Shapes of Graphs (AQA GCSE Further Maths)

Here is a sketch of the curve  where  and  are positive constants.

and lie on the curve.

Work out the values of  and .

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Here is a sketch of the curve

The curve intersects the -axis at and .

Complete the coordinates of and .

Write down the range of values for for which   

Here is the graph of   for values of  from to

By drawing a suitable linear graph on the grid, work out approximate solutions to

Here is a sketch of    where and are constants.

The graph intersects the -axis at and  and the -axis at point

Work out the coordinates of point .

You must show your working.

The graph of is shown, where .

The line intersects the graph exactly once.

Find the value of .

 is a cubic curve with a maximum and a minimum stationary point.

The -coordinate of the minimum point is  .

The -coordinate of the maximum point is  .

is a point on the curve.

The tangent at  has a negative gradient.

Sketch the curve on the grid below and show the coordinates of the stationary points.

The continuous curve g()  has exactly two stationary points.

The stationary points are

• a maximum point at where and

•  a minimum point at

On the axes below, sketch the curve.

Label points and on your sketch.

The graph of is shown, where and are positive constants.

The graph has a -intercept of and passes through the point

By finding the values of and , work out the equation of the graph.

Give your answer in the form where and are integers and where is the smallest positive integer possible.