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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. Ifodaning oxirgi raqamini aniqlang: $3^{279}\cdot 7^{298}-3^{178}\cdot 7^{197}$

A) 6

B) 1

C) 0

D) 3

2 / 25

2. Agar lg5=a va lg3=b bo`lsa, log₃₀⁡8 ni toping.

A) 1+b

B) 3(1−a)

C) (3(1-a))/(1+b)

D) (1−a)(1+b)

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3. 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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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) 1.4

B) √6/2

C) √5/2

D) 4/3

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

A) 1

B) √5

C) 2

D) 4

6 / 25

6. Hisoblang:

A) 85/104

B) 81/109

C) 172/249

D) 95/243

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7. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) A

B) C

C) D

D) B

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

A) 2

B) 0

C) 3

D) 1

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

A) -4⁴

B) -2¹¹

C) -2⁹

D) -4⁵

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

A) B

B) A

C) D

D) C

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

A) 2

B) 3

C) 1

D) 4

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13. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 12

C) 6

D) 8

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

A) 6√5 + 1

B) √5 + 6

C) 6√5 + 2

D) 3√5 + 6

15 / 25

15. 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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16. Soddalashtiring:

A) 3sin2x

B) 3cosx

C) 3cos2x

D) cosx

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17. 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) 4

C) 3

D) 5

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18. bo‘lsa, ?² + ?² ni toping.

A) 61/20

B) 65/21

C) 20.2

D) 20

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19. 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) 423

C) 444

D) 443

20 / 25

20. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 29

B) 27

C) 26

D) 28

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

A) 16

B) 15

C) 12

D) 14

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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) 211/47

B) 3

C) 175/48

D) 177/48

23 / 25

23. 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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24. Soddalashtiring:

A) 2sinα

B) 2

C) cosα

D) 1

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25. 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) 53

B) 73

C) 65

D) 55