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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. tenglama t ning qanday qiymatida uchta ildizga ega bo‘ladi?

A) 2

B) 5

C) 3

D) Ø

2 / 30

2. GH kesmani O nuqta, G nuqtadan boshlab hisoblaganda, 5 : 7 kabi, P nuqtaesa 5:11 kabi nisbatda bo’ladi. O va P nuqtalar orasidagi masofa 30 sm bo’lsa, GH kesmaning uzunligini toping.

A) 234

B) 288

C) 18

D) 72

3 / 30

3. ni hisoblang.

A) 12

B) -12

C) 13

D) -13

4 / 30

4. bo‘lsa, ?² + ?² ni toping.

A) 20.2

B) 61/20

C) 65/21

D) 20

5 / 30

5. Hisoblang:

A) 1

B) 1.5

C) 0

D) 2

6 / 30

6. 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) 12

D) 6

7 / 30

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

A) 12°

B) 6°

C) 9°

D) 18°

8 / 30

8. 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) 37/3

D) 83/6

9 / 30

9. bo’lsa, P(−1) ni toping.

A) 120

B) 105

C) 115

D) 100

10 / 30

10. 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

11 / 30

11. 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) √3

C) 2√3

D) √5

12 / 30

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

A) 3

B) 5

C) 2

D) 4

13 / 30

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

A) 6320

B) 6320

C) 6230

D) 5320

14 / 30

14. 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

15 / 30

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

A) 96

B) 106

C) 89

D) 100

16 / 30

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

A) 30°

B) 20°

C) 40°

D) 50°

17 / 30

17. 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

18 / 30

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

A) 10/3

B) 13/3

C) 16/3

D) 8/3

19 / 30

19. 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) 15

D) 16

20 / 30

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

A) 521

B) 123

C) 216

D) 265

21 / 30

21. Soddalashtiring:

A) D

B) B

C) A

D) C

22 / 30

22. Hisoblang:

A) A

B) C

C) D

D) B

23 / 30

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

A) 10

B) 14

C) 12

D) 8

24 / 30

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.