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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. Geometrik progressiyada dastlabki to‘rtta hadlari mos ravishda 6; 24; 96; bo‘lsa, ni toping.

A) 22

B) 15

C) 16

D) 14

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2. Hisoblang: cos 10^o− 2 cos 50^o− cos 70^o

A) –cos40°

B) cos40°

C) –sin40°

D) sin40°

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3. Тенгламани ечинг: ((0,001 ∙ ? + 2): 0,3) ∙ 0,01 − 11,2 = 22,2

A) 1 000 000

B) 1

C) 100 000

D) 1000

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

A) 5°

B) 30°

C) 45°

D) 15°

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5. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 6

C) 8

D) 12

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6. bo‘lsa, ? + ? ni toping.

A) 12

B) 13

C) 16

D) 11

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7. Hisoblang: bunda,

A) -49

B) -144

C) -64

D) -100

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8. 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) 6

C) 5

D) 3

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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) 2

B) 3

C) 4

D) 5

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10. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 424

B) 384

C) 420

D) 376

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

A) 130

B) 125

C) 115

D) 120

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12. 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) 30

B) 28

C) 55

D) 36

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13. 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) 12

C) 18

D) 16

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

A) 950

B) 900

C) 850

D) 800

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

A) 45

B) 55

C) 50

D) 40

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

A) 6

B) 4

C) 5

D) 3

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

A) 161

B) 169

C) 151

D) 159

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

A) 16

B) 13

C) 18

D) 22

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