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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. Tenglamani yeching: |x+6|=|x+10|

A) 6

B) -6

C) -8

D) 4

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2. f(x) funksiyani toping.

A) (1-x)/(1+x)

B) 1/(1-x)

C) 1/x

D) (1+x)/(1-x)

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

A) 1000

B) 1

C) 1 000 000

D) 100 000

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4. bo‘lsa, ? + ? ni toping.

A) 11

B) 16

C) 13

D) 12

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

A) 109

B) 150

C) 108

D) 111

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6. Yig‘indini toping:

A) 2020

B) 2023

C) 2021

D) 2022

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

A) 2

B) 1.5

C) 2.5

D) 4

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8. 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) 800

C) 900

D) 950

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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) 15

B) 22

C) 20

D) 12

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10. 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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11.

A) -6

B) -216

C) -1

D) -36

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

A) 12.6

B) 18.2

C) 9.8

D) 11.4

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

A) 4

B) 5

C) 3

D) 6

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

A) 161

B) 151

C) 169

D) 159

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15. Hisoblang: bunda,

A) -100

B) -144

C) -49

D) -64

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

A) 30°

B) 5°

C) 15°

D) 45°

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17. tengsizlikning butun yechimlari yig‘indisini toping.

A) 18

B) 21

C) 12

D) 20

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

A) 4

B) 4.5

C) 3.5

D) 4.8

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

A) 5

B) 3

C) 6

D) 9

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

A) 130

B) 120

C) 115

D) 125

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

A) 1.8

B) 0

C) 1.2

D) 1

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22. 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) 12

B) 16

C) 18

D) 10

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23. 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) 36

C) 55

D) 28

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24. 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

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25. 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