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Grade 11 · Equations
Solving Quadratic Equations: Every Method & Type
MEMORANDUM
Name: 
Class: 
Date: 
Mark
  / 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Solve x2 − 7x + 12 = 0. (factorise)
    (2)
    (x−3)(x−4)=0 → x = 3 or 4✓✓ (2)
  2. 2
    Solve x2 + 2x − 8 = 0. (factorise)
    (2)
    (x+4)(x−2)=0 → x = −4 or 2✓✓ (2)
  3. 3
    Solve x2 − 9x = 0. (common factor)
    (2)
    x(x−9)=0 → x = 0 or 9✓✓ (2)
  4. 4
    Solve x2 − 16 = 0. (difference of squares)
    (2)
    (x−4)(x+4)=0 → x = ±4✓✓ (2)
  5. 5
    Solve x2 + 4x + 1 = 0 (formula, 2 dp). (formula)
    (2)
    x = (−4±12)/2 ≈ −0,27 or −3,73✓✓ (2)
  6. 6
    Solve 2x2 − 5x + 1 = 0 (formula, 2 dp). (formula)
    (2)
    x = (5±17)/4 ≈ 2,28 or 0,22✓✓ (2)
  7. 7
    Solve x2 = 2x + 15. (rearrange)
    (2)
    x2−2x−15=0 → (x−5)(x+3)=0 → x = 5 or −3✓✓ (2)
  8. 8
    Solve 2x2 + 7x + 3 = 0. (leading coeff)
    (2)
    (2x+1)(x+3)=0 → x = −12 or −3✓✓ (2)
  9. 9
    Solve x + 5x = 6. (fraction)
    (2)
    x2−6x+5=0 → (x−1)(x−5)=0 → x = 1 or 5✓✓ (2)
  10. 10
    Solve (x − 2)(x + 1) = 4. (expand first)
    (2)
    x2−x−2=4 → x2−x−6=0 → (x−3)(x+2)=0 → x = 3 or −2✓✓ (2)
TOTAL: 20 marks
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