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Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

InfoMaster

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) 3

B) Ø

C) 5

D) 2

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2. ABCD tetraedrning D uchidagi barcha yassi burchaklari to`g`ri. Shu tetraedrda kub shunday ichki chizilganki, kubning bitta uchi D nuqtada, unga qarama−qarshi uchi esa ABC yoqda yotibdi. Agar DA=5, DB=6 va DC=10 bo`lsa, kub qirrasining uzunligini toping.

A) 2√2

B) 15/7

C) 25/12

D) 2

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3. ni hisoblang.

A) -12

B) 12

C) -13

D) 13

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4. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 8

C) 6

D) 12

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

A) -2¹¹

B) -2⁹

C) -4⁴

D) -4⁵

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

A) 216

B) 265

C) 123

D) 521

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8. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 4

B) 3

C) 2

D) 6

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

A) 9°

B) 6°

C) 12°

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) 6230

B) 6320

C) 6320

D) 5320

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

A) 50

B) 45

C) 60

D) 55

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13. 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) 8

C) 10

D) 6

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14. Agar ifodaning qiymatini toping.

A) 20

B) 0.8

C) 4

D) 0.05

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

A) 19

B) 17

C) 16

D) 15

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17. bo’lsa, P(−1) ni toping.

A) 100

B) 120

C) 105

D) 115

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18. 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) 20

C) 16

D) 15

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

A) 8/3

B) 13/3

C) 16/3

D) 10/3

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20. Hisoblang:

A) D

B) B

C) C

D) A

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21. 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) 8

C) 6

D) 9

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22. Soddalashtiring:

A) C

B) B

C) D

D) A

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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) 11

B) 13

C) 10

D) 12

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24. Agar bo‘lsa sin²α ni toping.

A) A

B) B

C) C

D) D

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25. 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) 91

C) 40

D) 81

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