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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. Tenglamaning natural sonlardagi yechimida ni toping:

A) 2

B) 5

C) 4

D) 3

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2. Funksiya berilgan. f(f(−1)) ni toping.

A) 18

B) 29

C) 15

D) 5

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3. n ∈ ? va bo’lsa, ? ning eng katta qiymatini toping.

A) 890

B) 790

C) 980

D) 680

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4. yig`indini toping.

A) 2

B) 1

C) 3

D) 4

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5. 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) 3

C) 5

D) 6

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6. Tenglamani yeching:

A) 29/220

B) Ø

C) 0

D) 10/11

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7. Soddalashtiring:

A) C

B) B

C) A

D) D

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8. 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) 6

B) 9

C) 2

D) 5

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9. Hisoblang:

A) 8

B) 5

C) 0

D) -6

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

A) 120°

B) 150°

C) 100°

D) 160°

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11. Hisoblang:

A) -4/3

B) -11/6

C) -22/12

D) -5/4

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12. Chizmadagi uchburchaklar sonini toping.

A) 30

B) 24

C) 26

D) 28

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13. 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) 14

D) 12

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14. Soddalashtiring:

A) B

B) C

C) A

D) D

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

A) (1/6 ; 1,1)

B) (0; 2,5)

C) (1/3 ; 1,2)

D) (1/6 ; 1,5)

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

A) 132°

B) 124°

C) 144°

D) 148°

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

A) 4

B) 2

C) 3

D) 1

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18. Soddalashtiring

A) 9

B) 5

C) 6

D) 0

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

A) 9

B) 7

C) 8

D) 10

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20. Soddalashtiring:

A) B

B) D

C) C

D) A

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

A) Barcha chorakdan o'tadi?

B) I,II,III

C) I, III, IV

D) II, III, IV

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22. Chizmada ∠AOD = 120∘, ∠BOD = 3∠AOB ?a ∠AOC = 2∠COD bo‘lsa, ∠BOC burchak nimaga teng?

A) 30°

B) 45°

C) 60°

D) 50°

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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) 28

B) 26

C) 27

D) 25

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24. Agar bo'lsa, ning qiymatini toping.

A) 0

B) 5

C) -4

D) 6

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25. 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) (1/3 ; 1,2)

D) (1/6 ; 1,5)

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26. 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) 2199

D) 2197

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