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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!

1 / 30

1. ko‘phadning barcha koeffitsientlari va ozod hadining yig‘indisini toping.

A) 245

B) -247

C) 125

D) -238

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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/3

C) π/2

D) π/4

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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. Berilgan natural son 400 dan katta va 500 dan kichik. Uning raqamlari yig‘indisi 9 va u berilgan sonning raqamlari teskari tartibda yozilgan sonning 47/36 qismiga teng. Berilgan sonni toping.

A) 443

B) 433

C) 423

D) 444

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

A) -5

B) -7

C) -6

D) -11

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

A) 30°

B) 20°

C) 40°

D) 50°

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7. Agar ifodaning qiymatini toping.

A) 0.8

B) 20

C) 4

D) 0.05

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8. 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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9. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!)

A) 16

B) 17

C) 15

D) 19

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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) 16

B) 20

C) 15

D) 18

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11. Soddalashtiring:

A) −сtg1°

B) −сtg²1°

C) −сtg13°

D) -1

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

A) 89

B) 106

C) 96

D) 100

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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) 85/6

B) 83/6

C) 35/3

D) 37/3

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14. Soddalashtiring:

A) B

B) C

C) A

D) D

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15. 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) 10

B) 6

C) 12

D) 8

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16. bo’lsa, P(−1) ni toping.

A) 100

B) 120

C) 105

D) 115

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17. 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) 81

D) 91

18 / 30

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

A) 22/3

B) 25/6

C) 20/3

D) 23/6

19 / 30

19. Hisoblang:

A) A

B) D

C) C

D) B

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

A) 11

B) 12

C) 13

D) 10

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21. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 4

B) 2

C) 6

D) 3

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

A) 2-2a

B) 4-2a

C) -2

D) 2a+4

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

A) 216

B) 123

C) 265

D) 521

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

A) 6°

B) 12°

C) 18°

D) 9°

25 / 30

25. Tenglamani yeching:

A) ∅

B) 29/462

C) 0

D) 10/21

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26. 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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27. Agar bo‘lsa sin²α ni toping.

A) A

B) D

C) B

D) C

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28. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 6

B) 7

C) 4

D) 5

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29. 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.