IGCSEMaths: CoreCIEExam QuestionsVectors & TransformationsVectors

Syllabus Edition

First teaching 2021

Last exams 2024

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Vectors (CIE IGCSE Maths: Core)

Exam Questions

48 mins20 questions
Easy
Medium
Hard
1a
Sme Calculator1 mark

Work out.

6 open parentheses table row 2 row cell negative 1 end cell end table close parentheses

open parentheses table row blank row blank end table close parentheses  

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1b
Sme Calculator1 mark

open parentheses table row 5 row cell negative 3 end cell end table close parentheses minus open parentheses table row 2 row 4 end table close parentheses

open parentheses table row blank row blank end table close parentheses  

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2
Sme Calculator1 mark

Work out open parentheses table row 2 row 5 end table close parentheses minus open parentheses table row cell negative 3 end cell row 4 end table close parentheses.

open parentheses table row blank row blank end table close parentheses  

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3
Sme Calculator2 marks

Work out.

i)
open parentheses table row 5 row cell negative 1 end cell end table close parentheses plus open parentheses table row 2 row 6 end table close parentheses
open parentheses table row blank row blank end table close parentheses   [1]
ii)
4 open parentheses table row cell negative 5 end cell row 2 end table close parentheses
open parentheses table row blank row blank end table close parentheses    [1]

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4a
Sme Calculator1 mark

Work out

open parentheses table row 2 row cell negative 3 end cell end table close parentheses plus open parentheses table row 5 row cell negative 1 end cell end table close parentheses

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4b
Sme Calculator1 mark

4 open parentheses table row 2 row cell negative 5 end cell end table close parentheses

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5a
Sme Calculator1 mark

Work out.

open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus open parentheses table row 2 row cell negative 4 end cell end table close parentheses

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5b
Sme Calculator1 mark

open parentheses table row 6 row 2 end table close parentheses minus open parentheses table row 1 row 5 end table close parentheses

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5c
Sme Calculator1 mark

4 open parentheses table row 2 row cell negative 5 end cell end table close parentheses

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6a
Sme Calculator1 mark

Work out.

open parentheses table row 4 row cell negative 2 end cell end table close parentheses minus open parentheses table row 1 row 5 end table close parentheses

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6b
Sme Calculator1 mark

Work out.

6 open parentheses table row 3 row 0 end table close parentheses

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7a
Sme Calculator1 mark

Work out.

open parentheses table row cell negative 2 end cell row 5 end table close parentheses minus open parentheses table row cell negative 1 end cell row 1 end table close parentheses

open parentheses table row blank row blank end table close parentheses 

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7b
Sme Calculator1 mark

7 open parentheses table row cell negative 3 end cell row 4 end table close parentheses

open parentheses table row blank row blank end table close parentheses

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8a
Sme Calculator1 mark

bold g space equals space open parentheses table row 2 row 5 end table close parentheses space space space space space space bold h bold space equals space open parentheses table row cell negative 3 end cell row 4 end table close parentheses

Write as a single vector

bold g bold space plus bold space bold h comma

open parentheses table row blank row blank end table close parentheses  

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8b
Sme Calculator1 mark

-h.

open parentheses table row blank row blank end table close parentheses  

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1
Sme Calculator3 marks

bold a equals open parentheses table row 3 row cell negative 2 end cell end table close parentheses       bold b equals open parentheses table row 5 row 7 end table close parentheses      bold c equals open parentheses table row cell negative 1 end cell row 4 end table close parentheses

Work out.

i)
bold a plus bold b
[1]
ii)
bold b minus bold 2 bold c
[2]

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2
Sme Calculator2 marks

bold p space equals space open parentheses table row 5 row 0 end table close parentheses space space space space space space space space space space space space space space space space space space space space space bold q space equals space open parentheses table row 1 row 6 end table close parentheses

Work out 2 bold p plus 3 bold q.

open parentheses table row blank row blank end table close parentheses 

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3
Sme Calculator2 marks

bold a bold space equals space open parentheses table row 5 row cell negative 2 end cell end table close parentheses space space space space space space space space space space bold b bold space equals space open parentheses table row cell negative 7 end cell row cell negative 3 end cell end table close parentheses

Work out a + 3b.

open parentheses table row blank row blank end table close parentheses 

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4
Sme Calculator1 mark

q17b-058013-mayjune2018-cie-igcse-maths-core

P is the point (-1, 2) and stack P Q with rightwards arrow on top = open parentheses table row 4 row cell negative 3 end cell end table close parentheses.

Find the co-ordinates of Q.

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5a
Sme Calculator1 mark

bold e space equals space open parentheses table row cell negative 5 end cell row 4 end table close parentheses space space space space space bold f space equals space open parentheses table row 0 row 6 end table close parentheses

Write as a single vector

3e,

open parentheses table row blank row blank end table close parentheses  

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5b
Sme Calculator1 mark

bold f bold minus bold e.

open parentheses table row blank row blank end table close parentheses 

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6
Sme Calculator1 mark

q23-058013-octnov2018-cie-igcse-maths-core

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

stack A B with rightwards arrow on top= open parentheses table row blank row blank end table close parentheses 

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7a
Sme Calculator2 marks

qp9-0580-11-paper-1-may-2020-cie-igcse-maths

Write stack P Q with rightwards arrow on top as a column vector.

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7b
Sme Calculator1 mark

Write 3stack P Q with rightwards arrow on top as a single vector.

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1a
Sme Calculator1 mark

The diagram shows a line A B on a 1cm2 grid.

qp2-0580-33-paper-3-may-2020-cie-igcse-maths

Write down the coordinates of point A.

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1b
Sme Calculator1 mark

Write down the vector stack A B with rightwards arrow on top.

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1c
Sme Calculator1 mark

stack B C with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 5 end table close parentheses

Mark point C on the grid.

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1d
Sme Calculator2 marks
i)
Work out  stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top.
[1]
ii)
Complete this statement.
stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals stack........... with rightwards arrow on top [1]

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1e
Sme Calculator2 marks

A comma space B and C are three vertices of a parallelogram, A B C D.

i)
Mark point space D spaceon the diagram and draw the parallelogram A B C D.
[1]
ii)
Work out the area of the parallelogram.
Give the units of your answer.
[2]

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2
Sme Calculator1 mark

Point P has coordinates (6, -2) and stack P Q with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 5 end table close parentheses.
Find the coordinates of point Q.

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3a
Sme Calculator1 mark

qp12-0580-12-paper-1-may-2020-cie-igcse-maths

Points A comma space B and C are shown on the grid.

Write down the coordinates of point C.

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3b
Sme Calculator1 mark

On the grid, plot point space D spaceso that A B C D is a parallelogram.

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3c
Sme Calculator2 marks

On the grid, plot point E so that stack E A with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 3 end table close parentheses

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4
Sme Calculator1 mark

Point A has coordinates (6, 4) and point B has coordinates (2, 7).
Write stack A B with rightwards arrow on top as a column vector.

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

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5
Sme Calculator5 marks

q6a-058031-octnov2018-cie-igcse-maths-core

i)
Write down the co-ordinates of point P.
[1]
ii)
Write down the column vector stack P Q with rightwards arrow on top.

stack P Q with rightwards arrow on top = open parentheses table row blank row blank end table close parentheses [1]

iii)
stack Q R space with rightwards arrow on top equals space open parentheses table row 3 row 2 end table close parentheses
On the grid, plot point R.
[1]
iv)
P Q R S is a parallelogram.

On the grid, complete the parallelogram P Q R S.
Write down the co-ordinates of point S.
[2]

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