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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. Ifodaning eng kichik qiymatini toping:

A) -12

B) -4

C) 12

D) 4

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2. x₀soni tenglamani ildizi bo`lsa, x²₀ -64 ni toping.

A) 20/69

B) -48

C) 0

D) 8

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3. n ∈ ? va bo’lsa, ? ning eng katta qiymatini toping.

A) 790

B) 980

C) 680

D) 890

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

A) 4

B) 3.5

C) 4.8

D) 4.5

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

A) 45°

B) 5°

C) 15°

D) 30°

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6. 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) 18

B) 16

C) 10

D) 12

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7. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 18.2

B) 12.6

C) 11.4

D) 9.8

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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) 13

B) 18

C) 16

D) 22

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

A) 130

B) 120

C) 125

D) 115

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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) √3

C) √2

D) 2

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12. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 384

B) 376

C) 424

D) 420

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

A) 264

B) 288

C) 294

D) 268

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

A) 36

B) 48

C) 56

D) 64

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15. 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) 5

B) 4

C) 3

D) 6

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

A) 45

B) 50

C) 40

D) 55

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

A) 108

B) 111

C) 150

D) 109

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18. bo‘lsa, ? + ? ni toping.

A) 16

B) 11

C) 13

D) 12

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

A) 169

B) 159

C) 161

D) 151

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20. 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) 3

C) 4

D) 2

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