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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. funksiyaning grafigi qaysi choraklardan o‘tadi?

A) II,III

B) III,IV

C) I,II

D) I,II,III,IV

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2. ni hisoblang.

A) 13

B) -12

C) -13

D) 12

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3. 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) 3

B) 211/47

C) 175/48

D) 177/48

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

A) 4

B) 2

C) 1

D) √5

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

A) 3

B) 1

C) 2

D) 4

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7. 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) 3

C) 5

D) 4

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

A) 14 sm

B) 12 sm

C) 18 sm

D) 7 sm

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

A) 60/7

B) 20/3

C) 260/17

D) 120/17

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

A) -2¹¹

B) -4⁴

C) -4⁵

D) -2⁹

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11. Soddalashtiring:

A) I

B) II

C) III

D) IV

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12. Soddalashtiring:

A) cosα

B) 2sinα

C) 1

D) 2

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

A) 1

B) 2

C) 3

D) 0

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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) C

D) A

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15. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 61/20

C) 20.2

D) 20

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16. 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) 433

C) 423

D) 443

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17. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -11

B) -6

C) -7

D) -5

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18. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) B

B) A

C) C

D) D

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19. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 10

B) 21

C) 19

D) 11

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20. Hisoblang:

A) 1

B) 2

C) 1.5

D) 0

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21. Tenglamalar sistemasi nechta yechimga ega?

A) 8

B) 10

C) 12

D) 6

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

A) 1

B) 3

C) 4

D) 2

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23. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping.

A) 0.2

B) 0.8

C) 0.6

D) 0.5

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24. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 28

B) 29

C) 26

D) 27

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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) 55

B) 73

C) 53

D) 65