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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. Tenglamani yeching: |x+6|=|x+10|

A) 4

B) -8

C) 6

D) -6

2 / 30

2. x₀soni tenglamani ildizi bo`lsa, x²₀ -64 ni toping.

A) 20/69

B) -48

C) 8

D) 0

3 / 30

3. ABC uchburchakda AL bissektrisa o’tkazildi. AB va BL kesmalarda E va D nuqtalar mos ravishda shunday olinganki, DL=LC, ED∥ AC. Agar
AE=15, AC=12 ekani ma’lum bo’lsa, ED kesma uzunligini toping.

A) 5

B) 3

C) 4

D) 2

4 / 30

4. Uchburchakning tomonlari lardan iborat bo‘lgan uchburchak yuzini toping.

A) 4

B) 2

C) 3

D) 1

5 / 30

5. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 376

B) 420

C) 384

D) 424

6 / 30

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

A) 120°

B) 100°

C) 150°

D) 160°

7 / 30

7. 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) 2

C) 5

D) 9

8 / 30

8. Chizmadagi uchburchaklar sonini toping.

A) 26

B) 30

C) 24

D) 28

9 / 30

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

A) 3

B) 7

C) 5

D) 2

10 / 30

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

A) 30°

B) 60°

C) 45°

D) 50°

11 / 30

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

A) 9

B) 6

C) 18

D) 12

12 / 30

12. Soddalashtiring

A) 6

B) 9

C) 5

D) 0

13 / 30

13. 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

14 / 30

14. Hisoblang:

A) -6

B) 0

C) 5

D) 8

15 / 30

15. 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)

16 / 30

16. Soddalashtiring:

A) B

B) D

C) A

D) C

17 / 30

17. Soddalashtiring:

A) C

B) B

C) D

D) A

18 / 30

18. 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

19 / 30

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

A) 63

B) 81

C) 95

D) 55

20 / 30

20. Agar bo'lsa, ning qiymatini toping.

A) -4

B) 6

C) 5

D) 0

21 / 30

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

A) 0

B) 1

C) 3

D) 2

22 / 30

22. 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) 2197

D) 2198

23 / 30

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

12 ∆ 1 operatsiya natijasini toping.

A) 132

B) 125

C) 136

D) 121

24 / 30

24. Tenglamani yeching:

A) Ø

B) 10/11

C) 0

D) 29/220

25 / 30

25. −16 ≤ 2(y − 7) ≤ 0 va −7 ≤ x ≤ 8 bo‘lsa, x² − y² ifodaning eng kichik qiymatini toping.

A) 0

B) 1

C) 3

D) 2

26 / 30

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

A) 12

B) 18

C) 16

D) 14

27 / 30

27. Soddalashtiring:

A) B

B) D

C) C

D) A

28 / 30

28. 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

29 / 30

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

A) 78

B) 69

C) 90

D) 84

30 / 30

30. 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) 27

B) 26

C) 28

D) 25