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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. Beshyulduzning uchidagi burchaklarining yig‘indisini toping.

A) 270°

B) 90°

C) 180°

D) 240°

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2. funksiyaning aniqlanish sohasini toping.

A) (2/3;∞)

B) (-∞;4/3)

C) (-∞;4/3)∪(4/3;∞)

D) (-∞;2/3)∪(2/3;∞)

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3. 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) 55

B) 65

C) 53

D) 73

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

A) 10

B) 8

C) 12

D) 6

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

A) 7 sm

B) 12 sm

C) 18 sm

D) 14 sm

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6. 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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7. Soddalashtiring:

A) II

B) I

C) IV

D) III

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8. bo‘lsa, ?² + ?² ni toping.

A) 20

B) 61/20

C) 20.2

D) 65/21

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9. Hisoblang:

A) 95/243

B) 81/109

C) 85/104

D) 172/249

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

A) 120°

B) 90°

C) 60°

D) 30°

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

A) 2

B) 1

C) 4

D) √5

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

A) -2⁹

B) -2¹¹

C) -4⁴

D) -4⁵

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

A) 3

B) 1

C) 4

D) 2

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14. (?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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15. 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) 211/47

B) 177/48

C) 175/48

D) 3

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

A) 2

B) 4

C) 1

D) 3

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17. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) B

B) C

C) D

D) A

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18. Soddalashtiring:

A) 3cos2x

B) cosx

C) 3sin2x

D) 3cosx

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19. 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) 120/17

C) 20/3

D) 260/17

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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) 4/3

B) 1.4

C) √5/2

D) √6/2

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

A) A

B) B

C) C

D) D

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22. 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) 3

D) 6

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23. 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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24. 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) 443

C) 433

D) 444

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