ALGEBRA
Manipulate algebraic expressions: (a) by completing the square; (b) simplifying algebraic fractions with binomial denominators.
Solve: (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
Solve: Equations in two unknowns:
one of which is linear and one of which is quadratic
algebraically or graphically.
Clarification
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.)