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Matematika olimpiada Viloyat 2021-2022 o'quv yili

9-sinf Matematika olimpiada №3.1

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Avgust 19, 2024

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9-sinf Matematika olimpiada №3.1

2021-2022 o'quv yil viloyat bosqichida tushgan savollar.

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1. Uchburchakning perimetri 24 sm ga teng bo‘lib, uning tomonlari uzunliklari arifmetik progressiya tashkil etadi. Shu uchburchakning kichik tomoni 6 sm bo‘lsa, uchburchak turini aniqlang.

A) O’tkir burchakli

B) O’tmas burchakli

C) Bunday uchburchak yo’q

D) To‘g‘ri burchakli

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2. Hisoblang: cos 10^o− 2 cos 50^o− cos 70^o

A) sin40°

B) –cos40°

C) cos40°

D) –sin40°

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3. Тенгламани ечинг: ((0,001 ∙ ? + 2): 0,3) ∙ 0,01 − 11,2 = 22,2

A) 1 000 000

B) 100 000

C) 1

D) 1000

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4. Chizmadagi 14 ta kvadratning perimetrlar yig‘indisi 400 sm ga teng. Ushbu kvadratlarning yuzlari yig‘indisi necha kv.sm ni tashkil qiladi?

A) 900

B) 800

C) 850

D) 950

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5. Soddalashtiring:

A) I

B) III

C) II

D) IV

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6. Beshta musbat son berilgan. Birinchi va beshinchi sonlar yig‘indisi 13 ga teng. Berilgan barcha sonlar yig‘indisidan ikkinchi son 3 marta, uchinchi son 4 marta, to‘rtinchi son esa 5 marta kichik. Berilgan sonlardan eng kattasini toping.

A) 15

B) 22

C) 12

D) 20

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7. Aylanaga tashqi chizilgan ABCD teng yonli trapetsiyaning yuzi √3 ga teng. Agar ВС : AD = 1 : 3 bo‘lsa, trapetsiyaning АВ yon tomonini toping.

A) 2

B) √6

C) √3

D) √2

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8. Uchburchakning to‘g‘ri burchagidan chiquvchi bissektrisa gipotenizani 15 va 20 ga teng qismlarga ajratadi. Uchburchak yuzini toping.

A) 288

B) 264

C) 294

D) 268

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9. to‘g‘ri chiziqlar orasidagi burchakni toping.

A) 5°

B) 15°

C) 45°

D) 30°

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10. Agar ? + ? + ? = 0 bo‘lsa, ni soddalashtiring.

A) 1

B) 0

C) 1.2

D) 1.8

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11. 1 dan 100 gacha bo‘lgan natural sonlar orasidagi ? sonlar shundayki, ? ning natural bo‘luvchilari ko‘paytmasi(1 va ? ham inobatga olinganda) ?³ ga teng. Shunday ? natural sonlar nechta?

A) 12

B) 18

C) 10

D) 16

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12. Hisoblang: bunda,

A) -49

B) -100

C) -144

D) -64

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13. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 384

B) 376

C) 424

D) 420

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14. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 12.6

B) 9.8

C) 18.2

D) 11.4

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15. Tenglama ildizlari yig‘indisini toping. (? − |?|)² + ? + |?| = 100 .

A) 50

B) 55

C) 40

D) 45

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16. f(x) kvadrat funksiyaga nisbatan ma’lumki, f(0) + f(1) = 0, f(2) + f(3) = 0. f(x) = 2022 tenglamaning ildizlari yig‘indisi nimaga teng? (bunda, f(x) = 2022 tenglama 2 ta turli yechimga ega).

A) 4

B) 5

C) 3

D) 6

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17. Yig‘indini toping:

A) 2023

B) 2022

C) 2021

D) 2020

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18. Ucburchakning tomonlari 13; 14; 15 ga teng. Ichki chizilgan aylana radiusini toping.

A) 4.5

B) 4.8

C) 4

D) 3.5

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19.

A) -216

B) -1

C) -6

D) -36

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20. Kenguru oldinga 1 metrga yoki 3 metrga sakraydi. U 10 metr masofani bosib o‘tishni xohlaydi. U bu ishni necha usulda amalga oshira oladi?

A) 55

B) 28

C) 30

D) 36

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21. tengsizlikning butun yechimlari yig‘indisini toping.

A) 18

B) 12

C) 20

D) 21

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22. Tenglamaning ildizlari yig‘indisini toping: [?] + {2?} = 2,5 (bu yerda, [?]⎯ ? sonining
butun qismi, {?}⎯ ? sonining kasr qismi, ya’ni {?} = ? − [?])

A) 3

B) 6

C) 5

D) 9

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23. ?₁ va ?₂ sonlari 2?² − 3? − 2 = 0 tenglamaning ildizlari, |?₁ − ?₂| ni toping.

A) 2

B) 3

C) 2.5

D) 3.5

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24. Raqamlari yig‘indisidan 12 marta katta bo‘lgan uch xonali sonlarni toping.