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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. To‘g‘ri burchakli uchburchakka ichki chizilgan aylana urinish nuqtasida gipotenuzani 5 va 12 ga teng kesmalarga ajratadi. Uchburchak yuzini toping

A) 48

B) 65

C) 35

D) 60

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2. Funksiya berilgan. f(f(−1)) ni toping.

A) 5

B) 29

C) 18

D) 15

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3. Agar biror oyda 5 ta payshanba bo’lsa, shu oyda … bo’la olmaydi.

A) 5 ta yakshanba

B) 5 ta seshanba

C) 5 ta shanba

D) 5 ta juma

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4. bo‘lsa, ? + ? ni toping.

A) 13

B) 12

C) 16

D) 11

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

A) 1

B) 0

C) 1.8

D) 1.2

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

A) 30°

B) 15°

C) 5°

D) 45°

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7. 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) 3

C) 5

D) 6

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8. 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) 12

C) 20

D) 22

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9. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 424

B) 420

C) 376

D) 384

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10. Tenglama butun sonlarda nechta yechimga ega? (? − 2021)² − ?² + 2? = 14

A) 4

B) 6

C) 5

D) 3

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

A) √6

B) √2

C) 2

D) √3

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12. Tenglamani yeching: (71² + 81²)(7² + 8²) = 1135² + ?²

A) 161

B) 169

C) 151

D) 159

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13. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 9.8

B) 11.4

C) 12.6

D) 18.2

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14. 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) 36

B) 30

C) 55

D) 28

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

A) 268

B) 288

C) 264

D) 294

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

A) 950

B) 900

C) 800

D) 850

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17. Aylanaga ichki chizilgan trapetsiyaning diagonallari o‘zaro perpendikulyar. Trapetsiya asoslari 1:7 nisbatda va perimetri 18 ga teng bo‘lsa, trapetsiya yuzini toping.

A) 13

B) 16

C) 18

D) 22

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

A) 50

B) 55

C) 45

D) 40

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20. Yig‘indini toping:

A) 2021

B) 2022

C) 2020

D) 2023

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21.

A) -36

B) -216

C) -6

D) -1

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

A) 150

B) 109

C) 111

D) 108

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23. Raqamlari joylashuvi kamayish tartibida bo‘ladigan nechta uch xonali natural son mavjud? (masalan, 983, 751,210)

A) 115

B) 130

C) 125

D) 120

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24. ABC uchburchak berilgan ∠B = 90°. AC va BC tomonlarida mos ravishda E va D nuqtalar shunday olinganki, bunda AE = EC, ∠ADB = ∠EDC. U holda CD: BD ni toping.

A) 5

B) 2

C) 3

D) 4

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

A) 2

B) 3.5

C) 2.5

D) 3