GCSEMathsAQAFoundationExam QuestionsGeometry & MeasuresVectors

Vectors (AQA GCSE Maths: Foundation): Exam Questions

Exam code: 8300

45 mins17 questions
Easy
Medium
Hard
1
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2 marks

Here are two column vectors.

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

On the grid below, draw and label the vector bold a plus bold b.

Empty grid for vectors

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2
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2 marks
Parallelogram ABCD

A B C D is a parallelogram.

stack A B with rightwards arrow on top equals bold p and stack A D with rightwards arrow on top equals bold q.

 

(i) Find the vector stack A C with rightwards arrow on top in terms of bold p and bold q.

[1]

 

(ii) Find the vector stack B D with rightwards arrow on top in terms of bold p and bold q.

[1]

 

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3
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2 marks

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

Work out bold a plus 2 bold b as a column vector.

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4
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1 mark

Here is vector bold a.

q2-paper-1h-nov-2020-aqa-gcse-maths

Circle the column vector that represents bold a.

open parentheses table row 3 row 2 end table close parentheses

open parentheses table row cell negative 3 end cell row 2 end table close parentheses

open parentheses table row 3 row cell negative 2 end cell end table close parentheses

open parentheses table row cell negative 3 end cell row cell negative 2 end cell end table close parentheses

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5
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3 marks

Vectors a, b, c, d and e are drawn on an isometric grid.

q1b-paper5-spec2015-ocr-gcse-maths

Write each of the vectors c, d and e in terms of a and/or b.

c = ....................

d = ....................

e = ....................

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1
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3 marks

Here are two column vectors.

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

On the grid below, draw and label the vector bold a plus 2 bold b.

Blank grid for vectors

How did you do?

2
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3 marks
Parallelogram ABCD where the diagonal BD is shown and M is marked as the midpoint of BD

A B C D is a parallelogram.

stack A B with rightwards arrow on top equals bold p and stack A D with rightwards arrow on top equals bold q.

M is the midpoint of the line B D.

Find the vector stack A M with rightwards arrow on top in terms of bold p and bold q.

 

How did you do?

3
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2 marks

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

Work out 3 bold a minus bold b as a column vector.

How did you do?

4a
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1 mark

The vector bold a bold spaceand the vector bold b are shown on the grid.

1oyXjMTR_q1a-medium-4-13-vectors-edexcel-gcse-maths

On the grid, draw and label vector negative 2 bold a

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4b
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2 marks

Work out bold a space plus space 2 bold b as a column vector.

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5a
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2 marks

Vectors bold a and 4 bold b are drawn on the grid.

q7-paper6-nov2020-ocr-gcse-maths

Write vector bold a as a column vector.

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5b
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2 marks

Find vector bold b as a column vector.

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6a
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2 marks

Vector bold a equals open parentheses table row 2 row 1 end table close parentheses , vector bold b equals open parentheses table row cell negative 2 end cell row 1 end table close parentheses.

On each grid below, draw a vector to represent

q11a-paper5-june2017-ocr-gcse-maths

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6b
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1 mark

Emma says that if she draws vector bold a and vector bold b they will be the same.

Explain why this is incorrect.

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1
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3 marks

Here are two column vectors.

bold a equals open parentheses table row 3 row cell negative 1 end cell end table close parentheses     bold b equals open parentheses table row 1 row cell 0.5 end cell end table close parentheses

On the grid below, draw and label the vector 2 bold a minus 4 bold b.

Empty grid for vectors

How did you do?

2
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3 marks

The shape in the diagram shows the vectors bold p, bold q and bold r.

M is the midpoint of the line A F.

Diagram of polygon ABCDEF with some vectors shown

 Find stack A M with rightwards arrow on top in terms of bold p, bold q and bold r.

How did you do?

3
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2 marks

bold a equals open parentheses table row cell negative 6 end cell row 4 end table close parentheses space space space space space space space space space space bold b equals open parentheses table row cell negative 2 end cell row cell negative 3 end cell end table close parentheses

Work out negative 2 bold a minus 4 bold b as a column vector.

How did you do?

4
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1 mark

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

Work out bold a space – space 3 bold b
Circle your answer.

open parentheses table row cell negative 6 end cell row 17 end table close parentheses

open parentheses table row cell negative 6 end cell row cell negative 13 end cell end table close parentheses

open parentheses table row 0 row 17 end table close parentheses

open parentheses table row 0 row cell negative 13 end cell end table close parentheses

How did you do?

5
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3 marks

Vector bold a equals open parentheses table row 3 row cell negative 1 end cell end table close parentheses and vector bold b equals open parentheses table row 1 row 3 end table close parentheses

Gavin starts to draw a diagram to show that bold a plus 2 bold b equals open parentheses table row 5 row 5 end table close parentheses

q9b-paper6-nov2019-ocr-gcse-maths

Complete Gavin’s diagram.

How did you do?

6a
2 marks

bold a equals open parentheses table row 6 row cell negative 2 end cell end table close parentheses and bold b equals open parentheses table row 10 row cell negative 5 end cell end table close parentheses

Work out 2 bold a minus bold b as a column vector.

How did you do?

6b
3 marks

Given that 3 bold a plus k bold b equals open parentheses table row cell negative 2 end cell row 4 end table close parentheses

Work out the value of k

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