9-sinf Matematika olimpiada №3.1

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1. stemadan ni toping.

A) 11/7

B) 3/7

C) 7/3

D) 7/11

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2. Agar arifmetik progressiyada bo`lsa, ayirmani toping.

A) 4

B) 1

C) 3

D) 2

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3. Teng yonli ABC (AC=BC) uchburchakning AC tomonida D nuqta olingan. K - BD kesma va AH balandlik kesishgan nuqta. Agar AD=AK bo‘lsa, u holda DBA burchakni toping.

A) 75°

B) 60°

C) 45°

D) 30°

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

A) 3.5

B) 4.5

C) 4

D) 4.8

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

A) 6

B) 5

C) 3

D) 9

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6. 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) 28

B) 30

C) 36

D) 55

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7. bo‘lsa, ? + ? ni toping.

A) 16

B) 11

C) 13

D) 12

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

A) 3

B) 5

C) 4

D) 6

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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) 12

B) 15

C) 22

D) 20

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10. 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) 900

D) 800

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

A) 264

B) 288

C) 268

D) 294

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12. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 12.6

B) 9.8

C) 11.4

D) 18.2

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13. tengsizlikning butun yechimlari yig‘indisini toping.

A) 20

B) 18

C) 12

D) 21

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14. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 10

C) 12

D) 8

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

A) 169

B) 159

C) 161

D) 151

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

A) 2.5

B) 3.5

C) 2

D) 3

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17. 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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18.

A) -36

B) -1

C) -216

D) -6

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19. 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) 10

C) 16

D) 12

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

A) 1

B) 1.8

C) 0

D) 1.2

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21. 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) 6

C) 4

D) 3

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22. Aylanaga tashqi chizilgan ABCD teng yonli trapetsiyaning yuzi √3 ga teng. Agar ВС : AD = 1 : 3 bo‘lsa, trapetsiyaning АВ yon tomonini toping.

A) √3

B) 2

C) √6

D) √2

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23. Hisoblang: bunda,

A) -144

B) -49

C) -64

D) -100

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24. Soddalashtiring:

A) II

B) IV

C) I

D) III

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25. 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) 2.5

D) 4

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