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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. stemadan ni toping.

A) 11/7

B) 7/3

C) 3/7

D) 7/11

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2. ABC uchburchakda O nuqta AD medianava BE bissektrisalar kesishishnuqtasi. AOEva BOD uchburchaklar yuzlari mos ravishda 1 va 3 ga teng bo`lsa, EOC uchburchakning yuzini toping.

A) 5

B) 4

C) 3

D) 2

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3. tengsizlikning butun yechimlari yig’indisini toping.

A) 9

B) 10

C) 7

D) 15

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4. Tenglamalar sistemasi nechta yechimga ega?

A) 8

B) 6

C) 12

D) 10

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5. 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) 16

C) 12

D) 18

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6. 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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A) -216

B) -6

C) -1

D) -36

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8. 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) 13

C) 22

D) 16

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9. tengsizlikning butun yechimlari yig‘indisini toping.

A) 20

B) 21

C) 18

D) 12

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

A) 2

B) 3

C) 3.5

D) 2.5

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

A) 0

B) 1.2

C) 1.8

D) 1

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

A) 268

B) 288

C) 294

D) 264

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13. 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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14. Hisoblang: bunda,

A) -49

B) -144

C) -100

D) -64

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

A) 48

B) 36

C) 64

D) 56

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

A) 169

B) 151

C) 159

D) 161

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

A) 12.6

B) 18.2

C) 9.8

D) 11.4

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18. 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) 30

D) 28

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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) 4

B) 5

C) 6

D) 3

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

A) 4.5

B) 3.5

C) 4

D) 4.8

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

A) 4

B) 3

C) 6

D) 5

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22. bo‘lsa, ? + ? ni toping.

A) 16

B) 12

C) 13

D) 11

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

A) 55

B) 45

C) 40

D) 50

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24. 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) 12

C) 15

D) 20

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25. Soddalashtiring: