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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. Abituriyentga 36 ta masala berildi. To‘g‘ri yechilgan har biriga 3 ball beriladi. Noto‘g‘risiga 2 ball chegiriladi. 88 ball to‘plashi uchun o‘quvchi nechta masalani to‘g‘ri yechishi kerak?

A) 34

B) 38

C) 32

D) 30

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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) 9

B) 4

C) 6

D) 12

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3. To’g’riburchakli uchburchakning o’tkir burchaklaridan chiquvchi medianalar √156 va √89 ga teng bo’lsa, uchburchak gipotenuzasini toping.

A) 14

B) 13

C) 12

D) 15

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

A) 15°

B) 5°

C) 30°

D) 45°

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

A) 4.5

B) 4.8

C) 3.5

D) 4

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6. Soddalashtiring:

A) IV

B) II

C) I

D) III

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

A) 40

B) 55

C) 50

D) 45

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

A) 4

B) 1.5

C) 2

D) 2.5

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10. Yig‘indini toping:

A) 2023

B) 2021

C) 2020

D) 2022

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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) √3

B) √2

C) √6

D) 2

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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) 4

D) 5

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13. bo‘lsa, ? + ? ni toping.

A) 13

B) 16

C) 11

D) 12

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

A) 0

B) 1.8

C) 1

D) 1.2

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15. 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) 16

C) 18

D) 13

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

A) 3

B) 5

C) 4

D) 6

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17. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 18.2

B) 9.8

C) 12.6

D) 11.4

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18. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 420

B) 384

C) 424

D) 376

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19. 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) 3

B) 6

C) 4

D) 5

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20.

A) -216

B) -1

C) -6

D) -36

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21. tengsizlikning butun yechimlari yig‘indisini toping.

A) 21

B) 18

C) 12

D) 20

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

A) 159

B) 161

C) 151

D) 169

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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. 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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25. 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) 22

B) 20

C) 15

D) 12