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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. bo‘lsa, nimaga teng?

A) 9

B) 3

C) 7

D) 5

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

A) (−∞;−2]

B) [−2;0]

C) [2;∞)

D) [−2;∞)

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3. funksiyaning aniqlanish sohasini toping.

A) (-∞;4/3)∪(4/3;∞)

B) (2/3;∞)

C) (-∞;4/3)

D) (-∞;2/3)∪(2/3;∞)

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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) 4

B) 3

C) 6

D) 5

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5. To‘g‘ri burchakli uchburchak o‘tkir burchaklari yarimlarining tangenslari ko‘paytmasi 1/6 ga teng bo‘lsa, uchburchak o‘tkir burchaklarining kosinuslari yig‘indisini toping.

A) 4/3

B) 1.4

C) √5/2

D) √6/2

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6. Soddalashtiring:

A) −сtg13°

B) −сtg²1°

C) -1

D) −сtg1°

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7. Soddalashtiring:

A) B

B) D

C) A

D) C

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

A) 12

B) 8

C) 10

D) 14

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

A) 25/6

B) 23/6

C) 20/3

D) 22/3

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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) 35/3

B) 37/3

C) 85/6

D) 83/6

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11. Agar ifodaning qiymatini toping.

A) 20

B) 0.05

C) 0.8

D) 4

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

A) 18

B) 15

C) 20

D) 16

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

A) 61

B) 54

C) 63

D) 56

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14. bo’lsa, P(−1) ni toping.

A) 120

B) 105

C) 100

D) 115

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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) 12

B) 6

C) 8

D) 10

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

A) 30°

B) 20°

C) 50°

D) 40°

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17. 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) 2√3

D) √5

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18. Hisoblang:

A) A

B) C

C) D

D) B

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19. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 4

B) 5

C) 2

D) 3

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

A) 3

B) 2

C) 4

D) 6

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21. Tenglamani yeching:

A) ∅

B) 10/21

C) 0

D) 29/462

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22. 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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23. Agar bo‘lsa sin²α ni toping.

A) D

B) A

C) B

D) C

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24. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 6

B) 7

C) 5

D) 4

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25. 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) 106

D) 89

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

A) 265

B) 521

C) 123

D) 216

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27. ∠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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28. Soddalashtiring: bunda, |?| < 1.

A) 2a+4

B) 4-2a

C) -2

D) 2-2a

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

A) 6320

B) 6230

C) 5320

D) 6320

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30. 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) 40

B) 91

C) 41

D) 81