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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. 60⁰ li burchakka bir-biriga tashqaridan urinuvchi ikkita aylana ichki chizilgan. Kichik aylananing radiusi ga teng. Katta aylananing radiusini toping.

A) 3r

B) 4r

C) 5r

D) 2r

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2. Agar bo’lsa , x va y sonlarning ko’paytmasini toping.

A) 6

B) -2

C) -4

D) 8

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3. bo‘lsa, 3? + ? ni toping.

A) 5

B) 2,5

C) 7,5

D) 10

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

A) 22

B) 18

C) 13

D) 16

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5. 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) 850

C) 800

D) 900

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

A) 3.5

B) 2

C) 3

D) 2.5

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

A) 151

B) 159

C) 169

D) 161

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A) -1

B) -216

C) -36

D) -6

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

A) 4

B) 2

C) 1.5

D) 2.5

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11. 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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12. 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) 376

C) 420

D) 384

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13. Tenglamaning ildizlari yig‘indisini toping: [?] + {2?} = 2,5 (bu yerda, [?]⎯ ? sonining
butun qismi, {?}⎯ ? sonining kasr qismi, ya’ni {?} = ? − [?])

A) 5

B) 6

C) 9

D) 3

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14. tengsizlikning butun yechimlari yig‘indisini toping.

A) 18

B) 20

C) 12

D) 21

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

A) 30°

B) 15°

C) 5°

D) 45°

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16. 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) 18

C) 12

D) 16

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

A) 50

B) 45

C) 55

D) 40

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

A) 1

B) 0

C) 1.2

D) 1.8

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19. bo‘lsa, ? + ? ni toping.

A) 12

B) 16

C) 13

D) 11

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

A) 4.5

B) 3.5

C) 4.8

D) 4

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

A) 111

B) 108

C) 150

D) 109

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

A) 6

B) 4

C) 3

D) 5

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