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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. 2, 3, 4, 5, 6, 7, 8, 9, 10 sonlariga bo‘lganda mos ravishda 1, 2, 3, 4, 5, 6, 7, 8, 9 qoldiqlar hosil bo‘ladigan eng kichik natural sonni toping

A) 5039

B) 2519

C) 1519

D) 1019

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

A) [−2;0]

B) [−2;∞)

C) [2;∞)

D) (−∞;−2]

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3. y=6sin2x+sin12x funksiyaning hosilasini toping.

A) 24sin5xcos7x

B) 24cos7xcos5x

C) 24sin7xsin5x

D) −24sin7xcos5x

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4. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping.

A) 10

B) 6

C) 12

D) 8

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5. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 2² + 4 ∙ 2³+. … + 100 ∙ 2⁹⁹

A) A

B) D

C) B

D) C

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6. Soddalashtiring:

A) D

B) C

C) A

D) B

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7. 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) 8

C) 6

D) 12

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8. 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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9. Tenglamani yeching:

A) 29/462

B) ∅

C) 0

D) 10/21

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

A) 50°

B) 20°

C) 30°

D) 40°

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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. Soddalashtiring: bunda, |?| < 1.

A) -2

B) 2-2a

C) 4-2a

D) 2a+4

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13. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 7

B) 4

C) 6

D) 5

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

A) 19

B) 15

C) 16

D) 17

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

A) 12

B) 10

C) 14

D) 8

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

A) 10

B) 13

C) 12

D) 11

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17. bo’lsa, P(−1) ni toping.

A) 100

B) 115

C) 120

D) 105

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18. Agar ifodaning qiymatini toping.

A) 20

B) 0.05

C) 0.8

D) 4

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

A) 45

B) 60

C) 55

D) 50

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20. Soddalashtiring:

A) −сtg1°

B) −сtg13°

C) -1

D) −сtg²1°

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

A) 56

B) 63

C) 61

D) 54

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

A) 10/3

B) 16/3

C) 8/3

D) 13/3

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

A) 18°

B) 12°

C) 6°

D) 9°

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25. 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) 18

C) 20

D) 15

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26. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 3

B) 2

C) 4

D) 5

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27. 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.