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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) 240°

C) 90°

D) 180°

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2. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping.

A) −7cos5x−5cos7x+c

B) 7sin5x−5sin7x+c

C) 7cos5x−5cos7x+c

D) 7sin5x+5sin7x+C

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3. Hisoblang:

A) 1

B) 1.5

C) 2

D) 0

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

A) 3

B) 4

C) 2

D) 1

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

A) -2⁹

B) -4⁵

C) -2¹¹

D) -4⁴

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

A) D

B) B

C) C

D) A

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

A) 16

B) 14

C) 12

D) 15

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

A) D

B) C

C) B

D) A

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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) 120/17

B) 20/3

C) 60/7

D) 260/17

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12. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 26

B) 27

C) 28

D) 29

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13. 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) 175/48

C) 3

D) 177/48

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14. 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) √5/2

B) √6/2

C) 1.4

D) 4/3

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15. Tenglamalar sistemasi nechta yechimga ega?

A) 12

B) 8

C) 10

D) 6

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16. bo‘lsa, ?² + ?² ni toping.

A) 61/20

B) 20.2

C) 65/21

D) 20

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

A) 12

B) 6

C) 10

D) 8

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18. 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) 53

C) 73

D) 65

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

A) 2

B) 0

C) 3

D) 1

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20. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -11

B) -5

C) -6

D) -7

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

A) 6√5 + 1

B) 3√5 + 6

C) √5 + 6

D) 6√5 + 2

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22. 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) 444

B) 423

C) 443

D) 433

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23. Soddalashtiring:

A) cosx

B) 3sin2x

C) 3cos2x

D) 3cosx

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24. 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) 0.5

C) 0.6

D) 0.2

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