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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. 7⁵⁰ning oxirgi ikkita raqamini toping.

A) 35

B) 51

C) 49

D) 25

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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) 0

B) π/2

C) π/3

D) π/4

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3. y=6sin2x+sin12x funksiyaning hosilasini toping.

A) 24sin7xsin5x

B) 24sin5xcos7x

C) −24sin7xcos5x

D) 24cos7xcos5x

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4. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 20.2

C) 61/20

D) 20

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

A) -11

B) -7

C) -6

D) -5

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6. 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) 81

B) 40

C) 41

D) 91

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7. Tenglamani yeching:

A) 0

B) 10/21

C) ∅

D) 29/462

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8. 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) 16

C) 20

D) 18

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

A) 10/3

B) 8/3

C) 16/3

D) 13/3

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10. 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) 3

B) 6

C) 8

D) 9

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

A) 18°

B) 9°

C) 6°

D) 12°

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12. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 3

B) 2

C) 4

D) 6

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13. Hisoblang:

A) B

B) C

C) A

D) D

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14. bo’lsa, P(−1) ni toping.

A) 115

B) 120

C) 105

D) 100

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

A) 61

B) 54

C) 56

D) 63

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

A) 14

B) 8

C) 12

D) 10

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17. Agar bo‘lsa sin²α ni toping.

A) B

B) D

C) C

D) A

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

A) 521

B) 123

C) 216

D) 265

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20. Soddalashtiring:

A) −сtg1°

B) -1

C) −сtg²1°

D) −сtg13°

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

A) 100

B) 106

C) 96

D) 89

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22. Agar ifodaning qiymatini toping.

A) 4

B) 0.05

C) 0.8

D) 20

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

A) 4-2a

B) 2-2a

C) -2

D) 2a+4

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

A) 30°

B) 40°

C) 20°

D) 50°

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26. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 4

B) 5

C) 6

D) 7

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

A) √5 +1

B) √5

C) 2√3

D) √3

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