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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. To‘g‘ri burchakli uchburchakda AC=3, BC=4, CD-balandlik va CE-bissektrisa. DE ni toping.

A) 12/35

B) 15/31

C) 21

D) 23/35

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2. ni hisoblang.

A) 13

B) 12

C) -12

D) -13

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3. 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) 1.4

C) 4/3

D) √5/2

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4. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) D

B) B

C) A

D) C

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5. 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) 65

C) 73

D) 55

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6. Hisoblang:

A) 95/243

B) 85/104

C) 81/109

D) 172/249

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

A) 14 sm

B) 18 sm

C) 12 sm

D) 7 sm

8 / 25

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

A) 120°

B) 30°

C) 60°

D) 90°

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9. Soddalashtiring:

A) 3sin2x

B) 3cosx

C) cosx

D) 3cos2x

10 / 25

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

A) 3

B) 1

C) 4

D) 2

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11. Soddalashtiring:

A) II

B) III

C) I

D) IV

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12. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 20.2

C) 20

D) 61/20

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13. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 21

B) 10

C) 19

D) 11

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

A) 2

B) 4

C) √5

D) 1

15 / 25

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

A) C

B) D

C) B

D) A

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16. Soddalashtiring:

A) 2sinα

B) 1

C) cosα

D) 2

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

A) 2

B) 1

C) 0

D) 3

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

A) 10

B) 6

C) 12

D) 8

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20. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 10

C) 12

D) 8

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21. 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) 175/48

B) 177/48

C) 3

D) 211/47

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22. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping.

A) A

B) B

C) C

D) D

23 / 25

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

A) 20/3

B) 260/17

C) 60/7

D) 120/17

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

A) 2

B) 3

C) 1

D) 4

25 / 25

25. Hisoblang: