1
Find 3m.
[1]
[Total: 1]
(a) Find .
[2]
(b) Find .
................................................... [2]
[Total: 4]
3 A is the point (4, 1) and .
Find the coordinates of B.
( .................... , .................... ) [1]
[Total: 1]
4
2
(a) Find 3a – 2b.
[2]
(b) Find .
................................................... [2]
(c)
Write down two simultaneous equations and solve them to find the value of m and the value of n.
Show all your working.
m = ...................................................
n = ................................................... [5]
[Total: 9]
3
(a) Find the column vector .
= [1]
(b) Find .
= ...................................................
[2]
(c) B is the mid-point of the line AC.
Find the co-ordinates of C.
( .............................. , .............................. ) [2]
(d) Find the equation of the straight line that passes through A and B.
................................................... [3]
4
(e) The straight line that passes through A and B cuts the y-axis at D.
Write down the co-ordinates of D.
( .............................. , .............................. ) [1]
[Total: 9]
6
y
6
5
4
3
A
2
1
B
–5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 x
–1
–2
–3
–4
–5
Describe fully the single transformation that maps triangle A onto triangle B.
....................................................................................................................................................................
.................................................................................................................................................................... [3]
[Total: 3]
5
7
y
10
2
C
–8 –6 –4 –2 0 2 4 6 8 10 x
–2
–4
–6
A B
–8
– 10
(a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
.............................................................................................................................................
............................................................................................................................................. [3]
(ii) triangle A onto triangle C.
.............................................................................................................................................
............................................................................................................................................. [3]
(b) Draw the image of triangle A after a translation by the vector . [2]
[Total: 8]
6
8 y
14
12
10
B
8
A
– 14 – 12 – 10 –8 –6 –4 –2 0 2 4 6 8 10 x
–2
–4
C
–6
–8
– 10
(a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
................................................................................................................................................
................................................................................................................................................ [3]
(ii) triangle A onto triangle C.
................................................................................................................................................
................................................................................................................................................ [3]
(b) Draw the image of triangle A after a translation by the vector . [2]
(c) Draw the image of triangle A after a reflection in the line y = 4. [2]
[Total: 10]
7
Describe fully the single transformation that maps triangle T onto triangle U.
....................................................................................................................................................................
.................................................................................................................................................................... [3]
[Total: 3]
8
10
(a) Draw the image of triangle T after a reflection in the line y = −1. [2]
(b) Draw the image of triangle T after a rotation through 90° clockwise about (0, 0). [2]
(c) Describe fully the single transformation that maps triangle T onto triangle A.
..........................................................................................................................................................
.......................................................................................................................................................... [2]
[Total: 6]
9
11
(a) (i) Draw the image of triangle A after a reflection in the line y = −x. [2]
(ii) Draw the image of triangle A after a translation by the vector . [2]
(b) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
................................................................................................................................................
................................................................................................................................................ [3]
(ii) triangle A onto triangle C.
................................................................................................................................................
................................................................................................................................................ [3]
[Total: 10]
10
12
(a) Describe fully the single transformation that maps shape T onto shape A.
..........................................................................................................................................................
.......................................................................................................................................................... [2]
(b) On the grid, reflect shape T in the line y = x. [2]
[Total: 4]
11
13
Describe fully the single transformation that maps
(a) triangle A onto triangle B,
..........................................................................................................................................................
.......................................................................................................................................................... [3]
(b) triangle A onto triangle C.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
[Total: 6]
12
14
(a)
Translate shape T by the vector .
Label the image A.
[2]
(b) Rotate shape T about the point (5, 3) through 180°.
Label the image B.
[2]
(c) Describe fully the single transformation that maps shape A onto shape B.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
[Total: 7]
13
15
Reflect shape T in the line y = x. [2]
[Total: 2]
14
16
(a) On the grid, draw the image of
(i) triangle A after a translation by the vector , [2]
(ii) triangle A after a reflection in the line y = x. [2]
(b) Describe fully the single transformation that maps triangle A onto triangle B.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
[Total: 7]
15
17
(a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
................................................................................................................................................
................................................................................................................................................ [2]
(ii) triangle A onto triangle C.
................................................................................................................................................
................................................................................................................................................ [3]
(b) On the grid, draw the image of
(i) triangle A after an enlargement, scale factor , centre (3, 0), [2]
(ii) triangle A after a translation by the vector . [2]
[Total: 9]
16
18
(a) Describe fully the single transformation that maps
(i) flag A onto flag B,
.............................................................................................................................................
............................................................................................................................................. [2]
(ii) flag A onto flag C,
.............................................................................................................................................
............................................................................................................................................. [3]
(iii) flag A onto flag D.
.............................................................................................................................................
............................................................................................................................................. [3]
17
(b) Draw the reflection of flag A in the line y = −1. [2]
[Total: 10]
19
(a) Describe fully the single transformation that maps triangle A onto triangle B.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
(b) On the grid, draw the image of
(i) triangle A after a reflection in the x-axis, [1]
(ii) triangle A after a translation by the vector . [2]
[Total: 6]
18
20
(a) Describe fully the single transformation that maps triangle T onto triangle P.
..........................................................................................................................................................
.......................................................................................................................................................... [2]
(b) Translate triangle T by the vector . [2]
(c) Rotate triangle T through 90° anticlockwise about (0, 0). [2]
(d) Enlarge triangle T by scale factor with centre (0, 0). [2]
[Total: 8]
19
21
(a) Describe fully the single transformation that maps triangle T onto triangle U.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
(b) On the grid, draw the image of triangle T after a rotation through 90° clockwise about the point
(7, 3).
[3]
[Total: 6]
20
22
(a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
................................................................................................................................................
................................................................................................................................................ [2]
(ii) triangle A onto triangle C,
................................................................................................................................................
................................................................................................................................................ [3]
(iii) triangle A onto triangle D.
................................................................................................................................................
................................................................................................................................................ [3]
(b) On the grid, draw the image of triangle A after an enlargement by scale factor 2, centre (7, 3). [2]
[Total: 10]
21
23
(a) (i) Draw the image of triangle A after a reflection in the line x = 2. [2]
(ii) Draw the image of triangle A after a translation by the vector . [2]
(iii) Draw the image of triangle A after an enlargement by scale factor , centre (3, 1). [3]
(b) Describe fully the single transformation that maps triangle A onto triangle B.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
[Total: 10]
22
24
Describe fully the single transformation that maps
(a) shape A onto shape B,
..........................................................................................................................................................
.......................................................................................................................................................... [3]
(b) shape A onto shape C.
..........................................................................................................................................................
.......................................................................................................................................................... [3]
[Total: 6]
23
y
3
2
A
1
x
–4 –3 –2 –1 0 1 2 3 4 5
–1
–2
–3
25 Draw the image of shape A after a translation by the vector . [2]
[Total: 2]
26
y
6
3
S
2
T
1
x
0
1 2 2 4 5 6 7 8 9
Describe fully the single transformation that maps triangle S onto triangle T.
Answer......................................................................................................................................................
.................................................................................................................................................................. [3]
[Total: 3]
