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

A) 125

B) -247

C) 245

D) -238

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2. Tenglamani yeching:

A) πk; π−arcctg4+πk; k∈Z

B) arccos0,8+2πk; k∈Z

C) πk; −arcctg4+πk; k∈Z

D) π −arcctg4+πk; k∈Z

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

A) 90°

B) 120°

C) 60°

D) 30°

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

A) 2

B) 3

C) 4

D) 1

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5. Soddalashtiring:

A) 1

B) 2

C) 2sinα

D) cosα

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6. 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) 0.8

C) 0.5

D) 0.2

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7. Soddalashtiring:

A) 3cos2x

B) cosx

C) 3cosx

D) 3sin2x

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8. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 28

B) 29

C) 26

D) 27

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9. 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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10. Hisoblang:

A) 2

B) 1.5

C) 1

D) 0

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

A) 3

B) 1

C) 2

D) 4

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12. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 19

B) 21

C) 10

D) 11

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

A) 7 sm

B) 12 sm

C) 14 sm

D) 18 sm

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

A) -6

B) -5

C) -11

D) -7

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

A) 8

B) 6

C) 10

D) 12

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

A) 4

B) 1

C) 2

D) √5

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17. 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

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

A) 1

B) 2

C) 0

D) 3

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19. Soddalashtiring:

A) II

B) I

C) III

D) IV

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20. 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) √5/2

B) 1.4

C) 4/3

D) √6/2

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

A) 6√5 + 2

B) 6√5 + 1

C) 3√5 + 6

D) √5 + 6

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22. 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) 433

B) 423

C) 444

D) 443

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23. Tenglamalar sistemasi nechta yechimga ega?