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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. bo‘lsa, ifodaning qiymatini toping

A) 2/3

B) 13/16

C) 15/16

D) 3/16

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2. Birinchi quvurdan ikkinchi quvurga qaraganda ikki barobar ko’p suv oqadi.Ikkalasi birgalikda bo’sh hovuzni 12 soatda to’ldiradi.Birinchi quvur hovuzning uchdan bir qismini necha soatda to’ldiradi?

A) 12

B) 4

C) 9

D) 6

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3. bo‘lsa, 3? + ? ni toping.

A) 10

B) 5

C) 7,5

D) 2,5

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4. 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) 36

C) 28

D) 30

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

A) 6

B) 3

C) 4

D) 5

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

A) 11.4

B) 9.8

C) 12.6

D) 18.2

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

A) 30°

B) 45°

C) 15°

D) 5°

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

A) 150

B) 109

C) 108

D) 111

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9. 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) 3

B) 4

C) 5

D) 2

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10. bo‘lsa, ? + ? ni toping.

A) 11

B) 12

C) 13

D) 16

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

A) 50

B) 40

C) 45

D) 55

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

A) 294

B) 288

C) 264

D) 268

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

A) 3.5

B) 3

C) 2.5

D) 2

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14.

A) -6

B) -216

C) -1

D) -36

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15. 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) √3

D) 2

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16. Soddalashtiring:

A) III

B) IV

C) II

D) I

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17. Tenglamalar sistemasi nechta yechimga ega?

A) 12

B) 8

C) 6

D) 10

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

A) 151

B) 161

C) 159

D) 169

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

A) 130

B) 120

C) 115

D) 125

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20. 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) 12

B) 20

C) 15

D) 22

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

A) 4

B) 4.5

C) 3.5

D) 4.8

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

A) 18

B) 16

C) 22

D) 13

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

A) 6

B) 3

C) 9

D) 5

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24. 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) 10

B) 18

C) 16

D) 12

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25. tengsizlikning butun yechimlari yig‘indisini toping.