1
1 The grid shows a point A.
y
4
2
A
1
–4 –3 –2 –1 0 1 2 3 4 x
–1
–2
–3
–4
(a) Write down the coordinates of point A.
( .................... , .................... ) [1]
(b) On the grid, plot the point B at (−1, 3). [1]
(c) C is a point on the grid whose coordinates are whole numbers.
On the grid, mark a point C so that triangle ABC is isosceles. [1]
[Total: 3]
2 The diagram shows a line L and two points, A and B, on a grid.
2
y
6
L
5
A
4
1
B
0 x
–6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8
–1
–2
(a) Write down the coordinates of point A.
( .............................. , .............................. ) [1]
(b) (i) Find the gradient of line L.
................................................... [1]
(ii) Write down the equation of line L in the form y = mx + c.
y = ................................................... [2]
(c) (i) Draw a line that is perpendicular to line L and passes through the point A. [1]
(ii) This line crosses the x-axis at point C.
Mark point C on the grid and write down the coordinates of point C.
( .............................. , .............................. ) [1]
[Total: 6]
3
3
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]
4 The diagram shows a point P and a line L.
4
(a) Write down the co-ordinates of point P.
( .............................. , .............................. ) [1]
(b) Find the gradient of line L.
................................................... [2]
(c) Write down the equation of line L in the form y = mx + c.
y = ................................................... [2]
[Total: 5]
5
5 A is the point (5, 7) and B is the point (9, −1).
Find the length AB.
................................................... [3]
[Total: 3]
6 A is the point (5, −5) and B is the point (9, 3).
Find the length of AB.
........................................ [3]
[Total: 3]
7 A is the point (8, 5) and B is the point (−4, 1).
(a) Calculate the length of AB.
................................................... [3]
6
(b) Find the co-ordinates of the midpoint of AB.
( .............................. , .............................. ) [2]
[Total: 5]
8 The grid shows a line L.
y
6
5
L 4
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1
–2
–3
–4
–5
–6
(a) Find the equation of line L.
Give your answer in the form .
y = ................................................... [2]
7
(b) (i) Complete the table of values for .
x −5 −3 0
y −5 5
[1]
(ii) On the grid, draw the graph of . [1]
(c) Write down the coordinates of the point which lies on both line L and the graph of .
( .................... , .................... ) [1]
(d) Write down the equation of the line that is parallel to and passes through the point (0, 18).
................................................... [1]
[Total: 6]
9 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]
8
10 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]
11 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]
9
(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]
[Total: 12]
12
y
6
A
5
4
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 x
–1
–2
–3
B
–4
–5
–6
–7
–8
A is the point (−6, 5) and B is the point (−2, −3).
10
(a) Find the equation of the straight line, l, that passes through point A and point B.
Give your answer in the form y = mx + c.
y = ................................................... [2]
(b) Find the equation of the line that is perpendicular to l and passes through the origin.
................................................... [2]
[Total: 4]
13 Factorise completely.
......................................................... [3]
[Total: 3]
11
14 Factorise completely.
................................................... [3]
[Total: 3]
15 Expand and simplify.
................................................... [3]
[Total: 3]
16 Expand and simplify.
................................................... [3]
[Total: 3]
12
17 The diagram shows a right-angled triangle ABC.
The area of this triangle is 30 cm2.
(a) Show that .
[3]
(b) Use factorisation to solve the equation .
x = .............................. or x = .............................. [3]
(c) Calculate BC.
BC = ................................................... cm [3]
[Total: 9]
