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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. 2, 3, 4, 5, 6, 7, 8, 9, 10 sonlariga bo‘lganda mos ravishda 1, 2, 3, 4, 5, 6, 7, 8, 9 qoldiqlar hosil bo‘ladigan eng kichik natural sonni toping

A) 2519

B) 5039

C) 1019

D) 1519

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2. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4

A) [2;∞)

B) [−2;∞)

C) [−2;0]

D) (−∞;−2]

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3. 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) 120/17

D) 260/17

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

A) 4

B) √5

C) 1

D) 2

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

A) C

B) A

C) B

D) D

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6. Soddalashtiring:

A) II

B) IV

C) III

D) I

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7. Soddalashtiring:

A) 2sinα

B) 2

C) 1

D) cosα

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8. bo‘lsa, ?² + ?² ni toping.

A) 61/20

B) 20.2

C) 20

D) 65/21

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9. 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) 12

D) 10

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

A) 12

B) 14

C) 16

D) 15

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11. 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) 4/3

C) 1.4

D) √5/2

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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) 10

B) 11

C) 21

D) 19

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

A) 2

B) 1

C) 4

D) 3

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14. 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) 28

D) 26

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

A) 2

B) 1

C) 0

D) 3

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

A) 18 sm

B) 7 sm

C) 14 sm

D) 12 sm

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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) D

D) A

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18. 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) 444

C) 423

D) 443

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19. 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) 65

B) 55

C) 73

D) 53

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20. Soddalashtiring:

A) 3sin2x

B) 3cosx

C) 3cos2x

D) cosx

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

A) 3√5 + 6

B) 6√5 + 1

C) √5 + 6

D) 6√5 + 2

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22. Hisoblang:

A) 95/243

B) 81/109

C) 85/104

D) 172/249

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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) 175/48

B) 3

C) 211/47

D) 177/48

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24. 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) 6

B) 3

C) 5

D) 4

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25. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) B

B) C

C) D

D) A