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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. Uchburchakning perimetri 24 sm ga teng bo‘lib, uning tomonlari uzunliklari arifmetik progressiya tashkil etadi. Shu uchburchakning kichik tomoni 6 sm bo‘lsa, uchburchak turini aniqlang.

A) O’tkir burchakli

B) Bunday uchburchak yo’q

C) To‘g‘ri burchakli

D) O’tmas burchakli

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2. ABCD parallelogramda AB=10, AD=16. BC tomonga AE va DF bissektrisalar o`tkazilganbo`lib, ular G nuqtada kesishadi. E va F nuqtalar BC tomonda bo`lsa, AGD va FGE uchgburchaklar yuzalari nisbatini toping.

A) 64

B) 36

C) 16

D) 4

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3. x, y, z tub sonlar uchun xyz = 5(x + y + z) bo’lsa, x² + y² + z² ni hisoblang.

A) 55

B) 70

C) 68

D) 78

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4. Soddalashtiring:

A) IV

B) I

C) III

D) II

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5. tengsizlikning butun yechimlari yig‘indisini toping.

A) 18

B) 20

C) 21

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) 384

B) 376

C) 420

D) 424

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7. Yig‘indini toping:

A) 2023

B) 2021

C) 2022

D) 2020

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

A) 4.8

B) 4

C) 4.5

D) 3.5

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

A) 115

B) 120

C) 130

D) 125

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10. ?(?) = 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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11. Hisoblang: bunda,

A) -49

B) -64

C) -144

D) -100

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

A) 30°

B) 15°

C) 45°

D) 5°

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13. bo‘lsa, ? + ? ni toping.

A) 12

B) 16

C) 11

D) 13

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

A) 1.2

B) 0

C) 1

D) 1.8

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15. 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

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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) 12

C) 16

D) 18

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

A) 2.5

B) 2

C) 3

D) 3.5

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18. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 12

C) 10

D) 8

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19. 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) 55

C) 28

D) 36

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

A) 108

B) 109

C) 111

D) 150

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

A) 268

B) 294

C) 288

D) 264

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

A) 3

B) 5

C) 6

D) 9

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23. 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) 13

C) 18

D) 16

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

A) 64

B) 48

C) 56

D) 36

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