CIE IGCSE ADDITIONAL MATHEMATICS
(0606)
TOPICAL PRACTICE QUESTIONS
TOPIC 13:
VECTORS IN TWO
DIMENSIONS
Compiled from:
Paper 1
Variants 1, 2 and 3
2016- 2020
"DON'T STRESS.
Do your best and forget the
rest."
Page 1
Source: 0606/11/M/J/17 - Question No. 5
1
(a)
B
A
a
M
O
c
b
C
The diagram shows a figure OABC, where OA = a , OB = b and OC = c . The lines AC and OB
intersect at the point M where M is the midpoint of the line AC.
(i) Find, in terms of a and c, the vector OM .
[2]
(ii) Given that OM : MB = 2 : 3, find b in terms of a and c.
[2]
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Compilation: www.mystudycompass.com
Source: 0606/11/M/J/17 - Question No. 5
Page 2
(b) Vectors i and j are unit vectors parallel to the x-axis and y-axis respectively.
The vector p has a magnitude of 39 units and has the same direction as -10i + 24j.
(i) Find p in terms of i and j.
[2]
(ii) Find the vector q such that 2p + q is parallel to the positive y-axis and has a magnitude of
12 units.
[3]
(iii) Hence show that q = k 5 , where k is an integer to be found.
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[2]
Compilation: www.mystudycompass.com
Source: 0606/11/M/J/18 - Question No. 8
2
(a) Given that p = 2i - 5j and q = i - 3j, find the unit vector in the direction of 3p - 4q.
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Page 3
[4]
Compilation: www.mystudycompass.com
Source: 0606/12/M/J/16 - Question No. 3
3
Page 4
J2N
J1N
J- 5N
K
O
K
O
Vectors a, b and c are such that a =
, b=
and c = K O .
y
3
L P
L P
L 5P
(i) Given that a = b - c , find the possible values of y.
[3]
(ii) Given that n ^b + ch + 4 ^b - ch = m ^2b - ch, find the value of n and of m.
[3]
© UCLES 2016
Compilation: www.mystudycompass.com
Source: 0606/12/M/J/17 - Question No. 3
4
Page 5
Vectors i and j are unit vectors parallel to the x-axis and y-axis respectively.
(a) The vector v has a magnitude of 3 5 units and has the same direction as i - 2 j. Find v giving
your answer in the form a i + b j, where a and b are integers.
[2]
(b) The velocity vector w makes an angle of 30° with the positive x-axis and is such that w = 2 .
Find w giving your answer in the form c i + d j, where c and d are integers.
[2]
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Compilation: www.mystudycompass.com
Page 6
Source: 0606/12/M/J/20 - Question No. 8
5
A
P
Q
O
B
R
The diagram shows a triangle OAB such that OA = a and OB = b . The point P lies on OA such that
3
OP = OA . The point Q is the mid-point of AB. The lines OB and PQ are extended to meet at the
4
point R. Find, in terms of a and b,
(a) AB,
[1]
(b) PQ. Give your answer in its simplest form.
[3]
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Compilation: www.mystudycompass.com
Source: 0606/12/M/J/20 - Question No. 8
Page 7
It is given that nPQ = QR and BR = kb, where n and k are positive constants.
(c) Find QR in terms of n, a and b.
[1]
(d) Find QR in terms of k, a and b.
[2]
(e) Hence find the value of n and of k.
[3]
© UCLES 2020
Compilation: www.mystudycompass.com
Source: 0606/12/O/N/18 - Question No. 7
6
- 12
o . Write v in the
(a) The vector v has a magnitude of 39 units and is in the same direction as e
5
a
form e o , where a and b are constants.
b
Page 8
[2]
r+s
5r + 1
o and q = e
o , where r and s are constants. Given that
(b) Vectors p and q are such that p = e
r+6
2s - 1
0
2p + 3q = e o , find the value of r and of s.
[4]
0
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Compilation: www.mystudycompass.com
Source: 0606/13/M/J/20 - Question No. 6
7
Page 9
5
o.
(a) Find the unit vector in the direction of e
- 12
[1]
4
-2
- 10
o, find the value of each of the constants k and r.
(b) Given that e o + k e o = r e
1
3
5
[3]
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Compilation: www.mystudycompass.com
Source: 0606/13/M/J/20 - Question No. 6
Page 10
(c) Relative to an origin O, the points A, B and C have position vectors p, 3q - p and 9q - 5p
respectively.
(i) Find AB in terms of p and q.
[1]
(ii) Find AC in terms of p and q.
[1]
(iii) Explain why A, B and C all lie in a straight line.
[1]
(iv) Find the ratio AB : BC.
[1]
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Page 11
Source: 0606/13/O/N/18 - Question No. 7
8
A
B
D
O
C
The diagram shows a quadrilateral OABC. The point D lies on OB such that OD = 2DB and AD = mAC ,
where m is a scalar quantity.
OA = a
OB = b
OC = c
(i)
Find AD in terms of m, a and c.
[1]
(ii)
Find AD in terms of a and b.
[2]
(iii)
Given that 15a = 16b - 9c , find the value of m.
[3]
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Page 12
Source: 0606/13/O/N/20 - Question No. 9
9
A
a
Y
X
O
b
C
B
The diagram shows the triangle OAC. The point B is the midpoint of OC. The point Y lies on AC such
that OY intersects AB at the point X where AX : XB = 3:1. It is given that OA = a and OB = b .
(a) Find OX in terms of a and b, giving your answer in its simplest form.
[3]
(b) Find AC in terms of a and b.
[1]
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Compilation: www.mystudycompass.com
Source: 0606/13/O/N/20 - Question No. 9
Page 13
(c) Given that OY = h OX , find AY in terms of a, b and h.
[1]
(d) Given that AY = mAC , find the value of h and of m.
[4]
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Compilation: www.mystudycompass.com