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Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

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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. Beshyulduzning uchidagi burchaklarining yig‘indisini toping.

A) 180°

B) 240°

C) 90°

D) 270°

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2. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi?

A) 71%

B) 61%

C) 60%

D) 70%

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3. Agar 2^a=27, 3^c=16 bo’lsa a ∙ ? ning qiymatini toping.

A) 10

B) 12

C) 11

D) 13

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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. bo‘lsa, ?² + ?² ni toping.

A) 20.2

B) 20

C) 65/21

D) 61/20

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6. Agar ifodaning qiymatini toping.

A) 4

B) 0.05

C) 0.8

D) 20

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7. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 2

B) 3

C) 4

D) 5

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8. Tenglamani yeching:

A) 10/21

B) 0

C) 29/462

D) ∅

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9. 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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10. 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) 91

B) 40

C) 41

D) 81

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

A) 106

B) 100

C) 96

D) 89

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

A) 8/3

B) 13/3

C) 10/3

D) 16/3

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13. 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) 35/3

B) 37/3

C) 85/6

D) 83/6

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

A) 18°

B) 12°

C) 9°

D) 6°

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

A) 12

B) 11

C) 13

D) 10

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16. Soddalashtiring:

A) −сtg²1°

B) −сtg1°

C) −сtg13°

D) -1

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17. Soddalashtiring:

A) B

B) A

C) C

D) D

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18. 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) 6

B) 10

C) 8

D) 12

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19. bo’lsa, P(−1) ni toping.

A) 100

B) 120

C) 105

D) 115

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

A) 25/6

B) 22/3

C) 23/6

D) 20/3

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

A) 60

B) 50

C) 55

D) 45

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22. Agar bo‘lsa sin²α ni toping.

A) C

B) D

C) B

D) A

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

A) 123

B) 265

C) 216

D) 521

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24. Arifmetik progressiyada ?₂ = 12, ?₇ − ?₄ = 9 bo‘lsa, ?₁₉ni toping.

A) 63

B) 61

C) 54

D) 56

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

A) 6320

B) 5320

C) 6320

D) 6230

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26. 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) √5

D) √3

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27. Hisoblang: