1
(x – 1) cm
x cm NOT TO
SCALE
(2x + 1) cm
x cm
The area of the rectangle is 29 cm2 greater than the area of the square.
The difference between the perimeters of the two shapes is k cm.
Find the value of k.
You must show all your working.
k = ................................................... [6]
[Total: 6]
2
2 Solve the simultaneous equations.
You must show all your working.
x = ...................................................
y = ................................................... [4]
[Total: 4]
3 Solve.
w = ................................................... [2]
[Total: 2]
4 Solve.
p = ................................................... [2]
[Total: 2]
3
5 Solve.
x = .............................. or x = .............................. [5]
[Total: 5]
6 Solve.
x = ................................................... [3]
[Total: 3]
4
7 Solve the simultaneous equations.
You must show all your working.
x = .............................. y = ..............................
x = .............................. y = .............................. [5]
[Total: 5]
5
8 Solve the simultaneous equations.
You must show all your working.
.................................................................
................................................................. [5]
[Total: 5]
9 Darpan runs a distance of 12 km and then cycles a distance of 26 km.
His running speed is x km/h and his cycling speed is 10 km/h faster than his running speed.
He takes a total time of 2 hours 48 minutes.
6
(a) An expression for the time, in hours, Darpan takes to run the 12 km is .
Write an equation, in terms of x, for the total time he takes in hours.
................................................... [3]
(b) Show that this equation simplifies to .
[4]
(c) Use the quadratic formula to solve .
You must show all your working.
x = .............................. or x = .............................. [4]
(d) Calculate the number of minutes Darpan takes to run the 12 km.
................................................... min [2]
[Total: 13]
7
10 Martin, Suki and Pierre make clocks.
In one week
• Martin makes x clocks.
• Suki makes 3 fewer clocks than Martin.
• Pierre makes twice as many clocks as Suki.
(a) Write an expression for the total number of clocks they make in one week.
Give your expression in its simplest form.
................................................... [3]
(b) The total number of clocks they make in one week is 35.
(i) Work out the value of x.
x = ................................................... [3]
(ii) Work out how many more clocks Pierre makes than Martin.
................................................... [2]
[Total: 8]
8
11
y
4
3
L
2
1
–3 –2 –1 0 1 2 x
–1
–2
–3
–4
–5
–6
Find the gradient of line L.
................................................... [2]
[Total: 2]
12 (a) Find the gradient of line l.
................................................... [2]
(b) Find the equation of line l in the form y = mx + c.
y = ................................................... [2]
9
(c) Find the equation of the line that is perpendicular to line l and passes through the point (12, −7).
Give your answer in the form y = mx + c.
y = ................................................... [3]
[Total: 7]
13 A is the point (7, 2) and B is the point (−5, 8).
(a) Calculate the length of AB.
................................................... [3]
(b) Find the equation of the line that is perpendicular to AB and that passes through the point (−1, 3).
Give your answer in the form .
y = ................................................... [4]
10
(c) AB is one side of the parallelogram ABCD and
• where and
• the gradient of BC is 1
• .
Find the coordinates of D.
( .................... , .................... ) [4]
[Total: 11]
14 (a) Find the gradient of line L.
................................................... [2]
(b) Write down the equation of line L in the form .
y = ................................................... [1]
11
[Total: 3]
15 A line, l, joins point F (3, 2) and point G (−5, 4).
(a) Calculate the length of line l.
................................................... [3]
(b) Find the equation of the perpendicular bisector of line l in the form y = mx + c.
y = ................................................... [5]
(c) A point H lies on the y-axis such that the distance GH = 13 units.
Find the coordinates of the two possible positions of H.
( .................... , .................... ) and ( .................... , .................... ) [4]
12
[Total: 12]
16 A has coordinates (−2, 7), B has coordinates (1, −5) and C has coordinates (5, 4).
(a) Find the coordinates of the midpoint of the line AB.
( .............................. , .............................. ) [2]
(b) Find .
= [2]
(c) Find .
................................................... [2]
(d) Find the equation of the line AB.
Give your answer in the form y = mx + c.
y = ................................................... [3]
13
(e) Find the equation of the line perpendicular to AB that passes through C.
Give your answer in the form y = mx + c.
y = ................................................... [3]
[Total: 12]
17 A is the point (5, −5) and B is the point (9, 3).
Find the length of AB.
........................................ [3]
[Total: 3]
18
Line L is shown on the grid.
14
(a) Find the equation of line L in the form .
y = ................................................ [2]
(b) Write down the equation of a line parallel to line L.
y = ................................................ [1]
[Total: 3]
19 Find the equation of the straight line that
• is parallel to the line y = 3x + 5
and
• passes through the point (1, 7).
Give your answer in the form y = mx + c.
y = ................................................... [2]
[Total: 2]
20 Find the equation of the line which is
• parallel to the line y = 3x − 5
and
• passes through the point (0, 17).
........................................ [1]
[Total: 1]
21 The coordinates of P are (−3, 8) and the coordinates of Q are (9, −2).
15
(a) Calculate the length PQ.
................................................... [3]
(b) Find the equation of the line parallel to PQ that passes through the point (6, −1).
................................................... [3]
(c) Find the equation of the perpendicular bisector of PQ.
................................................... [4]
[Total: 10]
22 Find the gradient of the line that is perpendicular to the line .
................................................... [2]
[Total: 2]
23 A rhombus ABCD has a diagonal AC where A is the point (−3, 10) and C is the point (4, −4).
16
(a) Calculate the length AC.
................................................... [3]
(b) Show that the equation of the line AC is .
[2]
(c) Find the equation of the line BD.
................................................... [4]
[Total: 9]
24 Line L passes through the points (0, −3) and (6, 9).
17
(a) Find the equation of line L.
................................................... [3]
(b) Find the equation of the line that is perpendicular to line L and passes through the point (0, 2).
................................................... [2]
[Total: 5]
18
25
The diagram shows the points C(–1, 2) and D(9, 7).
Find the equation of the line perpendicular to CD that passes through the point (1, 3).
Give your answer in the form y = mx + c.
y = ................................................... [4]
[Total: 4]
19
26 A is the point (2, 3) and B is the point (7, −5).
Find the equation of the line through A that is perpendicular to AB.
Give your answer in the form y = mx + c.
y = ................................................... [4]
[Total: 4]
