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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) 1019

B) 5039

C) 1519

D) 2519

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

A) 1

B) 4

C) √5

D) 2

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

A) 2

B) 1

C) 3

D) 4

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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) 4/3

D) √6/2

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6. Soddalashtiring:

A) 3cos2x

B) cosx

C) 3sin2x

D) 3cosx

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7. 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) 444

D) 433

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8. Hisoblang:

A) 172/249

B) 95/243

C) 81/109

D) 85/104

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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) 12

C) 10

D) 6

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

A) 90°

B) 60°

C) 120°

D) 30°

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

A) C

B) B

C) A

D) D

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

A) 2

B) 3

C) 4

D) 1

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

A) 14 sm

B) 18 sm

C) 7 sm

D) 12 sm

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14. bo‘lsa, ?² + ?² ni toping.

A) 61/20

B) 20

C) 65/21

D) 20.2

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15. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping.

A) 0.8

B) 0.6

C) 0.5

D) 0.2

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16. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 10

B) 21

C) 11

D) 19

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

A) 15

B) 12

C) 16

D) 14

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18. Soddalashtiring:

A) cosα

B) 2sinα

C) 1

D) 2

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

A) √5 + 6

B) 6√5 + 1

C) 6√5 + 2

D) 3√5 + 6

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20. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 8

C) 12

D) 10

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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) 60/7

B) 120/17

C) 260/17

D) 20/3

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22. Soddalashtiring:

A) II

B) III

C) IV

D) I

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

A) A

B) B

C) C

D) D

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24. Hisoblang:

A) 1

B) 2

C) 1.5

D) 0

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25. 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) 3

C) 5

D) 6