KEY STAGE 3: LEVEL 4 QUESTIONS

KEY STAGE 3: LEVEL 4 QUESTIONS
1) Some pupils are climbing up the ropes in the gym.
These are their positions after climbing for a few seconds.
Lena John Dylan Mindu Mary
(a) Dylan is about 1 2
of the way up the rope. Fill each gap with a
fraction.
Lena is about ………… of the way up the rope.
John is about ………… of the way up the rope.
(b)
Dylan is about 50% of the way up the rope.
Fill each gap with a percentage.
Mindu is about …………% of the way up the rope.
Mary is about …………% of the way up the rope.
(c)
Anna is climbing a longer rope.
She has climbed 2 of the way up the rope.
5
Put a X on the rope to show Anna’s position.
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Anna

2) (a) Lisa works in a shoe shop.
She recorded the size of each pair of trainers that she sold during
a week. This is what she wrote down.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
7
6
5
7
7
6
Sizes of trainers sold
7 5 6
4 4 8
8 6 7 5
4 5
4 9 5 7 8
5 7 6 9 4 7
Use a tallying method to make a table showing how many pairs of
trainers of each size were sold during the whole week.
(b)
(c)
Which size of trainer did Lisa sell the most of?
Lisa said,
How can you tell from your table that Lisa is wrong?
Most of the trainers sold
were bigger than size 6.
3)
s
s
t
t
t
The perimeter of this shape is 3t + 2s.
Write an expression for the perimeters of each of these shapes.
Write each expression in its simplest form.
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a
a
c
b
c
a
b
b
5
e
3
d
7
d
e
f
f
e
f
f
e
4) (a) At a sports center, people take part in one of five different sports.
This table shows the percentage of people who played badminton,
football and squash on Friday.
Friday
Badminton
Football
Squash
Swimming
Tennis
10%
40%
5%
?
?
badminton
Label the correct two sections of the pie chart football and
squash. Badminton has been labelled for you.
(b)
On Friday more people went swimming than played tennis.
Use the chart to estimate the percentage of people who went
swimming.
Use the chart to estimate the percentage of people who played
tennis.
Make sure you have accounted for all the people.
(c)
Altogether 260 people played the different sports on Friday.
Complete this table to show how many people played badminton,
football and squash on Friday.
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Friday
Sport Percentage Number of people
Badminton 10%
26
Football 40%
Squash 5%
(d)
Altogether 260 people played the different sports on Friday and
700 people played the different sports on Saturday.
40% of the people played football on Friday, but only 20% of the
people played football on Saturday.
Mike said : “40% is more than 20%, so more people played
football on Friday.”
Explain why Mike is wrong.
5) These patterns come from Egypt.
The first pattern looks the same after part of a turn.
It will look the same in 4 different positions.
In how many positions will each of these patterns look the same?
Write the number below each pattern.
(a)
(b)
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(c)
(d)
6) (a) Claire puts a 2 digit whole number into her calculator.
She multiplies the number by 10.
Fill in one other digit which you know must be on the calculator
display.
7
.
(b)
Claire starts again with the same 2 digit whole number.
This time she multiplies it by 100.
Fill in all the digits that might be on the calculator display.
4
7) Cubes
There are 30 cubes in a bag.
Kim takes a cube without looking inside the bag.
She writes down its colour and then puts the cube back in the bag.
She does this 30 times.
Kim records her results in a chart:
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Red
Black
White
Green
Yellow
7
3
11
4
5
(a)
Kim says:
There must be 7 red cubes
in the bag, because there are
7 reds in my chart.
Explain why Kim is wrong.
(b)
(c)
What is the smallest number of green cubes there could be in the
bag?
Kim says:
There cannot be any blue cubes
in the bag, because there are
no blues in my chart.
Explain why Kim is wrong.
(d)
Kim takes one more cube out of the bag.
What colour is the cube most likely to be?
Use the results in the chart to help you to decide.
8) Vegetables
Simon is growing vegetables in three vegetable patches.
(a)
About 50% of this vegetable patch is for carrots.
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carrots
cabbages
lettuces
Fill in each gap with a percentage.
About ………… % of the patch is for cabbages.
About ………… % of the patch is for lettuces.
(b)
About 1 8
of this vegetable patch is for betroth.
beetroot
broad beans
peas
Fill in each gap with a fraction.
About ………… of the patch is for broad beans.
About ………… of the patch is for peas.
(c)
About 4 of this vegetable patch is for potatoes.
5
Draw a straight line to show how much of the patch is for
potatoes. Shade in the area for potatoes.
The rest of the patch is for turnips.
About what fraction of the patch is for turnips?
9) Tiles
Alana has 3 tiles.
Whole edges of tiles must meet, like this:
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They cannot join like this:
Alana joins her 3 tiles together to make a shape.
She draws her shape on triangle dotty paper.
(a)
Draw one different shape made from Alana’s 3 tiles.
(b)
Draw another different shape made from Alana’s 3 tiles.
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(c)
The dots on the triangle dotty paper are 1cm apart.
What is the perimeter of Alana’s shape?
(d)
Draw a shape made from Alana’s 3 tiles which has a smaller
perimeter than Alana’s shape.
10) Cards
Here are some number cards:
0 1 2 3 4 5
Joan picked these three cards:
4
3
She made the number 314 with her cards.
1
(a)
(b)
Make a smaller number with Joan’s three cards.
Make the biggest number you can with Joan’s three cards.
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(c)
Joan made the number 314 with her three cards.
Which extra card should she pick to make her number 10 times as
big?
What number is 10 times as big as 314?
(d)
Andy has these cards:
0 1 2 3 4 5
He made the number 42.5 with four of his cards.
Use some of Andy’s cards to show the number 10 times as big as
42.5
Use some of Andy’s cards to show the number 100 times as big
as 42.5
11) Travel
There are 24 pupils in Jim’s class.
He did a survey of how the pupils in his class traveled to school.
He started to draw a pie chart to show his results.
(a)
4 pupils traveled to school by train.
Show this on Jim’s pie chart as accurately as you can.
Label this part train.
Label the remaining part car.
Jim's class (24 pupils)
bicycle
bus
walk
(b)
There are 36 pupils in Sara’s class.
She did the same survey and drew a pie chart to show her results.
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15 pupils traveled by bus and 6 pupils walked.
On Sara’s pie chart write how many pupils traveled to school by
train, car and bicycle.
Sara’s class (36 pupils)
bicycle ........
walk 6
train ........
car ........
bus 15
(c)
Jim says:
15 pupils in Sara's class travelled by bus.
Only 12 pupils in my class travelled by bus.
Sara's pie chart shows fewer people
travelling by bus than mine does.
So Sara's chart must be wrong.
12) Squares
Explain why Jim is wrong.
Kath puts 1 small square
tile on a square dotty grid,
like this:
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.
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.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
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.
.
Den makes a bigger square
with 4 small square tiles,
like this:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
.
.
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(a)
Scott has 9 small square tiles.
On the grid below, show how Scott can make a square in the
same way with 9 small square tiles.
(b) On the grid below, show how to make a square with more than 9
of these small square tiles.
How many tiles are there in your square?
(c)
Huw wants to make some more squares with the tiles.
Write 3 other numbers of tiles that he can use to make squares.
Huw can use:
1 tile or 4 tiles or 9 tiles or ............ tiles or ........... tiles or ...........
tiles
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13) Snacks
A machine in a youth club sells snacks.
Crisps:
20p
Chocolate bars: 35p
Drinks:
40p
Rolls:
75p
Sandwiches: £1.00
Len writes down the amounts of money which different people spend
one evening during each hour that the club is open:
Amounts of money spent during each hour
5 pm to 6 pm
40p
60p
55p
20p
40p
60p
55p
40p
6 pm to 7 pm
75p
55p
60p
40p
£1.15
40p
75p
40p
7 pm to 8 pm
£1.75
£1.40
£1.60
75p
£1.40
£1.10
60p
£1.50
(a)
Len says:
40p is the mode of the
amounts of money spent.
Explain why Len is right.
(b)
Len groups the amounts and starts to make a tally chart.
Fill in Len’s chart for 7 p.m. to 8 p.m..
Then fill in the column for the total number of people who spent
each amount.
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Amount of
money spent
5pm
to
6pm
Time
6pm
to
7pm
7pm
to
8pm
Total number
of people who
spent each
amount
Under 50p
I I I I
I I I
7
50p to 99p
I I I I
I I I I
£1.00 to £1.49
I
Over £1.49
(c)
Len says:
Now 50p to 99p is the mode.
Is Len right? Explain your answer.
(d)
Look at where the tally marks are on the chart.
What do you notice about the amounts of money people spent at
different times in the evening?
Give a reason which could explain the difference you notice.
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14) Lengths
(a) This triangle is accurately drawn
One side is 17.5cm long.
17.5 cm
Glyn says:
The perimeter of the triangle
is about 30cm.
How can you tell that he is wrong without measuring the other two
sides?
(b)
(c)
Measure each of the other two sides of the triangle.
Write their lengths to the nearest 0.1 of a centimetre.
Add up the lengths of the three sides of the triangle to find the
perimeter of the triangle.
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15) Symmetry
Catrin shades in a shape made of five squares on a grid:
She shades in 1 more square to make a shape which has the dashed
line as a line of symmetry:
(a)
Shade in 1 more square to make a shape which has the dashed
line as a line of symmetry.
You may use a mirror or tracing paper to help you.
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(b)
Shade in 1 more square to make a shape which has the dashed
line as a line of symmetry.
You may use a mirror or tracing paper to help you.
(c)
Shade in 2 more squares to make a shape which has the dashed
line as a line of symmetry.
You may use a mirror or tracing paper to help you.
(d)
Shade in 2 more squares to make a shape which has the dashed
line as a line of symmetry.
You may use a mirror or tracing paper to help you.
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16) Forty-five
(a) Fill in the missing numbers so that the answer is always 45.
The first one is done for you.
40 + ...... 5
142 – ..........
50% of ..........
=45
450 ÷ ..........
1
4
of ..........
(b) Fill in the gaps below to make the answer 45.
You may use any of these signs: + – × ÷
28 ........ 2 ........ 31 = 45
17) Symmetry
Some board games have pegs in holes.
(a) On each board below, shade 5 more pegs so that the dashed line
is a line of symmetry.
You may use a mirror or tracing paper to help.
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(b)
Shade 9 more pegs so that both dashed lines are lines of
symmetry.
18) Distances
This table shows the distances between some towns.
Distances in miles:
Hull
Exeter
305
Bangor
199 289
Dover
261 248 331
Hull Exeter Bangor Dover
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(a)
(b)
Which two towns are the shortest distance from each other?
Mrs. Davis drove from Bangor to Exeter.
What is the distance between Bangor and Exeter?
Then Mrs. Davis drove from Exeter to Dover.
What is the distance between Exeter and Dover?
How far did Mrs. Davis drive altogether?
19) Packs
(a) Carl is putting packs of biscuits into a box.
He said to put in the bottom layer.
The box holds 5 packs across and is 4 packs wide.
How many packs will fit altogether on the bottom layer?
The box holds 6 layers.
How many packs will fit in the box when it is full?
(b)
Aziz is putting packs of tea into a box.
The box holds 5 packs across and is 6 packs wide.
The box holds 3 layers.
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How many packs of tea will fit in the box when it is full?

(c)
Fill in the gaps below to show one way of filling a different box
with 24 packs in 2 layers.
total: 24 packs
2 layers
.......................... packs across
............................... pack wide
20) Cards
(a) Joe has these cards:
8 3 9 4 5 2 7 9
Sara takes a card without looking.
Joe says:
On Sara’s card,
is more likely than
Explain why Joe is wrong.
Here are some words and phrases:
impossible not likely certain likely
Choose a word or a phrase to fill in the gaps below.
It is ...................... that the number on Sara’s card will be smaller
than 10.
It is ...................... that the number on Sara’s card will be an odd
number.
(b)
Joe still has these cards:
8 3 9 4 5 2 7 9
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Joe mixes them up and puts them face down on the table.
Then he turns the first card over, like this:

5
Joe is going to turn the next card over.
Copy and complete this sentence:
On the next card, ………… is less likely than …………
The number on the next card could be higher than 5 or lower
than 5.
Which is more likely?
Tick the correct box.
higher than 5 lower than 5 cannot tell
Explain your answer.
21) Child
(a) The scale shows how long Laura was when she was born.
How long was Laura?
(b)
When Laura was one month old she was put on the scales.
3 4
kg
What mass do the scales show?
(c)
Now Laura is older. She is 1.03m tall.
Write Laura’s height in centimetres.
22) Playgroup
There are 50 children altogether in a playgroup.
(a)
How many of the children are girls?
boys
girls
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What percentage of the children are girls?

(b)
25 of the children are 4 years old.
20 of the children are 3 years old.
5 of the children are 2 years old.
Show this information on the diagram
below. Label each part clearly.
23) Cuboids
(a) These cuboids are made from small cubes.
Write how many small cubes there are in each cuboid.
The first is done for you.
2
2
1
2
3
Number of cubes: .......... 12
5
Number of cubes: ..........
2
4
2
2
3
5
Number of cubes: ..........
Number of cubes: ..........
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(b)
The following shape is made with two cuboids.
Write how many small cubes there are in this shape.
2
2
4
4
Number of cubes: ..........
24) Calculations
(a) Write what the missing numbers could be in the empty boxes.
+ – = 10 24
× × =
3 30
(b) Find the answer. 48 ÷ 4 =
(c) Find the answers. 524 – 249 =
46 × 8 =
144 ÷ 9 =
25) Cassettes
(a) A shop sells video tapes for £2.50 each.
What is the cost of 16 video tapes?
(b)
The shop sells audio cassettes.
Each cassette costs £1.49
What is the cost of 4 cassettes?
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(c) How many cassettes can you buy with £12?
(d)
The shop also sells cassettes in packs of three.
A pack costs £3.99
How many packs can you buy with £12?
(e) What is the greatest number of cassettes you can buy with £15?
You can buy some packs and some single cassettes.
26) Magic Squares
In a magic square, each row, column and diagonal adds up to the
same number.
For example, each row, column and diagonal in this magic square adds
up to 15
15
8 3 4 15 8 3 4 8 3 4
1 5 9 15 1 5 9 1 5 9
6 7 2 15 6 7 2 6 7 2
15
15
15
15
Here is another magic square.
Use the numbers in the first row of this magic square to work out what
each row, column and diagonal must add up to.
Then complete the magic square.
24 34 5
24 + 34 + 5 = ..........
2 .......... ..........
37 .......... 18
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27) Cakes
Here are the ingredients for 1 fruit cake:
1 fruit cake
200g self–raising flour
100g caster sugar
150g margarine
125g mixed fruit
3 eggs
(a)
Copy and complete the table to show how much of each
ingredient you need to make 10 fruit cakes.
Give your answers in grams and in kilograms.
2000 2
10 fruit cakes
............ g = ............ kg self–raising flour
............ g = ............ kg caster sugar
............ g = ............ kg margarine
............ g = ............ kg mixed fruit
30
eggs
(b)
6 eggs cost 70p
How much will 30 eggs cost?
28) Balancing
2 boxes balance 1 can.
2 cans balance 1 bottle.
How many boxes make each of the following balance?
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(a)
?
(b)
?
(c)
?
(d)
Joe has these four things:
He wants to put them on the scales to make them balance.
Show where each thing must go on the scales.
29) Patterns
Owen has some tiles like these:
He uses the tiles to make a series of patterns.
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Pattern
Number
1
Pattern
Number
2
Pattern
Number
3
Pattern
Number
4
(a)
Each new pattern has more tiles than the one before.
The number of tiles goes up by the same amount each time.
How many more tiles does Owen add each time he makes a
new pattern?
(b)
How many tiles will Owen need altogether to make pattern
number 6?
(c)
How many tiles will Owen need altogether to make pattern
number 9?
(d)
Owen uses 40 tiles to make a pattern.
What is the number of the pattern he makes?
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30) Spinners
Here are four spinners, labelled P, Q, R and S.
P
Q
R
S
Key
Plain
Shaded
Striped
(a)
(b)
(c)
Which spinner gives the greatest chance that the arrow will land
on plain?
Which spinner gives the smallest chance that the arrow will land
on shaded?
Shade this spinner so that it is certain that the arrow will land on
shaded.
(d)
Shade this spinner so that there is a 50% chance that the arrow
will land on shaded.
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31) Games
Jim, Bob, Liz and Meg had a games competition.
They played two games, Draughts and Ludo.
Each pupil played each of the others at the two different games.
Meg recorded how many Jim recorded who won
games each person won. each game.
Jim
/ / /
Draughts
Ludo
Meg
/ / /
Jim
Meg
Liz
/ / / /
Liz
Bob
Bob
/ /
Bob
Jim
Meg
Jim
Liz
Liz
Meg
(a)
(b)
(c)
(d)
Jim forgot to put one of the names on his table.
Use Meg's table to work out what the missing name is.
Who won the most games of Draughts?
Give one reason why Meg's table is a good way of recording the
results.
Give one reason why Jim's table is a good way of recording the
results.
32) Cuboids
This cuboid is made from 12 small cubes.
Number of cubes: .… 12 …..
2
2
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3

(a)
Write how many small cubes there are in this cuboid.
3
5
2
(b)
This shape is made with two cuboids.
Write how many small cubes there are in this shape.
2
2
4
4
33) Calculations
Find the answers. 524 – 249 =
46 × 8 =
144 ÷ 8 =
34) Missing Numbers
Write one number at the end of each equation to make it correct.
Example 26 + 34 = 16 + .....44....
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
400 + 150 = 500 + …………..……….……..
14 + 6 = 4 + …………..……….……..
37 – 20 = 27 – …………..……….……..
6 × 5 = 3 × …………..……….……..
38 + 17 = 28 + …………..……….……..
38 – 17 = 28 – …………..……….……..
40 × 10 = 4 × …………..……….……..
7000 ÷ 100 = 700 ÷ …………..……….……..
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35) Triangles
This is a right-angled
triangular tile:
You can fit 8 of the tiles into
a 4cm by a 4cm square like this:
2cm
2cm
4cm
4cm
Write how many of the tiles you can fit into each of these shapes.
4cm
6cm
2cm
4cm
2cm
6cm
2cm
2cm
2cm
4cm
4cm
2cm
4cm
2cm
36) Tiles
Daniel has some parallelogram tiles.
He puts them on a grid, in a continuing pattern.
He numbers each tile.
The diagram shows part of the pattern of tiles on the grid.
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y
6
3
x
4
2
x
2
1
x
0
2 4 6 8
Daniel marks the top right corner of each tile with a •
The co-ordinates of the corner with a • on tile number 3 are (6, 6)
(a) What are the co-ordinates of the corner with a • on tile number 4?
x
(b)
What are the co-ordinates of the corner with a • on tile number
20?
Explain how you worked out your answer.
(c)
Daniel says:
One tile in the pattern has a
in the corner at ( 25 , 25)
Explain why Daniel is wrong.
(d)
Daniel marks the bottom right corner of each tile with a X
Fill in the table to show the co-ordinates of each corner with a X.
tile number co-ordinates of the corner with a X
1 (...2..., ...1...)
2 (……, ……)
3 (……, ……)
4 (……, ……)
Fill in the missing numbers below.
(e)
Tile number 7 has a X in the corner at (………… , …………)
(f) Tile number ……………….. has a X in the corner at (20, 19)
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37) Relations
Look at these three signs:
<
is less than
=
is equal to
>
is greater than
Examples:
5 < 6
5 is less than 6
4 – 3 = 2 – 1
4 – 3 is equal to 2 – 1
6 – 2 > 9 – 6
6 – 2 is greater than 9 – 6
Put the correct sign, < or = or >, into each number sentence.
(a) 8 + 2 ........ 7 + 6
(b) 6 – 3 ........ 1 + 2
(c) 0 ........ –3
(d) –7 ........ –2
(e) 3 – 2 ........ –5
(f) 5 – 5 ........ 4 – 6
38) Beads
Bryn has some bags with some black beads and some white beads.
He is going to take a bead from each bag without looking.
(a)
Match the pictures to the statements. The first is done for you.
It is impossible that Bryn will take a black bead from bag …D…
It is unlikely that Bryn will take a black bead from bag .......………
It is equally likely that Bryn will take a black bead or a white bead
from bag .…….…...
It is likely that Bryn will take a black bead from bag .......…….
It is certain that Bryn will take a black bead from bag .......…….
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(b)
Bryn has 5 white beads in a bag.
He wants to make it more likely that he will take a black bead
than a white bead out of the bag.
How many black beads should Bryn put into the bag?
(c)
There are 20 beads altogether in another bag.
All the beads are either black or white.
It is equally likely that Bryn will take a black bead or a white bead
from the bag.
How many black beads and how many white beads are there in
the bag?
39) Arrangements
Here are some number cards:
1 7 3 5
You can use each card once to make the number 1735, like this:
1 7 3 5
(a)
(b)
What is the biggest number you can make with the four cards?
Explain why you cannot make an even number with the four
cards.
(c) 1 7 3 5
Use some of the four number cards to make numbers that are as
close as possible to the numbers written below.
Examples
80
7
5
30
3
1
You must not use the same card more than once in each answer.
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50
60
4000
1500
1600
40) Holiday
The table shows the cost for an adult for one week in a Holiday Camp.
It is for holidays between June and September in 1999.
Holiday starting between
June 5 – July 2
July 3 – July 16
July 17 – September 3
September 4 – September 10
September 11 – September 24
Cost
£85
£105
£130
£90
£75
(a)
All the holidays start on a Saturday.
The graph shows the cost of the holidays starting on each
Saturday. Copy and complete the graph for the last four weeks.
Cost
£160
Cost of holidays
£140
£120
£100
£80
£60
£40
£20
£0
5 12 19 26 3 10 17 24 31 7 14 21 28 4 11 18
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June July August September
Starting Date (Saturdays)

(b)
(c)
(d)
What is the cost for an adult for one week in the Holiday Camp,
beginning on August 14?
The holidays cost more at some times than at others.
Give a reason which could explain this difference.
The cost in June for an adult for one week in the Holiday Camp is
£85. The cost for a child is 25% less.
Child:
25% off
adult cost
What is the cost in June for a child for one week in the Holiday
Camp? Show your working.
What is the total cost for an adult and a child for one week in the
Holiday Camp in June?
41) Clock
(a) The time on this clock is 3 o'clock.
11
12
1
10
2
9
3
8
7
6
5
4
What is the size of the angle between the hands?
(b)
Use a whole number to complete this sentence:
At ..……………..... o'clock the size of the angle between the hands
is 180°
(c)
(d)
What is the size of the angle between the hands at 1 o'clock?
What is the size of the angle between the hands at 5 o'clock?
(e) How long does it take for the minute hand to move 360°?
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42) Missing Numbers
Write one number at the end of each equation to make it correct.
Example 26 + 34 = 16 + 44
(a)
(b)
(c)
(d)
38 + 17 = 28 + …………..……….……..
38 – 17 = 28 – …………..……….……..
40 × 10 = 4 × …………..……….……..
7000 ÷ 100 = 700 ÷ …………..……….……..
43) Sixty-fives
Here is the 65 times table.
1
×
65
=
65
2
×
65
=
130
3
×
65
=
195
4
×
65
=
260
5
×
65
=
325
6
×
65
=
390
7
×
65
=
455
8
×
65
=
520
9
×
65
=
585
10
×
65
=
650
(a)
Use the 65 times table to help you fill in the missing numbers.
65 x 5 = .....………
390 ÷ 65 = .....………
12 x 65 = .....………
20 x 65 = .....………
(b) Use the 65 times table to help you work out 16 × 65
Show how you do it.
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44) Spinners
(a) The diagram shows spinner A and spinner B.
A
3
2
4
1
5
B
2
3
1
4
6
5
Which spinner gives you the best chance to get 1?
Indicate one of the following answers.
spinner A spinner B doesn’t matter
Explain why you chose that answer.
(b)
Here are two different spinners.
The spinners are the same shape but different sizes.
C
6
5
1
2
3
4
D
6
5
1
4
2
3
Which spinner gives you the best chance to get 3?
Indicate one of the following answers.
spinner C spinner D doesn’t matter
Explain why you chose that answer
(c)
Each section of spinner E is the same size.
Copy and fill in numbers on spinner E so that both of these
statements are true.
It is equally likely that you will spin 3 or 2
It is more likely that you will spin 4 than 2
1
2
E
2
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45) Shapes
Look at the shaded shape.
y
10
8
6
4
2
0
0
2
4
6
8
10
x
(a)
Two statements below are correct.
Indicate which two you think are correct.
The shape is a quadrilateral.
The shape is a trapezium.
The shape is a pentagon.
The shape is a kite.
The shape is a parallelogram.
(b) What are the co-ordinates of point B?
y
10
8
6
B
4
2
A
0
0
2
4
6
8
10
x
(c)
The shape is reflected in a mirror line.
Point A stays in the same place. Where is point B reflected to?
Put a cross on the grid to show the correct place.
y
10
8
6
B
4
2
A
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0
0
2
4
6
8
10
x

(d)
Now the shape is rotated.
Point A stays in the same place. Where is point B rotated to?
Put a cross on the grid to show the correct place.
y
10
8
6
B
4
2
A
0
0
2
4
6
8
10
x
46) Birthdays
Mark and James have the same birthday.
They were born on 15th March in different years.
(a) Mark will be 12 years old on 15th March, 2001
How old will he be on 15th March, 2010?
(b)
In what year was Mark born?
(c) James will be half of Mark’s age on 15th March, 2001
In what year was James born?
47) Rainfall
A pupil recorded how much rain fell on 5 different days.
Results:
Amount in cm
Monday 0.2
Tuesday 0.8
Wednesday 0.5
Thursday 0.25
Friday 0.05
(a)
Fill in the gaps with the correct day
The most rain fell on ...................
The least rain fell on ...................
(b)
(c)
How much more rain fell on Wednesday than on Thursday?
How much rain fell altogether on Monday, Tuesday and
Wednesday?
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Now write your answer in millimetres.

48) Shapes
The shaded rectangle has an area of 4 cm 2 and a perimeter of 10 cm.
(a)
Look at the cross-shape.
Copy and complete the following statements.
The cross-shape has
an area of …………… cm 2 and a perimeter of ………… cm.
(b) Draw a shape with an area of 6 cm 2
(c)
(d)
What is the perimeter of your shape?
Look at the octagon below.
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What is the area of the octagon?
(e)
Explain how you know that the perimeter of the octagon is more
than 8cm.
49) Tokens
A class has some gold tokens and some silver tokens.
The tokens are all the same size.
(a)
The teacher puts 4 gold tokens and 1 silver token in a bag.
Leah is going to take one token out of the bag without looking.
She says:
There are two colours, so it is just as likely
that I will get a gold token as a silver token.
Explain why Leah is wrong.
(b)
(c)
How many more silver tokens should the teacher put in the bag to
make it just as likely that Leah will get a gold token as a silver
token?
Jack has a different bag with 8 tokens in it.
It is more likely that Jack will take a gold token than a silver token
from his bag. How many gold tokens might there be in Jack’s bag?
50) Temperatures
A book shows two ways to change °C to °F
exact rule
multiply the °C temperature by 1.8
then add 32
approximate rule
double the °C temperature
then add 30
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(a)
Copy and complete the following statements.
Using the exact rule, 25°C is …………… °F
Using the approximate rule, 25°C is ……………°F
(b)
Copy and complete the following statements.
Using the exact rule, 0°C is …………… °F
Using the approximate rule, 0°C is …………… °F
(c)
Show that at 10°C, the exact rule and the approximate rule give
the same answers.
51) Coaches
(a) A club wants to take 3000 people on a journey to London
The club secretary says:
We can go in coaches.
Each coach can carry 52 people.
How many coaches do they need for the journey?
Show your working.
(b)
(c)
Each coach costs £420. What is the total cost of the coaches?
How much is each person’s share of the cost?
52) Temperature
The arrow by this thermometer shows a temperature
of 20°C
ºC
30
(a) Draw an arrow by the thermometer to show 7°C
Label your arrow 7°C
20
20ºC
(b)
Draw an arrow by the thermometer to show –5°C
Label your arrow – 5°C
10
(c)
In New York the temperature was –2°C
In Atlanta the temperature was 7°C warmer.
What was the temperature in Atlanta?
0
(d) In Amsterdam the temperature was 3°C
In Helsinki the temperature was –8°C
How many degrees warmer was it in
Amsterdam than in Helsinki?
–10
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53) Twenty-seven
(a) Fill in the missing numbers.
25½ + ………………… = 27
150 ………………… = 27
50% of ………………… = 27
a quarter of ………………… = 27
(b)
Copy and complete the following calculations.
………………… × ………………… = 27
………………… × ………………… = 27
54) Clocks
My clock shows:
The hours and the minutes are both multiples of 3
multiple of 3
multiple of 3
(a)
Write a different time when the hours and the minutes are both
multiples of 3.
multiple of 3
multiple of 3
(b)
Later, my clock shows:
How many minutes will it be before the hours and the minutes are
both multiples of 6?
55) Folding and Cutting
(a) I start with a rectangle of paper.
I fold it in half, then I cut out three shapes.
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Then I unfold my paper.
Circle the diagram below that shows what my paper looks like now.
(b)
I start again with a different rectangle of paper.
I fold it in half, then in half again, then I cut out two shapes.
Then I unfold my paper.
Circle the diagram below that shows what my paper looks like now.
(c)
I start with a square of paper.
I fold it in half, then in half again, then I cut out one shape.
Then I unfold my paper.
Circle the diagram below that shows what my paper looks like now.
1 mark
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56) Motorway
The diagram shows how many miles there are between junctions on a
motorway.
junction
6
junction
junction
4
5
3 miles
22 miles
junction
3
15 miles
junction
2
7 miles
junction
1
6 miles
(a) How many miles is it from 2 to 4 ?
(b) Which junction is 31 miles from 1 ?
(c)
Mr. Patel uses the motorway.
He drives from 2 to 3 and back again from 3 to 2 .
He does this every day for five days.
How many miles does he drive on the motorway altogether?
57) Using Brackets
(a) Write the answers.
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(4 + 2) × 3 = …………………………
4 + (2 × 3) = …………………………
(b) Work out the answer to (2 + 4) × (6 + 3 + 1)
(c) Put brackets in the following calculation to make the answer 50
4 + 5 + 1 × 5
(d) Now put brackets in the calculation to make the answer 34
4 + 5 + 1 × 5

58) Box
The diagram shows a box.
1.5 cm
1 cm
6 cm
1.5 cm
1 cm
1 cm
1 cm
3 cm
Using square paper, copy and complete the net for the box.
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59) Fractions
(a) Look at these fractions.
1
2
1
3
5
6
Mark each fraction on the number line.
The first one is done for you.
0 1
1
2
(b)
Copy and complete the following equivalencies by filling in the
missing numbers in the boxes.
2
=
12 6
1
2
=
12
1 6
=
24
60) Sunshine
The diagrams show the number of hours of sunshine in two different
months.
Number of hours
of sunshine in month A
20
15
Number
of days
10
5
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less than 4 4 to 8 more than 8
Hours of sunshine

Number of hours
of sunshine in month B
Key:
number of days with
less than 4 hours
number of days with
4 to 8 hours
number of days with
more than 8 hours
(a) How many days are there in month A?
Indicate one of the following answers.
28 29 30 31 not possible
to tell
(b) How many days are there in month B?
Indicate one of the following answers.
28 29 30 31 not possible
to tell
(c)
Which month had more hours of sunshine?
Indicate one of the following answers.
month A
month B
Explain how you know.
61) Map
The map shows the positions of seven towns, numbered 1 to 7
The dashed lines show the roads between the towns.
1
2 3 4
North
7
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6
5

(a) A girl cycled from town 1
She went south to a town.
Then she went east to a different town, where she stopped for a
drink. In which town did she stop for a drink?
(b)
Copy and complete the missing directions in the boxes below.
Start at town 5, go north to town 4,
Thengo............totown 3
Start at town 6, go north–west to town 7,
Thengo............totown 1
(c)
Steve lives in one of these towns.
Town 3 is west of where Steve lives.
In which town does Steve live?
62) Ruler
(a) The diagram shows part of a ruler.
A B C D
3 4 5 6 7 8 9 10 11 12 13
cm
Copy and complete these sentences.
The distance between A and B is ……………………… cm.
The distance between C and D is ……………………… cm.
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(b)
Look at the ruler below.
E
3 4 5 6 7 8 9 10 11 12 13
cm
I want the distance between E and F to be 3½ cm.
There are two places F could be.
Show the two places by copying the ruler and drawing arrows.
63) Getting There
Look at this number chain.
3 + 4 7 × 2
14
(a)
Copy and fill in the missing numbers in the circles below.
16 + 48 × 13.5
÷ 13.5 50
(b)
Copy and fill in the missing numbers in the arrows below.
+
180 2700
×
180 2700
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64) Squares
Alika has a box of square tiles.
The tiles are three different sizes.
1 cm
1 by 1 tile
1 cm
.
.
.
.
.
.
2 cm
. .
. .
. .
. .
. .
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2 cm
3 cm
3 cm
2 by 2 tile
3 by 3 tile
She also has a mat that is 6cm by 6cm.
36 of the 1 by 1 tiles will cover the mat.
6 cm
6 cm
(a)
(b)
(c)
How many of the 2 by 2 tiles will cover the mat?
How many of the 3 by 3 tiles will cover the mat?
Alika glues three tiles on her mat like this:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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Copy and complete the following statements.
She could cover the rest of the mat by using
another two 3 by 3 tiles, and
another . . . . . . . 1 by 1 tiles.
She could cover the rest of the mat by using
another two 2 by 2 tiles, and
another . . . . . . . 1 by 1 tiles.
65) Computation
Work out
238 + 1487 = ..........................
723 154 = …………………
66) Areas
(a) What is the area of this rectangle?
4 cm
3 cm
(b)
I use the rectangle to make four triangles.
Each triangle is the same size.
What is the area of one of the triangles?
4 cm
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3 cm

(c)
I use the four triangles to make a trapezium.
What is the area of the trapezium?
67) Signs
Use +, –, × or ÷ to make each calculation correct.
Examples:
2 .....+...... 4 = 7 .....–..... 1
5 .....×..... 3 = 3 .....×..... 5
5 ............. 2 = 10 .......... 3
12 ........... 3 = 3 .......... 3
2 ........... 1 = 9 .......... 3
6 ........... 6 = 7 .......... 7
68) Angles
Two pupils drew angles on square grids.
Angle A
Angle B
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(a) Which word below describes angle A?
Indicate one of the following answers.
acute
obtuse
right-angled
reflex
(b)
Is angle A bigger than angle B? Yes or No?
Explain your answer.
69) Factors
There are four different ways to put 6 pupils into equal size groups.
1 group of 6
6
pupils
2 groups of 3
3 groups of 2
6 groups of 1
(a)
Show the different ways to put 16 pupils into equal size groups.
group of
groups of
16
pupils
groups of
groups of
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groups of

(b)
Circle the numbers below that are factors of twelve.
1 2 3 4 5 6 7 8 9 10 11 12
70) Thinking of rules
(a) I can think of three different rules to change 6 to 18
6 18
Complete these sentences to show what these rules could be.
first rule
second rule
third rule
add ……………………
multiply by ……………………
multiply by 2 then ……………………
(b)
Now I think of a new rule.
The new rule changes 10 to 5 and it changes 8 to 4
10 5 8 4
Write what the new rule could be.
71) Car parking
P
Car Park
Car Park Charges
15p for 8 minutes
How much does it cost to park for 40 minutes?
Show your working.
72) Heights
(a) Peter's height is 0.9m. Lucy is 0.3m taller than Peter.
What is Lucy's height?
(b)
(c)
Lee's height is 1.45m. Misha is 0.3m shorter than Lee.
What is Misha's height?
Zita's height is 1.7m. What is Zita's height in centimetres?
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73) Place names
Some towns and villages have very long names.
The table shows information about the ten longest place names in the
UK.
Number of letters
67
58
27
22
21
21
19
18
18
17
Country
Wales
Wales
England
Wales
Wales
Wales
England
England
Scotland
Scotland
(a)
(b)
The longest place name in Wales has more letters than the
longest place name in Scotland.
How many more?
50% of the ten longest place names are in Wales.
What percentage of the ten longest place names are in England?
74) Dinner time
The diagram shows what pupils in years 7, 8 and 9 choose to do at
dinner time.
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Key
Year 7
Year 8
Year 9
50
40
30
Number
of
pupils
20
10
0
Eat a
packed lunch
Eat at
home
Eat a
school dinner
(a)
A pupil from each year group is chosen at random.
Are they most likely to eat a packed lunch, or eat at home, or eat
a school dinner?
For each pupil, indicate one of the following answers.
Eat a
packed
lunch
Eat
at
home
Eat a
school
dinner
Pupil from year 7
Pupil from year 8
Pupil from year 9
(b) How many more pupils are there in year 8 than year 9?
Show your working.
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75) Which calculation?
Here is some information about a school.
There are 3 classes in year 8. Each class has 27 pupils.
There are 4 classes in year 9. Each class has 25 pupils.
(a)
Use the information to match each question with the correct
calculation. The first one is done for you.
Question
Calculation
3+4
Howmany classes are there
altogether in
years 8 and 9?
3–4
4–3
There are more classes
inyear9thaninyear8.
Howmany more?
(3×27)+(4×25)
Howmany pupils are there
altogether in
years 8 and 9?
(3+27)+(4+25)
(3 × 27) – (4 × 25)
There are more pupils
in year 9 than in year 8.
Howmany more?
(4 + 25) – (3 + 27)
(4 × 25) – (3 × 27)
(b)
Use the information about the school to write what the missing
question could be in the following diagram.
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Question
Calculation
4×25
76) Throwing coins
I throw a fair coin. For each statement below, write down whether it is
True or False. Explain your answer.
(a) On each throw, the probability of getting a head is
2
1
(b)
On four throws, it is certain that I will get two heads and two tails.
77) Folding
(a) I have a rectangle made out of paper.
The rectangle measures 12cm by 8cm.
8 cm
12 cm
I want to fold the rectangle in half to make a smaller rectangle.
I can do this in two different ways.
What size could the smaller rectangle be? Write both ways.
(b)
I have a square made out of paper. The square measures 20cm by
20cm.
I keep folding it in half until I have a rectangle that is 5cm by 10cm.
20 cm
10 cm
5 cm
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20 cm
How many times did I fold it?

ANSWERS.
1) (a) About '3 /4 ' .
About '1 /3 ' .
(b) About 25% for Mindu.
About 40% for Mary.
(c) Indicates a position between 3.8cm and 6.2cm inclusive up the
rope.
2) (a) Size Number Sold
4 5
5 6
6 5
7 8
8 3
9 2
(b) 7.
3) 3a. 3b + 2c. 2d + 7. 4e + 4f + 8.
4) (a) Labels correct sections.
squash
football
badminton
(b) Estimates between 25% and 35% inclusive went swimming.
Estimates between 10% and 20% inclusive played tennis.
(c) Indicates 104 for football. Indicates 13 for squash.
(d) 20% of 700 is more than 40% of 260 etc.
5) (a) 2. (b) 3. (c) 4. (d) 3.
6) (a) 0. (b) 7400.
7) (a) E.g. there could be just 1 red cube.
(b) 1 cube.
(c) Could have been unlucky enough not to pick a blue cube.
(d) Indicates that white is the most probable.
8) (a) About 30% for cabbages, 20% for lettuces.
(b) For broad beans estimates a fraction close to 1 . 2
For peas estimates a fraction close to 3 . 8
(c) 'About 1 /5 turnips.'
9) (c) 11.
10) (a) 134 or 143.
(b) 431.
(c) Should pick 0. 3140.
(d) 425. 4250.
11) (b) Train = 3, car = 3, bicycle = 9.
(c) The pie-charts show the proportion of those travelling by bus.
12) (b) Can use 16 tiles.
(c) 16, 25 or 36 tiles.
13) (a) Since 40 p is the most frequent amount spent.
(c) Yes since more people spent between 50p to 99p than any other
amount.
(d) Observes a difference in the amounts spent, e.g.: 'Spent more at
night.'
Makes a hypothesis which could explain the difference in the
amounts stated, e.g.: 'People spend less in the morning when they
just have tea. Then they have a snack for lunch but they have
dinner in the evening and spend more.'
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14) (a) The sum of the lengths of the other two sides must be greater than
the length of the third side
(b) Indicates a length in the range 14.2cm to 14.6cm inclusive.
Indicates a length in the range 9.4cm to 9.8cm inclusive.
(c) Add up the 3 lengths.
15) (a) Indicates correct square, and no other square(s).
(b)
Indicates correct square, and no other square(s).
(c)
Indicates correct squares, and no other square(s).
(d)
Indicates correct squares, and no other square(s).
16) (a) 40 + 5, 142 – 97, 50% of 90, 450 ÷ 10, ¼ of 180.
(b) 28 ÷ 2 + 31.
17) (a) Indicates the correct pegs, e.g.:
(b)
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18) (a) Bangor and Hull.
(b) 289 miles. 248 miles. 537 miles in total.
19) (a) 20 packs. 120 packs.
(b) 90 packs.
(c) Indicates any two positive integers which multiply together to make
12.
20) (a) The two symbols are equally likely. ‘Certain’. ‘Likely’.
(b) ‘Triangle is less likely than a square’.
Higher than 5.
21) (a) 48 cm.
(b) 3.8 kg.
(c) 103 cm.
22) (a) 30 girls. 60%.
(b) 4 years old = 180 o .
3 years old = 144 o .
2 years old = 36 o .
23) (a) 10, 16, 30.
(b) 24.
24) (a) Any 2 numbers adding up to 34.
Any 2 numbers which multiply to give 10.
(b) 12.
(c) 275. 368. 16.
25) (a) £40.
(b) £5.96.
(c) 8.
(d) 3.
(e) 3 packs of 3 + 2 singles cassettes = 11 cassettes in total.
26) Adds up to 63.
21 40
8
27) (a) '1 kg caster sugar
1.5 kg margarine
1¼ kg mixed fruit'
(b) £3.50.
28) (a) 4 boxes.
(b) 5 boxes.
(c) 6 boxes.
(d)
29) (a) 4.
(b) 24.
(c) 36.
(d) 10.
30) (a) S.
(b) R.
(c) Shade the entire spinner.
(d) Shade half the spinner.
31) (a) Liz.
(b) Jim.
(c) Meg’s table allows us to see how many games each person won.
(d) Jim’s table gives more detailed information.
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32) (a) 30 cubes.
(b) 24 cubes.
33) 275, 368 and 16.
34) (a) 50.
(b) 16.
(c) 10.
(d) 10.
(e) 27.
(f) 7.
(g) 100.
(h) 10.
35) 4, 4, 7 and 9 respectively.
36) (a) (8, 8).
(b) (40, 40).
(c) Because the co-ordinates of each ‘dot’ must be even.
(d) Missing co-ordinates are: (4, 3), (6, 5) and (8, 7).
(e) (14, 13).
(f) Tile number 10.
37) (a) < or less than.
(b) = or equal to.
(c) > or greater than.
(d) < or less than.
(e) > or greater than.
(f) > or greater than.
38) (a) unlikely, equally likely, likely, certain.
(b) More than 5 !
(c) 10 of each colour.
39) (a) 7531.
(b) An even number must end with an even digit and all the digits are
odd.
(c) 51
57.
3751.
1537.
1573.
40) (a) Cost
Cost of holidays
£160
£140
£120
£100
£80
£60
£40
£20
£0
5 12 19 26 3 10 17 24 31 7 14 21 28 4 11 18
June July August September
Starting Date (Saturdays)
(b) £130.
(c) E.g. 'More people want to go when the weather is best.'
(d) Child = £63.75. Total = £148.75.
41) (a) 90 o .
(b) 6.
(c) 30 o .
(d) 150 o .
(e) 1 hour.
42) (a) 27.
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(b) 7.
(c) 100.
(d) 10.
43) (a) 325.
6.
780.
1300.
(b) E.g. 10 × 65 = 650, 6 × 65 = 390. Thus 16 × 65 = 650 + 390 =
1040.
44) (a) Spinner A since it has fewer numbers to choose from.
(b)
It does not matter since each spinner is split into 6 identical
sectors.
(c) Label two sectors 3 and three sectors 4.
45) (a) The first and fourth statements are correct.
(b) (5, 7).
(c)
x
(d)
x
46) (a) 21.
(b) 1989.
(c) 1995.
47) (a) Tuesday and Friday.
(b) 0.25 cm.
(c) 1.5 cm which equals 15 mm.
48) (a) Area 5 cm 2 , perimeter 12 cm.
(b) Any shape of area 6cm 2 .
(d) 7 cm 2 .
(e) Since the diagonals of each centimeter square are longer than 1
cm.
49) (a) There are more gold tokens than silver and so it is more likely that
a gold token will be chosen.
(b) 3.
(c) 5 or 6 or 7 or 8.
50) (a) 77 and 80 respectively.
(b) 32 and 30 respectively.
(c) Both rules give a value of 50.
51) (a) 58.
(b) 24360.
(c) 8.12.
52) (c) 5.
(d) 11.
53) (a) 1½.
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123
54
108.
(b) E.g. 3 × 9.
2 × 13.5.
54) (a) Any different time to 09:15 with both hours and minutes as
multiples of 3; e.g. 09:18.
(b) 2 or 81
55) (a) Indicates the 4 th diagram.
(b) Indicates the 5 th diagram.
(c) Indicates the 5 th diagram.
56) (a) 22.
(b) 5.
(c) 70.
57) (a) 18 and 10 respectively.
(b) 60.
(c) (4 + 5 + 1) × 5.
(d) 4 + (5 + 1) × 5.
58)
N
6 × 1.5
both 1 × 3 6 × 1
both 1 × 3
W
E
6 × 1
6 × 1.5
S
59) (a)
1
5
(b)
3
6
1, 24, and 4.
60) (a) Indicates the answer of 28.
(b) Indicates ‘not possible to tell’.
(c) Month B. B has a higher proportion of days with more than 8
hours sunshine.
61) (a) 5.
(b) West.
Northeast.
(c) Town 4.
62) (a) 1.5.
5.
(b) 4.5 and 11.5.
63) (a) 64, 864 and 675.
(b) 2520 and 15.
64) (a) 9.
(b) 4.
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(c) 4.
14.
65) 1725.
569.
66) (a) 12 cm 2 .
(b) 3 cm 2 .
(c) 12 cm 2 .
67) 5 + 2 = 10 – 3.
12 – 3 = 3 × 3.
2 + 1 = 9 ÷ 3.
6 – 6 = 7 – 7 or 6 ÷ 6 = 7 ÷ 7.
68) (a) Acute.
(b) No. The two angles are the same size (45 o ).
69) (a) 1, 16
2, 8
4, 4
8, 2
16, 1
(b) Indicates 1, 2, 3, 4, 6 and 12.
70) (a) Add 12.
Multiply by 3.
Multiply by 2 add 6.
(b) Divide by 2.
71) 75 pence.
72) (a) 1.2 m.
(b) 1.15 m.
(c) 170 cm.
73) (a) 49.
(b) 30%.
74) (a)
(b) 12.
75) (a) Joins the first to 4 – 3.
Joins the second to (3 × 27) + (4 × 25).
Joins the third to (4 × 25) – (3 × 27).
(b) The question refers to the total number of pupils in year 9.
76) (a) True. There are two equally likely outcomes.
(b)
(b)
False.
Indicates. The result of each throw is essentially random. For
example we could end up with 4 heads.
77) (a) 12 by 4 and 6 by 8.
(b) 3 times.
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