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Matematika olimpiada Tuman 2022-2023 o'quv yili

9-sinf Matematika olimpiada №4

InfoMaster

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!

1 / 30

1. Ifodaning eng kichik qiymatini toping:

A) -4

B) 12

C) -12

D) 4

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2. f(x) funksiyani toping.

A) 1/x

B) (1-x)/(1+x)

C) 1/(1-x)

D) (1+x)/(1-x)

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3. bo‘lsa, 3? + ? ni toping.

A) 5

B) 7,5

C) 10

D) 2,5

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4. Mahsulot narxi ketma-ket ikki marta bir xil foizga oshirilgandan so’ng dastlabki narxidan 90,44% ga oshdi.Mahsulot narxi har safar necha foizga oshgan?

A) 40 %

B) 39 %

C) 38 %

D) 37 %

5 / 30

5. 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) 18

D) 16

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6. Soddalashtiring

A) 9

B) 5

C) 0

D) 6

7 / 30

7. Tenglamani yeching:

A) 29/220

B) Ø

C) 10/11

D) 0

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8. Agar ac < 0 bo‘lsa, y=ax-bx²-c funksiya grafigi koordinatalar tekisligining qaysi choraklaridan o‘tadi?

A) I, III, IV

B) II, III, IV

C) Barcha chorakdan o'tadi?

D) I,II,III

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9. Chizmadagi uchburchaklar sonini toping.

A) 28

B) 26

C) 30

D) 24

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10. Soddalashtiring:

A) A

B) D

C) C

D) B

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

A) 18

B) 9

C) 12

D) 6

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12. 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) 2

C) 5

D) 6

13 / 30

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

12 ∆ 1 operatsiya natijasini toping.

A) 125

B) 136

C) 121

D) 132

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14. f(x)=ax+b funksiya grafigi A(-1;3) va B(1;7) nuqtalar orqali o‘tadi. f(4- f( -1)) ni toping

A) 10

B) 7

C) 9

D) 12

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

A) (1/6 ; 1,5)

B) (0; 2,5)

C) (1/3 ; 1,2)

D) (1/6 ; 1,1)

16 / 30

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

A) 2

B) 7

C) 3

D) 5

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

A) 78

B) 69

C) 90

D) 84

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

A) 100°

B) 160°

C) 120°

D) 150°

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19. −16 ≤ 2(y − 7) ≤ 0 va −7 ≤ x ≤ 8 bo‘lsa, x² − y² ifodaning eng kichik qiymatini toping.

A) 3

B) 2

C) 1

D) 0

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

A) 1

B) 0

C) 3

D) 2

21 / 30

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

A) (1/6 ; 1,1)

B) (0; 2,5)

C) (1/3 ; 1,2)

D) (1/6 ; 1,5)

22 / 30

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

A) 9

B) 25

C) 10

D) 15

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23. Hisoblang:

A) 8

B) 5

C) 0

D) -6

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24. Soddalashtiring:

A) A

B) B

C) C

D) D

25 / 30

25. Hisoblang:

A) -4/3

B) -11/6

C) -5/4

D) -22/12

26 / 30

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

A) 10

B) 9

C) 8

D) 7

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

A) 124°

B) 132°

C) 144°

D) 148°

28 / 30

28. Anvar 2 dan boshlab barcha natural sonlarni doskaga yozdi. U yozayotganda to‘la kub bo‘lgan sonlarni qoldirib ketdi (8, 125 kabi). Doskaga 2186-o‘rinda yozilgan sonni toping.

A) 2200

B) 2198

C) 2197

D) 2199

29 / 30

29. Agar bo'lsa, ning qiymatini toping.