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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. Tenglamaning natural sonlardagi yechimida ni toping:

A) 3

B) 4

C) 2

D) 5

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2. Sonlarni o`sish tartibida yozing.

A) a

B) c

C) c

D) b

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3. А punktdan В punktga qarab yuk poyezdi yo‘lga chiqdi. Oradan 3 soat o‘tgandan keyin, uning ortidan tezligi yuk poyezdi tezligidan 40 km/soat ortiq bo‘lgan yo‘lovchi poyezdi yo‘lga chiqdi. Yuk poyezdi yo‘lga chiqqanidan 15 soat o‘tib yo‘lovchi poyezdi yuk poyezdidan 300 km oldinda ekani ma’lum bo‘ldi. Yuk poyezdining tezligini toping.

A) 60 km/soat

B) 80 km/soat

C) 100 km/soat

D) 50 km/soat

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

A) 15°

B) 30°

C) 5°

D) 45°

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

A) 1.5

B) 2

C) 4

D) 2.5

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6. 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) 20

B) 15

C) 22

D) 12

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

A) 3.5

B) 2.5

C) 3

D) 2

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8. 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) 12

C) 10

D) 18

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

A) 115

B) 125

C) 130

D) 120

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

A) 36

B) 64

C) 56

D) 48

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

A) 5

B) 4

C) 6

D) 3

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12. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 12

C) 8

D) 6

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13. Hisoblang: bunda,

A) -64

B) -100

C) -49

D) -144

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14. 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) 6

B) 5

C) 3

D) 4

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

A) 4.8

B) 4.5

C) 4

D) 3.5

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16. tengsizlikning butun yechimlari yig‘indisini toping.

A) 20

B) 18

C) 21

D) 12

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

A) 288

B) 268

C) 264

D) 294

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18. bo‘lsa, ? + ? ni toping.

A) 13

B) 12

C) 16

D) 11

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19. 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) 4

C) 2

D) 5

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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) 18

C) 22

D) 13

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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. Soddalashtiring: