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Grade 11 · Equations and Inequalities
Solving Quadratic Equations: Factorising, Formula and Completing the Square
WORKSHEET
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Mark
  / 36

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Solve x2 − 7x + 12 = 0. (factorise)
    (2)
  2. 2
    Solve x2 + 2x − 8 = 0. (factorise)
    (2)
  3. 3
    Solve x2 − 9x = 0. (common factor)
    (2)
  4. 4
    Solve x2 − 16 = 0. (difference of squares)
    (2)
  5. 5
    Solve x2 + 4x + 1 = 0 (formula, 2 decimal places). (formula)
    (3)
  6. 6
    Solve 2x2 − 5x + 1 = 0 (formula, 2 decimal places). (formula)
    (3)
  7. 7
    Solve x2 + 8x − 9 = 0 by completing the square. (complete the square)
    (3)
  8. 8
    Solve 3x2 − 12x + 5 = 0 by completing the square, correct to TWO decimal places. (complete the square)
    (4)
  9. 9
    Write x2 − 10x + 3 in the form (x + p)2 + q. (complete the square)
    (2)
  10. 10
    Solve x2 = 2x + 15. (rearrange)
    (3)
  11. 11
    Solve 2x2 + 7x + 3 = 0. (leading coeff)
    (3)
  12. 12
    Solve x + 5/x = 6. (fraction)
    (4)
  13. 13
    Solve (x − 2)(x + 1) = 4. (expand first)
    (3)
TOTAL: 36 marks
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