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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. va a,b>0 bo‘lsa, ifodaning eng kichik qiymatini toping.

A) 2

B) 3

C) 4

D) 1

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2. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/12+πk; k∈Z

B) π/6+πk; k∈Z

C) π/12+2πk; k∈Z

D) π/12+πk/2; k∈Z)

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3. Hisoblang:

A) 2

B) 0

C) 1.5

D) 1

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4. Soddalashtiring:

A) 1

B) 2sinα

C) 2

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) 1.4

B) √5/2

C) √6/2

D) 4/3

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

A) 1

B) 2

C) 4

D) √5

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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) 444

B) 423

C) 443

D) 433

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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) 4

B) 5

C) 6

D) 3

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10. Hisoblang:

A) 81/109

B) 95/243

C) 85/104

D) 172/249

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11. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 20.2

C) 61/20

D) 20

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12. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 27

B) 29

C) 26

D) 28

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13. 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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14. 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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15. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) B

B) A

C) D

D) C

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16. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 6

C) 8

D) 12

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

A) 1

B) 2

C) 3

D) 4

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18. Soddalashtiring:

A) 3cos2x

B) 3cosx

C) 3sin2x

D) cosx

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19. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -7

B) -5

C) -11

D) -6

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

A) -4⁵

B) -2¹¹

C) -2⁹

D) -4⁴

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21. 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) 60/7

C) 20/3

D) 120/17

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22. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 19

B) 11

C) 21

D) 10

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

A) 90°

B) 30°

C) 120°

D) 60°

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

A) 6√5 + 1

B) √5 + 6

C) 6√5 + 2

D) 3√5 + 6

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25. 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) 0.6

C) 0.2

D) 0.8