Syllabus Edition

First teaching 2021

Last exams 2024

|

Vectors (CIE IGCSE Maths: Extended)

Exam Questions

2 hours38 questions
1
Sme Calculator
6 marks

stack A B with rightwards arrow on top space equals space open parentheses 6
minus 1 close parentheses               stack B C with rightwards arrow on top space equals space open parentheses negative 2
5 close parentheses                stack D C with rightwards arrow on top space equals space open parentheses 2
minus 3 close parentheses

Find

i)
stack A C with rightwards arrow on top,
 
stack A C with rightwards arrow on top space equals space open parentheses
space space space
space space space space space space space close parentheses  [2]
ii)
stack B D with rightwards arrow on top,
 
stack B D with rightwards arrow on top space equals space open parentheses
space space space
space space space space space space space close parentheses  [2]
iii)
open vertical bar stack B C with rightwards arrow on top close vertical bar.
  
  [2]

Did this page help you?

2
Sme Calculator
4 marks

bold p equals open parentheses table row 4 row 5 end table close parentheses       bold q equals open parentheses table row cell negative 2 end cell row 7 end table close parentheses

i)

Find 2 bold p plus bold q.
 

open parentheses table row cell space space space space space end cell row blank end table close parentheses [2]

ii)

Find open vertical bar bold p close vertical bar.
 

[2]

Did this page help you?

3
Sme Calculator
1 mark

A is the point left parenthesis 4 comma space 1 right parenthesis and stack A B with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 1 end table close parentheses.
 
Find the coordinates of B.
 

( ...................... , ...................... )

Did this page help you?

4
Sme Calculator
4 marks

bold a equals open parentheses table row cell negative 3 end cell row 2 end table close parentheses space space space space space space space bold b equals open parentheses table row 5 row 4 end table close parentheses space space space space space space space bold c equals open parentheses table row 14 row 9 end table close parentheses

i)
Find  3 bold a minus 2 bold b .
 
 

 open parentheses table row cell space space space space space end cell row cell space space space space space end cell end table close parentheses [2]

ii)
Find  vertical line space bold a bold space vertical line.
 
 

[2]

Did this page help you?

5
Sme Calculator
3 marks

cie-igcse-2018-oct-nov-p4-tz3-q1b

i)
Find the column vector stack A B with rightwards arrow on top.
 
 

stack A B with rightwards arrow on top equals open parentheses table row cell space space space space end cell row cell space space space space space space end cell end table close parentheses [1]

ii)
Find  vertical line stack A B with rightwards arrow on top vertical line.
 
 

vertical line stack A B with rightwards arrow on top vertical line equals................................................. [2]

Did this page help you?

6
Sme Calculator
2 marks

Find the magnitude of the vector open parentheses table row cell negative 1 end cell row 7 end table close parentheses.

Did this page help you?

7
Sme Calculator
2 marks

cie-igcse-2019-oct-nov-p4-tz2-q8b

i)table row blank row blank end table
Write stack O A with rightwards arrow on top as a column vector.

 

stack O A with rightwards arrow on top equals open parentheses table row cell space space space space space space space space end cell row blank end table close parentheses  [1]

ii)table row blank row blank end table
Write stack A B with rightwards arrow on top as a column vector.

 

stack A B with rightwards arrow on top equals open parentheses table row cell space space space space space space space space end cell row blank end table close parentheses  [1]

Did this page help you?

8
Sme Calculator
5 marks

stack O A with rightwards arrow on top equals open parentheses table row 4 row 3 end table close parentheses      stack A B with rightwards arrow on top equals open parentheses table row 8 row cell negative 7 end cell end table close parentheses      stack A C with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 6 end table close parentheses

Find

i)
open vertical bar stack O B with rightwards arrow on top close vertical bar,


open vertical bar stack O B with rightwards arrow on top close vertical bar equals............................................... [3]

ii)
stack B C with rightwards arrow on top.


stack B C with rightwards arrow on top equalsopen parentheses table row blank row blank end table space space space close parentheses [2] 

Did this page help you?

1
Sme Calculator
3 marks

cie-igcse-2020-may-jun-p4-tz2-q2d

In the diagram, O is the origin, O T equals 2 T D and M is the midpoint of T C.
stack O C with rightwards arrow on top equals bold c and stack O D with rightwards arrow on top equals bold d.
 
Find the position vector of M.
Give your answer in terms of bold c and bold d in its simplest form.

Did this page help you?

2a
Sme Calculator
3 marks

screenshot-2022-09-15-at-10-34-46-am

OAB is a triangle and ABC and PQC are straight lines.
P is the midpoint of OA, Q is the midpoint of PC and OQ : QB = 3 : 1.

stack O A with rightwards arrow on top equals 4 bold a and stack O B with rightwards arrow on top equals 8 bold b.

Find, in terms of bold a and/or bold b, in its simplest form

i)
stack A B with rightwards arrow on top,

 

stack A B with rightwards arrow on top = ................................................... [1]

ii)
stack O Q with rightwards arrow on top,

 

stack O Q with rightwards arrow on top = ................................................... [1]

iii)
stack P Q with rightwards arrow on top,

 

stack P Q with rightwards arrow on top = ................................................... [1]

2b
Sme Calculator
3 marks

By using vectors, find the ratio A B space colon space B C.

......................... : ........................

Did this page help you?

3
Sme Calculator
5 marks

bold a equals open parentheses table row cell negative 3 end cell row 2 end table close parentheses space space space space space space space bold b equals open parentheses table row 5 row 4 end table close parentheses space space space space space space space bold c equals open parentheses table row 14 row 9 end table close parentheses

m bold a plus n bold b equals text bold c end text
 
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 = ................................................      

Did this page help you?

4
Sme Calculator
2 marks

cie-igcse-2018-may-jun-1-p4-q11b
P Q R S is a parallelogram with diagonals P R and P R intersecting at X.
stack P Q with rightwards arrow on top equals bold a and stack P S with rightwards arrow on top equals bold b.

Find stack Q X with rightwards arrow on top in terms of bold a and bold b.
Give your answer in its simplest form.

stack Q X with rightwards arrow on top equals ...............................................

Did this page help you?

5a
Sme Calculator
2 marks

q2a-hard-4-13-vectors-edexcel-gcse-maths

O P T R spaceis a trapezium.

stack O P with rightwards arrow on top equals bold a space space
stack P T with rightwards arrow on top equals bold b space
stack O R with rightwards arrow on top space equals space 3 bold b

i)
Find stack O T with rightwards arrow on top in terms of bold a andbold space bold b
[1]
ii)
Find stack P R with rightwards arrow on top in terms of bold a and bold b
Give your answer in its simplest form.
[1]
5b
Sme Calculator
2 marks

S is the point on P R such that P S space colon space S R = 1 : 3

Find stack O S with rightwards arrow on top in terms of bold a and bold b.
Give your answer in its simplest form.

5c
Sme Calculator
2 marks

What does your answer to part (b) tell you about the position of point S?

Did this page help you?

1
Sme Calculator
6 marks

cie-igcse-2020-oct-nov-p4-tz3-q8b

In the diagram, O A B and O E D are straight lines.
O is the origin, A is the midpoint of O B and E is the midpoint of A C.
stack A C with rightwards arrow on top space equals space bold a spaceand stack C B with rightwards arrow on top space equals space bold b.
 
Find, in terms of bold a and bold b, in its simplest form 

i)
stack A B with rightwards arrow on top,
    
stack space A B with rightwards arrow on top space equals space................................................ [1]
ii)
stack O E with rightwards arrow on top,
    
stack space O E with rightwards arrow on top space equals space................................................ [2]
iii)
the position vector of D.
    
 [3]

Did this page help you?

2
Sme Calculator
3 marks

stack M T with rightwards arrow on top space space equals space open parentheses 2 k
minus k close parentheses  and  open vertical bar stack M T with rightwards arrow on top space close vertical bar equals space square root of 180.
 
Find the positive value of k.


k space equals
..............................................

Did this page help you?

3a
Sme Calculator
5 marks

cie-igcse-2018-oct-nov-p4-tz2-q11b

O A B is a triangle and C is the mid-point of O B.
D is on A B such that A D : D B = 3 : 5.
O A E is a straight line such that O A colon A E = 2 : 3.
stack O A with rightwards arrow on top equals bold a and stack O C with rightwards arrow on top equals bold c.
 
Find the following vectors, in terms of bold a and bold c, in their simplest form

i)
stack A B with rightwards arrow on top,
 
 

stack A B with rightwards arrow on top equals................................................ [1]

ii)
stack A D with rightwards arrow on top,
 
 

stack A D with rightwards arrow on top equals................................................ [1]

iii)
stack C E with rightwards arrow on top,
 
 

stack C E with rightwards arrow on top equals................................................ [1]

iv)
stack C D with rightwards arrow on top.
 
 

stack C D with rightwards arrow on top equals................................................ [2]

3b
Sme Calculator
1 mark

stack C E with rightwards arrow on top equals k stack C D with rightwards arrow on top

Find the value of k.

 

 

k = ................................................

Did this page help you?

4a
Sme Calculator
3 marks

cie-igcse-spec-p4-q6a-diagram

O P Q R is a rectangle and O is the origin.
M is the midpoint of R Q and P T space colon space T Q space equals space 2 space colon space 1.
stack O P with rightwards arrow on top space equals space bold p and  stack O R with rightwards arrow on top space equals space bold r.

Find, in terms of bold p and/or bold r, in its simplest form

i)
stack M Q with rightwards arrow on top,

stack M Q with rightwards arrow on top space equals
..............................................  [1]
ii)
stack M T with rightwards arrow on top,

stack M T with rightwards arrow on top space equals
.............................................. [1]
iii)
stack O T with rightwards arrow on top,

stack O T with rightwards arrow on top space equals .............................................. [1]
4b
Sme Calculator
2 marks

R Q spaceand space O T spaceare extended and meet at U.

Find the position vector of U in terms of bold p and bold r.
Give your answer in its simplest form.

Did this page help you?

5
Sme Calculator
4 marks

q2-vhard-4-13-vectors-edexcel-gcse-maths

A B C spaceis a straight line.

A B space colon thin space B C space equals space 2 colon 5

stack O A space with rightwards arrow on top equals space 2 bold a plus bold b
stack O B with rightwards arrow on top space equals 3 bold a space plus 2 bold b

Express stack space O C space with rightwards arrow on top in terms of space bold a bold spaceand bold b.
Give your answer in its simplest form.

Did this page help you?