

B) -2⁹

C) -2¹¹

D) -4⁴

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13. Soddalashtiring:

A) 3cosx

B) 3sin2x

C) 3cos2x

D) cosx

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14. 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) 3

C) 6

D) 4

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

A) B

B) D

C) C

D) A

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16. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 12

C) 10

D) 8

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

A) B

B) C

C) D

D) A

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18. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping.

A) 6

B) 10

C) 8

D) 12

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19. Hisoblang:

A) 85/104

B) 81/109

C) 95/243

D) 172/249

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

A) 1

B) 2

C) 3

D) 0

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

A) 18 sm

B) 14 sm

C) 7 sm

D) 12 sm

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22. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 26

B) 29

C) 28

D) 27

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23. Ikki xonali sonni qandaydir natural songa bo‘lganda bo‘linmada 3 va qoldiqda 8 hosil bo‘ladi. Agar bo‘linuvchining raqamlari o‘rni almashtirilsa va bo‘luvchi son o‘zgarishsiz qoldirilsa, u holda bo‘linmada 2 va qoldiqda 5 hosil bo‘ladi. Bo‘linuvchning dastlabki qiymatini toping.

A) 53

B) 73

C) 65

D) 55

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24. Uchburchakning tomonlari 10, 24 va 26. Aylananing markazi uchburchakning katta tomonida yotadi va ikki kichik tomonlari bu aylanaga urinadi. Aylana radiusini toping.

A) 20/3

B) 120/17

C) 60/7

D) 260/17

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25. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -11

B) -6

C) -5

D) -7