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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!

1 / 30

1. Sonlarni kamayish tartibida joylashtiring:

A) a>b>c

B) c>b>a

C) b>c>a

D) c>a>b

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2. 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) √30

B) 6

C) √10

D) 12√30

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3. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping.

A) 7sin5x−5sin7x+c

B) −7cos5x−5cos7x+c

C) 7sin5x+5sin7x+C

D) 7cos5x−5cos7x+c

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4. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) B

B) C

C) D

D) A

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5. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping.

A) 2

B) 1

C) 3

D) 4

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6. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta?

A) 100

B) 106

C) 89

D) 96

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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) 12

B) 6

C) 8

D) 10

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8. 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) 81

D) 40

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9. Agar ifodaning qiymatini toping.

A) 0.05

B) 20

C) 0.8

D) 4

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10. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 6

B) 5

C) 7

D) 4

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11. Hisoblang:

A) A

B) C

C) D

D) B

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

A) 50°

B) 40°

C) 20°

D) 30°

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13. ? 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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14. Agar bo‘lsa sin²α ni toping.

A) B

B) D

C) A

D) C

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15. Tenglamani yeching:

A) ∅

B) 0

C) 29/462

D) 10/21

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16. bo’lsa, P(−1) ni toping.

A) 100

B) 105

C) 115

D) 120

17 / 30

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

A) 23/6

B) 22/3

C) 25/6

D) 20/3

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

A) 2-2a

B) 4-2a

C) -2

D) 2a+4

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

A) 123

B) 216

C) 521

D) 265

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

A) 45

B) 50

C) 60

D) 55

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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) 35/3

B) 37/3

C) 85/6

D) 83/6

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

A) 10

B) 8

C) 14

D) 12

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24. Soddalashtiring:

A) D

B) C

C) B

D) A

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

A) 17

B) 19

C) 16

D) 15

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

A) 5

B) 2

C) 4

D) 3

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

A) 61

B) 63

C) 56

D) 54

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28. Soddalashtiring:

A) -1

B) −сtg1°

C) −сtg²1°

D) −сtg13°

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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) 5320

C) 6230

D) 6320

30 / 30

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.