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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. Tenglamani yeching:

A) (1;-2)

B) (2;1)

C) (1;-2)

D) (-2;1)

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2. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/12+2πk; k∈Z

B) π/6+πk; k∈Z

C) π/12+πk/2; k∈Z)

D) π/12+πk; k∈Z

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3. Asosi ga teng bo`lgan muntazam to`rtburchakli piramidaning uchidan o`tkazilgan kesma asos tomonini 2:4 nisbatda bo`ladi va asos tekisligi bilan 60^o li burchakhosilqiladi. Piramidahajmini toping.

A) √10

B) 6

C) √30

D) 12√30

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4. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 19

B) 10

C) 11

D) 21

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5. 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) 6

B) 4

C) 3

D) 5

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

A) 55

B) 45

C) 50

D) 60

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7. Soddalashtiring:

A) B

B) C

C) D

D) A

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

A) 40°

B) 30°

C) 50°

D) 20°

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9. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 7

B) 5

C) 6

D) 4

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10. 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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11. Agar ifodaning qiymatini toping.

A) 0.8

B) 20

C) 4

D) 0.05

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12. Hisoblang:

A) D

B) C

C) A

D) B

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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) 6

D) 10

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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) 17

B) 15

C) 16

D) 19

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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 +1

B) 2√3

C) √5

D) √3

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16. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 3

B) 4

C) 2

D) 6

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

A) -2

B) 2a+4

C) 4-2a

D) 2-2a

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18. 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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19. bo’lsa, P(−1) ni toping.

A) 120

B) 105

C) 100

D) 115

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20. Soddalashtiring:

A) −сtg²1°

B) −сtg13°

C) -1

D) −сtg1°

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21. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 5

B) 4

C) 2

D) 3

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22. Agar bo‘lsa sin²α ni toping.

A) B

B) C

C) D

D) A

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

A) 8/3

B) 16/3

C) 10/3

D) 13/3

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24. 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) 37/3

C) 85/6

D) 35/3

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

A) 9°

B) 18°

C) 6°

D) 12°

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

A) 10

B) 11

C) 12

D) 13

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

A) 521

B) 265

C) 123

D) 216

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

A) 12

B) 8

C) 14

D) 10

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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.