UCSI INTERNATIONAL SCHOOL
Vectors
13.1.16
44 min
42 marks
To be completed in class and at home
 2
 and q =
p = 
 3 
1.
(a)
 3
  .
1 
Write p + q as a column vector.


Answer (a) p + q = 







[2]
(b)
The point O is marked on the grid below.
Draw the vector OP where OP = p
y
3
2
1
–3
–2
–1
O
1
2
3
x
–1
–2
–3
[1]
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1
2.
  1
AB =   and CD = 3 AB
 4
(a)
Write CD as a column vector.
Answer (a) CD =






[1]
(b)
Make two statements about the relationship between the lines AB and CD.
Statement 1 …………………………………………………………………
Statement 2 …………………………………………………………………
[2]
3.
Write the following as single vectors.
(a)
 2  1   3 
       
 3   0    1

Answer (a) 




[2]
(b)
 5
6  
  4

Answer (b) 




[2]
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4.
The points A and B are marked on the diagram.
y
4
3
2
B
1
–4
–3
–2
–1 0
–1
–2
1
2
3
4
x
A
–3
–4
(a)
Write AB as a column vector.

Answer (a) AB = 




[1]
(b)
  3
BC =  .
  2
Write down the co-ordinates of C.
Answer (b) (……… , …………)
[1]
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3
5.
y
5
4
3
2
1
–4
–3
–2
–1
0
1
–1
x
2
3
4
5
6
K
–2
–3
–4
–5
(a)
  3
KL =   . The point K is marked on the diagram.
 3
(i)
Draw KL on the diagram.
[1]
(ii)
Write down the co-ordinates of the point L.
Answer (a)(ii) (……… , ………)
[1]
(b)
P is the point (–3, –3).
 2
PR =   and PS = 2 PR .
1 
Find the co-ordinates of S.
Answer (b) (………… , ………)
[2]
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4
6.
y
5
4
3
2
1
–4
–3
–2
–1
0
1
x
3
2
5
4
6
–1
–2
–3
K
–4
–5
(a)
  2
KL =   .The point K is marked on the diagram.
 5
(i)
Draw KL on the diagram.
[1]
(ii)
Write down the co-ordinates of the point L.
Answer (a)(ii) (…..… , …….…)
[1]
(b)
P is the point (–4, –4).
3
PR =   and PS = 2 PR .
 2
Find the co-ordinates of S.
Answer (b) (……… , …………)
[2]
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 3
a =   and b =
  2
7.
(a)
  1


 2
Work out
(i)
a + 3b,

Answer (a)(i) 




[2]
(ii)
b – a.

Answer (a)(ii) 




[2]
(b)
PQ = 2b.
The point P is marked on the grid below.
Draw the vector PQ on the grid.
y
7
6
5
4
3
P
2
1
–3
–2
–1
0
1
2
3
4
5
6
x
–1
–2
[2]
8.
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6
y
6
5
4
3
C
2
1
B
–6
–5
–4
–3
A
–2
–1 0
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
Triangle ABC is drawn on the grid.
(a)
(i)
Write down the coordinates of A.
Answer (a)(i) (……… , ………)
[1]
(ii)
Write AB and BC as column vectors.

Answer (a)(ii) AB = 



 BC = 





[2]
(b)
 4
Translate triangle ABC by the vector   . Label the image T.
  3
[2]
(c)
AP = 2 AB and AQ = 2 AC .
(i)
Plot the points P and Q on the grid.
[2]
(ii)
Describe fully the single transformation which maps triangle ABC onto triangle
APQ.
Answer (c)(ii) ……….…………………………………………………………
…………………………………………………………………………………
[3]
(d)
Rotate triangle ABC through 180° about the midpoint of the side AB. Label the image R.
[2]
9.
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7
y
10
C
8
6
4
B
2
0
A
2
4
6
8
10
x
Points A, B and C are shown on the grid.
(a)
Plot the point D on the grid above so that ABCD is a rhombus.
[1]
(b)
Write BD as a column vector.

Answer (b) BD = 




[2]
(c)
M is the mid-point of AC.
Write AM as a column vector.

Answer (c) AM = 




[1]
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