Name: ___________________________
GCSE (1 – 9)
Vectors
Instructions
• Use black ink or ball-point pen.
• Answer all questions.
• Answer the questions in the spaces provided
– there may be more space than you need.
• Diagrams are NOT accurately drawn, unless otherwise indicated.
• You must show all your working out.
Information
• The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.
• Keep an eye on the time.
• Try to answer every question.
• Check your answers if you have time at the end
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1 a= 2
3 ( ) and b=(15)
(a) Write down as a column vector
(i) a + b
…..........................
(1)
(ii) 2a + 3b
…..........................
(2)
The vector c is drawn on the grid.
(b) From the point P, draw the vector 4c
P
Ï
(1)
(Total for question 1 is 4 marks)
2 a= 4
1 ( ) and b=(32)
(a) Write down as a column vector
(i) a + b
…..........................
(1)
(ii) 2a – b
…..........................
(2)
( )
c= 5
-4
(b) From the point P, draw the vector c
P
Ï
(1)
(Total for question 2 is 4 marks)
3 a= - 2
3 ( ) and b=(-51)
(a) Write down as a column vector
(i) a + b
…..........................
(1)
(ii) 2a – b
…..........................
(2)
(b) Translate the triangle by the vector
( )
3
-2
(1)
(Total for question 3 is 4 marks)
4 A is the point (3, 2) and B is the point (4, –1).
(a) Write down as a column vector ⃗
AB
…..........................
(1)
C is the point (5, –2) and D is the point (2, 1).
(b) Write down as a column vector ⃗
CD
….........................
(1)
(Total for question 4 is 2 marks)
5 A is the point (5, –1) and B is the point (4, –3).
(a) Write down as a column vector ⃗
AB
…..........................
(1)
C is the point (1, 6) and D is the point (–3, 9).
(b) Write down as a column vector ⃗
CD
….........................
(1)
(Total for question 5 is 2 marks)
6 ABCDEF is a regular hexagon with centre O.
A B
a b
F C
O
E D
⃗
OA = a
⃗
OB = b
(a) Find, in terms of a, the vector ⃗
AD
…..........................
(1)
(b) Find, in terms of a and b, the vector ⃗
AB
…..........................
(c) Find, in terms of b, the vector ⃗
AF (1)
…..........................
(1)
(Total for question 6 is 3 marks)
7 The diagram shows a parallelogram.
A B
2a
2b
C D
⃗
OA = 2a
⃗
OB = 3 b
(a) Find, in terms of a, the vector ⃗
DA
…..........................
(1)
(b) Find, in terms of a and b, the vector ⃗
AB
…..........................
(1)
(c) Find, in terms of a and b, the vector ⃗
AC
…..........................
(1)
(Total for question 7 is 3 marks)
8
A
5a
M
O 3b B
⃗
OA = 5a
⃗
OB = 3 b
M is the midpoint of AB
(a) Find, in terms of a and b, the vector ⃗
AB
…..........................
(1)
(b) Find, in terms of a and b, the vector ⃗
AM
…..........................
(1)
(c) Find, in terms of a and b, the vector ⃗
OM
…..........................
(1)
(Total for question 8 is 3 marks)
