1
1 The grid shows point P and point R.
y
5
P 4
3
2
1
–5 –4 –3 –2 –1 0 1 2 3 4 5 x
–1
–2
–3
R
–4
–5
(a) Write down the coordinates of point P.
( .................... , .................... ) [1]
(b)
Mark point Q on the grid. [1]
(c) Find .
[1]
(d) Complete this statement.
[1]
[Total: 4]
2 The grid shows a point A.
2
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]
3 The diagram shows a line L and two points, A and B, on a grid.
3
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]
4 The diagram shows a point P, a shape S and lines A and B on a 1 cm2 grid.
4
y
9
P
8
6
A
S
5
1
B
–2 –1 0 1 2 3 4 5 6 7 8 9 10 x
(a) Line A is parallel to line B.
Explain what parallel means.
.......................................................................................................................................................... [1]
(b) Write down the coordinates of point P.
( .................... , .................... ) [1]
(c) (i) Write down the mathematical name for shape S.
................................................... [1]
(ii) Work out the area of shape S.
................................................... cm2 [1]
(d) (i) Find the gradient of line A.
................................................... [1]
(ii) Write down the equation of line A.
................................................... [2]
5
[Total: 7]
Points A, B and C are shown on the grid.
(a) Write down the coordinates of point C.
( .............................. , .............................. ) [1]
(b) On the grid, plot point D so that ABCD is a parallelogram. [1]
(c) On the grid, plot point E so that . [2]
[Total: 4]
6 The diagram shows a line AB on a 1 cm2 grid.
6
(a) Write down the coordinates of point A.
( .................... , .................... ) [1]
(b) Write down the vector .
[1]
(c)
Mark point C on the grid. [1]
(d) (i) Work out .
[1]
(ii) Complete this statement.
[1]
(e) A, B and C are three vertices of a parallelogram, ABCD.
7
(i) Mark point D on the diagram and draw the parallelogram ABCD. [1]
(ii) Work out the area of the parallelogram.
Give the units of your answer.
.............................. .................... [2]
[Total: 8]
7 The diagram shows a point P and a line L.
(a) Write down the co-ordinates of point P.
( .............................. , .............................. ) [1]
(b) Find the gradient of line L.
................................................... [2]
8
(c) Write down the equation of line L in the form y = mx + c.
y = ................................................... [2]
[Total: 5]
8 (a) On the grid, draw the line through the point (−3, −2) that is perpendicular to the y-axis.
[1]
(b) On the grid, draw the line y = −2x.
[1]
[Total: 2]
9 A straight line joins the points A (−2, -3) and C (1, 9).
(a) Find the equation of the line AC in the form y = mx + c.
y = ................................................... [3]
(b) Calculate the acute angle between AC and the x-axis.
................................................... [2]
(c) ABCD is a kite, where AC is the longer diagonal of the kite.
B is the point (3.5, 2).
9
(i) Find the equation of the line BD in the form y = mx + c.
y = ................................................... [3]
(ii) The diagonals AC and BD intersect at (−0.5, 3).
Work out the co-ordinates of D.
( .............................. , .............................. ) [2]
[Total: 10]
10 (a) Write down the co-ordinates of point A.
( .................... , .................... ) [1]
(b) On the grid, plot point B (1, –3). [1]
[Total: 2]
11 (a) Write down the co-ordinates of point A.
( .................... , .................... ) [1]
(b) Plot the point C at (4, −3). [1]
(c) Find the vector .
= [1]
10
[Total: 3]
