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Matematika olimpiada Viloyat 2021-2022 o'quv yili

9-sinf Matematika olimpiada №3.1

InfoMaster

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. ni hisoblang.

A) 3

B) 4

C) -2

D) 2

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2. Bahodir o`zidagi 411 dona yong`oqni 4 ta bolaga bo`lib berdi. Agar Sanjar va O`ktamning olgan yong`oqlari soni 2 va 3 sonlariga to`g`ri proporsional ,O`ktam va Sohibning yong`oqlari 7 va 5 sonlariga teskari proporsional , Sanjar va G`anisherning yong`oqlari esa 9 va 4 sonlariga teskari proporsional ekanligi ma`lum bo`lsa, G`anisher nechta yong`oq olgan?

A) 135

B) 180

C) 126

D) 145

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3. ABC teng yonli uchburchakning AC asosida D nuqta olingan, bunda CD = 2 va CL bissektrisa (L ∈ AB) DL kesmaga perpendikulyar. AL ni toping.

A) 3

B) 2

C) 5

D) 1

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A) -216

B) -1

C) -6

D) -36

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5. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 420

B) 424

C) 376

D) 384

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6. Tenglamalar sistemasi nechta yechimga ega?

A) 12

B) 6

C) 10

D) 8

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

A) √6

B) √3

C) √2

D) 2

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

A) 161

B) 151

C) 159

D) 169

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

A) 1.2

B) 0

C) 1.8

D) 1

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

A) 2

B) 2.5

C) 3.5

D) 3

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11. bo‘lsa, ? + ? ni toping.

A) 12

B) 16

C) 11

D) 13

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12. Soddalashtiring:

A) II

B) IV

C) III

D) I

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

A) 4

B) 3.5

C) 4.8

D) 4.5

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

A) 294

B) 288

C) 264

D) 268

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15. Yig‘indini toping:

A) 2020

B) 2022

C) 2023

D) 2021

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16. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 11.4

B) 9.8

C) 18.2

D) 12.6

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

A) 13

B) 22

C) 18

D) 16

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

A) 2.5

B) 2

C) 1.5

D) 4

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

A) 5

B) 4

C) 6

D) 3

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

A) 45

B) 50

C) 55

D) 40

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21. 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) 15

C) 20

D) 12

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22. 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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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) 55

B) 28

C) 30

D) 36

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

A) 3

B) 6

C) 9

D) 5

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

A) 109

B) 108

C) 111

D) 150