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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!

1 / 30

1. Rombning diagonallari 6 va 8 ga teng bo‘lsa, uning tomonini toping.

A) 6

B) 3

C) 5

D) 8

2 / 30

2. Agar cheksiz kamayuvchi geometrik progressiyaning hadlari yig`indisi ga teng bo`lsa, uning hadlari kublari yig`indisining hadlari kvadratlari yig`indisiga nisbatini toping.

A) 2

B) 1

C) 4

D) 3

3 / 30

3. Agar biror oyda 5 ta payshanba bo’lsa, shu oyda … bo’la olmaydi.

A) 5 ta juma

B) 5 ta shanba

C) 5 ta seshanba

D) 5 ta yakshanba

4 / 30

4. a parametrining qanday qiymatlarida tenglama uchta ildizga ega bo‘ladi.

A) -6

B) 6

C) 4

D) 0

5 / 30

5. 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) 22

C) 18

D) 16

6 / 30

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

A) 60°

B) 30°

C) 45°

D) 50°

7 / 30

7. Hisoblang:

A) -5/4

B) -22/12

C) -11/6

D) -4/3

8 / 30

8. Agar bo'lsa, ning qiymatini toping.

A) 0

B) -4

C) 5

D) 6

9 / 30

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

A) 18

B) 12

C) 6

D) 9

10 / 30

10. 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) (1/3 ; 1,2)

D) (1/6 ; 1,1)

11 / 30

11. Hisoblang:

A) 5

B) -6

C) 0

D) 8

12 / 30

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

A) 148°

B) 124°

C) 132°

D) 144°

13 / 30

13. −16 ≤ 2(y − 7) ≤ 0 va −7 ≤ x ≤ 8 bo‘lsa, x² − y² ifodaning eng kichik qiymatini toping.

A) 0

B) 1

C) 2

D) 3

14 / 30

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

A) 25

B) 15

C) 10

D) 9

15 / 30

15. Soddalashtiring:

A) C

B) A

C) B

D) D

16 / 30

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

A) 84

B) 69

C) 90

D) 78

17 / 30

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

A) 7

B) 3

C) 5

D) 2

18 / 30

18. Soddalashtiring

A) 9

B) 5

C) 0

D) 6

19 / 30

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

12 ∆ 1 operatsiya natijasini toping.

A) 132

B) 136

C) 121

D) 125

20 / 30

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

A) 160°

B) 100°

C) 120°

D) 150°

21 / 30

21. Soddalashtiring:

A) D

B) A

C) C

D) B

22 / 30

22. 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 ; 1,1)

D) (1/6 ; 1,5)

23 / 30

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

A) 55

B) 81

C) 63

D) 95

24 / 30

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

A) 9

B) 8

C) 7

D) 10

25 / 30

25. 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) 25

C) 26

D) 27

26 / 30

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

A) 9

B) 10

C) 12

D) 7

27 / 30

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