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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

1 / 25

1. ko‘phadning barcha koeffitsientlari va ozod hadining yig‘indisini toping.

A) -238

B) 125

C) 245

D) -247

2 / 25

2. ifodani soddalshtiring

A) 2sinα

B) 2cosα

C) 1

D) cosα

3 / 25

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

A) 0

B) 2

C) 3

D) 1

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

A) 12

B) 6

C) 10

D) 8

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6. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 28

B) 27

C) 29

D) 26

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7. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°)

A) 1

B) 4

C) 3

D) 2

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8. 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

9 / 25

9. 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

10 / 25

10. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping.

A) 3√5 + 6

B) 6√5 + 1

C) 6√5 + 2

D) √5 + 6

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11. 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) 423

B) 444

C) 443

D) 433

12 / 25

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

A) -4⁴

B) -2¹¹

C) -4⁵

D) -2⁹

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

A) 1

B) 4

C) 2

D) √5

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14. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) B

B) C

C) A

D) D

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15. 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) √6/2

B) 4/3

C) 1.4

D) √5/2

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16. 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) 6

B) 5

C) 4

D) 3

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17. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -5

B) -6

C) -11

D) -7

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18. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 20.2

C) 20

D) 61/20

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19. 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) 73

B) 55

C) 53

D) 65

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

A) D

B) B

C) A

D) C

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21. Soddalashtiring:

A) 3cosx

B) 3cos2x

C) 3sin2x

D) cosx

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22. Tenglamalar sistemasi nechta yechimga ega?

A) 8

B) 12

C) 6

D) 10

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

A) 260/17

B) 120/17

C) 20/3

D) 60/7

24 / 25

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

A) 0.5

B) 0.2

C) 0.6

D) 0.8

25 / 25

25. Hisoblang: