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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. Koordinata boshidan o‘tuvchi, simmetriya o‘qi ordinata o‘qiga parallel, cho‘qqisi y=x va y+x-2=0 to‘g‘ri chiziqlar kesishgan nuqtada bo‘lgan parabolaning tenglamasini toping.

A) y=-x²+1

B) y=-x²-2x

C) y=-x²+2x

D) y=x²-2x

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2. ifodani soddalshtiring

A) 2sinα

B) 1

C) cosα

D) 2cosα

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3. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4

A) [−2;0]

B) [2;∞)

C) (−∞;−2]

D) [−2;∞)

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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) 8

B) 12

C) 6

D) 10

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5. Hisoblang:

A) 2

B) 1.5

C) 1

D) 0

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

A) -2

B) 4-2a

C) 2a+4

D) 2-2a

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7. 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) 91

D) 40

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

A) 6°

B) 9°

C) 18°

D) 12°

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

A) 50

B) 55

C) 60

D) 45

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10. 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) 85/6

B) 83/6

C) 35/3

D) 37/3

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

A) 12

B) 10

C) 13

D) 11

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12. Tenglamani yeching:

A) 29/462

B) ∅

C) 0

D) 10/21

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13. Soddalashtiring:

A) B

B) D

C) A

D) C

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14. Hisoblang:

A) A

B) D

C) C

D) B

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

A) 23/6

B) 22/3

C) 25/6

D) 20/3

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16. a²b⁵ = 6²⁰ tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud?

A) 12

B) 14

C) 10

D) 8

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17. Agar ifodaning qiymatini toping.

A) 0.05

B) 0.8

C) 4

D) 20

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

A) 6320

B) 6320

C) 6230

D) 5320

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

A) 15

B) 20

C) 18

D) 16

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20. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 4

B) 2

C) 3

D) 6

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

A) 521

B) 123

C) 265

D) 216

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22. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 4

B) 6

C) 5

D) 7

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

A) 56

B) 63

C) 54

D) 61

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25. bo’lsa, P(−1) ni toping.

A) 100

B) 115

C) 120

D) 105

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26. 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) 12

D) 8

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27. 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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28. 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.