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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. tenglama nechta ildizga ega?

A) 4

B) 3

C) 2

D) 1

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2. Ifodani soddalashtiring:

A) 0

B) 1−√(a-1)

C) √(a²-1)

D) 1+√(a+1)

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3. f(x)=x³/3-x²-35x+2 funksiya uchun f `(x)=0 bo`lsa x ni toping.

A) −7 va −5

B) −5 va 7

C) 5 va 7

D) −7 va 5

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4. АВCDE beshburchak berilgan, М, N, Р va Q nuqtalar —АВ, ВС, CD va DE tomonlarning o‘rtalari. Agar U va V — МP? va NQ ning o‘rtasi bo‘lsa, АЕ: UV nisbatni toping.

A) 3

B) 5

C) 6

D) 4

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5. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)⁵ − 4(2? + 6)⁴, bunda |? + 3| ≤ 2.

A) -4⁵

B) -4⁴

C) -2¹¹

D) -2⁹

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

A) 22/3

B) 23/6

C) 20/3

D) 25/6

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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) 91

B) 40

C) 81

D) 41

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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) 16

B) 20

C) 18

D) 15

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9. bo’lsa, P(−1) ni toping.

A) 105

B) 115

C) 100

D) 120

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

A) 16/3

B) 10/3

C) 8/3

D) 13/3

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11. Agar bo‘lsa sin²α ni toping.

A) D

B) B

C) A

D) C

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

A) 8

B) 12

C) 14

D) 10

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

A) 2a+4

B) 2-2a

C) -2

D) 4-2a

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

A) 63

B) 61

C) 56

D) 54

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

A) 96

B) 100

C) 89

D) 106

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16. 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) 35/3

C) 83/6

D) 37/3

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17. Soddalashtiring:

A) D

B) A

C) C

D) B

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

A) 12°

B) 6°

C) 9°

D) 18°

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19. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 4

B) 6

C) 5

D) 7

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

A) 4

B) 3

C) 5

D) 2

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21. Tenglamani yeching:

A) 10/21

B) ∅

C) 29/462

D) 0

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

A) 123

B) 521

C) 216

D) 265

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

A) 16

B) 19

C) 17

D) 15

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24. 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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25. 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) 8

C) 10

D) 12

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26. Hisoblang:

A) C

B) A

C) B

D) D

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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) √3

C) √5

D) 2√3

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28. Soddalashtiring:

A) −сtg1°

B) -1

C) −сtg13°

D) −сtg²1°

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

A) 50°

B) 20°

C) 30°

D) 40°

30 / 30

30. 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.