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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. Hisoblang:

A) 1

B) 1,5

C) 0,5

D) 5

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2. tengsizlikni yeching.

A) xℇR

B) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

C) (-∞;3)∪(3;∞)

D) (-∞;-1/2)∪(-1/2;∞)

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3. Baliq og‘irliklari 14:12:11:8:15 kabi nisbatda bo‘lgan besh bo‘lakka bo‘lindi. Ikkinchi bo‘lakning og‘irligi 1,12 kg bo‘lsa, butun baliqning og‘irligini qancha?

A) 5,6 kg

B) 4,48 kg

C) 6,72 kg

D) 6,4 kg

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4. Agar $f(x)=(a+b-4)\cdot x^{2}+2x^{2}+(b-2)x$ juft funksiya bo’lsa, $f(a)$ ning qiymatini toping.

1. $a^{3}-2a^{2}+a^{2}b+ab-2a$

2.ab-2a+ba

3. $a^{2}+2a^{2}+a^{2}b+ab-2a$

4.a-b+2a-3b

A) 4

B) 2

C) 3

D) 1

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5. bo‘lsa, ? + ? ni toping.

A) 11

B) 13

C) 16

D) 12

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

A) 5

B) 2

C) 7

D) 3

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

A) 7

B) 10

C) 12

D) 9

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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 ; 1,5)

C) (1/6 ; 1,1)

D) (1/3 ; 1,2)

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9. Ikkinchi raqami uchinchi raqamidan 1 ta kam bo‘lgan uch xonali sonlar sonini toping.

A) 63

B) 55

C) 81

D) 95

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10. Soddalashtiring:

A) D

B) C

C) A

D) B

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11. Soddalashtiring:

A) D

B) B

C) A

D) C

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12. Hisoblang:

A) -6

B) 0

C) 5

D) 8

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13. Agar bo'lsa, ning qiymatini toping.

A) 5

B) 0

C) 6

D) -4

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

A) 69

B) 78

C) 84

D) 90

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15. −16 ≤ 2(y − 7) ≤ 0 va −7 ≤ x ≤ 8 bo‘lsa, x² − y² ifodaning eng kichik qiymatini toping.

A) 1

B) 3

C) 0

D) 2

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

A) 2

B) 1

C) 4

D) 3

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17. Chizmadagi uchburchaklar sonini toping.

A) 24

B) 28

C) 26

D) 30

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

A) (0; 2,5)

B) (1/3 ; 1,2)

C) (1/6 ; 1,5)

D) (1/6 ; 1,1)

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19. 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) 2

B) 6

C) 9

D) 5

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20. 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) 12

C) 18

D) 14

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21. Soddalashtiring:

A) B

B) A

C) D

D) C

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

A) 120°

B) 150°

C) 160°

D) 100°

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23. 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) 25

B) 26

C) 27

D) 28

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

A) 3

B) 2

C) 0

D) 1

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

12 ∆ 1 operatsiya natijasini toping.

A) 121

B) 132

C) 136

D) 125

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

A) 8

B) 7

C) 9

D) 10

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27. 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) 2199

B) 2200

C) 2198

D) 2197

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28. Tenglamani yeching: