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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 t ning qanday qiymatida uchta ildizga ega bo‘ladi?

A) 5

B) 3

C) 2

D) Ø

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2. Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping.

A) 6-2√3

B) 4√3-6

C) 2√2−1

D) 1

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3. ni hisoblang.

A) -13

B) 12

C) -12

D) 13

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4. Soddalashtiring:

A) I

B) IV

C) III

D) II

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5. Hisoblang:

A) 81/109

B) 95/243

C) 85/104

D) 172/249

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6. 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) 83/6

B) 85/6

C) 37/3

D) 35/3

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7. (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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8. Tenglamani yeching:

A) ∅

B) 29/462

C) 0

D) 10/21

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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) 15

B) 16

C) 17

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) 20

B) 16

C) 15

D) 18

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

A) 5320

B) 6320

C) 6320

D) 6230

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

A) 40°

B) 20°

C) 30°

D) 50°

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13. 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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14. 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) 6

B) 9

C) 3

D) 8

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15. Agar bo‘lsa sin²α ni toping.

A) A

B) C

C) B

D) D

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

A) 45

B) 55

C) 60

D) 50

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

A) 54

B) 63

C) 56

D) 61

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

A) 2a+4

B) 2-2a

C) -2

D) 4-2a

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

A) 12

B) 14

C) 10

D) 8

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20. Agar ifodaning qiymatini toping.

A) 0.05

B) 20

C) 0.8

D) 4

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

A) 6

B) 2

C) 4

D) 3

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

A) 265

B) 216

C) 123

D) 521

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

A) 13

B) 10

C) 11

D) 12

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24. Hisoblang:

A) D

B) A

C) B

D) C

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

A) 18°

B) 12°

C) 6°

D) 9°

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26. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 5

B) 6

C) 4

D) 7

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27. Soddalashtiring:

A) D

B) C

C) B

D) A

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

A) √5

B) √5 +1

C) 2√3

D) √3

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29. Soddalashtiring: