1
1
(a) Complete the table of values for
x
−6
−4
−3
−3
y
.
−2
−1
1
−6
2
3
4
6
6
3
[3]
(b) On the grid, draw the graph of
for
and
.
y
12
10
8
6
4
2
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6 x
–2
–4
–6
–8
– 10
– 12
[4]
(c) On the grid, draw the line y = 5.
(d) Use your graph to solve the equation
[1]
.
x = ...................................................
[1]
[Total: 9]
2
2
On the axes, sketch the graph of the function
.
y
O
x
[2]
[Total: 2]
3
y
5
4
3
2
1
–2
–1
0
–1
–2
1
2
x
3
(a) The grid shows the graph of
.
The graph passes through the points with coordinates (0, 4) and (1, 1).
(i)
Find the value of a and the value of b.
a = ...................................................
b = ...................................................
[2]
(ii) Write down the equation of the tangent to the graph at (0, 4).
...................................................
(iii) The equation of the tangent to the graph at
is
[1]
.
Find the equation of the tangent to the graph at x = 1.
...................................................
(b) The table shows some values for
(i)
x
−2
−1.5
y
2
2.11
for
−1
(i)
.
0
0.5
2.43
1
1.5
3
4.33
Complete the table.
(ii) On the grid, draw the graph of
(c)
−0.5
[2]
[3]
for
.
[4]
Write down the values of x where the two graphs intersect.
x = .............................. or x = .............................. [2]
4
(ii) The answers to part(c)(i) are two solutions of a cubic equation in terms of x.
Find this equation in the form
, where a, b, c and d are integers.
..................................................................................
[4]
[Total: 18]
4
(a) Complete the table of values for
x
−6
−4
y
−2
−3
−3
,
−2
.
−1
1
12
2
3
4
6
2
[3]
5
(b) On the grid, draw the graph of
for
and
.
[4]
(c) On the grid, draw the line y = 8.
(d) Use your graph to solve
[1]
.
x = ...................................................
[1]
[Total: 9]