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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. Agar va bo‘lsa, ni toping.

A) 25

B) 11

C) 31

D) 39

2 / 25

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

A) π/12+2πk; k∈Z

B) π/12+πk; k∈Z

C) π/6+πk; k∈Z

D) π/12+πk/2; k∈Z)

3 / 25

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

A) 2

B) 1

C) 4

D) √5

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4. 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) √5/2

D) 4/3

5 / 25

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

A) 90°

B) 120°

C) 60°

D) 30°

6 / 25

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

A) 3√5 + 6

B) √5 + 6

C) 6√5 + 1

D) 6√5 + 2

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7. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 19

B) 10

C) 21

D) 11

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8. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) A

B) B

C) D

D) C

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9. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -6

B) -5

C) -7

D) -11

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10. 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) 6

D) 8

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11. Hisoblang:

A) 2

B) 1

C) 0

D) 1.5

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12. 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

13 / 25

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

A) 15

B) 16

C) 12

D) 14

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

A) C

B) D

C) A

D) B

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15. bo‘lsa, ?² + ?² ni toping.

A) 20

B) 65/21

C) 20.2

D) 61/20

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16. Soddalashtiring:

A) 3cosx

B) 3cos2x

C) cosx

D) 3sin2x

17 / 25

17. Soddalashtiring:

A) 2

B) cosα

C) 1

D) 2sinα

18 / 25

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

A) 4

B) 1

C) 2

D) 3

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

A) 7 sm

B) 14 sm

C) 12 sm

D) 18 sm

20 / 25

20. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 10

C) 12

D) 8

21 / 25

21. Soddalashtiring:

A) IV

B) II

C) I

D) III

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22. 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

23 / 25

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

A) 2

B) 1

C) 4

D) 3

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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) 3

B) 6

C) 5

D) 4

25 / 25

25. 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