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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. ABC uchburchakka aylana tashqi chizilgan. Uchburchakning AM medianasi aylana bilan K nuqtada kesishguncha davom ettirilgan. Agar AM=18,MK=8,BK=10 bo‘lsa, AC tomonini toping.

A) 15

B) 16

C) 14

D) 12

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

A) 7sin5x−5sin7x+c

B) 7cos5x−5cos7x+c

C) −7cos5x−5cos7x+c

D) 7sin5x+5sin7x+C

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3. Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping .

A) π/4

B) 0

C) π/2

D) π/3

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

A) 4

B) 2

C) 1

D) 3

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5. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping.

A) 14 sm

B) 7 sm

C) 18 sm

D) 12 sm

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

A) 6320

B) 6320

C) 5320

D) 6230

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7. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 2

B) 4

C) 3

D) 6

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8. Hisoblang:

A) D

B) A

C) C

D) B

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

A) 20°

B) 40°

C) 50°

D) 30°

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10. 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) 6

B) 8

C) 10

D) 12

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11. Soddalashtiring:

A) -1

B) −сtg²1°

C) −сtg13°

D) −сtg1°

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12. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 3

B) 4

C) 5

D) 2

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

A) 20/3

B) 23/6

C) 22/3

D) 25/6

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14. Tenglamani yeching:

A) 29/462

B) 10/21

C) ∅

D) 0

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15. Agar ifodaning qiymatini toping.

A) 0.8

B) 20

C) 0.05

D) 4

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

A) 521

B) 216

C) 123

D) 265

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17. ? 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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18. bo’lsa, P(−1) ni toping.

A) 100

B) 115

C) 105

D) 120

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19. 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) 15

C) 18

D) 20

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

A) 2a+4

B) -2

C) 2-2a

D) 4-2a

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

A) √3

B) √5 +1

C) 2√3

D) √5

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

A) 16

B) 17

C) 15

D) 19

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23. Agar bo‘lsa sin²α ni toping.

A) A

B) B

C) C

D) D

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24. 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) 9

D) 6

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

A) 12°

B) 6°

C) 9°

D) 18°

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

A) 50

B) 60

C) 45

D) 55

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27. 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) 37/3

B) 83/6

C) 35/3

D) 85/6

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28. 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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29. Soddalashtiring:

A) B

B) A

C) D

D) C

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30. 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) 81

C) 91

D) 40