Solve a quadratic inequality by first making a quadratic equation to find the critical values - the points at which the graph changes from positive to negative, and vice versa.

Draw a sign diagram to represent three intervals, and determine for each interval if the graph is positive or negative.

State the inequality OR inequalities that represent the required interval(s).

Quadratic Inequalities - Test Yourself

Simultaneous Equations - Key Facts

Simultaneous equations can always be solved by substitution - rearrange the 'easier' equation to make it or , then substitute it into the 'harder' equation.

Use these to find the points of intersection between a line and a curve or a circle and a curve.

The discriminant - remember, - will identify how many points of intersection there are:
- there are TWO points of intersection
- there is ONE point of intersection (the line is a tangent)
- there are NO points of intersection

Drag the red line below to see the changes to the discriminant when the two equations are solved simultaneously: