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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. Tarkibida 85% suv bo‘lgan 0,5 t sellyuloza qorishmasida 75% suv bo‘lgan qorishma olish uchun necha kg suvni bug‘lantirish kerak?

A) 400

B) 200

C) 100

D) 300

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

A) –sin40°

B) cos40°

C) –cos40°

D) sin40°

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3. olti xonali son 72 ga bo’linsa, ? + ? ni toping.

A) 15

B) 10

C) 13

D) 12

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

A) 850

B) 900

C) 800

D) 950

5 / 25

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) 16

B) 18

C) 10

D) 12

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6. 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) 2

D) √3

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

A) 6

B) 5

C) 4

D) 3

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8. Hisoblang: bunda,

A) -100

B) -144

C) -49

D) -64

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

A) 268

B) 288

C) 264

D) 294

10 / 25

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

A) 1.5

B) 4

C) 2

D) 2.5

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

A) 130

B) 115

C) 120

D) 125

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12. ?(?) = 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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13. bo‘lsa, ? + ? ni toping.

A) 13

B) 16

C) 11

D) 12

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

A) 151

B) 161

C) 169

D) 159

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

A) 3.5

B) 4.5

C) 4.8

D) 4

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

A) 64

B) 36

C) 48

D) 56

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

A) 3.5

B) 2.5

C) 2

D) 3

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18. tengsizlikning butun yechimlari yig‘indisini toping.

A) 21

B) 18

C) 20

D) 12

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

A) 109

B) 108

C) 111

D) 150

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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) 3

B) 2

C) 4

D) 5

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

A) 1.8

B) 1

C) 1.2

D) 0

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22. Soddalashtiring:

A) II

B) I

C) IV

D) III

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23. 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

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

A) 45°

B) 5°

C) 30°

D) 15°

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25. 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) 22

C) 18

D) 13