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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. funksiyaning grafigi qaysi choraklardan o‘tadi?

A) III,IV

B) I,II,III,IV

C) I,II

D) II,III

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2. Perimetri 4 ga o`tkir burchagi 30^oga va shu burchak qarshisidagi tomoni √3 ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping.

A) 4√3+7

B) (1+√3)/2

C) (√3-1)/2

D) 7-4√3

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

A) 3

B) 4

C) 2

D) 1

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4. 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) 3

B) 5

C) 6

D) 4

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

A) 2

B) 4

C) 1

D) 3

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7. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) D

B) A

C) B

D) C

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8. 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) 1.4

C) √5/2

D) √6/2

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

A) 6√5 + 1

B) √5 + 6

C) 3√5 + 6

D) 6√5 + 2

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10. Soddalashtiring:

A) 3cos2x

B) 3sin2x

C) cosx

D) 3cosx

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

A) 60/7

B) 20/3

C) 260/17

D) 120/17

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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) 11

D) 10

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13. Soddalashtiring:

A) IV

B) I

C) III

D) II

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

A) 12

B) 16

C) 14

D) 15

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15. 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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16. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 29

B) 27

C) 28

D) 26

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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) A

D) D

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18. Tenglamalar sistemasi nechta yechimga ega?

A) 8

B) 10

C) 12

D) 6

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

A) -4⁵

B) -2⁹

C) -4⁴

D) -2¹¹

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

A) 0

B) 3

C) 2

D) 1

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21. Hisoblang:

A) 1

B) 2

C) 0

D) 1.5

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

A) 30°

B) 90°

C) 120°

D) 60°

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23. Teng yonli АВС uchburchakda: АВ = ВС = 25 sm va АС = 14 sm. ВС tomonga AD balandlikning D asosida urinuvchi va АС tomon o‘rtasidan o‘tuvchi aylana radiusini toping.

A) 177/48

B) 3

C) 175/48

D) 211/47

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24. Hisoblang: