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Paper 1

Manipulate algebraic expressions:
(a) by completing the square;
(b) simplifying algebraic fractions with binomial denominators.

(a) quadratic equations:

  • by factorisation
  • by completing the square
  • by using the quadratic formula
(b) quadratic inequalities:
  • in one variable
  • and interpret the solution graphically

Equations in two unknowns:

  • one of which is linear and one of which is quadratic
  • algebraically or graphically.
  • To avoid unnecessary assumptions the binomial denominators should be linear expressions.
  • Completing the square is necessary in the teaching process to determine the turning point of a parabola.
  • Solving quadratic equations by completing the square will not be examined.
  • Solution of non-quadratic inequalities should be seen in context of the graphs of functions.
    For example:
    Determine the value(s) if x for which:

    (The solution to this question should be read off the graph of the two functions.)