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Vector Addition and Subtraction of Multiples

In this worksheet, students add and subtract multiples of simple 2D vectors.

'Vector Addition and Subtraction of Multiples' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Apply Addition, Subtraction, Multiplication and Diagrammatic Representation of Vectors

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

A vector is a "carrier" of information regarding a shifting movement.

A 2D vector can be written in the form

 

( x )
y

 

where x is the horizontal shift and y is the vertical shift.

 

The following diagram shows how a positive of negative number affects the direction of the shift.

 

 

To add or subtract vectors, we add or subtract the top numbers and the bottom numbers separately.

To find multiples of vectors, we simply multiply the top and bottom numbers by the multiple.

 

Example 1

 

Work out:

 

( 3 ) + 2
( -2 )
5 6

 

 

Answer

 

( 3 + -4
)

5 + 12

 

 

( -1 )
17

 

 

Example 2

 

Work out:

 

4 ( 3 ) -
( -2 )
-5 6

 

Answer

 

( 12 - -2
)

-20 - 6

 

 

( 14 )
-26

 

Select the correct answer to: 

 

( 3 ) + 2
( -2 )
4 3

 

Answers

1. ( -1 )   2. ( 4 )   3. ( -1 )
10 10 7

 

1.

2.

3.

Select the correct answer to: 

 

2 ( 3 ) +
( -2 )
4 3

 

Answers

1. ( -1 )   2. ( 4 )   3. ( -1 )
10 11 7

 

1.

2.

3.

Select the correct answer to: 

 

3 ( 3 ) +
( 4 )
-1 -1

 

Answers

1. ( 13 )   2. ( 7 )   3. ( 13 )
-2 -2 -4

 

1.

2.

3.

Select the correct answer to: 

 

  ( 3 ) - 2
( 4 )
-1 -1

 

Answers

1. ( 11 )   2. ( 7 )   3. ( -5 )
-2 -3 1

 

1.

2.

3.

Select the correct answer to: 

 

  ( 3 ) -
( 4 )
-1 -1

 

Answers

1. ( -1 )   2. ( -1 )   3. ( -7 )
0 -2 -2

 

1.

2.

3.

Select the correct answer to: 

 

3 ( 3 ) - 2
( 4 )
-1 -1

 

Answers

1. ( 13 )   2. ( 1 )   3. ( 13 )
-2 -1 -4

 

1.

2.

3.

Select the correct answer to: 

 

2 ( -5 ) - 3
( 1 )
0 -1

 

Answers

1. ( -13 )   2. ( 1 )   3. ( 13 )
3 -2 -3

 

1.

2.

3.

Select the correct answer to: 

 

3 ( -4 ) -
( 4 )
1 -2

 

Answers

1. ( -16 )   2. ( 0 )   3. ( -16 )
1 -1 5

 

1.

2.

3.

Select the correct answer to: 

 

3 ( 4 ) + 2
( 2 )
-1 -3

 

Answers

1. ( 14 )   2. ( 16 )   3. ( -16 )
-4 -9 -7

 

1.

2.

3.

Select the correct answer to: 

 

4 ( -2 ) - 2
( -2 )
-1 -1

 

Answers

1. ( 4 )   2. ( -8 )   3. ( -4 )
-4 2 -2

 

1.

2.

3.

  • Question 1

Select the correct answer to: 

 

( 3 ) + 2
( -2 )
4 3

 

Answers

1. ( -1 )   2. ( 4 )   3. ( -1 )
10 10 7

 

CORRECT ANSWER
1.
  • Question 2

Select the correct answer to: 

 

2 ( 3 ) +
( -2 )
4 3

 

Answers

1. ( -1 )   2. ( 4 )   3. ( -1 )
10 11 7

 

CORRECT ANSWER
2.
  • Question 3

Select the correct answer to: 

 

3 ( 3 ) +
( 4 )
-1 -1

 

Answers

1. ( 13 )   2. ( 7 )   3. ( 13 )
-2 -2 -4

 

CORRECT ANSWER
3.
  • Question 4

Select the correct answer to: 

 

  ( 3 ) - 2
( 4 )
-1 -1

 

Answers

1. ( 11 )   2. ( 7 )   3. ( -5 )
-2 -3 1

 

CORRECT ANSWER
3.
  • Question 5

Select the correct answer to: 

 

  ( 3 ) -
( 4 )
-1 -1

 

Answers

1. ( -1 )   2. ( -1 )   3. ( -7 )
0 -2 -2

 

CORRECT ANSWER
1.
  • Question 6

Select the correct answer to: 

 

3 ( 3 ) - 2
( 4 )
-1 -1

 

Answers

1. ( 13 )   2. ( 1 )   3. ( 13 )
-2 -1 -4

 

CORRECT ANSWER
2.
  • Question 7

Select the correct answer to: 

 

2 ( -5 ) - 3
( 1 )
0 -1

 

Answers

1. ( -13 )   2. ( 1 )   3. ( 13 )
3 -2 -3

 

CORRECT ANSWER
1.
  • Question 8

Select the correct answer to: 

 

3 ( -4 ) -
( 4 )
1 -2

 

Answers

1. ( -16 )   2. ( 0 )   3. ( -16 )
1 -1 5

 

CORRECT ANSWER
3.
  • Question 9

Select the correct answer to: 

 

3 ( 4 ) + 2
( 2 )
-1 -3

 

Answers

1. ( 14 )   2. ( 16 )   3. ( -16 )
-4 -9 -7

 

CORRECT ANSWER
2.
  • Question 10

Select the correct answer to: 

 

4 ( -2 ) - 2
( -2 )
-1 -1

 

Answers

1. ( 4 )   2. ( -8 )   3. ( -4 )
-4 2 -2

 

CORRECT ANSWER
3.
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