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Ecolint Campus des NationsMathématiques
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Pack B — Fluency

Ecolint Campus des NationsMathematics
Year 10 · Quadratic Equations

Pack B · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    Solve x2=49x^2 = 49.
     
  2. 2.
    Solve (x−5)2=0(x - 5)^2 = 0.
     
  3. 3.
    Solve (x−3)(x−7)=0(x - 3)(x - 7) = 0.
     
  4. 4.
    Factorise x2+8x+15x^2 + 8x + 15.
     
  5. 5.
    Factorise x2−9x+20x^2 - 9x + 20.
     
  6. 6.
    Solve x2+7x+10=0x^2 + 7x + 10 = 0.
     
  7. 7.
    Factorise x2−81x^2 - 81.
     
  8. 8.
    Solve x2−36=0x^2 - 36 = 0.
     
  9. 9.
    State the roots of y=(x−5)(x+1)y = (x - 5)(x + 1).
     
  10. 10.
    Verify that x=2x = 2 is a root of x2−7x+10=0x^2 - 7x + 10 = 0.
     
SilverQuestions 11–20
  1. 11.
    Solve x2−2x−15=0x^2 - 2x - 15 = 0.
     
  2. 12.
    Solve x2=4x+12x^2 = 4x + 12.
     
  3. 13.
    Solve x2=7xx^2 = 7x.
     
  4. 14.
    Expand (x+7)2(x + 7)^2.
     
  5. 15.
    Write x2+10xx^2 + 10x as (x+p)2−q(x + p)^2 - q.
     
  6. 16.
    Write x2+4x+9x^2 + 4x + 9 in completed-square form (x+p)2+q(x + p)^2 + q.
     
  7. 17.
    Use the quadratic formula to solve x2+7x+12=0x^2 + 7x + 12 = 0.
     
  8. 18.
    Solve (x+2)(x−5)=8(x + 2)(x - 5) = 8.
     
  9. 19.
    How many real roots does x2−6x+9=0x^2 - 6x + 9 = 0 have?
     
  10. 20.
    Solve (x+2)2=25(x + 2)^2 = 25.
     
GoldQuestions 21–30
  1. 21.
    Factorise 3x2+10x+73x^2 + 10x + 7.
     
  2. 22.
    Use the quadratic formula to solve 3x2+10x+7=03x^2 + 10x + 7 = 0.
     
  3. 23.
    Write x2−10x+18x^2 - 10x + 18 in completed-square form.
     
  4. 24.
    Solve x2+4x+1=0x^2 + 4x + 1 = 0 by completing the square (give exact answers).
     
  5. 25.
    Solve x2+4x+10=0x^2 + 4x + 10 = 0.
     
  6. 26.
    Solve x2−6x−2=0x^2 - 6x - 2 = 0, giving exact answers.
     
  7. 27.
    The roots of x2+7x+12=0x^2 + 7x + 12 = 0 are α\alpha and β\beta. State α+β\alpha + \beta and αβ\alpha \beta.
     
  8. 28.
    If x=4x = 4 is a root of x2+bx−4=0x^2 + bx - 4 = 0, find bb.
     
  9. 29.
    Find a monic quadratic equation with roots −1-1 and 66.
     
  10. 30.
    Solve (x−3)2=11(x - 3)^2 = 11, giving exact answers.
     
PlatinumQuestions 31–40
  1. 31.
    For what values of kk does x2+4x+k=0x^2 + 4x + k = 0 have two distinct real roots?
     
  2. 32.
    A rectangular garden is xx m wide and (x+4)(x + 4) m long. Its area is 6060 m². Find xx.
     
  3. 33.
    Write 2x2−12x+72x^2 - 12x + 7 in the form a(x+p)2+qa(x + p)^2 + q.
     
  4. 34.
    A ball is thrown upward and its height hh (m) after tt s is given by h=30t−5t2h = 30t - 5t^2. When does it hit the ground (other than at t=0t = 0)?
     
  5. 35.
    Solve 2x2−7x−4=02x^2 - 7x - 4 = 0 exactly.
     
  6. 36.
    A right-angled triangle has legs of length xx and (x+1)(x + 1) cm. Its hypotenuse is 55 cm. Find xx.
     
  7. 37.
    The quadratic x2−6x+c=0x^2 - 6x + c = 0 has roots that differ by 2. If one root is 44, find cc and bb.
     
  8. 38.
    Solve x2+6x+4=0x^2 + 6x + 4 = 0 exactly, in surd form.
     
  9. 39.
    The equation x2+kx+9=0x^2 + kx + 9 = 0 has exactly one (repeated) real root. Find kk.
     
  10. 40.
    The product of two consecutive positive integers is 132132. Find the integers.