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YEAR 7
MATHS

Name: ______________________________
1

Contents
Number:
Types of number
Place value
Algebra:
Coordinates
Patterns and sequences
Collecting like terms (simplifying)
Solving linear equations
Shape, Space and Measure:
Types of shapes and properties
Area and perimeter of rectangles and triangles
Data Handling:
Averages
Tally charts and bar graphs
Probability:
Probability

2

Types of Numbers
Things to remember:
 A factor is a whole number that divides exactly into another number
...

 A prime number only has 2 factors – 1 and itself
...

 A square number is the result of multiplying an integer (whole number) by itself
...

(a)
Write down the square of 8
……………………
...

(1)

(c)

Estimate the value of √20
……………………
...


Here is a list of eight numbers:
From the list, write down
(i)
a factor of 20

4 5 14 25 29 30 33 39 40
……………………
...


(iii)

the prime number that is greater than 15
……………………
...


Express 180 as a product of its prime factors
...

(Total for Question is 3 marks)
3

4
...

(1)

(b)

(c)

Write down the value of √25

……………………
...

(1)
(Total for Question is 3 marks)

5
...

(1)

5² + 2³

……………………
...


Here is a list of numbers:
2
3
10
12
15
From the list write down
(i)
an odd number

16

24
……………………
...

(1)

(c)

a factor of 18
……………………
...


Here is a list of numbers
...

(1)

(b)

write down the square number
……………………
...

(1)
(Total for Question is 3 marks)
4

8
...

1
2
4
5
7
11
13
14
15
17
From the list, write down three different prime numbers that add together to make 20

…
...

(a)
Write the number seven thousand and twenty five in figures
...

(1)
(b)

Write the number 9450 in words
...

(1)
Write the number 28
...


(d)

…
...

…
...


Write down the value of the 3 in the number 4376
…
...


Write down the value of the 3 in 16
...

(Total for question is 1 mark)

4
...

(1)
Write these numbers in order of size
...

2
...
71
0
...
4
…………………………………………………………………………………………………
...

…
...


(a)

(b)

Write these numbers in order of size
...

3517
7135
5713
1357
…………………………………………………………………………………………………
...
Start with the smallest number
...
354
0
...
35
0
...

(1)
(Total for Question is 2 marks)

6
...
There is a number on each card
...

…
...

…………………………………………………………………………………………………
...


(a)

(b)

(c)

Write these numbers in order of size
...

3007
4435
399
4011
3333
…………………………………………………………………………………………………
...
Start with the smallest number
...
7
5
...
7
14
...

(1)
9
Write 10 as a decimal
...

(1)
(Total for question = 3 marks)

7

Coordinates
y
4

Things to remember:
Along the corridor, up the stairs  (x,y)

3

Questions:
1
...

(…
...
Label the point Q
...
Label the point R
...


(a)

(b)

Write down the coordinates of the point
(i)
A,
( ……… , ……
...

( ……… , ……
...

(1)
(Total 3 marks)

y
4
3
2

A
B

1

0

3
...

(……………,…………
...

(……………,…………
...

On the grid, mark the point (3, 0) with
the letter Q
...


5
...


(a)

(b)

Write down the coordinates of
the point
(i)
A,
(…
...

(…
...

(ii)
Write down the
coordinates of D
...
)
(2)
(Total 4 marks)

(a)

Write down the coordinates of the point A
...
)
(1)
Write down the coordinates of the point B
...
)
(1)
On the grid, mark with a cross (×) the point
(−3, −1)
...

(1)
(Total for question = 3 marks)

(a)

(i)

Write down the coordinates of
the point A
...
)

(ii)

(b)

Write down the coordinates of
the point B
...
)
(2)
On the grid, mark with a cross the
point (3, –4)
...

(1)
(Total for Question is 3 marks)

9

Patterns and Sequences
Things to remember:
 If there is a pattern, look carefully at how many sticks/blocks are being added on each time
...

Questions:
1
...


In the space below, draw Pattern number 4

(1)
(b)

Complete the table
...

(1)
(Total for Question is 3 marks)

2
...

6
10
14
(a)
Write down the next term in this sequence
...

(1)

(b)

Find the 10th term in this sequence
...

(1)
The number 101 is not a term in this sequence
...

…
...

(1)
(Total for Question is 3 marks)
10

3
...

3
7
11
15
(a)
Write down the next term of this sequence
...

(1)
The 50th term of this number sequence is 199
(b)
Write down the 51st term of this sequence
...

(1)
The number 372 is not a term of this sequence
...

…
...

(1)
(Total for Question is 3 marks)

4
...


(a)

In the space below, draw Pattern 4

(b)

Find the number of grey squares in Pattern 6

(1)

…
...

(c) Work out how many white squares there are in this Pattern
...

(2)
(Total for Question is 4 marks)
11

5
...


(a)

Draw Pattern number 4 in the space below
...

(2)
Sunil says that he will need 70 sticks for Pattern number 20
(c)
Is Sunil correct? You must give a reason for your answer
...

…
...

(2)
(Total for Question is 5 marks)
6
...

5
9
13
17
(a)
Write down the next term of the sequence
...

(1)
Work out the eleventh term of the sequence
...


…
...

…
...

(2)
(Total for Question is 3 marks)
12

7
...


(a)

In the space below, draw pattern number 4

(1)
(b)

Find the total number of tiles in pattern number 20
…
...


Here is a sequence of patterns made from sticks
...

(2)
(Total for question = 3 marks)
13

Collecting Like Terms (Simplifying)
Things to remember:
 2a means a + a or 2 lots of a
 a² means a x a
 The sign (+ or -) belongs to the term following it
...

Questions:
1
...

(1)
(b)

Simplify 3 × c × d
…
...

(1)
(Total for Question is 3 marks)

2
...

(1)

(b)

Simplify

8n – 3n
…
...

(1)

(d)

Simplify

3x + 7y + 2x – y
…
...


Simplify

3x + 5y + x + 4y
…
...


(a)

Simplify

a×c×3

…
...

(1)
(c)

Simplify

5x – 4y + 3x – 3y

…
...


(a)

Simplify 5a – 2a

…
...

(1)
(c)

Simplify 3e + 4f + 2e – f

…
...


(a)

Simplify

m+m+m
…
...

(1)
(c)

Simplify

5 × 3g

…
...


(a)

Simplify

d+d+d+d
…
...

(1)
(c)

Simplify

2x + 3y + 3x – y

…
...


(a)

Simplify

f+f+f+f–f
…
...

(1)

(c)

Simplify

3a + 2h + a + 3h
…
...

 The inverse of + is – and the inverse of x is ÷
 Work one step at a time, keeping you = signs in line on each new row of working
...

A two step function machine is shown
...

(1)

(b)

If the output is 25, what was the input?
…
...

(2)
(Total for Question is 4 marks)
2
...

Total cost = £4 per hour plus £12
Arun hires a car for 5 hours
...


£…
...

The total cost is £40
(b)
Work out how many hours Raj hires the car for
...
hours
(3)
(Total for Question is 5 marks)
17

3
...

(1)
(b)

Solve 5h + 7 = 17

h=
...


(a)

Solve x + 9 = 19

x=
...

(1)
(c)

Solve

w⁄4=

8

w=
...


(a)

Solve

=2

n=
...

(2)
(Total for Question is 3 marks)

18

6
...

(1)
(b)

Solve y − 9 = 17

y=
...


Solve

3x + 7 = 1

x=
...


Solve 4x + 5 = x + 26

x=
...

 Edges, faces and vertices belong on 3D shapes
...

Here is a triangular prism
...

(ii)

the number of faces

...


The net is folded to make the prism
...

(b)
Mark this point on the net with the letter P
...


Here is a cuboid
...

Complete each sentence by writing the correct number in the gap
...
faces
...
edges
...
vertices
...


(a)

On the grid, draw a kite
...


(1)

Write down the special name of this quadrilateral
...

(1)
(Total for Question is 2 marks)

21

4
...


(Total for Question is 1 marks)
5
...


(i)

6
...


(ii)


...


(a)

(b)

(c)

(d)

Write down the letter of the shape that is a sphere
...

(1)
Write down the mathematical name of shape A
...

(1)
How many faces does shape B have?

...

(1)

22

Area and Perimeter of Rectangles and Triangles
Things to remember:
 Area of a rectangle = base x height
 Area of a triangle = ½ x base x height
 The perimeter is the distance around the outside of shape
Questions:
1
...


(Total for Question is 2 marks)
2
...


(Total for Question is 2 marks)

23

3
...
Work out the area of this rectangle
...
cm2
(Total for Question is 2 marks)
4
...


(a)

Find the perimeter of the shaded shape
...
cm
(1)

(b)

Find the area of the shaded shape
...
cm2
(1)
(Total for Question is 2 marks)

24

5
...

(a)
Find the perimeter of the shaded shape
...
cm
(2)
On the grid below, draw a square with the same area as the shaded shape
...


Dilys buys a new house
...

The lawn is going to be in the shape of a rectangle
...
The lawn will have a width of 8 m
...

The length of the edging strip needs to be equal to the perimeter of her lawn
...
50 per metre
...

(Total for Question is 4 marks)

26

Tally Charts and Bar Graphs
Things to remember:
 The fifth tally mark should make a gate – this makes it easier to count the tally as you can
count up in 5s
...

 If you are drawing a bar chart, the axes must be labelled
...

Ray and Clare are pupils at different schools
...
Here is Ray’s bar chart of his teachers’ favourite colours
...

…………………………………………………………………………………………………
...

(2)
Clare drew a bar chart of her teachers’ favourite colours
...

6
5
4
Frequency

3
2
1
0

Red

Blue

Yellow

Green

Colours

4 teachers said that Yellow was their favourite colour
...

(b)
Complete Clare’s bar chart
...

(1)
Work out the number of teachers Clare asked
...

(1)
Write down the fraction of the number of teachers that Clare asked who said Red
was their favourite colour
...

(1)
(Total 7 marks)
27

A shop has a sale
...

£
100
90
80

Key

70
60
Reduction
in price

50
40
30

Sale
price

20

Fryer

Mixer

Cook set

Iron

0

Microwave

10

Vacuum
cleaner

2
...

£
...
and
...

(1)

Mixer

Fryer

Normal price

£90

Normal price

£85

Sale price

£70

Sale price

£70

(d)

Complete the bar chart for the mixer and the fryer
...


Daniel carried out a survey of his friends’ favourite flavour of crisps
...

Plain
Chicken
Bovril
Salt & Vinegar
Salt & Vinegar
Plain
Chicken
Plain
Plain
Chicken
Bovril
Salt & Vinegar
Bovril
Plain
Plain
Salt & Vinegar
(a)

Complete the table to show Daniel’s results
...


Write down the number of Daniel’s friends whose favourite flavour was Salt &
Vinegar
...

(1)
Which was the favourite flavour of most of Daniel’s friends?
……………………
...

Hours of TV watched last week
9
8
7
6
Number
of hours 5

Helen

4

Robin

3
2
1
0

Sunday

Monday

Tuesday Wednesday Thursday

Friday

Saturday

Day

(a)

(b)

(c)

Write down the number of hours of TV that Helen watched on Monday
...

………………………hours
(ii)
Who watched the greater number of hours of TV on Friday and Saturday?
Show your working
...


Heather carried out a survey about her friends’ pets
...

Cat
Cat
Dog
Hamster
Cat
Dog
Hamster
Cat
Cat
Dog
Hamster
Dog
Hamster
Dog
Fish
Cat
Dog
Fish
Cat
Cat
Complete the table to show Heather’s results

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