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Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

1022 Ko'rishlar 2 izohlar

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11-sinf Matematika olimpiada №4

2022-yil 12-oktyabr:

2022-2023 o'quv yilida tuman bosqichida tushgan savollar!

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1. 3²⁰¹⁷ sonning oxirgi ikkita raqamini toping.

A) 63

B) 83

C) 13

D) 03

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2. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi.

A) a=3

B) 1

C) (0;3)

D) a>3, a=0

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3. ifodani soddalshtiring

A) 2cosα

B) cosα

C) 2sinα

D) 1

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

A) 3

B) 1

C) 2

D) 4

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

A) 14 sm

B) 7 sm

C) 18 sm

D) 12 sm

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6. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping.

A) 2√3

B) √5 +1

C) √3

D) √5

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7. Tenglamani yeching:

A) ∅

B) 0

C) 29/462

D) 10/21

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8. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada?

A) 12°

B) 6°

C) 18°

D) 9°

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9. Soddalashtiring: bunda, |?| < 1.

A) -2

B) 4-2a

C) 2-2a

D) 2a+4

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10. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 4

B) 5

C) 3

D) 2

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11. Agar bo‘lsa sin²α ni toping.

A) C

B) A

C) D

D) B

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12. Doskaga ?₁, ?₂, ?₃, . . . , ?₂₀₀ sonlari yozilgan. Ma’lumki, ?₁ = 3, ?₂ = 9. Agar ixtiyoriy n natural son uchun ?_n+2 = ?_n+1 − ?_n tenglik o‘rinli bo‘lsa, ?₂₀₀ ni toping.

A) 9

B) 8

C) 3

D) 6

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13. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta?

A) 106

B) 89

C) 96

D) 100

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14. O‘tkir burchakli uchburchakning ikki tomon uzunliklari ayirmasi 8, bu tomonlarning uchinchi tomondagi proyeksiyalari mos ravishda 8 va 20 ga teng. Berilgan uchburchakka tashqi chizilgan aylana radiusini toping.

A) 83/6

B) 37/3

C) 35/3

D) 85/6

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15. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping.

A) 23/6

B) 20/3

C) 22/3

D) 25/6

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16. Soddalashtiring:

A) B

B) A

C) C

D) D

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17. Nargizada 2 ta olma va 3 ta nok bor. U 5 kun ketma-ket har kuni singliga bittadan meva beradi. Bu ishni necha usul bilan amalga oshirish mumkin?

A) 12

B) 6

C) 8

D) 10

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18. ? soniga teskari bo‘lgan son ? ning 9% ini tashkil qiladi. ? ni toping. (?u yerda, ? > 0)

A) 8/3

B) 16/3

C) 13/3

D) 10/3

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19. Agar ifodaning qiymatini toping.

A) 20

B) 0.05

C) 0.8

D) 4

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20. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!).

A) 50

B) 60

C) 55

D) 45

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21. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping.

A) 13

B) 11

C) 12

D) 10

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22. y = x² − 2x + 3 parabolaga y = 3 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing.

A) y =-x² + 2x + 3

B) y = x² − 2x - 3

C) y =-x² + 2x - 3

D) y = -x² − 2x + 3

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23. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 4

B) 2

C) 6

D) 3

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24. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 4

B) 7

C) 6

D) 5

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25. Hisoblang:

A) D

B) A

C) B

D) C

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26. Natural son roppa-rosa 2 ta tub bo‘luvchiga, bu sonning kvadrati esa 45 ta turli natural bo‘luvchiga ega. Berilgan sonning kubi eng ko‘pi bilan nechta natural bo‘luvchiga ega bo‘lishi mumkin?

A) 41

B) 40

C) 91

D) 81

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27. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping.

A) 521

B) 216

C) 123

D) 265

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28. u_nketma-ketlik quyidagicha berilgan: u₁ = 1, u_n+1 = u_n + 8n. U holda, u₅₀ −u₃₀ ni toping.