Revision Paper Calculus
Revision Paper Calculus
Revision Paper Calculus
(i) f (x - 3) ,
................................................. [1]
(ii) g (5x) .
................................................. [1]
................................................. [3]
2
[2]
x = ................................................. [2]
3
( .................... , ....................)
[3]
O x
[3]
5
a = ................................................ [2]
(ii) On the axes, sketch the graph of y = x 3 - 4x 2 + 4x , indicating the values where the graph
meets the axes.
O x
[4]
7
y = ................................................ [7]
8
6 (a)
y
12
11
10
–1 0 1 2 3 4 5 x
–1
–2
–3
–4
–5
–6
–7
–8
9
The diagram shows the graph of y = f (x) for -1.5 G x G 5.
................................................. [1]
k = ................................................. [1]
(iv) On the grid, draw a line y = mx so that f (x) = mx has exactly one solution for -1.5 G x G 5.
[2]
(b) y = 3x 2 - 12x + 7
dy
(i) Find the value of when x = 5.
dx
................................................. [3]
(ii) Find the coordinates of the point on the graph of y = 3x 2 - 12x + 7 where the gradient is 0.
[5]
O x
12
O x
[4]
9 f (x) = x (x - 1) (x - 2)
(a) Find the coordinates of the points where the graph of y = f (x) crosses the x-axis.
( ..................... , ..................... )
( ..................... , ..................... )
[2]
(c) Find the coordinates of the turning points of the graph of y = f (x) .
Show all your working and give your answers correct to 1 decimal place.
15
O x
[2]
16
2
10 (a) (i) Factorise 24 + 5x - x .
................................................. [2]
y
NOT TO
c
SCALE
a O b x
a = ................................................
b = ................................................
c = ................................................ [3]