Aller au contenu principal
Ecolint Campus des NationsMathématiques
← Dossiers de révision

Pack A — Fluency

Ecolint Campus des NationsMathematics
Year 10 · Quadratic Equations

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

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

BronzeQuestions 1–10
  1. 1.
    Solve x2=25x^2 = 25.
     
  2. 2.
    Solve (x−3)2=0(x - 3)^2 = 0.
     
  3. 3.
    Solve (x−2)(x−5)=0(x - 2)(x - 5) = 0.
     
  4. 4.
    Factorise x2+7x+12x^2 + 7x + 12.
     
  5. 5.
    Factorise x2−7x+12x^2 - 7x + 12.
     
  6. 6.
    Solve x2+5x+6=0x^2 + 5x + 6 = 0.
     
  7. 7.
    Factorise x2−16x^2 - 16.
     
  8. 8.
    Solve x2−16=0x^2 - 16 = 0.
     
  9. 9.
    State the roots of y=(x−3)(x+2)y = (x - 3)(x + 2).
     
  10. 10.
    Verify that x=3x = 3 is a root of x2−5x+6=0x^2 - 5x + 6 = 0.
     
SilverQuestions 11–20
  1. 11.
    Solve x2−3x−10=0x^2 - 3x - 10 = 0.
     
  2. 12.
    Solve x2=5x+6x^2 = 5x + 6.
     
  3. 13.
    Solve x2=5xx^2 = 5x.
     
  4. 14.
    Expand (x+5)2(x + 5)^2.
     
  5. 15.
    Write x2+8xx^2 + 8x as (x+p)2−q(x + p)^2 - q.
     
  6. 16.
    Write x2+6x+11x^2 + 6x + 11 in completed-square form (x+p)2+q(x + p)^2 + q.
     
  7. 17.
    Use the quadratic formula to solve x2+5x+6=0x^2 + 5x + 6 = 0.
     
  8. 18.
    Solve (x+1)(x−4)=6(x + 1)(x - 4) = 6.
     
  9. 19.
    How many real roots does x2−4x+4=0x^2 - 4x + 4 = 0 have?
     
  10. 20.
    Solve (x+3)2=16(x + 3)^2 = 16.
     
GoldQuestions 21–30
  1. 21.
    Factorise 2x2+7x+32x^2 + 7x + 3.
     
  2. 22.
    Use the quadratic formula to solve 2x2+7x+3=02x^2 + 7x + 3 = 0.
     
  3. 23.
    Write x2−6x+4x^2 - 6x + 4 in completed-square form.
     
  4. 24.
    Solve x2+6x+7=0x^2 + 6x + 7 = 0 by completing the square (give exact answers).
     
  5. 25.
    Solve x2+2x+5=0x^2 + 2x + 5 = 0.
     
  6. 26.
    Solve x2−4x−1=0x^2 - 4x - 1 = 0, giving exact answers.
     
  7. 27.
    The roots of x2+5x+6=0x^2 + 5x + 6 = 0 are α\alpha and β\beta. State α+β\alpha + \beta and αβ\alpha \beta.
     
  8. 28.
    If x=3x = 3 is a root of x2+bx−6=0x^2 + bx - 6 = 0, find bb.
     
  9. 29.
    Find a monic quadratic equation with roots 22 and 55.
     
  10. 30.
    Solve (x−4)2=7(x - 4)^2 = 7, giving exact answers.
     
PlatinumQuestions 31–40
  1. 31.
    For what values of kk does x2+6x+k=0x^2 + 6x + k = 0 have two distinct real roots?
     
  2. 32.
    A rectangular garden is xx m wide and (x+3)(x + 3) m long. Its area is 4040 m². Find xx.
     
  3. 33.
    Write 2x2−8x+52x^2 - 8x + 5 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=20t−5t2h = 20t - 5t^2. When does it hit the ground (other than at t=0t = 0)?
     
  5. 35.
    Solve 2x2−5x−3=02x^2 - 5x - 3 = 0 exactly.
     
  6. 36.
    A right-angled triangle has legs of length xx and (x+7)(x + 7) cm. Its hypotenuse is 1313 cm. Find xx.
     
  7. 37.
    The quadratic x2−8x+c=0x^2 - 8x + c = 0 has roots that differ by 2. If one root is 55, 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 5656. Find the integers.