9-sinf Matematika olimpiada №3.1

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2021-2022 o'quv yil viloyat bosqichida tushgan savollar.

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1. Teng yonli trapetsiyaning diagonali uni ikkita teng yonli uchburchakka ajratadi. Trapetsiyaning burchaklarini toping.

1. $82^{0},98^{0}$

2. $135^{0},45^{0}$

3. $100^{0},80^{0}$

4. $72^{0},108^{0}$

A) 4

B) 1

C) 2

D) 3

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2. ABC uchburchakning AB tomonidan M va N nuqtalar shunday tanlab olinganki, BN=NM=MA. AC tomonidan K va L nuqtalar shunday tanlab olindiki AK=3KL=1,5LC bo'ldi. S_MNLK: S_MNLK=?

A) 2

B) 3

C) 0,5

D) 1

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3. Hisoblang

A) 18

B) 11

C) 16

D) 15

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

A) 159

B) 151

C) 161

D) 169

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

A) 56

B) 36

C) 48

D) 64

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6. 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) 12

C) 22

D) 15

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7. Hisoblang: bunda,

A) -100

B) -144

C) -49

D) -64

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8. Yig‘indini toping:

A) 2022

B) 2023

C) 2020

D) 2021

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A) -216

B) -36

C) -1

D) -6

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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. 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) 36

C) 30

D) 55

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

A) 1

B) 0

C) 1.8

D) 1.2

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

A) 1.5

B) 2.5

C) 4

D) 2

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14. 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) 16

B) 18

C) 10

D) 12

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15. 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) 16

C) 22

D) 18

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

A) 18.2

B) 11.4

C) 9.8

D) 12.6

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

A) 3.5

B) 3

C) 2.5

D) 2

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

A) 111

B) 108

C) 109

D) 150

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

A) 5°

B) 30°

C) 15°

D) 45°

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

A) 264

B) 288

C) 294

D) 268

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

A) 4

B) 3

C) 6

D) 5

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24. Soddalashtiring:

A) III

B) I

C) IV

D) II

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25. 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) 5

C) 3

D) 6

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