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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) III,IV

B) I,II,III,IV

C) II,III

D) I,II

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2. Ifodani soddalashtiring:

A) 1+√(a+1)

B) 1−√(a-1)

C) √(a²-1)

D) 0

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3. Soddalashtiring:

A) 2

B) 1

C) cosα

D) 2sinα

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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) 6

C) 8

D) 12

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5. Soddalashtiring:

A) III

B) II

C) I

D) IV

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

A) 15

B) 12

C) 14

D) 16

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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) 5

B) 3

C) 6

D) 4

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

A) 18 sm

B) 14 sm

C) 7 sm

D) 12 sm

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

A) 120°

B) 30°

C) 90°

D) 60°

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10. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 21

B) 19

C) 10

D) 11

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

A) 20/3

B) 60/7

C) 260/17

D) 120/17

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

A) B

B) A

C) C

D) D

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

A) -2¹¹

B) -4⁵

C) -2⁹

D) -4⁴

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14. Soddalashtiring:

A) 3cos2x

B) 3sin2x

C) 3cosx

D) cosx

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15. Hisoblang:

A) 1.5

B) 1

C) 2

D) 0

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

A) 0.5

B) 0.2

C) 0.6

D) 0.8

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17. 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

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

A) 1

B) 3

C) 2

D) 0

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

A) A

B) D

C) C

D) B

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21. 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) √5/2

C) 4/3

D) 1.4

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

A) 1

B) 3

C) 4

D) 2

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24. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 8

C) 6

D) 12

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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) 65

C) 55

D) 73