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Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

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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) 90°

B) 240°

C) 180°

D) 270°

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2. Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping .

A) π/3

B) 0

C) π/4

D) π/2

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3. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/6+πk; k∈Z

B) π/12+πk/2; k∈Z)

C) π/12+πk; k∈Z

D) π/12+2πk; k∈Z

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4. Soddalashtiring:

A) 3cosx

B) 3cos2x

C) cosx

D) 3sin2x

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5. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -6

B) -7

C) -11

D) -5

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

A) 2-2a

B) 4-2a

C) -2

D) 2a+4

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7. ? 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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8. 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) 10

D) 12

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9. Agar bo‘lsa sin²α ni toping.

A) A

B) D

C) B

D) C

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10. Uchlari A(2; −3), B(6; −1), C(6; 4) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping.

A) 20

B) 18

C) 15

D) 16

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11. bo’lsa, P(−1) ni toping.

A) 105

B) 120

C) 115

D) 100

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12. Tenglamani yeching:

A) ∅

B) 0

C) 10/21

D) 29/462

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13. Soddalashtiring:

A) B

B) D

C) C

D) A

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

A) 265

B) 216

C) 123

D) 521

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

A) √5

B) √3

C) √5 +1

D) 2√3

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17. 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) 37/3

B) 83/6

C) 85/6

D) 35/3

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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) 12

B) 8

C) 6

D) 10

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19. 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) 81

C) 40

D) 91

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20. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang)

A) 40°

B) 50°

C) 30°

D) 20°

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21. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 2

B) 4

C) 5

D) 3

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

A) 63

B) 56

C) 61

D) 54

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23. 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.