IGCSEMathsCambridge (CIE)ExtendedExam QuestionsVectors & TransformationsVectors

Vectors (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Exam code: 0580 & 0980

2 hours41 questions

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Vectors

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1
Sme Calculator2 marks

stack V W with rightwards arrow on top equals open parentheses table row 10 row cell negative 24 end cell end table close parentheses
Find  open vertical bar stack V W with rightwards arrow on top close vertical bar.

How did you do?

2
Sme Calculator6 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]

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3
Sme Calculator4 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]

How did you do?

4
Sme Calculator4 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]

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5
Sme Calculator3 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]

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6
Sme Calculator5 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] 

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7
Sme Calculator2 marks

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

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1a4 marks

The diagram shows triangle O P T.

q22-paper4-spec-2025-cie-igcse-further-maths

In the diagram stack O T with rightwards arrow on top space equals space bold t and stack O P with rightwards arrow on top space equals space bold p. O K space colon space K T space equals space 2 space colon 1 and T L space colon space L P space equals space 2 space colon 1.

Find, in terms of t and p, in its simplest form

i)   stack P L with rightwards arrow on top

[2]

ii)  stack K L with rightwards arrow on top

[2]

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1b2 marks

K L is extended to the point M.

stack K M with rightwards arrow on top space equals space minus 2 over 3 bold t bold space plus space 4 over 3 bold p.

Show that M lies on O P extended.

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24 marks

P is the point (16, 9) and Q is the point (22, 24).

N is the point on PQ such that PN = 2NQ.
Find the co-ordinates of N.

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

How did you do?

33 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.

How did you do?

4
Sme Calculator5 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 = ................................................      

How did you do?

5a2 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]

How did you do?

5b2 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.

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5c2 marks

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

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16 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]

How did you do?

2a3 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]

How did you do?

2b2 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.

How did you do?

3a5 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]

How did you do?

3b1 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 = ................................................

How did you do?

44 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.

How did you do?