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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. 1!+2!+3!+.....+10! sonining oxirgi raqamini toping.

A) 7

B) 3

C) 0

D) 6

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2. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/12+πk; k∈Z

B) π/6+πk; k∈Z

C) π/12+πk/2; k∈Z)

D) π/12+2πk; k∈Z

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

A) 14

B) 12

C) 16

D) 15

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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) 12

C) 8

D) 6

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

A) B

B) A

C) C

D) D

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6. Hisoblang:

A) 2

B) 1

C) 1.5

D) 0

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

A) 27

B) 28

C) 26

D) 29

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

A) -5

B) -11

C) -6

D) -7

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9. 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) √5/2

C) √6/2

D) 1.4

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10. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) D

B) B

C) C

D) A

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11. Hisoblang:

A) 172/249

B) 95/243

C) 85/104

D) 81/109

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12. 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) 443

B) 433

C) 423

D) 444

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13. 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) 73

C) 65

D) 53

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14. Soddalashtiring:

A) 3sin2x

B) 3cosx

C) cosx

D) 3cos2x

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15. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 8

C) 6

D) 12

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

A) 2

B) 4

C) 1

D) √5

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

A) 18 sm

B) 7 sm

C) 12 sm

D) 14 sm

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18. 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) 211/47

D) 3

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

A) 90°

B) 30°

C) 60°

D) 120°

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20. Soddalashtiring:

A) 2sinα

B) 1

C) cosα

D) 2

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21. Soddalashtiring:

A) I

B) III

C) II

D) IV

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

A) -4⁵

B) -4⁴

C) -2¹¹

D) -2⁹

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

A) 2

B) 3

C) 4

D) 1

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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) 5

B) 3

C) 6

D) 4

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

A) 6√5 + 2

B) 3√5 + 6

C) √5 + 6

D) 6√5 + 1