9 sinf Matematika fanidan olimpiada test savollari

9 sinf Matematika fanidan olimpiada test savollari

1. 
   Parabolaning koordinata o’qlari bilan kesishish nuqtalarining muqtalarining koordinatalarini toping? y = -x²-4x+5
   
   1. 
      (-1;2)
      
   2. 
      (2,-1)
      
   3. 
      (-5,0)
      
   4. 
      (0,-5)
      

E) (0,0)

2. 
   Parabola uchini koordunatalarini toping? y=x²+6x+5
   
   1. 
      (3,-4)
      
   2. 
      (-5.-1)
      
   3. 
      (3,4)
      
   4. 
      (-3,-4)
      
   5. 
      (2,3)
      
3. 
   T englamalar sistemasini yeching? √x- √y=1
   

x-y=5

A) (16;9) B) (9;4) C) (7;2) D) (10;5) E) (5,7)

4. (a-b)/a=4 ekanligi ma’lum bo’lsa, (6a+5b)/b ni toping?

A)5 B)-4 C)-2 D)3 E) 2

5. ABCD to’g’ri to’rtburchakning AB tomoni BC tomonidan 2 marta qisqa. Agar K nuqta BC

tomonning o’rtasida yotsa, AKD burchakni toping?

A) 45⁰ B)60⁰ C) 90⁰ D) 75⁰ E)55⁰

6. trapetsiya asoslari 6sm va 9sm balandligi 10 sm trapetsiya diagnallarini kesishish nuqtasidan

asosigacha bo’lgan masofani toping,

A) 3va7 B) 2va 8 C) 4 va 6 D) 20 va 10 E) 6va8

7, Kvadrat funksiyaga taaluqli bo’lgan qaysi tushunchalar noto’g’ri berilgan,

A) y=ax²+bx+c ko’rinishdagi funksiya kvadrat funksiya deyiladi, bunda a≠0,b,c sonlar

B) y=ax²+bx+c ko’rinishdagi funksiya grafigi paraboladan iborat bo’ladi.

C) y=ax²+bx+c ko’rinishdagi funksiya grafigi har doim koordinata boshidan o’tadi.

D y=ax²+bx+c ko’rinishdagi funksiya a>0bo’lsa parabola tarmoqlari yuqoriga a<0 bo’lsa parabola

tarmoqlari pastga yo’nalgan bo’ladi.

E) to’g’ri javob berilmagan

8. m va a ning qanday qiymatlarida (x²-3x+m)/(x+a)=x-5 kasr togri qisqartirilgan?

A) -6,-1 B)-5,1 C) 10,-2 D)-10,2 E) -5,4

9. Ikkita o’xshash ko’pburchaklar uchun qaysi jumla noto’g’ri?

A) yuzalarini nisbati o’xshashlik koyfissentiga teng

B) ularning burchaklari soni teng

C) mos tomonlari proporsional

D) ularning tomonlari soni teng

E) xammasi to’g’ri

10. K ning shunday qiymatini topingki y=-x² parabola bilan y=kx-5 to’g’ri chiziq kesishish nuqtalarida

X=2 bo’lsin.

A) 2 B) 1/2 C) -1/2 D) -2 E) 3

11. x²+(9/x)=5(x-(3/x)) tenglamani butun yechimlari yig’indisini toping?

A) 5 B) 3 C) 2 D)9 E) 1

12. Absissalar o’qini x=-1 va x=3 nuqtalarda ordinatalar o’qini esa y=3 nuqtada kesib o’tuvchi parabola

tenglamasini ko’rsating

A) y=x²+2x+1 B) y= x²+2x+3 C) y=- x²+2x+3 D) y=- x²+2x+1 E) y=x²-3x+3
13. Quyidagi funksiyalardan qaysi biri kvadrat funksiya emas?

1. y=2x+1 2. y=2x²+3 3. y=2x³+3

A) 1 va 3 B) 2 va 3 C) 1 va 2 D) barchasi E) hech qaysisi

14. Parabola qaysi chorakda joylashgan? Y=-x²+5x

A) 1,3,4 B) 1,2,3 C) 2,3,4 D) 1,2,3,4 E)1,4,2

15. 4x²-16≤0 tengsizlikni yeching.

A) -4≤x≤0 B) 0≤x≤4 C)-4≤x≤4 D) -2≤x≤2 E) -1≤x≤1

16. a va b parallel to’g’ri chiziqlarni c kesuvchi kesib o’tganda hosil bo’lgan ichki bir tomonli

burchaklarni ayrimasi 24⁰ ga teng. Shu burchaklarni kattasini toping?

A) 114⁰ B)112⁰ C) 102⁰ D) 120⁰ E) 140⁰

17. to’g’ri to’rtburchakning bo’yi 3,8 sm eni bo’yidan 1,3 sm qisqa uning yuzini toping?

A) 3,25sm² B) 4,84sm ² C) 9,5sm² D) 8,5sm² E) 7,5sm²

18. Aylananig radiusi 6sm ga teng. Aylanaga ichki chizilgan mutazam uchburchakning yuzini toping?

A) 27 B) 27√2 C) 27√3 D) 18√5 E) 18√3 E) 35

19. Uzunliklari 10 va 15 sm bo’lgan ikki kesmaning uchlari o’zaro parallel teksliklarda yotadi. Birinchi

kesmaning tekslikdagi proeksiyasi √19 sm bolsa, ikkinchi kesmaning proyeksiyasi necha sm bo’ladi?

A)12 B) 11 C) 10 D) 13 E) 9

20. Teng yonli trapetsiyaning asoslari 4,2 va 5,4 ga, kichik asosidagi burchagi esa 135⁰ ga teng.

Trapetsiyaning yuzini toping?

A) 24,8 B) 9,6 C) 16,8 D) 4,8 E) 2,88

21. Uzunligi 30 π bo’gan aylanani 60⁰ li yoyini tortib turuvchi vatar uzunligi qancha?

A) 12 B) 16 C) 15 D) 13 E) 17

22. Balandligi 6 ga teng bo’lgan teng yonli uchburchakning asosi yon tomonidan 6 ga ortiq,

uchburchakning asosini toping.

A) 16 B) 15 C)18 D) 24 E)20

23. Aylanaga ichki chizilgan to’g’ri to’rtburchakning tomonlari 32 va 24 ga teng. aylanani uzunligini

toping?

A) 40π B) 20π C) 80 π D) 48π E) 32π

24. ABCD teng yonli trapetsiya ABD burchak 90⁰ ga teng. BE ┴ AD, AE=4 va ED=9. trapetsiyaning

balandligini toping.

A) 4 B) 5 C) 6 D) 7 E) 8

25. Romb dioganallarining tomonlari bilan hosil qilgan burchaklarining nisbati 2:7 ga teng. Rombning

kichik burchagini toping?

A) 20⁰ B) 30⁰ C) 40⁰ D) 60⁰ E) 70⁰

26. ABC uchburchakning AD medianasi AB va AC tomonlari bilan mos ravishda 30⁰ va 60⁰ li burchak

hosil qiladi. Agar AB=3 bo’lsa, AC ni toping?

A) 1 B) √3/2 C) √3/3 D) 3/2 E) 4/3

27. Muntazam ABC uchburchakning perimetri 3 ga teng. Agar AB₁=2AB va AC₁=2AC bo’lsa, AB₁C₁

uchburchakning perimetrini toping?

A) 5 B)6 C)7 D) 8 E) 9

28. 15 sonining oldiga va so’ngiga 1tadan raqamlar shunday yozildiki, natijada hosil bo’lgan 4 xonali

sonlar 15ga qoldiqsiz bo’lindi. Bunday 4 xonali sonlar eng ko’pi bilan nechta?

A) 6 B) 8 C) 12 D) 4 E) 16

29. 3/2, 5/4, 9/8, 17/16….. ketma-ketlikning dastlabki 40ta xadining yig’indisini toping?

A) 43 B) 40+1/2540 C) 41+1/2540 D) 41-1/2540 E) 42

30. Hisoblang. 1/35+1/63+1/99+1/143+…+1/575

A) 0,004 B) 0,08 C) 1/6 D) 0,07 E) 0,085

3 1. Sistemani qanoatlantiruvchi x lar yig’indisini toping. x⁷y⁹=64

x⁹ y⁷=1024

A) -1 B) 1 C) 0 D) -3 E) -2

32. x²+4x-4=0 bo’lsa, x₁⁴+x₂⁴ ni toping?

A)524 B)640 C)645 D)544 E) 560

33. Nechta butun son 3^√6-x≥(x-4)sin(x-4)3 tengsizlikni qanoatlantiradi.

A) 3ta B) 2ta C) 1ta D) 0ta E) aniqlab bo’lmaydi

34. (4/3)5cosx0=sinx tenglamaning. [0,12π ] dagi yechimlari yig’indisini aniqlang.

A) 7π B) 8π C) 9π D) 33π E) 5π/14

35. Agar a,b>0 sonlarning o’rta arifmetigi o’rta geometrigidan 4marta katta bo’lsa, a/b ning qiymatini

Aniqlang?

A) 31≥8√15 B) 32≥8√15 C) 32+8√15 D) 31+8√15 E) 30≥8√15

36. Agar 2

A)[4;56] B)(4;56] C)(4;56) D)[4;56) E)to’g’ri javob yo’q

37. y=x²-6x+11 funksiyaning a(1;-2) vektor bo’ylab parallel ko’chirish natijasida qanday funksiya hosil bo’ladi.

A) (x-2)² B)(x-2)²+2 C)(x-4)²+2 D)(x-4)² E)(x-2)²-2

38. √x²-ax+2=x-1 tenglama qaysi butun a da yechimga ega?

A)0 va 3 B) 2va3 C)0 va 2 D)3 E)2

39. Uch xonali sonda yuzlar xonasing raqami o’chirildi va hosil bo’lgan ikki xonali sonni 7 ga ko’

paytirildi.. Natijada dastlabki uch xonali sonning o’zini hosil qilindi. Shu son raqamlari yig’indisini

xisoblang.

A) 13 B) 5 C) 16 D) 17 E) 8

40. [(4x+9)/3]=16(x+1)/11 tenglama yechimlari ichida eng kichigini toping.

A) 127/16 B) 135/17 C) 191/24 D) 188/24 E) 123/16

√x+√y=5

41. √xy=4 bo’lsa, x+y ni toping.
A) 17 B) 18 C) 19 D) 16 E) 15

42. 17∙28∙41∙35-24∙12∙87 ayrima qanday raqm bilan tugaydi?

A) 0 B) 2 C) 4 D) 6 E) 8

43. p ning nechta butun qiymatida x²+px+9=0 tenglama xaqiqiy ildizga ega emas.

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44. ((x-3)/(x+2))≤0 tengsizlikni barcha butun yechimlari yig’indisini toping.

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45. x²+mx-x-m=0 (m=1) tenglama berilgan shu tenglama ildizlari kvadratlarining yig’indisini toping.

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46. Perimetrlari 18sm va 27sm bo’lgan ikkita romb o’zaro gomotetik, bu romblar tomonlari va

yuzalarining nisbatlarini toping? ____________________________________

47. Agar sinα=0,5 bo’lsa, cosα, tgα,ctgα ni toping?

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48. (x-3)(x+4)>0 tengsizlikni yeching. __________________________________
49. a ning qanday qiymatlarida ax²-8x-2≤0 tengsizlik x ning barcha qiymatlarida o’rinli bo’ladi?

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50. ABCD trapetsiyada AC dioganal uni o’xshash ABC va ACD uchburchaklarga ajratadi. Bunda

BC=4m AD=9m bo’lsa, AC dioganal uzunligini toping?

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