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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) 100

B) 300

C) 200

D) 400

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2. ABCD trapetsiyaning yuzi 36 gateng, asoslari DC=6, AB=2. BC tomonidan E nuqta olingan bo’lib, BE=2EC bo’lsa, ADE uchbutchakning yuzini toping.

A) 14

B) 21

C) 16

D) 12

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3. ABC uchburchakda AL bissektrisa o’tkazildi. AB va BL kesmalarda E va D nuqtalar mos ravishda shunday olinganki, DL=LC, ED∥ AC. Agar
AE=15, AC=12 ekani ma’lum bo’lsa, ED kesma uzunligini toping.

A) 2

B) 4

C) 3

D) 5

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4. 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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5. 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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6. 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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7. 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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8. Hisoblang: bunda,

A) -144

B) -49

C) -64

D) -100

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

A) 64

B) 56

C) 36

D) 48

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

A) 3

B) 4

C) 5

D) 6

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11. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 9.8

B) 12.6

C) 11.4

D) 18.2

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12. Soddalashtiring:

A) II

B) III

C) IV

D) I

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

A) 2

B) √3

C) √6

D) √2

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14.

A) -1

B) -6

C) -216

D) -36

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

A) 3

B) 5

C) 9

D) 6

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

A) 111

B) 150

C) 108

D) 109

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

A) 40

B) 50

C) 45

D) 55

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

A) 15°

B) 30°

C) 5°

D) 45°

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19. bo‘lsa, ? + ? ni toping.

A) 11

B) 12

C) 16

D) 13

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

A) 4.5

B) 4

C) 3.5

D) 4.8

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22. tengsizlikning butun yechimlari yig‘indisini toping.

A) 20

B) 21

C) 12

D) 18

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23. 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) 950

D) 900

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24. Yig‘indini toping:

A) 2021

B) 2020

C) 2023

D) 2022

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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) 5

D) 4