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Matematika olimpiada Tuman 2022-2023 o'quv yili

9-sinf Matematika olimpiada №4

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Avgust 19, 2024

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9-sinf Matematika olimpiada №4

2022-yil 12-oktabr:

2022-2023 o'quv yili tuman bosqichida tushgan savollar!

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1. Ifodaning eng kichik qiymatini toping:

A) -4

B) 4

C) 12

D) -12

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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) 12

B) 16

C) 14

D) 21

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3. ?, ? natural sonlari uchun 3? + 2? soni 11 ga qoldiqsiz bo‘linadi. u holda quyidagi sonlardan qaysi biri 11 ga qoldiqsiz bo’linmasligi mumkin?

A) 8(10? + 3?)

B) 58? + 90?

C) 47? + 34?

D) 14? + 13b

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4. yig`indini 2012 ga bo‘lgandagi qoldiqni toping.

A) 3

B) 0

C) 2

D) 1

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5. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 9.8

B) 18.2

C) 11.4

D) 12.6

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6. Soddalashtiring:

A) B

B) D

C) C

D) A

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7. Ikki son o’rtasidagi ∆ operatsiyasiga ko‘ra quyidagi natijalar olindi:

12 ∆ 1 operatsiya natijasini toping.

A) 132

B) 125

C) 136

D) 121

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8. a parametrning qanday qiymatlarida 9 + 3a, 5 − 2a va 15 − 5a uzunlikdagi kesmalardan uchburchak
yashash mumkin?

A) (0; 2,5)

B) (1/6 ; 1,1)

C) (1/6 ; 1,5)

D) (1/3 ; 1,2)

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9. Agar 3x − y = 7 va 5x + 4y = 21 bo‘lsa, 24x + 9y ni hisoblang.

A) 90

B) 78

C) 84

D) 69

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10. x₀haqiqiy son x³ +1 = (x² − x −1)² − 4 tenglama ildizi bo‘lsa, (x₀ − 1)² ni toping.

A) 5

B) 7

C) 3

D) 2

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11. a parametrning qanday qiymatlarida 9 + 3a, 5 − 2a va 15 − 5a uzunlikdagi kesmalardan uchburchak
yashash mumkin?

A) (1/6 ; 1,1)

B) (1/3 ; 1,2)

C) (1/6 ; 1,5)

D) (0; 2,5)

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12. Uchlari A(2; −3), B(6; 0), C(6; 2) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping.

A) 16

B) 18

C) 12

D) 14

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13. a = 0,12(12), ? = 0,1(21), c = 0,12(11). Agar a+ b+ c= 0, x₁x₂x₃x₄... x₂₀₂₁x₂₀₂₂x_2023...bo‘lsa, x₂₀₂₂ni toping (bunda, x₁, x₂... raqamlar).

A) 9

B) 6

C) 5

D) 2

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14. ABC uchburchakning AE va BF medianalari P nuqtada kesishadi. Agar ABC uchburchak yuzi 36 bo‘lsa, PEСF to‘rtburchak yuzini toping.

A) 9

B) 12

C) 6

D) 18

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15. Raqamlari yig‘indisi 2 ga teng bo‘lgan o‘n xonali natural sonlar nechta?

A) 25

B) 10

C) 15

D) 9

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16. Soddalashtiring:

A) A

B) C

C) D

D) B

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17. ABCD to‘rtburchakda: AB=CD, BC= AD. Agar A burchak B burchakdan 4 marta katta bo‘lsa, to‘rtburchakning A burchagini toping.

A) 144°

B) 124°

C) 148°

D) 132°

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18. Hisoblang:

A) 8

B) 5

C) 0

D) -6

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19. Soddalashtiring

A) 9

B) 6

C) 0

D) 5

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20. Ikkinchi raqami uchinchi raqamidan 4 marta katta, birinchi raqami esa ikkinchi raqamidan 3 ta kam bo‘lgan uch xonali sonlar nechta?

A) 4

B) 3

C) 1

D) 2

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21. Chizmadagi uchburchaklar sonini toping.

A) 24

B) 26

C) 30

D) 28

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22. −16 ≤ 2(y − 7) ≤ 0 va −7 ≤ x ≤ 8 bo‘lsa, x² − y² ifodaning eng kichik qiymatini toping.

A) 0

B) 2

C) 1

D) 3

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23. Hisoblang:

A) -11/6

B) -22/12

C) -4/3

D) -5/4

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24. tengsizlikning (−5; 5) oraliqda nechta butun yechimi mavjud?

A) 8

B) 7

C) 10

D) 9

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25. Soddalashtiring:

A) D

B) B

C) C

D) A

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26. Agar a + b − 2c = 0 bo’lsa, ni hisoblang.

A) 2

B) 3

C) 1

D) 0

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27. Oila erkak kishi, uning ayoli va talaba qizidan iborat. Agar erkak kishining maoshi 2 barobar oshsa, u holda oila daromadi 67%ga ortadi, agar talaba qizning stipendiyasi 3 barobar kamaysa, oila daromadi 4%ga qisqaradi. Ayolning maoshi oila daromadining necha foizni tashkil qiladi?

A) 28

B) 26

C) 25

D) 27

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28. Soat strelkasi 5 soat vaqt o‘tgandan keyin qanday burchakka buriladi?

A) 150°

B) 160°

C) 100°

D) 120°

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29. Tenglamani yeching: