1
1
When
,
.
Find the value of p and the value of q.
p = ...................................................
q = ...................................................
[2]
[Total: 2]
2
(a) Find the value of
when x = 5.
...................................................
(b) Find the coordinates of the point on the graph of
[3]
where the gradient is 0.
( .................... , .................... ) [2]
[Total: 5]
3
(a) Show that
can be written as
.
[2]
2
3
(b) Calculate the x–values of the turning points of
.
Show all your working and give your answers correct to 2 decimal places.
x = ......................................... , x = ......................................... [7]
(c) The equation
where a and b are integers.
has one solution only when
and when
,
Find the maximum value of a and the minimum value of b.
a = ...................................................
b = ...................................................
[3]
[Total: 12]
3
4
A curve has equation
.
The stationary points of the curve have coordinates
and
.
Work out the value of a, the value of b and the value of k.
a = .............................. , b = .............................. , k = .............................. [6]
[Total: 6]
5
Find the x-coordinates of the points on the graph of
where the gradient is 0.
...................................................
[4]
4
[Total: 4]
6
A curve has equation
.
Find the coordinates of its two stationary points.
( .................... , .................... ) and ( .................... , .................... ) [5]
[Total: 5]
7
when x = −2.
Find the gradient of the curve
...................................................
[3]
[Total: 3]
8
A curve has the equation
.
5
(a) Work out the coordinates of the two turning points.
( .............................. , .............................. ) and ( .............................. , .............................. ) [6]
(b) Determine whether each of the turning points is a maximum or a minimum.
Give reasons for your answers.
[3]
[Total: 9]
6
9
, where
is the derived function.
Find the value of p and the value of q.
p = ...................................................
q = ...................................................
[2]
[Total: 2]
10
(a) Find the value of y when x = −1.
y = ...................................................
(b) Find the two stationary points on the graph of
[2]
.
( .................... , .................... )
( .................... , .................... ) [6]
[Total: 8]
11
A curve has equation
.
7
(a) Find the coordinates of the two stationary points.
( .................... , .................... ) and ( .................... , .................... ) [5]
(b) Determine whether each of the stationary points is a maximum or a minimum.
Give reasons for your answers.
[3]
[Total: 8]