1. (a) (i) Write down, in figures, the number twenty four thousand, five hundred and seven.
(ii) Write down, in words, the number 6014.
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
[1]
(b) Using the following list of numbers
22 81 24 35 78 59 3 61
69
write down
(i) two numbers that have a sum of 100,
[1]
(ii) the number that must be added to 36 to make 95,
[1]
(iii) a multiple of 7,
[1]
(iv) the square of 9.
[1]
(c) Write down all the factors of 55.
[2]
(d) How many torches at £3.85 each can be bought with £20?
[2]
1. (a) (i) Write down, in figures, the number twenty four thousand, five hundred and seven.
Don’t miss out 0 in tens
24,507
(ii) Write down, in words, the number 6014.
[1]
Six thousand and fourteen
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
[1]
(b) Using the following list of numbers
22 81 24 35 78 59 3 61
69
write down
(i) two numbers that have a sum of 100,
(ii) the number that must be added to 36 to make 95,
Numbers
must be
from the list
22 and 78
95 – 36 = 59
35
(iii) a multiple of 7,
81
Not 9 × 2 = 18
(iv) the square of 9.
(c) Write down all the factors of 55.
[1]
[1]
[1]
[1]
[2]
1, 5, 11, 55
(d) How many torches at £3.85 each can be bought with £20?
20 ≈
3.85
20
4
[2]
20 = 5
4
Reveal
1. (a) (i) Write down, in figures, the number twenty four thousand, five hundred and seven.
(ii) Write down, in words, the number 6014.
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
[1]
(b) Using the following list of numbers
22 81 24 35 78 59 3 61
69
write down
(i) two numbers that have a sum of 100,
ASSESSMENT
AO1 to– 36
Recall
and
(ii) the number that must be added
to make
95,use
OBJECTIVE
knowledge
of properties of numbers
[1]
[1]
(iii) a multiple of 7,
[1]
(iv) the square of 9.
[1]
(c) Write down all the factors of 55.
[2]
(d) How many torches at £3.85 each can be bought with £20?
[2]
1. (a) (i) Write down, in figures, the number twenty four thousand, five hundred and seven.
(ii) Write down, in words, the number 6014.
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
[1]
(b) Using the following list of numbers
22 81 24 35 78 59 3 61
69
write down
(i) two numbers that have a sum of 100,
[1]
(ii) the number that must be added to 36 to make 95,
[1]
(iii) a multiple of 7,
[1]
(iv) the square of 9.
[1]
(c) Write down all the factors of 55.
[2]
(d) How many torches at £3.85 each can be bought with £20?
[2]
the volume of water in a bucket,
the area of the floor of a classroom,
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
2. Which metric unit is best used to measure
the distance from Llandudno to Swansea,
[3]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
2. Which metric unit is best used to measure
the volume of water in a bucket,
litre
the area of the floor of a classroom,
m2
the distance from Llandudno to Swansea,
km
Area must be a
square unit
[3]
Use metric units, not Imperial units
e.g. use kilometres and litres not
miles and gallons
Reveal
the volume of water in a bucket,
the area of the floor of a classroom,
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
2. Which metric unit is best used to measure
the distance from Llandudno to Swansea,
ASSESSMENT
OBJECTIVE
AO1 – Recall and use knowledge
of metric units
[3]
the volume of water in a bucket,
the area of the floor of a classroom,
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
2. Which metric unit is best used to measure
the distance from Llandudno to Swansea,
[3]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3. (a) Complete the following shape so that it is symmetrical about
the line AB.
[2]
Part b
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3. (a) Complete the following shape so that it is symmetrical about
the line AB.
[2]
Part b
Reveal
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3. (a) Complete the following shape so that it is symmetrical about
the line AB.
ASSESSMENT
OBJECTIVE
Part b
AO1 – Recall and use knowledge
of line symmetry
[2]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3. (a) Complete the following shape so that it is symmetrical about
the line AB.
[2]
Part b
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3 (b) Draw all the lines of symmetry on each of the following
diagrams.
[3]
Part a
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3 (b) Draw all the lines of symmetry on each of the following
diagrams.
[3]
Part a
Reveal
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3 (b) Draw all the lines of symmetry on each of the following
diagrams.
ASSESSMENT
OBJECTIVE
Part a
AO1 – Recall and use knowledge
of line symmetry
[3]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
3 (b) Draw all the lines of symmetry on each of the following
diagrams.
[3]
Part a
Circle (C)
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
4. A bag contains a large number of cards. Drawn on each card there is either a circle, a
triangle, a parallelogram or a hexagon.
Triangle (T)
Parallelogram (P) Hexagon (H)
Thirty two pupils were asked to
select a card at random, note
down the shape and replace the
card in the bag.
Here are the results.
(a) Using the centimetre squared grid,
draw a bar chart of the data given.
Part b
[6]
Triangle (T)
Thirty two pupils were asked to
select a card at random, note
down the shape and replace the
card in the bag.
Here are the results.
Parallelogram (P) Hexagon (H)
12
11
10
9
7
6
4
3
2
1
0
Part b
Triangle (T)
5
Circle (C)
Frequency
8
(a) Using the centimetre squared grid,
draw a bar chart of the data given.
Hexagon (H)
FOUNDATION Paper 1
Circle (C)
Parallelogram (P)
GCSE MATHEMATICS - LINEAR
4. A bag contains a large number of cards. Drawn on each card there is either a circle, a
triangle, a parallelogram or a hexagon.
Shape
Tally
Frequency
C
5
T
7
P
11
H
9
Total
Check that you’ve got
all (4 × 8) = 32
32
Reveal
[6]
Circle (C)
Triangle (T)
Parallelogram (P) Hexagon (H)
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
4. A bag contains a large number of cards. Drawn on each card there is either a circle, a
triangle, a parallelogram or a hexagon.
Thirty two pupils were asked to
select a card at random, note
down the shape and replace the
card in the bag.
Here are the results.
(a) Using the centimetre squared grid,
draw a bar chart of the data given.
ASSESSMENT
OBJECTIVE
Part b
AO3 – Generating a strategy to
collate the data e.g. tally chart
[6]
Circle (C)
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
4. A bag contains a large number of cards. Drawn on each card there is either a circle, a
triangle, a parallelogram or a hexagon.
Triangle (T)
Parallelogram (P) Hexagon (H)
Thirty two pupils were asked to
select a card at random, note
down the shape and replace the
card in the bag.
Here are the results.
(a) Using the centimetre squared grid,
draw a bar chart of the data given.
Part b
[6]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
4 (b) One of the pupils is selected at random and asked to show their
card. What is the probability that the card has a triangle drawn on it?
[2]
Part a
7
32
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
4 (b) One of the pupils is selected at random and asked to show their
card. What is the probability that the card has a triangle drawn on it?
7 because there are 7 triangles
32 because there are 32 cards in total
Answer has to be written as a fraction, decimal or percentage.
[2]
NOT ‘7 out of 32’, ‘7 in 32’ or ‘7 : 32’
Part a
Reveal
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
4 (b) One of the pupils is selected at random and asked to show their
card. What is the probability that the card has a triangle drawn on it?
[2]
ASSESSMENT
OBJECTIVE
Part a
AO1 – Recall and use knowledge
of the probability of equally likely
events
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
4 (b) One of the pupils is selected at random and asked to show their
card. What is the probability that the card has a triangle drawn on it?
[2]
Part a
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
5. The chart shows the times five friends spent at a gym.
(a) Who was the first person to arrive at the gym?
(b) For how long was Jake at the gym?
[1]
[2]
(c) State the times when at least 3 of the friends were in the gym together.
[2]
As 4 squares represent
1 hour, 1 square
represents 15 minutes
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
5. The chart shows the times five friends spent at a gym.
(a) Who was the first person to arrive at the gym?
Lisa
[1]
(b) For how long was Jake at the gym?
4:30pm to 6:15pm so 1 hour and 45 minutes
[2]
(c) State the times when at least 3 of the friends were in the gym together.
4:30pm to 5:15pm and 5:30pm to 6:15pm
Reveal
[2]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
5. The chart shows the times five friends spent at a gym.
ASSESSMENT
OBJECTIVE
AO1 – Recall and use knowledge
of diagrams and scales
(a) Who was the first person to arrive at the gym?
(b) For how long was Jake at the gym?
[1]
[2]
(c) State the times when at least 3 of the friends were in the gym together.
[2]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
5. The chart shows the times five friends spent at a gym.
(a) Who was the first person to arrive at the gym?
(b) For how long was Jake at the gym?
[1]
[2]
(c) State the times when at least 3 of the friends were in the gym together.
[2]
6. (a) Write down the next term in each of the following sequences.
10, 18, 26,
(ii) 100, 84, 68, 52,
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
(i) 2,
(b) Susan thinks of a number.
She multiplies her number by 5
and subtracts 6.
Her answer is 34.
What was her number?
(c) Simplify 6g + 2g + g.
[2]
[2]
[1]
(d) Find the value of 3c + 4d, when c = 4 and d = 2.
[2]
Part e
6. (a) Write down the next term in each of the following sequences.
+8
(i) 2,
+8
– 16
(ii) 100, 84, 68, 52,
FOUNDATION Paper 1
+8
10, 18, 26,
– 16 – 16
GCSE MATHEMATICS - LINEAR
+8
34
– 16
[2]
36
(b) Susan thinks of a number.
She multiplies her number by 5
and subtracts 6.
Her answer is 34.
What was her number?
Input
8
×5
–6
Output
÷5
+6
34
Her number was 8
[2]
g is the same as 1g
(c) Simplify 6g + 2g + g.
9g
[1]
3c means 3  c
(d) Find the value of 3c + 4d, when c = 4 and d = 2.
(3 × 4) + (4 × 2)
= 12 + 8
= 20
Part e
(Not 34 + 42 or 12c + 8d)
[2]
Reveal
6. (a) Write down the next term in each of the following sequences.
10, 18, 26,
[2]
(ii) 100, 84, 68, 52,
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
(i) 2,
(b) Susan thinks of a number.
She multiplies her number by 5
and subtracts 6.
Her answer is 34.
What was her number?
[2]
(c) Simplify 6g + 2g + g.
[1]
(d) Find the value of 3c + 4d, when c = 4 and d = 2.
ASSESSMENT
OBJECTIVE
Part e
(a), (c) and (d) – AO1 – Recall and use
knowledge of basic algebra
(b) – AO2 – Select and apply a method
to find an unknown
[2]
6. (a) Write down the next term in each of the following sequences.
10, 18, 26,
(ii) 100, 84, 68, 52,
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
(i) 2,
(b) Susan thinks of a number.
She multiplies her number by 5
and subtracts 6.
Her answer is 34.
What was her number?
(c) Simplify 6g + 2g + g.
[2]
[2]
[1]
(d) Find the value of 3c + 4d, when c = 4 and d = 2.
[2]
Part e
(1, 4)
(2, 5)
(3, 6)
(4, 7)
. . . . . . . . . (x, y)
Write down the formula connecting x and y.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
6 (e) There is a relation between the x-coordinate and the y-coordinate of
each of the following points.
[2]
Parts a-d
(1, 4)
+3
(2, 5)
+3
(3, 6)
(4, 7)
+3
+3
. . . . . . . . . (x, y)
Write down the formula connecting x and y.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
6 (e) There is a relation between the x-coordinate and the y-coordinate of
each of the following points.
For each point, the y-coordinate is 3 more than the x-coordinate.
So, the formula is
y=x +3
[2]
Parts a-d
Reveal
(1, 4)
(2, 5)
(3, 6)
(4, 7)
. . . . . . . . . (x, y)
Write down the formula connecting x and y.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
6 (e) There is a relation between the x-coordinate and the y-coordinate of
each of the following points.
[2]
ASSESSMENT
OBJECTIVE
Parts a-d
AO2 – Select and apply a method
to find the relationship between x
and y
(1, 4)
(2, 5)
(3, 6)
(4, 7)
. . . . . . . . . (x, y)
Write down the formula connecting x and y.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
6 (e) There is a relation between the x-coordinate and the y-coordinate of
each of the following points.
[2]
Parts a-d
Use the data in the table to
draw a conversion graph
between acres and hectares.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
7. (a) A unit used in the Imperial system for measuring the area of a field is the acre.
The unit used in the metric system is the hectare.
The table shows the number of acres and the number of hectares in each of three areas.
[2]
(b) Find an estimate for the
number of hectares in 200
acres.
[2]
Use the data in the table to
draw a conversion graph
between acres and hectares.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
7. (a) A unit used in the Imperial system for measuring the area of a field is the acre.
The unit used in the metric system is the hectare.
The table shows the number of acres and the number of hectares in each of three areas.
[2]
(b) Find an estimate for the
number of hectares in 200
acres.
As 200 acres is
not on the
graph, pick a
smaller number
that is a factor
of 200. e.g. 2
2 acres  0.8 hectares
× 100
200 acres  80 hectares
0.8
[2]
Reveal
Use the data in the table to
draw a conversion graph
between acres and hectares.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
7. (a) A unit used in the Imperial system for measuring the area of a field is the acre.
The unit used in the metric system is the hectare.
The table shows the number of acres and the number of hectares in each of three areas.
ASSESSMENT
OBJECTIVE
(a) AO1 – recall and use knowledge of
conversion graphs
(b) Find an estimate for the
(b) AO2 – select an appropriate
number of hectares in 200
method to convert a value
that is
acres.
not on either axis
[2]
[2]
Use the data in the table to
draw a conversion graph
between acres and hectares.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
7. (a) A unit used in the Imperial system for measuring the area of a field is the acre.
The unit used in the metric system is the hectare.
The table shows the number of acres and the number of hectares in each of three areas.
[2]
(b) Find an estimate for the
number of hectares in 200
acres.
[2]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
8. Petra and Steve are organising a packed lunch and a bottle of water for each pupil going
on a school trip.
Petra puts the packed lunches into boxes with each box holding 20 lunches.
Steve puts the bottles of water into crates with each crate holding 18 bottles.
When they have finished Petra has filled 45 boxes and Steve has filled 52 crates.
Showing all your calculations, explain whether or not Steve has enough water to give one
bottle with each lunch?
[6]
52 × 18
The number of water bottles is
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
8. Petra and Steve are organising a packed lunch and a bottle of water for each pupil going
on a school trip.
Petra puts the packed lunches into boxes with each box holding 20 lunches.
Steve puts the bottles of water into crates with each crate holding 18 bottles.
When they have finished Petra has filled 45 boxes and Steve has filled 52 crates.
Showing all your calculations, explain whether or not Steve has enough water to give one
bottle with each lunch?
5
You must show
your working!
0
9
2
0
0
5
2
1
4
6
0
3
1
There are other methods
you could use for long
multiplication.
8
6
936 bottles
The number of packed lunches is 45 × 20
45 × 20 = (45 × 2) × 10
= 90 × 10
= 900 lunches
Steve has 936 bottles and there are 900
lunches, so yes, he does have enough.
[6]
Reveal
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
8. Petra and Steve are organising a packed lunch and a bottle of water for each pupil going
on a school trip.
Petra puts the packed lunches into boxes with each box holding 20 lunches.
Steve puts the bottles of water into crates with each crate holding 18 bottles.
When they have finished Petra has filled 45 boxes and Steve has filled 52 crates.
Showing all your calculations, explain whether or not Steve has enough water to give one
bottle with each lunch?
ASSESSMENT
OBJECTIVE
AO3 – Interpret and analyse the
problem and develop a strategy to
solve it
[6]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
8. Petra and Steve are organising a packed lunch and a bottle of water for each pupil going
on a school trip.
Petra puts the packed lunches into boxes with each box holding 20 lunches.
Steve puts the bottles of water into crates with each crate holding 18 bottles.
When they have finished Petra has filled 45 boxes and Steve has filled 52 crates.
Showing all your calculations, explain whether or not Steve has enough water to give one
bottle with each lunch?
[6]
(a) Complete the following table to show all the possible scores.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
9. A red box contains four discs numbered 3, 6, 9 and 12 respectively.
A green box contains four discs numbered 4, 7, 10 and 13 respectively.
In a game, a player takes one disc at random from each of the two boxes.
The score for the game is the smaller of the two numbers on the discs.
[2]
(b) A player wins if the score is less than 6.
It costs 50p to play the game once.
The prize for winning the game is £1.
If 80 people play the game once, find the expected profit.
[6]
(a) Complete the following table to show all the possible scores.
6
6
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
9. A red box contains four discs numbered 3, 6, 9 and 12 respectively.
A green box contains four discs numbered 4, 7, 10 and 13 respectively.
In a game, a player takes one disc at random from each of the two boxes.
The score for the game is the smaller of the two numbers on the discs.
9
9
12
10
[2]
Less than 6 does
include 6
(b) A player wins if the score is less than 6.
not
It costs 50p to play the game once.
The prize for winning the game is £1.
If 80 people play the game once, find the expected profit.
Probability of winning = 7
16
10
7
80
= 70 = 35
Expected number of winners =
×
2 Alternatively, if 16 play the game, we
16
2
Cost to play = 50p × 80 = 0.5 × 80 = £40
expect 7 to win. If 160 play, we
expect 70 to win. So, if 80 play, we
expect 35 to win.
Expected pay out for winning = £1 × 35 = £35
Expected profit = 40 – 35 = £5
[6]
Reveal
(a) Complete the following table to show all the possible scores.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
9. A red box contains four discs numbered 3, 6, 9 and 12 respectively.
A green box contains four discs numbered 4, 7, 10 and 13 respectively.
In a game, a player takes one disc at random from each of the two boxes.
The score for the game is the smaller of the two numbers on the discs.
(a) AO1 – Recall and use knowledge of
ASSESSMENT
diagrams
(b) A player wins if the score is sample
less thanspace
6.
(b)once.
AO2 – Selecting and applying
It costs
50p to play the game
OBJECTIVE
The prize for winning the game methods
is £1.
to find the expected profit
[2]
If 80 people play the game once, find the expected profit.
[6]
(a) Complete the following table to show all the possible scores.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
9. A red box contains four discs numbered 3, 6, 9 and 12 respectively.
A green box contains four discs numbered 4, 7, 10 and 13 respectively.
In a game, a player takes one disc at random from each of the two boxes.
The score for the game is the smaller of the two numbers on the discs.
[2]
(b) A player wins if the score is less than 6.
It costs 50p to play the game once.
The prize for winning the game is £1.
If 80 people play the game once, find the expected profit.
[6]
(a) How far did Helen cycle in
the first hour?
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
10. Helen cycles home from a village that is 30 miles from her home.
The travel graph below represents her journey.
(b) For how many minutes did
Helen stop on her journey?
[1]
(c) Without calculating any speeds, explain how you can decide whether Helen was
cycling faster before stopping or after she had stopped.
(d) At what time did she arrive home?
[1]
[1]
1 hour (60 minutes)
= 20 little squares.
So, 1 little square = 3 minutes
(a) How far did Helen cycle in
the first hour?
30 – 17 = 13 miles
17
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
10. Helen cycles home from a village that is 30 miles from her home.
The travel graph below represents her journey.
[1]
(b) For how many minutes did
Helen stop on her journey?
11:09 to 11:45  36
minutes
(Or, line is 12 squares long.
12 × 3 = 36 minutes.)
[1]
(c) Without calculating any speeds, explain how you can decide whether Helen was
cycling faster before stopping or after she had stopped.
The line before she stops is steeper. So, she was cycling faster
before she stopped.
(d) At what time did she arrive home?
[1]
13:30 + 6(mins) = 13:36
Reveal
[1]
(a) How far did Helen cycle in
the first hour?
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
10. Helen cycles home from a village that is 30 miles from her home.
The travel graph below represents her journey.
(b) For how many minutes did
Helen stop on her journey?
ASSESSMENT
OBJECTIVE
(a), (d) AO1 – Recall and use
knowledge of distance-time graphs
(b), (c) AO2 – Select and apply
methods using scale and gradient
[1]
(c) Without calculating any speeds, explain how you can decide whether Helen was
cycling faster before stopping or after she had stopped.
(d) At what time did she arrive home?
[1]
[1]
(a) How far did Helen cycle in
the first hour?
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
10. Helen cycles home from a village that is 30 miles from her home.
The travel graph below represents her journey.
(b) For how many minutes did
Helen stop on her journey?
[1]
(c) Without calculating any speeds, explain how you can decide whether Helen was
cycling faster before stopping or after she had stopped.
(d) At what time did she arrive home?
[1]
[1]
Part of rail timetable
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
11. Sarah and Paige live in Nottingham and are planning a trip to Liverpool.
They need to be in Liverpool by 2:00 pm. They can travel by train, bus or in Sarah’s car.
Showing all your reasoning, how do you recommend they travel from Nottingham to
Liverpool?
Give one advantage and one disadvantage for your choice of transport.
[8]
Part of the national bus timetable information
Travelling by car:
Distance from Nottingham to Liverpool is 105 miles.
Expected average speed of car on this journey is
35 m.p.h.
Cost of running Sarah’s car is 30p per mile.
Part of rail timetable
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
11. Sarah and Paige live in Nottingham and are planning a trip to Liverpool.
They need to be in Liverpool by 2:00 pm. They can travel by train, bus or in Sarah’s car.
Showing all your reasoning, how do you recommend they travel from Nottingham to
Liverpool?
Give one advantage and one disadvantage for your choice of transport.
[8]
One possible solution is
to work out the cost and
quickest time for each
mode of transport.
Note!!
Part of the national bus timetable information
Travelling by car:
Distance from Nottingham to Liverpool is 105 miles.
Expected average speed of car on this journey is
35 m.p.h.
Cost of running Sarah’s car is 30p per mile.
By Car
By Train
The fastest train to get there before 2 p.m.:
10:52 to 13:27
2hrs 35min
Cost = £39.50 + £39.50 = £79.00
By Bus
Double the
£31.50 to
include the
return journey
The fastest bus to get there before 2 p.m.:
7:15 to 11:55
4hrs 40min
Cost = £32.00
Speed = Distance
Time
Time = Distance
Speed
Time = 105 ÷ 35 = 3hrs
Cost = £0.30 ×105 = £31.50
£31.50 × 2 = £63.00
I recommend the bus because it’s a lot cheaper, but it
takes longer.
This could be a different answer
Reveal
Part of rail timetable
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
11. Sarah and Paige live in Nottingham and are planning a trip to Liverpool.
They need to be in Liverpool by 2:00 pm. They can travel by train, bus or in Sarah’s car.
Showing all your reasoning, how do you recommend they travel from Nottingham to
Liverpool?
Give one advantage and one disadvantage for your choice of transport.
Part of the national bus timetable information
ASSESSMENT
OBJECTIVE
[8]
Travelling
by applying
car:
AO2 – selecting
and
Distance from Nottingham to Liverpool is 105 miles.
mathematical
methods
to speed
justify
a on this journey is
Expected
average
of car
35 m.p.h.of transport.
selected mode
Cost of running Sarah’s car is 30p per mile.
Part of rail timetable
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
11. Sarah and Paige live in Nottingham and are planning a trip to Liverpool.
They need to be in Liverpool by 2:00 pm. They can travel by train, bus or in Sarah’s car.
Showing all your reasoning, how do you recommend they travel from Nottingham to
Liverpool?
Give one advantage and one disadvantage for your choice of transport.
[8]
Part of the national bus timetable information
Travelling by car:
Distance from Nottingham to Liverpool is 105 miles.
Expected average speed of car on this journey is
35 m.p.h.
Cost of running Sarah’s car is 30p per mile.
12. (a) Solve
x= 3
6
(ii) 7x – 10 = 11.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
(i)
(b) Simplify 2a – 7b – 5a – 6b.
[1]
[2]
[2]
12. (a) Solve
x= 3
6
x=3×6
Check:
x = 18
18 ÷ 6 = 3
[1]
(ii) 7x – 10 = 11.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
(i)
7x = 11 + 10
7x = 21
x = 21
7
x =3
(b) Simplify 2a – 7b – 5a – 6b.
Check:
(7×3) – 10
= 21 – 10
= 11
[2]
= 2a – 7b – 5a – 6b
= – 3a – 13b
[2]
Reveal
12. (a) Solve
x= 3
6
[1]
(ii) 7x – 10 = 11.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
(i)
ASSESSMENT
OBJECTIVE
AO1 – Recall and use knowledge
of solving linear equations and
collecting like terms
(b) Simplify 2a – 7b – 5a – 6b.
[2]
[2]
12. (a) Solve
x= 3
6
(ii) 7x – 10 = 11.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
(i)
(b) Simplify 2a – 7b – 5a – 6b.
[1]
[2]
[2]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13. (a)
Part b
Draw an enlargement of the shape shown below using
a scale factor of 2.
Use the point A as the centre of the enlargement.
[3]
Draw an enlargement of the shape shown below using
a scale factor of 2.
Use the point A as the centre of the enlargement.
This is the correct size but
drawn in the wrong place.
[3]
Make sure you use the
centre of enlargement, A
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13. (a)
Part b
Reveal
Draw an enlargement of the shape shown below using
a scale factor of 2.
Use the point A as the centre of the enlargement.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13. (a)
ASSESSMENT
OBJECTIVE
Part b
AO1 – Recall and use knowledge
of enlargement
[3]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13. (a)
Part b
Draw an enlargement of the shape shown below using
a scale factor of 2.
Use the point A as the centre of the enlargement.
[3]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13 (b) Rotate the shape shown below through 90° anticlockwise about the
point (2, 1).
[2]
Part a
Remember the three key
facts:
Angle: 90°
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13 (b) Rotate the shape shown below through 90° anticlockwise about the
point (2, 1).
[2]
Centre: (2, 1)
Direction: anticlockwise
Part a
Reveal
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13 (b) Rotate the shape shown below through 90° anticlockwise about the
point (2, 1).
[2]
ASSESSMENT
OBJECTIVE
Part a
AO1 – Recall and use knowledge
of rotation
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
13 (b) Rotate the shape shown below through 90° anticlockwise about the
point (2, 1).
[2]
Part a
14. (a) Showing all your working, find an estimate for:
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
503 × 20.3
4.1
[2]
(b) The value of  is approximately 3.14. Estimate the circumference
of a circle with radius 20 cm.
[2]
14. (a) Showing all your working, find an estimate for:
Round all numbers to 1 significant figure
 500 × 20
4
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
503 × 20.3
4.1
= 10000
4
=
2500
[2]
(b) The value of  is approximately 3.14. Estimate the circumference
of a circle with radius 20 cm.
Circumference =  × diameter
= 3.14 × 40
= 3.14 × 4 × 10
Remember to use
diameter.
i.e. 2 × 20 = 40
= 12.56 × 10
= 125.6 cm
[2]
Reveal
14. (a) Showing all your working, find an estimate for:
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
503 × 20.3
4.1
[2]
AO1 – Recall and use knowledge
ASSESSMENT
of estimation3.14.
and Estimate
significantthe circumference
(b) The
value of  is approximately
OBJECTIVE
figures.
of a circle with radius
20 cm.
[2]
14. (a) Showing all your working, find an estimate for:
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
503 × 20.3
4.1
[2]
(b) The value of  is approximately 3.14. Estimate the circumference
of a circle with radius 20 cm.
[2]
(a) Fill in the numbers on these houses.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
15. The houses on one side of a long street have odd numbers and the houses on the other
side of the street have even numbers.
[1]
(b) The numbers on five houses next to each other on one side of the street total 65.
What are the numbers on these five houses?
[3]
(c) The product of the numbers on two houses which are directly opposite each other is 90.
What are the numbers on these two houses?
[1]
15. The houses on one side of a long street have odd numbers and the houses on the other
side of the street have even numbers.
+2 +2
(a) Fill in the numbers on these houses.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
+1
+2 +2
97 99 101
105
98 100 102 104 106
[1]
(b) The numbers on five houses next to each other on one side of the street total 65.
What are the numbers on these five houses?
[3]
This must be the middle house number.
So, the solution is:
65 ÷ 5 = 13
9
11
13
15
17
(c) The product of the numbers on two houses which are directly opposite each other is 90.
What are the numbers on these two houses?
The numbers will be consecutive i.e.
(number) × (number + 1) = 90
By investigation :
9 and 10
[1]
Product means
“multiply”
Reveal
(a) Fill in the numbers on these houses.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
15. The houses on one side of a long street have odd numbers and the houses on the other
side of the street have even numbers.
[1]
(b) The numbers on five houses next to each other on one side of the street total 65.
WhatASSESSMENT
are the numbers on these fiveAO2
houses?
– Select and apply
OBJECTIVE
appropriate numerical methods
[3]
(c) The product of the numbers on two houses which are directly opposite each other is 90.
What are the numbers on these two houses?
[1]
(a) Fill in the numbers on these houses.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
15. The houses on one side of a long street have odd numbers and the houses on the other
side of the street have even numbers.
[1]
(b) The numbers on five houses next to each other on one side of the street total 65.
What are the numbers on these five houses?
[3]
(c) The product of the numbers on two houses which are directly opposite each other is 90.
What are the numbers on these two houses?
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
16. The diagram represents an aerial view of a building.
A dog, D, on a lead is tied to a side of the building at X.
Draw the boundary of the region in which the dog can roam.
[3]
[3]
3cm
The lead is shortened
by the corner, so the
answer is not a circle.
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
16. The diagram represents an aerial view of a building.
A dog, D, on a lead is tied to a side of the building at X.
Draw the boundary of the region in which the dog can roam.
1.9cm
Reveal
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
16. The diagram represents an aerial view of a building.
A dog, D, on a lead is tied to a side of the building at X.
Draw the boundary of the region in which the dog can roam.
ASSESSMENT
OBJECTIVE
AO2 – Select and apply
appropriate rules of loci
[3]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
16. The diagram represents an aerial view of a building.
A dog, D, on a lead is tied to a side of the building at X.
Draw the boundary of the region in which the dog can roam.
[3]
Mrs. Roberts is travelling to Hong Kong on business.
(a) There is a time difference between the UK and Hong Kong.
When the time is 6 a.m. in the UK the time is 2 p.m. on the same day in Hong Kong.
(i) When it is 10 a.m. in the UK what time is it in Hong Kong?
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
17. You will be assessed on the quality of your written communication in part (b) of this
question.
(ii) Mr. Roberts stays in the UK and has given his wife his time schedule, shown below.
Mrs. Roberts will be in meetings most of
the day in Hong Kong from 8 a.m. until 11
a.m., then from 12 noon to 6 p.m.
She plans to telephone her husband at a
convenient time during the day.
During which time period should Mrs.
Roberts telephone her husband?
Give your answer in UK and Hong Kong
times.
Part b
[2]
17. You will be assessed on the quality of your written communication in part (b) of this
question.
(i) When it is 10 a.m. in the UK what time is it in Hong Kong?
6am (UK) is 2pm (HK) (+8hrs)
so
10am (UK) is 6pm (HK)
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
Hong Kong is 8
Mrs. Roberts is travelling to Hong Kong on business.
hours ahead of UK
(a) There is a time difference between the UK and Hong Kong.
When the time is 6 a.m. in the UK the time is 2 p.m. on the same day in Hong Kong.
pm
meeting
am
(ii) Mr. Roberts stays in the UK and has given his wife his time schedule, shown below.
Mrs. Roberts will be in meetings most of
the day in Hong Kong from 8 a.m. until 11
a.m., then from 12 noon to 6 p.m.
She plans to telephone her husband at a
convenient time during the day.
During which time period should Mrs.
Roberts telephone her husband?
Give your answer in UK and Hong Kong
times.
HK
2:00
2:30
3:30
7:30
8:30
10:00
0:00
2:00
5:00
6:00
Between
8:30pm – 10:00pm HK time [Mrs Roberts has finished work]
12:30pm – 2:00pm UK time [Mr Roberts is having lunch]
So they are both free to talk
Part b
Reveal
[2]
Mrs. Roberts is travelling to Hong Kong on business.
(a) There is a time difference between the UK and Hong Kong.
When the time is 6 a.m. in the UK the time is 2 p.m. on the same day in Hong Kong.
(i) When it is 10 a.m. in the UK what time is it in Hong Kong?
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
17. You will be assessed on the quality of your written communication in part (b) of this
question.
(ii) Mr. Roberts stays in the UK and has given his wife his time schedule, shown below.
Mrs. Roberts will be in meetings most of
the day in Hong Kong from 8 a.m. until 11
a.m., then from 12 noon to 6 p.m.
She plans to telephone her husband at a
convenient time during the day.
During which time period should Mrs.
Roberts telephone her husband?
Give your answer in UK and Hong Kong
times.
ASSESSMENT
OBJECTIVE
Part b
(a) (i) AO2 – Select and apply
appropriate numerical
technique to calculate time
difference.
(ii) AO3 – Interpret times and
select appropriately.
[2]
Mrs. Roberts is travelling to Hong Kong on business.
(a) There is a time difference between the UK and Hong Kong.
When the time is 6 a.m. in the UK the time is 2 p.m. on the same day in Hong Kong.
(i) When it is 10 a.m. in the UK what time is it in Hong Kong?
[1]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
17. You will be assessed on the quality of your written communication in part (b) of this
question.
(ii) Mr. Roberts stays in the UK and has given his wife his time schedule, shown below.
Mrs. Roberts will be in meetings most of
the day in Hong Kong from 8 a.m. until 11
a.m., then from 12 noon to 6 p.m.
She plans to telephone her husband at a
convenient time during the day.
During which time period should Mrs.
Roberts telephone her husband?
Give your answer in UK and Hong Kong
times.
Part b
[2]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
17 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights.
She finds two suitable hotels on the internet.
Which hotel should Mrs. Roberts choose? You must show your working and give a
reason for your answer.
Part a
[5]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
17 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights.
She finds two suitable hotels on the internet.
Which hotel should Mrs. Roberts choose? You must show your working and give a
reason for your answer.
Hotel Gelton
£80 × 4 = £320
Hotel Bear
B&B
£107 × 3 = £321 B&B + dinner
Remember to include a
valid reason for your choice
Choose Hotel Bear as you also get dinner for 4 nights
for an extra £1, so this is better value for money.
Part a
Reveal
[5]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
17 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights.
She finds two suitable hotels on the internet.
Which hotel should Mrs. Roberts choose? You must show your working and give a
reason for your answer.
ASSESSMENT
OBJECTIVE
Part a
AO3 – Interpret, analyse and
compare both options presented
and justify their choice of hotel.
[5]
FOUNDATION Paper 1
GCSE MATHEMATICS - LINEAR
17 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights.
She finds two suitable hotels on the internet.
Which hotel should Mrs. Roberts choose? You must show your working and give a
reason for your answer.
Part a
[5]
1. Ashley visits a computer store.
(a) She sees the following display.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i)
Ashley buys a box of rewritable discs, 2 packets of
photo paper, 3 printer
cartridges and 6 packets of
printer paper.
Complete the following
table to show her bill for
these items.
[4]
Part (ii)
1. Ashley visits a computer store.
(a) She sees the following display.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i)
Ashley buys a box of rewritable discs, 2 packets of
photo paper, 3 printer
cartridges and 6 packets of
printer paper.
Complete the following
table to show her bill for
these items.
Don’t forget to
include this in
the total.
Remember you
can use your
calculator.
2 packets of photo paper
Remember
to write
down the ‘0’
 91.40
3 printer cartridges
6 packets of printer paper
2 × £6.39
12.78
3 × £16.78
50.34
6 × £3.47
20.82
7.46 + 12.78 + 50.34 + 20.82
Part (ii)
91.40
[4]
Reveal
1. Ashley visits a computer store.
(a) She sees the following display.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i)
Ashley buys a box of rewritable discs, 2 packets of
photo paper, 3 printer
cartridges and 6 packets of
printer paper.
Complete the following
table to show her bill for
these items.
ASSESSMENT
OBJECTIVE
Part (ii)
AO1 – Recall and use knowledge
of money using a calculator
[4]
1. Ashley visits a computer store.
(a) She sees the following display.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i)
Ashley buys a box of rewritable discs, 2 packets of
photo paper, 3 printer
cartridges and 6 packets of
printer paper.
Complete the following
table to show her bill for
these items.
[4]
Part (ii)
[2]
(b) (i) What percentage of the following shape is shaded?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
1a (ii) The store gives a discount of 5% of the total cost of these items.
What discount does Ashley receive?
[1]
(ii) What percentage of the shape is NOT shaded?
[1]
Part (i)
5 × 91.4 = £4.57
100
0.05
or
× 91.4 = £4.57
Use a calculator!
[2]
(b) (i) What percentage of the following shape is shaded?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
1a (ii) The store gives a discount of 5% of the total cost of these items.
What discount does Ashley receive?
1
3
2
4
4 shaded out of 10
4 = 40
10
100
= 40%
[1]
(ii) What percentage of the shape is NOT shaded?
100% – 40% = 60%
[1]
Part (i)
Reveal
[2]
(b) (i) What percentage of the following shape is shaded?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
1a (ii) The store gives a discount of 5% of the total cost of these items.
What discount does Ashley receive?
[1]
(ii) What percentage of the shape is NOT shaded?
ASSESSMENT
OBJECTIVE
Part (i)
AO1 – Recall and use knowledge
of percentages
[1]
[2]
(b) (i) What percentage of the following shape is shaded?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
1a (ii) The store gives a discount of 5% of the total cost of these items.
What discount does Ashley receive?
[1]
(ii) What percentage of the shape is NOT shaded?
[1]
Part (i)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2. (a) (i) What is the mass of Mia’s pet hamster?
[1]
The mass of Mia’s pet hamster is
Part (ii)
g.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2. (a) (i) What is the mass of Mia’s pet hamster?
Each
section is
10g
[1]
The mass of Mia’s pet hamster is
Part (ii)
340
g.
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2. (a) (i) What is the mass of Mia’s pet hamster?
AO1 – Recall and use knowledge
of metric units of mass and reading
OBJECTIVE
scales
The mass of Mia’s pet hamster is
g.
ASSESSMENT
Part (ii)
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2. (a) (i) What is the mass of Mia’s pet hamster?
[1]
The mass of Mia’s pet hamster is
Part (ii)
g.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2a (ii) She puts her hamster on a different scale.
Draw the pointer to show the hamster’s mass.
[1]
(b) Mia goes out in her car.
What speed is she doing, correct to the nearest 10 miles per hour?
Part (i)
m.p.h.
[1]
Each section
is 20g
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2a (ii) She puts her hamster on a different scale.
Draw the pointer to show the hamster’s mass.
[1]
(b) Mia goes out in her car.
What speed is she doing, correct to the nearest 10 miles per hour?
Arrow is
nearer to
60 than 50
50 60
60
Part (i)
m.p.h.
[1]
Reveal
ASSESSMENT
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2a (ii) She puts her hamster on a different scale.
Draw the pointer to show the hamster’s mass.
OBJECTIVE
AO1 – Recall and use knowledge
of metric units of mass and
interpreting scales
[1]
(b) Mia goes out in her car.
What speed is she doing, correct to the nearest 10 miles per hour?
ASSESSMENT
OBJECTIVE
Part (i)
AO1 – Recall and use knowledge
of reading scales and rounding to
nearest 10
m.p.h.
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
2a (ii) She puts her hamster on a different scale.
Draw the pointer to show the hamster’s mass.
[1]
(b) Mia goes out in her car.
What speed is she doing, correct to the nearest 10 miles per hour?
Part (i)
m.p.h.
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
3. (a)
The above shape, drawn on a square grid, represents a large garden.
Estimate the area of the garden if every square represents an area of 5 m2.
Part b
[3]
Count whole squares
and squares more
than half full
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
3. (a)
The above shape, drawn on a square grid, represents a large garden.
Estimate the area of the garden if every square represents an area of 5 m2.
Counting gives 77 squares
Area = 77 × 5
= 385 m2
Part b
[3]
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
3. (a)
The above shape, drawn on a square grid, represents a large garden.
Estimate the area of the garden if every square represents an area of 5 m2.
ASSESSMENT
OBJECTIVE
Part b
AO1 – Recall and use knowledge
of estimation of the area of an
irregular shape drawn on a square
grid
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
3. (a)
The above shape, drawn on a square grid, represents a large garden.
Estimate the area of the garden if every square represents an area of 5 m2.
Part b
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(b) Write down the special name of the straight line shown in each diagram below.
[2]
(c) Write down the name of each of the shapes shown below.
B
A
A
B
C
C
[3]
Part a
(b) Write down the special name of the straight line shown in each diagram below.
Diameter
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Chord
[2]
(c) Write down the name of each of the shapes shown below.
B
A
A
Trapezium
B
Pentagon
C
Cylinder
C
[3]
Part a
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(b) Write down the special name of the straight line shown in each diagram below.
[2]
(c) Write down the name of each of the shapes shown below.
B
A
A
B
C
ASSESSMENT
OBJECTIVE
Part a
AO1
C – Recall and use knowledge
of vocabulary of circles, polygons
and solid figures
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(b) Write down the special name of the straight line shown in each diagram below.
[2]
(c) Write down the name of each of the shapes shown below.
B
A
A
B
C
C
[3]
Part a
4. The formula to find the Total Cost, in pounds, of hiring a carpet cleaner is
(a) Find the Total Cost when the Number of days is 3 and the Hire charge is £10.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Total Cost = Number of days × £6.75 + Hire charge.
[2]
(b) Find the Number of days, when the Total Cost is £61 and the Hire charge is £7.
Total Cost = Number of days × £6.75 + Hire charge.
[2]
4. The formula to find the Total Cost, in pounds, of hiring a carpet cleaner is
20.25
(a) Find the Total Cost when the Number of days is 3 and the Hire charge is £10.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Total Cost = Number of days × £6.75 + Hire charge.
6.75
×3
20.25
20.25
+10.00
30.25
Add on the
hire charge
Total cost = £30.25
[2]
(b) Find the Number of days, when the Total Cost is £61 and the Hire charge is £7.
Total Cost = Number of days × £6.75 + Hire charge.
Number of days × £6.75 = Total cost – Hire charge
= 61 – 7
= 54
Number of days = 54 ÷ 6.75
=8
Reveal[2]
4. The formula to find the Total Cost, in pounds, of hiring a carpet cleaner is
(a) Find the Total Cost when the Number of days is 3 and the Hire charge is £10.
ASSESSMENT
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Total Cost = Number of days × £6.75 + Hire charge.
OBJECTIVE
AO1 – Recall and use knowledge
of substitution of positive integers
into simple formulae
[2]
(b) Find the Number of days, when the Total Cost is £61 and the Hire charge is £7.
Total Cost = Number of days × £6.75 + Hire charge.
ASSESSMENT
OBJECTIVE
AO1 – Recall and use knowledge
of rearranging simple formulae
[2]
4. The formula to find the Total Cost, in pounds, of hiring a carpet cleaner is
(a) Find the Total Cost when the Number of days is 3 and the Hire charge is £10.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Total Cost = Number of days × £6.75 + Hire charge.
[2]
(b) Find the Number of days, when the Total Cost is £61 and the Hire charge is £7.
Total Cost = Number of days × £6.75 + Hire charge.
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
5.
(a) Write down the coordinates of
the points A and B.
Coordinates of A are:
(
,
)
Coordinates of B are:
(
,
)
[2]
(b) C is the mid-point of AB.
Mark the point C on the graph.
[1]
(c) The perpendicular to the line AB from the point D meets AB at the point E.
Mark the point E on the graph paper above.
[1]
The x-coordinate
is always first.
C
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
5.
(a) Write down the coordinates of
the points A and B.
E
Coordinates of A are:
(
–3
,
4
)
Coordinates of B are:
(
–3
,
–2
)
[2]
(b) C is the mid-point of AB.
Mark the point C on the graph.
[1]
(c) The perpendicular to the line AB from the point D meets AB at the point E.
Mark the point E on the graph paper above.
[1]
Perpendicular means ‘at right angles to…’
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
5.
(a) Write down the coordinates of
the points A and B.
ASSESSMENT
OBJECTIVE
AO1 – Recall
and use
Coordinates of A are:
knowledge of Cartesian
(
,
coordinates in 4 quadrants
and
vocabulary of geometrical terms
)
Coordinates of B are:
(
,
)
[2]
(b) C is the mid-point of AB.
Mark the point C on the graph.
[1]
(c) The perpendicular to the line AB from the point D meets AB at the point E.
Mark the point E on the graph paper above.
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
5.
(a) Write down the coordinates of
the points A and B.
Coordinates of A are:
(
,
)
Coordinates of B are:
(
,
)
[2]
(b) C is the mid-point of AB.
Mark the point C on the graph.
[1]
(c) The perpendicular to the line AB from the point D meets AB at the point E.
Mark the point E on the graph paper above.
[1]
6. (a) The diagram shows a number of cubes of side 1 cm forming a solid shape.
Volume of the shape =
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Find the volume of the shape and state the units of your answer.
(b) (i) Measure the size of ABC.
ABC =
º
Show/hide protractor
[1]
Part b
1
2
3
4
5
Find the volume of the shape and state the units of your answer.
Number of cubes = 7 × 2
67
Volume of the shape =
14 cm3
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
6. (a) The diagram shows a number of cubes of side 1 cm forming a solid shape.
2 layers
(b) (i) Measure the size of ABC.
Make sure the
correct reading is
used: the angle is
acute, so it is less
than 90°
ABC =
53
º
53º
[1]
Part b
Reveal
6. (a) The diagram shows a number of cubes of side 1 cm forming a solid shape.
Volume of the shape =
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Find the volume of the shape and state the units of your answer.
(b) (i) Measure the size of ABC.
ABC =
ASSESSMENT
OBJECTIVE
Part b
º
AO1 – Recall and use knowledge
of volume of composite solids by
counting cubes and accurate use
of a protractor
[1]
6. (a) The diagram shows a number of cubes of side 1 cm forming a solid shape.
Volume of the shape =
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Find the volume of the shape and state the units of your answer.
(b) (i) Measure the size of ABC.
ABC =
º
[1]
Part b
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
6 (ii) On the diagram below, draw XYZ, which is 124°.
X
Y
Show/hide protractor
[1]
Part a
Make sure the
correct reading is
used: the angle is
greater than 90°,
so it is obtuse.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
6 (ii) On the diagram below, draw XYZ, which is 124°.
X
Y
[1]
Part a
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
6 (ii) On the diagram below, draw XYZ, which is 124°.
X
Y
ASSESSMENT
OBJECTIVE
Part a
AO1 – Recall and use knowledge
of accurately using a protractor
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
6 (ii) On the diagram below, draw XYZ, which is 124°.
X
Y
[1]
Part a
7. Siân, Ryan and Dafydd are neighbours and have houses on a new housing estate.
4m
9m
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Siân makes a rectangular front lawn measuring 9m by 4m.
(a) Ryan makes a square lawn, which has the same perimeter as Siân’s lawn.
Find the length of a side of Ryan’s lawn.
[3]
(b) Dafydd also makes a square lawn, but his lawn has the same area as Siân’s lawn.
Find the length of a side of Dafydd’s lawn.
[3]
7. Siân, Ryan and Dafydd are neighbours and have houses on a new housing estate.
4m
9m
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Siân makes a rectangular front lawn measuring 9m by 4m.
(a) Ryan makes a square lawn, which has the same perimeter as Siân’s lawn.
Find the length of a side of Ryan’s lawn.
Perimeter of Siân’s lawn = 4 + 9 + 4 + 9
= 26 cm
Length of Ryan’s lawn = 26 ÷ 4 = 6.5 cm
[3]
(b) Dafydd also makes a square lawn, but his lawn has the same area as Siân’s lawn.
Find the length of a side of Dafydd’s lawn.
Area of Siân’s lawn = 4 × 9 = 36 cm2
Length of Dafydd’s square lawn = √36 = 6 cm
[3]
Reveal
7. Siân, Ryan and Dafydd are neighbours and have houses on a new housing estate.
4m
9m
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Siân makes a rectangular front lawn measuring 9m by 4m.
(a) Ryan makes a square lawn, which has the same perimeter as Siân’s lawn.
Find the length of a side of Ryan’s lawn.
ASSESSMENT
OBJECTIVE
AO2 – Select and apply
mathematical methods of perimeter
and area to find the lengths of the
lawns
[3]
(b) Dafydd also makes a square lawn, but his lawn has the same area as Siân’s lawn.
Find the length of a side of Dafydd’s lawn.
[3]
7. Siân, Ryan and Dafydd are neighbours and have houses on a new housing estate.
4m
9m
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
Siân makes a rectangular front lawn measuring 9m by 4m.
(a) Ryan makes a square lawn, which has the same perimeter as Siân’s lawn.
Find the length of a side of Ryan’s lawn.
[3]
(b) Dafydd also makes a square lawn, but his lawn has the same area as Siân’s lawn.
Find the length of a side of Dafydd’s lawn.
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
8.
The above picture shows two houses each with a front door.
Write down an estimate for the actual height of a door.
Using this estimate for the height of a door, estimate the actual distance between the two
houses shown by the arrowed line.
Show/hide ruler (vertical)
You must show all your working.
Show/hide ruler (horizontal)
[4]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
8.
The above picture shows two houses each with a front door.
Write down an estimate for the actual height of a door.
2m
Using this estimate for the height of a door, estimate the actual distance between the two
houses shown by the arrowed line.
You must show all your working.
Door measures 2cm
Therefore 2cm ≡ 2m

Scale 1cm ≡ 1m
Measured distance between two houses = 9cm
Actual distance between two houses = 9m
[4]
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
8.
The above picture shows two houses each with a front door.
Write down an estimate for the actual height of a door.
Using this estimate for the height of a door, estimate the actual distance between the two
houses shown by the arrowed line.
You must show all your working.
ASSESSMENT
OBJECTIVE
AO2 – Select and apply
mathematical methods of
estimation and scale to find the
actual distance between the two
houses
[4]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
8.
The above picture shows two houses each with a front door.
Write down an estimate for the actual height of a door.
Using this estimate for the height of a door, estimate the actual distance between the two
houses shown by the arrowed line.
You must show all your working.
[4]
[1]
(ii) A pencil costs 32 pence.
What is the cost of g pencils?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
9. (a) (i) The mass of a donkey is x kg. During the year the donkey’s mass increases by 8 kg.
What is the mass of the donkey at the end of the year?
[1]
(b) Describe in words the rule for continuing each of the following sequences.
(i)
48,
42,
36,
30, ….
Rule:
(ii)
2,
8,
32,
128, …
[1]
Rule:
[1]
Part (c)
9. (a) (i) The mass of a donkey is x kg. During the year the donkey’s mass increases by 8 kg.
What is the mass of the donkey at the end of the year?
To increase is to ADD
[1]
(ii) A pencil costs 32 pence.
What is the cost of g pencils?
32g pence
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(x + 8) kg
32 × g
= 32g
[1]
(b) Describe in words the rule for continuing each of the following sequences.
(i)
48,
Rule:
(ii)
2,
42,
36,
30, ….
Take away 6 from previous number
8,
32,
128, …
[1]
Rule:
Multiply previous number by 4
[1]
Part (c)
Reveal
ASSESSMENT
(ii) A pencil costs 32 pence.
What is OBJECTIVE
the cost of g pencils?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
9. (a) (i) The mass of a donkey is x kg. During the year the donkey’s mass increases by 8 kg.
What is the mass of the donkey at the end of the year?
AO1 – Recall and use knowledge
of formation of simple algebraic
expressions,
[1]
[1]
(b) Describe in words the rule for continuing each of the following sequences.
(i)
48,
42,
36,
30, ….
Rule:
ASSESSMENT
(ii)
2,
OBJECTIVE
32, 128, …
8,
AO1 – Recall and use knowledge
of describing the rule for the next
term of a sequence
[1]
Rule:
[1]
Part (c)
[1]
(ii) A pencil costs 32 pence.
What is the cost of g pencils?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
9. (a) (i) The mass of a donkey is x kg. During the year the donkey’s mass increases by 8 kg.
What is the mass of the donkey at the end of the year?
[1]
(b) Describe in words the rule for continuing each of the following sequences.
(i)
48,
42,
36,
30, ….
Rule:
(ii)
2,
8,
32,
128, …
[1]
Rule:
[1]
Part (c)
9 (c) Solve each of the following equations.
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i) 6x = 48
(ii) y + 6 = 19
[1]
Part (a) & (b)
9 (c) Solve each of the following equations.
x = 48
6
x =8
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i) 6x = 48
(ii) y + 6 = 19
y = 19 – 6
y = 13
[1]
Part (a) & (b)
Reveal
9 (c) Solve each of the following equations.
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i) 6x = 48
(ii) y + 6 = 19
[1]
ASSESSMENT
OBJECTIVE
Part (a) & (b)
AO1 – Recall and use knowledge
of solving simple linear equations
9 (c) Solve each of the following equations.
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
(i) 6x = 48
(ii) y + 6 = 19
[1]
Part (a) & (b)
A group of 3 adults and a number of
children travel in a minibus to visit
Arthur’s Castle.
It costs a total of £58 to park the
minibus and pay for the tickets for
everyone to visit the castle.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
10.
How many were there in the group
altogether?
[6]
A group of 3 adults and a number of
children travel in a minibus to visit
Arthur’s Castle.
It costs a total of £58 to park the
minibus and pay for the tickets for
everyone to visit the castle.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
10.
How many were there in the group
altogether?
Total cost of tickets = 58 – 5 = £53
Take away
cost of minibus
Cost for 3 adults = 3 × 7 = £21
Cost for children = 53 – 21 = £32
Number of children = 32 ÷ 4 = 8 children
Total on trip = 8 + 3 = 11 people
Don’t forget to add
on the 3 adults
[6]
Reveal
A group of 3 adults and a number of
children travel in a minibus to visit
Arthur’s Castle.
It costs a total of £58 to park the
minibus and pay for the tickets for
everyone to visit the castle.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
10.
How many were there in the group
altogether?
ASSESSMENT
OBJECTIVE
AO2 – Select and apply
mathematical methods by using
the numerical information to find
the number of people in the group
[6]
A group of 3 adults and a number of
children travel in a minibus to visit
Arthur’s Castle.
It costs a total of £58 to park the
minibus and pay for the tickets for
everyone to visit the castle.
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
10.
How many were there in the group
altogether?
[6]
11. Fran needs at least £800 in euros (€) to go on a visit to France.
The exchange rate is £1 = €1.14.
What is the least number of euros that Fran buys to ensure he has at least
£800 worth and how much did he pay for them?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
When he goes to the bank he finds that the lowest euro note the bank will
give him is the 5 euro note.
[5]
11. Fran needs at least £800 in euros (€) to go on a visit to France.
The exchange rate is £1 = €1.14.
What is the least number of euros that Fran buys to ensure he has at least
£800 worth and how much did he pay for them?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
When he goes to the bank he finds that the lowest euro note the bank will
give him is the 5 euro note.
Euros = 800 × 1.14 = 912 euro
Round UP to the nearest 5 …. = 915 euro
He needs 915 euro
Cost in pounds = 915 ÷ 1.14
= £802.63
Must round up as
910 euro would
not be enough
Reasonable answer:
you are expecting it to
cost more than £800
as you are getting
more than 912 euro
[5]
Reveal
11. Fran needs at least £800 in euros (€) to go on a visit to France.
The exchange rate is £1 = €1.14.
What is the least number of euros that Fran buys to ensure he has at least
£800 worth and how much did he pay for them?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
When he goes to the bank he finds that the lowest euro note the bank will
give him is the 5 euro note.
ASSESSMENT
OBJECTIVE
AO2 – Select and apply
mathematical methods involving
foreign currencies and exchange
rates
[5]
11. Fran needs at least £800 in euros (€) to go on a visit to France.
The exchange rate is £1 = €1.14.
What is the least number of euros that Fran buys to ensure he has at least
£800 worth and how much did he pay for them?
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
When he goes to the bank he finds that the lowest euro note the bank will
give him is the 5 euro note.
[5]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
12. Year 11 and 12 pupils in a comprehensive school were asked:
“In the election for a pupil governor, for whom would you vote?”
The two pie charts below were drawn by a pupil to illustrate the results for Year 11 and
Year 12 separately.
Year 11
Year 12
(a) Estimate the fraction of Year 11 pupils who would vote for Jitesh.
[1]
(b) Can you tell from the pie charts whether fewer Year 11 pupils than Year 12
pupils would vote for Tom?
Put a circle around your choice.
Yes / No
Explain the reasoning for your answer.
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
12. Year 11 and 12 pupils in a comprehensive school were asked:
“In the election for a pupil governor, for whom would you vote?”
The two pie charts below were drawn by a pupil to illustrate the results for Year 11 and
Year 12 separately.
Year 11
Year 12
(a) Estimate the fraction of Year 11 pupils who would vote for Jitesh.

[1]
(b) Can you tell from the pie charts whether fewer Year 11 pupils than Year 12
pupils would vote for Tom?
Put a circle around your choice.
Yes / No
Explain the reasoning for your answer.
You do not know the number of pupils surveyed in each year.
[2]
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
12. Year 11 and 12 pupils in a comprehensive school were asked:
“In the election for a pupil governor, for whom would you vote?”
The two pie charts below were drawn by a pupil to illustrate the results for Year 11 and
Year 12 separately.
ASSESSMENT
Year 11
Year 12
AO1 – Recall and use knowledge
of pie charts
OBJECTIVE
(a) Estimate
the fraction of Year 11 pupils who would vote for Jitesh.
[1]
(b) Can you tell from the pie charts whether fewer Year 11 pupils than Year 12
pupils would vote for Tom?
Put a circle around your choice.
Yes / No
Explain the reasoning for your answer.
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
12. Year 11 and 12 pupils in a comprehensive school were asked:
“In the election for a pupil governor, for whom would you vote?”
The two pie charts below were drawn by a pupil to illustrate the results for Year 11 and
Year 12 separately.
Year 11
Year 12
(a) Estimate the fraction of Year 11 pupils who would vote for Jitesh.
[1]
(b) Can you tell from the pie charts whether fewer Year 11 pupils than Year 12
pupils would vote for Tom?
Put a circle around your choice.
Yes / No
Explain the reasoning for your answer.
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13. (a) Reflect the triangle A in the y-axis.
[1]
Part (b)
Count squares
at right angles
to mirror line
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13. (a) Reflect the triangle A in the y-axis.
[1]
Part (b)
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13. (a) Reflect the triangle A in the y-axis.
ASSESSMENT
OBJECTIVE
AO1 – Recall and knowledge of
reflection in 4 quadrants
[1]
Part (b)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13. (a) Reflect the triangle A in the y-axis.
[1]
Part (b)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13 (b) In the diagram below, describe the translation that maps A to B.
[1]
Part (a)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13 (b) In the diagram below, describe the translation that maps A to B.
3 to the left and 4 up
[1]
Part (a)
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13 (b) In the diagram below, describe the translation that maps A to B.
ASSESSMENT
OBJECTIVE
AO1 – Recall and use knowledge
of translation in 4 quadrants
[1]
Part (a)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
13 (b) In the diagram below, describe the translation that maps A to B.
[1]
Part (a)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
14. a) The diagram on the next page, drawn to the scale of 1 cm represents 10 km, shows
a coastline with harbours at A and B. Find the actual distance, in kilometres,
between the two harbours.
Open map in order to try find a solution
b) At 1:00 p.m. a ship sets off from A and another ship sets off from B. Each
ship travels in a straight line. The ship from A maintains an average speed of
40 km/hour whilst the ship from B keeps to an average speed of 30 km/hour.
The ships meet at 4:00 p.m.
Giving full details of your working and reasoning, find the position where the
two ships meet.
Write down the bearing of this point from B.
Open map in order to try find a solution
[3]
[6]
AB = 15.5 cm
Actual distance = 15.5 × 10
= 155 km
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
14. a) The diagram on the next page, drawn to the scale of 1 cm represents 10 km, shows
a coastline with harbours at A and B. Find the actual distance, in kilometres,
between the two harbours.
Remember to
b) At 1:00 p.m. a ship sets off from A and another ship sets off from B. Each
give full details
ship travels in a straight line. The ship from A maintains an average speed of
40 km/hour whilst the ship from B keeps to an average speed of 30 km/hour.
The ships meet at 4:00 p.m.
Giving full details of your working and reasoning, find the position where the
two ships meet.
Write down the bearing of this point from B.
[3]
[6]
Time taken is from 1.00pm to 4.00pm = 3 hrs
Ship A travels 40 × 3 = 120 km
Find distances travelled
in 3hrs
Ship B travels 30 × 3 = 90 km
(Distance = speed × time)
120 = 12 cm
10
90 = 9 cm
10
Scale 1cm ≡ 10km
Open map to show the rest of the solution
Reveal
14. a) The diagram on the next page, drawn to the scale of 1 cm represents 10 km, shows
a coastline with harbours at A and B. Find the actual distance, in kilometres,
between the two harbours.
OBJECTIVE
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
ASSESSMENT
AO1 – Recall and use knowledge
of scale
b) At 1:00 p.m. a ship sets off from A and another ship sets off from B. Each
ship travels in a straight line. The ship from A maintains an average speed of
40 km/hour whilst the ship from B keeps to an average speed of 30 km/hour.
The ships meet at 4:00 p.m.
Giving full details of your working and reasoning, find the position where the
two ships meet.
Write down the bearing of this point from B.
ASSESSMENT
OBJECTIVE
AO3 – Interpret and analyse the
problem and generate a strategy to
find the bearing using speed,
distance, time of where the two
ships meet
[3]
[6]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
14. a) The diagram on the next page, drawn to the scale of 1 cm represents 10 km, shows
a coastline with harbours at A and B. Find the actual distance, in kilometres,
between the two harbours.
b) At 1:00 p.m. a ship sets off from A and another ship sets off from B. Each
ship travels in a straight line. The ship from A maintains an average speed of
40 km/hour whilst the ship from B keeps to an average speed of 30 km/hour.
The ships meet at 4:00 p.m.
Giving full details of your working and reasoning, find the position where the
two ships meet.
Write down the bearing of this point from B.
[3]
[6]
Back to question
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
14.
Show/hide protractor
Show/hide ruler
Show/hide arc
Rotate ruler
3cm 6cm 9cm 12cm
Back to question
Cannot be
here as
cannot travel
over land
12cm
(120km)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
14.
9cm
(90km)
Bearing is
303º
Reveal
GCSE MATHEMATICS - LINEAR
14.
GCSE MATHEMATICS - LINEAR
14.
15. The owner of a takeaway coffee shop uses two types of paper cups.
Hi-rim cup
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
They can be stacked like this...
Base-stay cup
Hi-rim cup
Base-stay cup
Diagrams are not drawn to scale.
(a) How high is a stack of 25 Hi-rim cups?
[2]
(b) A stack of Base-stay cups is 18.6 cm high.
How many Base-stay cups are in the stack?
[2]
Part (c)
15. The owner of a takeaway coffee shop uses two types of paper cups.
Hi-rim cup
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
They can be stacked like this...
Hi-rim cup
Base-stay cup
Base-stay cup
Diagrams are not drawn to scale.
(a) How high is a stack of 25 Hi-rim cups?
Remember there are 24 cups
above the bottom cup
Therefore 24 × 0.5 NOT 25 × 0.5
Height of cup 1 = 14 cm
Height of cups 2 to 25 = 24 × 0.5 = 12 cm
Total height = 14 + 12 = 26 cm
Add height of bottom cup
[2]
(b) A stack of Base-stay cups is 18.6 cm high.
How many Base-stay cups are in the stack?
Remove cup 1: 18.6 – 9 = 9.6
Number of cups 9.6 ÷ 1.2 = 8
8 cups + 1 cup = 9 cups
[2]
Part (c)
Reveal
15. The owner of a takeaway coffee shop uses two types of paper cups.
Hi-rim cup
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
They can be stacked like this...
Hi-rim cup
Base-stay cup
Base-stay cup
Diagrams are not drawn to scale.
(a) How high is a stack of 25 Hi-rim cups?
[2]
(b) A stack of Base-stay cups is 18.6 cm high.
How many Base-stay cups are in the stack?
ASSESSMENT
OBJECTIVE
Part (c)
AO2 – Select and apply
mathematical methods using the
visual information of how the cups
are stacked
[2]
15. The owner of a takeaway coffee shop uses two types of paper cups.
Hi-rim cup
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
They can be stacked like this...
Base-stay cup
Hi-rim cup
Base-stay cup
Diagrams are not drawn to scale.
(a) How high is a stack of 25 Hi-rim cups?
[2]
(b) A stack of Base-stay cups is 18.6 cm high.
How many Base-stay cups are in the stack?
[2]
Part (c)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
15 (c) A stack of Hi-rim cups is the same height as a stack of Base-stay cups.
There are 21 Base-stay cups in the stack.
How many cups are there in the stack of Hi-rim cups?
[3]
Part (a) & (b)
Height of Base-stay
20 × 1.2 + 9 = 33 cm
To find number of Hi-rim
33 – 14 = 19
19 ÷ 0.5 = 38 cups
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
15 (c) A stack of Hi-rim cups is the same height as a stack of Base-stay cups.
There are 21 Base-stay cups in the stack.
How many cups are there in the stack of Hi-rim cups?
38 + 1 = 39 cups
Don’t forget the bottom cup
[3]
Part (a) & (b)
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
15 (c) A stack of Hi-rim cups is the same height as a stack of Base-stay cups.
There are 21 Base-stay cups in the stack.
How many cups are there in the stack of Hi-rim cups?
ASSESSMENT
OBJECTIVE
AO3 – Interpret and analyse the
problem and generate a strategy to
find the number of cups
[3]
Part (a) & (b)
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
15 (c) A stack of Hi-rim cups is the same height as a stack of Base-stay cups.
There are 21 Base-stay cups in the stack.
How many cups are there in the stack of Hi-rim cups?
[3]
Part (a) & (b)
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
16. (a) Find the value of 3.72 + √21.16
(b) In a shop, the marked price of a television is £542.
The shop offers a discount of 28% of the marked price.
Find the discounted price of the television.
[3]
16. (a) Find the value of 3.72 + √21.16
Use your calculator!
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
18.29
(b) In a shop, the marked price of a television is £542.
The shop offers a discount of 28% of the marked price.
Find the discounted price of the television.
28 × 542 = £151.76
100
Discounted price = 542 – 151.76
= £390.24
As you have a calculator,
you could do…:
28% = 0.28
1 – 0.28 = 0.72
0.72 x 542 = £390.24
[3]
Reveal
ASSESSMENT
OBJECTIVE
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
16. (a) Find the value of 3.72 + √21.16
AO1 – Recall and use knowledge
of squares and square roots using
a calculator
[1]
(b) In a shop, the marked price of a television is £542.
The shop offers a discount of 28% of the marked price.
Find the discounted price of the television.
ASSESSMENT
OBJECTIVE
AO1 – Recall and use knowledge
of percentage reduction
[3]
[1]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
16. (a) Find the value of 3.72 + √21.16
(b) In a shop, the marked price of a television is £542.
The shop offers a discount of 28% of the marked price.
Find the discounted price of the television.
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
17. The table below shows the probabilities of selecting one ball at random
from a bag of coloured balls.
(a) Are there any balls of another colour in the bag?
Give a reason for your answer.
[2]
(b) What is the probability of selecting either a yellow or a purple ball?
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
17. The table below shows the probabilities of selecting one ball at random
from a bag of coloured balls.
(a) Are there any balls of another colour in the bag?
Give a reason for your answer.
0.25 + 0.14 + 0.06 + 0.15 + 0.40 = 1
There are no balls of any other colour because the
probabilities add up to 1.
[2]
(b) What is the probability of selecting either a yellow or a purple ball?
P(yellow or purple)
= P(yellow) + P(purple)
= 0.06 + 0.40
= 0.46
The ball can’t be yellow and purple at
the same time, so the rule
P(A or B) = P(A) + P(B) works.
[2]
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
17. The table below shows the probabilities of selecting one ball at random
from a bag of coloured balls.
(a) Are there any balls of another colour in the bag?
Give a reason for your answer.
ASSESSMENT
OBJECTIVE
AO3 – Generating a strategy
involving the law of total probability
to solve the problem
[2]
(b) What is the probability of selecting either a yellow or a purple ball?
ASSESSMENT
OBJECTIVE
AO2 – Select and apply the
probability law for mutually
exclusive events
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
17. The table below shows the probabilities of selecting one ball at random
from a bag of coloured balls.
(a) Are there any balls of another colour in the bag?
Give a reason for your answer.
[2]
(b) What is the probability of selecting either a yellow or a purple ball?
[2]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
18. Solve the equation
6x – 7 = 4(x + 3).
[3]
GCSE MATHEMATICS - LINEAR
18. Solve the equation
6x – 7 = 4(x + 3).
6x – 7 = 4x + 12 Expand brackets
6x – 4x = 12 + 7 Collect terms
2x = 19
x = 19
2
x = 9.5
[3]
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
18. Solve the equation
ASSESSMENT
OBJECTIVE
6x – 7 = 4(x + 3).
AO1 - Recall and use knowledge
of expanding brackets and solving
linear equations with x on both
sides
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
18. Solve the equation
6x – 7 = 4(x + 3).
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
19. You will be assessed on the quality of your written communication in this question.
A number is written on each of five cards.
The cards are arranged in ascending order.
It is known that the mean of the five numbers is 9.6, the range is 12, the median is 10,
the greatest number is 16 and the fourth number is twice the second number.
Explaining your reasoning, find the five numbers written on the cards.
[7]
4
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
19. You will be assessed on the quality of your written communication in this question.
6 10 12 16
A number is written on each of five cards.
The cards are arranged in ascending order.
It is known that the mean of the five numbers is 9.6, the range is 12, the median is 10,
the greatest number is 16 and the fourth number is twice the second number.
Explaining your reasoning, find the five numbers written on the cards.
[7]
The median is 10. Therefore, the number on the middle card is 10.
The largest number is 16.
The range is 12. Therefore, the smallest number is 16 – 12 = 4
Now, mean × number of cards = total
So, 9.6 × 5 = 48
total of 5 cards – total of 3 cards = 48 – (4 + 10 + 16)
= 18
The fourth number is twice the second, and the two add up to 18.
The fourth number is 12, the second is 6.
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
19. You will be assessed on the quality of your written communication in this question.
A number is written on each of five cards.
The cards are arranged in ascending order.
It is known that the mean of the five numbers is 9.6, the range is 12, the median is 10,
the greatest number is 16 and the fourth number is twice the second number.
Explaining your reasoning, find the five numbers written on the cards.
ASSESSMENT
OBJECTIVE
AO3 – Interpret and analyse the
problem to generate a strategy
using knowledge of mean, median
and range
[7]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
19. You will be assessed on the quality of your written communication in this question.
A number is written on each of five cards.
The cards are arranged in ascending order.
It is known that the mean of the five numbers is 9.6, the range is 12, the median is 10,
the greatest number is 16 and the fourth number is twice the second number.
Explaining your reasoning, find the five numbers written on the cards.
[7]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
20. Jaspal invests £2500 for 2 years at 7% per annum compound interest.
What is the value of his investment after 2 years?
[3]
20. Jaspal invests £2500 for 2 years at 7% per annum compound interest.
What is the value of his investment after 2 years?
7% of £2500 =
7 × 2500 = £175
100
Add this on: 2500 + 175 = £2675
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
1st year:
So, Jaspal has £2675 in his account after 1 year.
2nd year:
7% of £2675 =
7 × 2675 = £187.25
100
Add this on: 2675 + 187.25 = £2862.25
So, Jaspal has £2862.25 in his account after 2 years.
[3]
Reveal
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
20. Jaspal invests £2500 for 2 years at 7% per annum compound interest.
What is the value of his investment after 2 years?
ASSESSMENT
OBJECTIVE
AO1 - Recall and use knowledge
of compound interest
[3]
FOUNDATION Paper 2
GCSE MATHEMATICS - LINEAR
20. Jaspal invests £2500 for 2 years at 7% per annum compound interest.
What is the value of his investment after 2 years?
[3]