Shapes of Graphs (AQA GCSE Further Maths)

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

(0, 3) and (2, 0.48) lie on the curve.

Work out the values of  and .

...............................    

...............................[4]

Here is a sketch of    where   

is a point on the curve.

Work out the value of .

[2]

 is a point on the curve with -coordinate –1

Work out the -coordinate of .

[1]

Here is a sketch of the curve

The curve intersects the axis at and .

Complete the coordinates of and .

[2]

Write down the range of values for for which   

[1]

Here is the graph of  for values of  from −1 to 4

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

[4]

 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.

Show the coordinates of the stationary points.

[4]

The function      has domain    

Here is the graph of   

Write down the equation of the line of symmetry of the graph.

[1]

Use the graph to work out the solutions of   

Give your answers to 1 decimal place.

[2]

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.

[4]

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

The stationary points are

• a point of inflection at
•  a minimum point at where > 1 and < 0

On the axes below, sketch the curve.
Label points and on your sketch.

[3]