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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. Ifodaning eng kichik qiymatini toping:

A) 12

B) 4

C) -4

D) -12

2 / 30

2. Agar f(x) = (a + b − 4)x³+ 2x²+ (b − 3)x +6 juftfunksiyaberilganbo’lsa, f(b) ningqiymatini toping.

A) 27

B) 20

C) 24

D) 7

3 / 30

3. Massasi 228 g tuzli aralashma tarkibida 88,2% suv bor. Aralashma tarkibida 81% suv bo’lishi uchun qancha suvni bug’lantirish kerak?

A) 86,4

B) 72,4

C) 84,6

D) 76,4

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4. Agar ABC uchburchakning AB va AC tomonlarida M va N nuqtalar olinib, ular tomonlarni mos ravishda AM:BM=3:5 va AN:CN=4:5 kabi nisbatda bo’lsa, CM to’g’ri chiziq BN kesmani qanday nisbatda bo’ladi?

A) 4:3

B) 3:1

C) 5:3

D) 3:2

5 / 30

5. Kenguru oldinga 1 metrga yoki 3 metrga sakraydi. U 10 metr masofani bosib o‘tishni xohlaydi. U bu ishni necha usulda amalga oshira oladi?

A) 55

B) 30

C) 28

D) 36

6 / 30

6. Soddalashtiring:

A) A

B) B

C) D

D) C

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

A) 63

B) 95

C) 81

D) 55

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8. Soddalashtiring

A) 0

B) 6

C) 5

D) 9

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9. Agar bo'lsa, ning qiymatini toping.

A) 0

B) 5

C) -4

D) 6

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

A) 2

B) 1

C) 0

D) 3

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

A) 3

B) 7

C) 2

D) 5

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12. Hisoblang:

A) 5

B) 0

C) 8

D) -6

13 / 30

13. 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) 5

B) 2

C) 6

D) 9

14 / 30

14. 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) 16

C) 14

D) 18

15 / 30

15. Agar AB =12, BC =14, CD = 2 bo’lsa, aylana radiusini aniqlang.

A) 8

B) 10

C) 9

D) 11

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

A) (1/3 ; 1,2)

B) (0; 2,5)

C) (1/6 ; 1,5)

D) (1/6 ; 1,1)

17 / 30

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

A) 160°

B) 100°

C) 120°

D) 150°

18 / 30

18. 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) 9

C) 12

D) 10

19 / 30

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

12 ∆ 1 operatsiya natijasini toping.

A) 125

B) 132

C) 136

D) 121

20 / 30

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

A) 3

B) 2

C) 4

D) 1

21 / 30

21. Soddalashtiring:

A) B

B) A

C) C

D) D

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 ; 1,5)

D) (1/6 ; 1,1)

23 / 30

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

A) 84

B) 78

C) 90

D) 69

24 / 30

24. Chizmadagi uchburchaklar sonini toping.

A) 30

B) 28

C) 26

D) 24

25 / 30

25. Tenglamani yeching:

A) 0

B) 10/11

C) Ø

D) 29/220

26 / 30

26. 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°

27 / 30

27. 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

28 / 30

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

A) 45°

B) 30°

C) 50°

D) 60°

29 / 30

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

A) 7

B) 10

C) 9

D) 8

30 / 30

30. 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