Matematika fanidan 9-sinflar o’rtasidagi I tur olimpiada testlari

Matematika fanidan 9-sinflar o’rtasidagi I tur olimpiada testlari

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

E) (0,0)

2. 
   Parabola uchini koordinatalarini toping? y=x²+6x+5
   
   1. 
      (3,-4)
      
   2. 
      (-5.-1)
      
   3. 
      (3,4)
      
   4. 
      (-3,-4)
      
   5. 
      (2,3)
      
3. 
   Tenglamalar 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, 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
7. 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
8. 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
9. 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
10. 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

11. 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
12. 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
13. 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
14. 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
15. To’g’ri to’rtburchakning bo’yi 3,8 sm eni bo’yidan 1,3 sm qisqa uning yuzini toping?
16. 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
17. 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
18. Sistemani qanoatlantiruvchi x lar yig’indisini toping. x⁷y⁹=64
x⁹ y⁷=1024
A) -1 B) 1 C) 0 D) -3 E) -2
19. x²+4x-4=0 bo’lsa, x₁⁴+x₂⁴ ni toping?
A)524 B)640 C)645 D)544 E) 560
20. 17∙28∙41∙35-24∙12∙87 ayrima qanday raqam bilan tugaydi?
A) 0 B) 2 C) 4 D) 6 E) 8
21. p ning nechta butun qiymatida x²+px+9=0 tenglama xaqiqiy ildizga ega emas.
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22. ((x-3)/(x+2))≤0 tengsizlikni barcha butun yechimlari yig’indisini toping.

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

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24. Tenglamani yeching:
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25. Yuzi 96 sm², balandliklari 6 sm va 8 sm bo‘lgan parallelogrammning perimetrini toping.
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26. Tarkibida 85% suv bo‘lgan 0,5 t sellyuloza qorishmasida 75% suv bo‘lgan qorishma olish uchun necha kg suvni bug‘lantirish kerak?
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27. Hisoblang:
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28. ni hisoblang
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29. ABCD teng yonli trapetsiya ABD burchak 90⁰ ga teng. BE ┴ AD, AE=4 va ED=9. trapetsiyaning balandligini toping.
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30. x²+(9/x)=5(x-(3/x)) tenglamani butun yechimlari yig’indisini toping?
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