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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. bo‘lsa, nimaga teng?

A) 3

B) 7

C) 5

D) 9

2 / 25

2. Tengsizlikni yeching.

A) (5/3;2)

B) (4/3;3)

C) (2/3;2)

D) (1/2;∞)

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

A) 3

B) 2

C) 1

D) 4

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

A) -2¹¹

B) -4⁴

C) -2⁹

D) -4⁵

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5. Hisoblang:

A) 95/243

B) 172/249

C) 85/104

D) 81/109

6 / 25

6. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 19

B) 11

C) 10

D) 21

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

A) 30°

B) 120°

C) 60°

D) 90°

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8. Soddalashtiring:

A) IV

B) III

C) I

D) II

9 / 25

9. 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) 433

C) 443

D) 444

10 / 25

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

A) 14

B) 12

C) 16

D) 15

11 / 25

11. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 8

C) 12

D) 6

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12. 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) 177/48

B) 175/48

C) 211/47

D) 3

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13. 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) 4/3

D) 1.4

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

A) D

B) B

C) A

D) C

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

A) 1

B) 2

C) √5

D) 4

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16. Hisoblang:

A) 1.5

B) 0

C) 2

D) 1

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17. 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

18 / 25

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

A) C

B) B

C) D

D) A

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

A) 2

B) 4

C) 1

D) 3

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21. 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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22. Soddalashtiring:

A) 2

B) 1

C) cosα

D) 2sinα

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23. 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) 6

D) 10

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

A) 14 sm

B) 7 sm

C) 12 sm

D) 18 sm

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25. Uchburchakning tomonlari 10, 24 va 26. Aylananing markazi uchburchakning katta tomonida yotadi va ikki kichik tomonlari bu aylanaga urinadi. Aylana radiusini toping.

A) 260/17

B) 20/3

C) 120/17

D) 60/7