Cambridge IGCSE®
Vectors – Past paper questions
The questions in this document have been compiled from a number of past papers, as indicated in the table
below.
Use these questions to formatively assess your learners’ understanding of this topic. Some questions have
additional ‘Challenge questions’ included. These do not form part of the original questions, but have been
added as part of the lesson plans included in Resource Plus.
Question Year Series Paper number
13 2017 June 11
13 2017 June 13
18 2017 June 21
17 2017 June 23
14 2017 November 11
8 2017 November 13
14a 2017 November 21
14b 2017 November 21
4a 2017 November 31
The mark scheme for each question is provided at the end of the document.
You can find the complete question papers and the complete mark schemes (with additional notes where
available) on the School Support Hub www.cambridgeinternational.org/support.
Vectors – Past paper questions Copyright © UCLES 2018 1
13
a =c m b =c m
5 -3
-1 -4
Write a + 2b as a single vector.
f p [2]
Vectors – Past paper questions Copyright © UCLES 2018 2
(a) GH = c m
6
13
-4
Find
(i) 5GH ,
f p [1]
(ii) HG .
f p [1]
(b) c m + c m = c m
6 2 8
7 y 3
Find the value of y.
y = ............................................ [1]
Vectors – Past paper questions Copyright © UCLES 2018 3
18 The diagram shows a parallelogram OCEG.
C D E
NOT TO
SCALE
B
H F
b
O A G
a
O is the origin, OA = a and OB = b.
BHF and AHD are straight lines parallel to the sides of the parallelogram.
OG = 3OA and OC = 2OB.
(a) Write the vector HE in terms of a and b.
HE = .................................. [1]
(b) Complete this statement.
a + 2b is the position vector of point ......................... [1]
(c) Write down two vectors that can be written as 3a - b.
............................... and ............................... [2]
Vectors – Past paper questions Copyright © UCLES 2018 4
17
P
NOT TO
p Z SCALE
O Q
q
O is the origin, OP = p and OQ = q.
Z is a point on PQ such that PZ : ZQ = 5 : 2.
Work out, in terms of p and q, the position vector of Z.
Give your answer in its simplest form.
................................................... [3]
Vectors – Past paper questions Copyright © UCLES 2018 5
14 Work out.
3 -1
(a) d n + d n
2 5
f p [1]
6 4
(b) d n - d n
3 -2
f p [1]
2
(c) 4d n
5
f p [1]
Vectors – Past paper questions Copyright © UCLES 2018 6
3 4
8 s =f p t =f p
-1 2
Work out 5s – t.
f p [2]
Vectors – Past paper questions Copyright © UCLES 2018 7
(a) D is the point (2, ‒5) and DE = c m .
7
14
1
Find the co-ordinates of the point E.
( ..................... , ..................... ) [1]
Vectors – Past paper questions Copyright © UCLES 2018 8
(b) v = c m and v = 13.
t
14
12
Work out the value of t, where t is negative.
t = .................................................. [2]
Vectors – Past paper questions Copyright © UCLES 2018 9
4 (a)
2
B
1
x
–5 –4 –3 –2 –1 0 1 2 3 4 5
–1
–2
A
–3
–4
(i) Plot point C at (–4, 2). [1]
(ii) Write down the mathematical name of the triangle formed by joining the points A, B and C.
................................................. [1]
(iii) Write down the vector AB.
AB = f p [1]
(iv) (a) Find the gradient of the line AB.
................................................. [2]
(b) Write down the equation of the line AB.
y = ................................................ [1]
Vectors – Past paper questions Copyright © UCLES 2018 10
Mark schemes
Question Answer Marks Part marks
13 −1 2 −6 𝜅
( ) B1 for ( ) seen or answer ( )
−9 −8 −9
−1
( )
𝑘
Question Answer Marks Part marks
13(a)(i) 30 1
( )
−20
13(a)(ii) −6 1
( )
4
13(b) −4 1
Question Answer Marks Part marks
18(a) 2a + b 1
18(b) D 1
18(c) ⃗⃗⃗⃗⃗
𝐶𝐹 and ⃗⃗⃗⃗⃗
𝐵𝐺 2 B1 for each
Question Answer Marks Part marks
17 2 5 3 5 2
p+ q M1 for QZ= (q−p) oe or QZ= (p−q)oe
7 7 7 7
M1 for correct route from O to Z or
identifying OZ
Question Answer Marks Part marks
14(a) 2 1
( )
7
14(b) 2 1
( )
5
14(c) 8 1
( )
20
Question Answer Marks Part marks
8 11 2 11 𝜅 15
( ) B1 for ( ) or ( ) or ( ) seen
−7 𝑘 −7 −5
Question Answer Marks Part marks
14(a) (9, −4) 1
Question Answer Marks Part marks
14(b) −5 2 M1 for 𝑡2 + 122 = 132 oe
or SC1 for answer 5 or ± 5
Vectors – Past paper questions Copyright © UCLES 2018 11
Question Answer Marks Part marks
4(a)(i) Correct point plotted 1
4(a)(ii) Right-angled or scalene 1
4(a)(iii) 8 1
4
4(a)(iv)(a) 0.5 oe 2 M1 for attempt at rise ÷ run
4(a)(iv)(b) [𝑦 =] 0.5𝑥 oe 1FT Correct or FT their (iv)(a)
Vectors – Past paper questions Copyright © UCLES 2018 12
