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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. ifodani a=4, b=5 bo‘lgandagi qiymatini toping.

A) 2

B) 1

C) 0

D) -1

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2. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 30

B) 48

C) 39

D) 33

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3. Massasi 228 g tuzli aralashma tarkibida 88,2% suv bor. Aralashma tarkibida 81% suv bo’lishi uchun qancha suvni bug’lantirish kerak?

A) 86,4

B) 72,4

C) 76,4

D) 84,6

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

A) 2.5

B) 3.5

C) 2

D) 3

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5. Dastlab tarvuzning 99% i suv edi, quritilgandan so‘ng esa 98% suv bo‘ldi. Tarvuzning massasi necha marta kamaydi?

A) 2.5

B) 2

C) 1.5

D) 4

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6. bo‘lsa, ? + ? ni toping.

A) 16

B) 12

C) 11

D) 13

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7. 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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A) -6

B) -1

C) -216

D) -36

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9. 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) 28

B) 30

C) 55

D) 36

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10. Yig‘indini toping:

A) 2023

B) 2020

C) 2021

D) 2022

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

A) 40

B) 55

C) 45

D) 50

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12. 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) 2

B) 3

C) 5

D) 4

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

A) 22

B) 18

C) 16

D) 13

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

A) 108

B) 150

C) 109

D) 111

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15. Soddalashtiring:

A) II

B) I

C) IV

D) III

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

A) 15°

B) 5°

C) 30°

D) 45°

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17. 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) √2

C) √6

D) √3

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

A) 3

B) 5

C) 4

D) 6

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19. Hisoblang: bunda,

A) -100

B) -49

C) -64

D) -144

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

A) 1.8

B) 1

C) 1.2

D) 0

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21. Teng yonli trapetsiyaning asoslari 6 va 10 ga, diagonali 10 ga teng. Trapetsiya yuzini
toping.

A) 64

B) 36

C) 48

D) 56

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

A) 6

B) 5

C) 9

D) 3

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

A) 120

B) 115

C) 125

D) 130

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