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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. Doiraga ichki chizilgan kvadrat undan yuzasi $2\pi-4$ ga teng bo‘lgan segmentni ajratadi. Kvadratning yuzasini toping.

A) 16

B) 2

C) 4

D) 8

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2. f(x)=x³/3-x²-35x+2 funksiya uchun f `(x)=0 bo`lsa x ni toping.

A) −7 va −5

B) 5 va 7

C) −5 va 7

D) −7 va 5

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

A) 15

B) 14

C) 12

D) 16

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4. 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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5. 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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6. Soddalashtiring:

A) III

B) I

C) II

D) IV

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

A) -4⁴

B) -2⁹

C) -2¹¹

D) -4⁵

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8. Soddalashtiring:

A) cosα

B) 2

C) 1

D) 2sinα

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

A) D

B) C

C) A

D) B

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10. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 28

B) 27

C) 29

D) 26

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11. 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) 53

C) 65

D) 73

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12. Hisoblang:

A) 1

B) 0

C) 2

D) 1.5

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13. 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) 444

D) 443

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14. (?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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15. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping.

A) 2

B) 3

C) 4

D) 1

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16. Soddalashtiring:

A) 3cosx

B) 3cos2x

C) cosx

D) 3sin2x

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

A) 0.6

B) 0.8

C) 0.5

D) 0.2

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18. bo‘lsa, ?² + ?² ni toping.

A) 20.2

B) 20

C) 61/20

D) 65/21

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19. 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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20. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) A

B) B

C) C

D) D

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

A) 1

B) 0

C) 3

D) 2

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22. 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) 120/17

C) 260/17

D) 60/7

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23. 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) 4/3

B) 1.4

C) √6/2

D) √5/2

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24. Tenglamalar sistemasi nechta yechimga ega?