Equations, Inequalities & Graphs (CIE IGCSE Additional Maths)

The diagram shows the graph of  .
Use the graph to solve the inequality .

On the axes, sketch the graph of , stating the intercepts with the coordinate axes. 

Hence find the values of  for which .

On the axes below sketch the graph of , showing the coordinates of the points where the curve intersects the coordinate axes.

Hence find the values of  for which .

On the axes below, sketch the graph of , showing the coordinates of the points where the graph meets the coordinate axes.

Solve .

On the axes below, sketch the graph of , showing the coordinates of the points where the graph meets the coordinate axes.

Hence solve .

The diagram shows the graph of a cubic curve .

Find an expression for .

Solve .

Write in the form , where  and  are constants.

Hence write down the coordinates of the stationary point on the curve .

On the axes below, sketch the graph of , showing the exact values of the intercepts of the curve with the coordinate axes.

Find the value of for which  has exactly 3 values of .

The diagram shows the graph of  , where  is a cubic function. Find the two possible expressions for .

Solve the inequality .