Specimen Assessment Materials 2 GCSE Mathematics – Numeracy 2017
Question papers
Unit 1: Non-calculator, Foundation tier
Unit 1: Non-calculator, Intermediate tier
Unit 1: Non-calculator, Higher tier
Unit 2: Calculator-allowed, Foundation tier
Unit 2: Calculator-allowed, Intermediate tier
Unit 2: Calculator-allowed, Higher tier
Mark schemes
Unit 1: Non-calculator, Foundation tier
Unit 1: Non-calculator, Intermediate tier
Unit 1: Non-calculator, Higher tier
Unit 2: Calculator-allowed, Foundation tier
Unit 2: Calculator-allowed, Intermediate tier
Unit 2: Calculator-allowed, Higher tier
Assessment grids
Candidate Name
Centre
Number
Candidate Number
0
GCSE
MATHEMATICS - NUMERACY
UNIT 1: NON - CALCULATOR
FOUNDATION TIER
2nd SPECIMEN PAPER SUMMER 2017
1 HOUR 30 MINUTES
ADDITIONAL MATERIALS
The use of a calculator is not permitted in this examination.
A ruler, protractor and a pair of compasses may be required.
INSTRUCTIONS TO CANDIDATES
Write your name, centre number and candidate number in
the spaces at the top of this page.
Answer all the questions in the spaces provided in this
booklet.
Take π as 3∙14.
INFORMATION FOR CANDIDATES
You should give details of your method of solution when
appropriate.
Unless stated, diagrams are not drawn to scale.
Scale drawing solutions will not be acceptable where you are
asked to calculate.
For Examiner’s use only
Maximum
Mark
Question
Mark
Awarded
1.
4
2.
3
3.
2
4.
3
5.
5
6.
5
7.
6
8.
4
9.
5
10.
5
11.
4
12.
5
13.
5
14.
3
15.
4
16.
2
TOTAL
65
The number of marks is given in brackets at the end of each
question or part-question.
The assessment will take into account the quality of your linguistic and mathematical
organisation, communication and accuracy in writing in question 7.
Formula list
Area of a trapezium =
1
( a  b) h
2
1. Every week, Sarah does her family shopping on the Internet.
She has to be careful to order things in the correct quantities.
The following table shows the items and quantities that Sarah has ordered.
Place a ‘X’ by the items that do not appear to have a sensible quantity and a ‘’ by those that do.
Two have been completed for you.
[4]
Item
Quantity
Orange juice
2 litres
Mushrooms
50 kilograms
A bag of sugar
1 kilogram
Tomato sauce
350 litres
Potatoes
5 grams
Chocolate bar
100 grams
Bottle of vinegar
250 millilitres
Butter
500 grams
Milk
4 litres
Washing-up liquid
500 litres
X or 

X
2. The diagram shows the ground layout of the Liberty Stadium.
During a recent game, the number of spectators in the
West Stand was
East Stand was
South Stand was
7345
6339
4991.
The North Stand is kept for away team spectators.
All 1093 away supporters were in the North Stand.
Showing all your working, calculate the total attendance at the game, giving your answer correct to
the nearest 100.
[3]
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3. Jay and Alex design a game for their school fete. They each have a copy of a fair spinner as
shown below.
•
The game is based on the probability of obtaining certain numbers on the spinner, when the
spinner is spun once.
(a) Jay decides that she wants to place numbers on her spinner that would give an even chance of
getting a number greater than 4.
Place 4 numbers on Jay’s spinner to show this.
[1]
Jay’s Spinner
•
(b) Alex decides that he wants to place numbers on his spinner that would make it certain that you
would get a number less than 3.
Place 4 numbers on Alex’s spinner to show this.
[1]
Alex’s Spinner
•
4. A jewellery shop wishes to create boxes to use for packaging gifts.
(a) Which one of the following patterns cannot be used to form a box in the shape of a cube?
Circle your answer.
[1]
(b) The net of a gift box is shown below.
What is the name of the 3D shape made from this net?
Circle your answer.
[1]
Cuboid
Triangular prism
Cylinder
Sphere
Cone
(c) The shape of another gift box is a triangular based pyramid (tetrahedron).
Which of the following diagrams shows the top view of this gift box?
Circle your answer.
[1]
A
B
C
D
5. The table below shows the scores in the final of the Langford Bay Golf Championship.
The player with the lowest score wins the championship.
Name
Score
A. Jenkins
-2
H. Smith
8
J. Evans
1
L. Hakami
-3
F. Loxley
-7
P.J. Ames
5
G. Francis
-1
(a) Complete the table below to show the names and scores of the players in order from 1st place to
7th place.
[3]
Position Name
Score
1st
2nd
L. Hakami
-3
5th
J. Evans
1
6th
P.J. Ames
5
3rd
4th
7th
(b) What was the difference between the scores of the players in 2nd and 6th places?
Circle your answer.
[1]
2
-4
8
7
-2
(c) How much less would H. Smith need to score in order to win the championship?
[1]
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6. Gethin wants to organise a mountain walk in the Brecon Beacons with his 3 friends Chloe, Robert
and Martyn during 2015.
He has the following information:
 He (Gethin) can only go on a Sunday;
 Chloe cannot go during the last 4 months of the year;
 Martyn works on the first 3 Sundays of each month;
 Robert cannot go during the school holidays;
 All his friends agree that the months of November, December and January are unsuitable for
the walk.
The calendar shown on the opposite page is for 2015.
The school holidays are represented by
What would be the latest date that they could all go for the mountain walk?
You may use the calendar provided to show your working.
[5]
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JANUARY 2015
S
M
T
W
FEBRUARY 2015
T
F
S
1
2
3
S
M
T
W
T
MARCH 2015
F
S
S
M
T
W
T
APRIL 2015
F
S
S
M
T
W
T
F
S
1
2
3
4
4
5
6
7
8
9
10
1
2
3
4
5
6
7
1
2
3
4
5
6
7
5
6
7
8
9
10
11
11
12
13
14
15
16
17
8
9
10
11
12
13
14
8
9
10
11
12
13
14
12
13
14
15
16
17
18
18
19
20
21
22
23
24
15
16
17
18
19
20
21
15
16
17
18
19
20
21
19
20
21
22
23
24
25
25
26
27
28
29
30
31
22
23
24
25
26
27
28
22
23
24
25
26
27
28
26
27
28
29
30
29
30
31
S
M
T
S
M
F
S
MAY 2015
S
M
T
W
T
JUNE 2015
F
S
1
2
S
JULY 2015
M
T
W
T
F
S
1
2
3
4
5
6
AUGUST 2015
W
T
F
S
1
2
3
4
T
W
T
1
3
4
5
6
7
8
9
7
8
9
10
11
12
13
5
6
7
8
9
10
11
2
3
4
5
6
7
8
10
11
12
13
14
15
16
14
15
16
17
18
19
20
12
13
14
15
16
17
18
9
10
11
12
13
14
15
17
18
19
20
21
22
23
21
22
23
24
25
26
27
19
20
21
22
23
24
25
16
17
18
19
20
21
22
24
25
26
27
28
29
30
28
29
30
26
27
28
29
30
31
23
24
25
26
27
28
29
30
31
31
SEPTEMBER 2015
S
M
6
7
13
OCTOBER 2015
T
W
T
F
S
S
M
T
W
1
2
3
4
5
8
9
10
11
12
4
5
6
7
14
15
16
17
18
19
11
12
13
20
21
22
23
24
25
26
18
19
27
28
29
30
25
26
NOVEMBER 2015
T
F
S
1
2
3
8
9
14
15
20
21
27
28
DECEMBER 2015
S
M
T
W
T
F
S
S
M
T
W
T
F
S
10
1
2
3
4
5
6
7
6
7
1
2
3
4
5
8
9
10
11
12
16
17
8
9
10
11
12
13
14
13
14
15
16
17
18
19
22
23
24
15
16
17
18
19
20
21
20
21
22
23
24
25
26
29
30
31
22
23
24
25
26
27
28
29
30
27
28
29
30
31
7. You will be assessed on the quality of your organisation, communication and
accuracy in writing in this question.
Marine Bay
West Wales
Camping & Caravan Park
Pitch fees per night.
Tent = £12
Caravan = £16
Motor-home = £15
The Jones family invited their friends, the Williams and the Phillips families to stay at the Marine Bay
Camping and Caravan Park, West Wales.
The Jones family have a caravan and stayed for 3 nights.
The Williams family have a motor-home and only stayed for one night.
The Phillips family stayed in a tent.
The total fee for the 3 pitches was £99.
For how many nights did the Phillips family stay?
You must show all your working.
[4 + OCW 2]
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8. The electricity meter readings at the beginning and at the end of a 3-month period were:
Reading at the end of the period
6
5
1
9
7
Reading at the beginning of the period
6
4
9
4
7
The cost of the electricity used was 30p per unit and there was a standing charge of £25.34 for the
3-month period.
Complete the following table to find the total cost.
[4]
Reading at the end of the period
Reading at the beginning of the period
Number of units used
Cost of the units, in £
Standing charge for the 3 months
Total cost
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9.
Ten people work at Dragon Fitness.
One of these people earns £1000 per week.
All the other 9 people earn the same weekly wage.
The mean wage for all of these 10 people is £280 per week.
(a)
Complete the table below to show the different types of average weekly wage for these 10
people.
[4]
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Mean
Median
Mode
£280
(b)
Complete the following sentence and give a reason for your choice of mode,
mean.
median or
[1]
‘The average wage of people working at Dragon Fitness is most typically £………’
Reason…………………………………………………………………………………………………………
…………………………………………………………………………………..………………………………
10. Carys is planning a visit to Blaenau Ffestiniog tomorrow.
Carys lives in Rhyl and plans to travel by train.
She will need to travel by train from Rhyl to
Llandudno Junction, then change train to travel on to
Blaenau Ffestiniog.
Carys has collected the timetables she needs to plan her day out.
Going to Blaenau Ffestiniog:
Departs
07:08
07:57
08:29
08:57
09:27
09:57
Departs
07:39
10:28
13:30
16:33
From
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
To
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
From
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Arrives
07:28
08:16
08:51
09:16
09:43
10:16
To
Blaenau Ffestiniog
Blaenau Ffestiniog
Blaenau Ffestiniog
Blaenau Ffestiniog
Duration
20m
19m
22m
19m
16m
19m
Arrives
08:42
11:30
14:32
17:35
Duration
1h 03m
1h 02m
1h 02m
1h 02 m
Arrives
15:57
18:35
21:21
Duration
1h 00m
58m
58m
Returning from Blaenau Ffestiniog:
Departs
14:57
17:37
20:23
Departs
16:18
16:25
17:15
17:37
18:39
18:53
19:26
19:51
From
Blaenau Ffestiniog
Blaenau Ffestiniog
Blaenau Ffestiniog
From
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
To
Llandudno Junction
Llandudno Junction
Llandudno Junction
To
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Arrives
16:34
16:43
17:33
17:53
18:55
19:12
19:42
20:10
Duration
16m
18m
18m
16m
16m
19m
16m
19m
(a) If Carys leaves Rhyl after 9 a.m., what is the earliest possible time at which she could arrive in
Blaenau Ffestiniog? Circle your answer.
[1]
10:28
11:30
13:30
14:32
14:57
(b)
Carys plans to be at the railway station in Blaenau Ffestiniog by 5 p.m. to begin her return
journey home.
How much time, in hours and minutes, will it take to travel back (from the time she leaves
Blaenau Ffestiniog to the time she arrives back at Rhyl station)?
[4]
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11. Gwesty Traeth is a guest house and has six bedrooms.
Two of the rooms are described as Double (they have a double bed).
Two of the rooms are described as Twin (they have two single beds).
Two of the rooms are described as Single (they have one single bed).
The diagram below shows a plan of these rooms.
w
The people listed below have contacted Gwesty Traeth requesting rooms for dates in
July 2016.
 Sasha and Mia want to share a twin room for the 6th and 7th.
 Mr & Mrs Jones want a double room for the 5th.
 Flavia wants a single room for the 5th and 6th.
 Mr & Mrs Evans want a double room for themselves and a twin room for their sons, Morys
and Ifan, to share for the three nights 5th, 6th and 7th.
 Their daughter Heledd will join them on the 6th and 7th, and she requires a single room.
 Mr & Mrs Igorson want a double room for the 6th and 7th.
Use the table below to show who is given which room for each of the dates from the 5th July until
the 7th July.
No-one should have to change rooms during their stay.
[4]
Room 1
5th July
6th July
7th July
Room 2
Room 3
Room 4
Room 5
Room 6
12.
Thomas buys a number of items from a market stall with two £20 notes and one £10 note.
These are the items Thomas buys:
7 cereal bars at 99p each
5 pairs of socks at £3.95 each
3 sweaters at £7.49 each
Thomas waits for the owner of the market stall to list all the items he has selected.
The owner then uses a calculator to add these costs individually and gives
Thomas 75p change.
(a)
Without the use of a calculator, how could Thomas check the calculation by using an
efficient method?
You must show all your working.
[4]
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(b)
Did Thomas receive the correct change? If not, state the correct amount.
[1]
…………………………………………………………………………………………………..........................
…………………………………………………………………………………………………..........................
13. Billy and Shaun both completed a survey.
They collected leaves from a number of trees and decided to measure them.
They agreed on the following decisions
 The length of the leaf does not include the stem
 The width of the leaf is measured at the widest section of the leaf
(a)
Why have they both agreed on these decisions about measuring the leaves?
[1]
……………………………………………………………………………………………....
……………………………………………………………………………………………....
(b)
Billy measured the length and width of each leaf he had collected.
Shaun did the same with his leaves.
They displayed the lengths and widths of their own leaves on separate scatter diagrams.
Billy’s scatter diagram is shown below and Shaun’s scatter diagram is shown opposite.
(i)
Who found the longest leaf?
Write down the length of this leaf.
……………….
.................. cm
[1]
(ii)
Only one of the two boys collected all his leaves from the same tree.
Who was this, Billy or Shaun? Give a reason for your answer.
[1]
…………………………………………………………………………………..………………………………
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…………………………………………………………………………………..………………………………
(iii)
Draw, by eye, a line of best fit on Shaun’s scatter diagram.
[1]
(iv)
Shaun realises he has one more leaf that he has not included on his scatter diagram.
The leaf is damaged in such a way that Shaun cannot measure its width.
The length of the leaf is 8·5 cm.
Write down a reasonable estimate for the width of this leaf.
Width ………. cm
[1]
14.
Ingredients to make 4 pancakes
55 g plain flour
1 egg
100 ml milk
37·5 ml water
25 g butter
Useful information: metric and imperial units
4 ounces is approximately 110 g
Using the recipe shown above, calculate the quantity of plain flour needed to make 48
pancakes. Give your answer in ounces.
[3]
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15.
In a supermarket, the same brand of shampoo is sold in two different-sized bottles.
Large bottle 800 ml for £1.28
Small bottle 300 ml for 45p
Which bottle of shampoo offers the better value for money?
You must show your working and give a reason for your choice.
[4]
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16. The three Welsh castles, shown below, are all within walking distance of each other.
White Castle
Skenfrith Castle
Grosmont Castle
These castles are shown on the map below.
The black lines represent the footpaths between the castles.
N
Complete the following statements.
The bearing of Skenfrith Castle from White Castle is .................... °
The bearing of White Castle from Grosmont Castle is .................... °
[2]
END OF PAPER
Candidate Name
Centre
Number
Candidate
Number
0
GCSE
MATHEMATICS - NUMERACY
UNIT 1: NON - CALCULATOR
INTERMEDIATE TIER
2nd SPECIMEN PAPER SUMMER 2017
1 HOUR 45 MINUTES
ADDITIONAL MATERIALS
The use of a calculator is not permitted in this examination.
A ruler, protractor and a pair of compasses may be
required.
INSTRUCTIONS TO CANDIDATES
Write your name, centre number and candidate number in
the spaces at the top of this page.
Answer all the questions in the spaces provided in this
booklet.
Take π as 3∙14.
INFORMATION FOR CANDIDATES
You should give details of your method of solution when
appropriate.
Unless stated, diagrams are not drawn to scale.
For Examiner’s use only
Question
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
TOTAL
Maximum
Mark
Mark
Awarded
5
9
4
5
5
6
4
9
2
4
7
8
4
8
80
Scale drawing solutions will not be acceptable where you
are asked to calculate.
The number of marks is given in brackets at the end of each
question or part-question.
The assessment will take into account the quality of your linguistic and mathematical
organisation, communication and accuracy in writing in question 2(c)(i).
Formula list
Area of a trapezium =
1
( a  b) h
2
Volume of a prism = area of cross section  length
1.
Ten people work at Dragon Fitness.
One of these people earns £1000 per week.
All the other 9 people earn the same weekly wage.
The mean wage for all of these 10 people is £280 per week.
(a)
Complete the table below to show the different types of average weekly wage
for these 10 people.
[4]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
Mean
Median
Mode
£280
(b)
Complete the following sentence and give a reason for your choice of mode,
median or mean.
[1]
‘The average wage of people working at Dragon Fitness is most typically £………’
Reason…………………………………………………………………………………………
…………………………………………………………………………………………………..
2. Carys is planning a visit to Blaenau Ffestiniog tomorrow.
Carys lives in Rhyl and plans to travel by train.
She will need to travel by train from Rhyl to
Llandudno Junction, then change train to travel on to
Blaenau Ffestiniog.
Carys has collected the timetables she needs to plan her day out.
Going to Blaenau Ffestiniog:
Departs
07:08
07:57
08:29
08:57
09:27
09:57
Departs
07:39
10:28
13:30
16:33
From
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
To
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
From
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Arrives
07:28
08:16
08:51
09:16
09:43
10:16
To
Blaenau Ffestiniog
Blaenau Ffestiniog
Blaenau Ffestiniog
Blaenau Ffestiniog
Duration
20m
19m
22m
19m
16m
19m
Arrives
08:42
11:30
14:32
17:35
Duration
1h 03m
1h 02m
1h 02m
1h 02m
Arrives
15:57
18:35
21:21
Duration
1h 00m
58m
58m
Returning from Blaenau Ffestiniog:
Departs
14:57
17:37
20:23
Departs
16:18
16:25
17:15
17:37
18:39
18:53
19:26
19:51
From
Blaenau Ffestiniog
Blaenau Ffestiniog
Blaenau Ffestiniog
From
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
Llandudno Junction
To
Llandudno Junction
Llandudno Junction
Llandudno Junction
To
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Rhyl
Arrives
16:34
16:43
17:33
17:53
18:55
19:12
19:42
20:10
Duration
16m
18m
18m
16m
16m
19m
16m
19m
(a) If Carys leaves Rhyl after 9 a.m., what is the earliest possible time at which she
could arrive in Blaenau Ffestiniog? Circle your answer.
[1]
10:28
11:30
13:30
14:32
14:57
(b)
Carys decides to leave Rhyl after 9 a.m.
She would like to spend the least time possible changing trains on her way to
Blaenau Ffestiniog, so she selects the most suitable train.
How long will she have to wait for her connecting train to Blaenau Ffestiniog
at Llandudno Junction station?
Circle your answer.
[1]
12 minutes
16 minutes
19 minutes
45 minutes
1h 2 minutes
(c)(i) You will be assessed on the quality of your organisation, communication and
accuracy in writing in this part of the question.
Carys plans to be at the railway station in Blaenau Ffestiniog by 5 p.m. to
begin her return journey home.
How much time, in hours and minutes, will it take to travel back (from the time
she leaves Blaenau Ffestiniog to the time she arrives back at Rhyl station)?
[4 + OCW 2]
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
(ii)
Delays on the Blaenau Ffestiniog to Llandudno Junction railway line are
expected tomorrow.
A delay may cause Carys to miss her connecting train on the way home.
If this happens, at what time will Carys arrive back at Rhyl station?
You may assume that Carys misses only one train.
Circle your answer.
18:35
21:21
18:55
Explain how you decided on your answer.
19:12
19:42
[1]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
3. Gwesty Traeth is a guest house and has six bedrooms.
Two of the rooms are described as Double (they have a double bed).
Two of the rooms are described as Twin (they have two single beds).
Two of the rooms are described as Single (they have one single bed).
The diagram below shows a plan of these rooms.
w
The people listed below have contacted Gwesty Traeth requesting rooms for dates in
July 2016.
 Sasha and Mia want to share a twin room for the 6th and 7th.
 Mr & Mrs Jones want a double room for the 5th.
 Flavia wants a single room for the 5th and 6th.
 Mr & Mrs Evans want a double room for themselves and a twin room for their
sons, Morys and Ifan, to share for the three nights 5th, 6th and 7th.
 Their daughter Heledd will join them on the 6th and 7th, and she requires a
single room.
 Mr & Mrs Igorson want a double room for the 6th and 7th.
Use the table below to show who is given which room for each of the dates from the
5th July until the 7th July.
No-one should have to change rooms during their stay.
[4]
Room 1
5th July
6th July
7th July
Room 2
Room 3
Room 4
Room 5
Room 6
4.
Thomas buys a number of items from a market stall with two £20 notes and
one £10 note.
These are the items Thomas buys:
7 cereal bars at 99p each
5 pairs of socks at £3.95 each
3 sweaters at £7.49 each
Thomas waits for the owner of the market stall to list all the items he has
selected.
The owner then uses a calculator to add these costs individually and gives
Thomas 75p change.
(a)
Without the use of a calculator, how could Thomas check the calculation by
using an efficient method?
You must show all your working.
[4]
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(b)
Did Thomas receive the correct change? If not, state the correct amount.
[1]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
5. Billy and Shaun both completed a survey.
They collected leaves from a number of trees and decided to measure them.
They agreed on the following decisions
 The length of the leaf does not include the stem
 The width of the leaf is measured at the widest section of the leaf
(a)
Why have they both agreed on these decisions about measuring the leaves?
[1]
……………………………………………………………………………………………....
……………………………………………………………………………………………....
(b)
Billy measured the length and width of each leaf he had collected.
Shaun did the same with his leaves.
They displayed the lengths and widths of their own leaves on separate scatter
diagrams.
Billy’s scatter diagram is shown below and Shaun’s scatter diagram is shown
opposite.
(i)
Who found the longest leaf?
Write down the length of this leaf.
……………….
.................. cm
[1]
(ii)
Only one of the two boys collected all his leaves from the same tree.
Who was this, Billy or Shaun? Give a reason for your answer.
[1]
……………………………………………………………………………………………....
……………………………………………………………………………………………....
……………………………………………………………………………………………....
(iii)
Draw, by eye, a line of best fit on Shaun’s scatter diagram.
[1]
(iv)
Shaun realises he has one more leaf that he has not included on his scatter
diagram.
The leaf is damaged in such a way that Shaun cannot measure its width.
The length of the leaf is 8·5 cm.
Write down a reasonable estimate for the width of this leaf.
Width ………. cm
[1]
6.
Ingredients to make 4 pancakes
55 g plain flour
1 egg
100 ml milk
37·5 ml water
25 g butter
Useful information: metric and imperial units
4 ounces is approximately 110 g
25 ml of milk or water is approximately 1 fluid ounce
(a)
Using the recipe shown above, calculate the quantity of plain flour needed to
make 48 pancakes. Give your answer in ounces.
[3]
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…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b)
Owen works in a school kitchen.
He uses the recipe information for pancakes shown above.
He has measured out the plain flour, milk and butter and placed them with the
eggs in a large bowl.
Owen measures out 150 fluid ounces of water to add to his other pancake
ingredients in the bowl.
How many pancakes is Owen making?
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
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7.
In a supermarket, the same brand of shampoo is sold in two different-sized
bottles.
Large bottle 800 ml for £1.28
Small bottle 300 ml for 45p
Which bottle of shampoo offers the better value for money?
You must show your working and give a reason for your choice.
[4]
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…………………………………………………………………………………………………
8. Derek works for a company which designs and fits kitchen cupboards.
Kitchen cupboards and worktops are usually measured in mm.
(a)(i)
A worktop is 4500 mm long.
How much is this in metres?
[1]
………………………………………………………………………………………………
………………………………………………………………………………………………
(ii)
A rectangular worktop needs to be covered in a special varnish.
The worktop measures 3000 mm long by 700 mm wide.
Calculate the area of the top surface of the worktop in m2.
[2]
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
(b)
A kitchen cupboard is in the shape of a cuboid.
Its capacity is 420 000 cm3.
Internally, the cupboard measures 60 cm wide and 70 cm deep.
Calculate the internal height of the cupboard in cm.
[2]
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
(c)
A kitchen worktop measures 301 cm, correct to the nearest 1 cm.
Derek needs to fit two of these worktops together along a wall measuring
605 cm, correct to the nearest 5 cm.
Unfortunately, he finds that the worktops do not fit.
Explain why this might have happened, and state the greatest possible
difference between the lengths of the wall and the two worktops.
[4]
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
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………………………………………………………………………………………………
………………………………………………………………………………………………
9.(a)
Lucy has been given pie charts showing the number of computers sold by 2
different companies.
RG computers
LF computers
Lucy says
‘More men buy RG computers than LF computers.’
Explain how this could be true.
[1]
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
(b)
Lucy sees a headline.
Sales of desktop computers are steadily falling.
A graph was printed under this headline.
Which of the following graphs was it most likely to have been?
Circle your answer.
[1]
10.
Coffee is often sold in a carton.
The height of one coffee carton is 13·4 cm.
Diagram not drawn to scale
A stack of 4 empty coffee cartons is shown below.
Diagram not drawn to scale
(a)
What is the total height of a stack of 21 coffee cartons?
Circle your answer.
32 cm
(b)
33·34 cm
33·6 cm
45·4 cm
[1]
47 cm
The height of a stack of x coffee cartons is 61·4 cm.
By forming an equation, or otherwise, calculate the number of coffee cartons
in the stack.
[3]
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11. The three Welsh castles, shown below, are all within walking distance of each
other.
White Castle
Skenfrith Castle
Grosmont Castle
These castles are shown on the map below.
The black lines represent the footpaths between the castles.
N
(a)
By road, White Castle is 11 km from Skenfrith Castle.
Complete the sentence below.
The map scale is approximately 1 cm to represent …………. km.
[3]
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…………………………………………………………………………………………………
…………………………………………………………………………………………………
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(b)
Complete the following statements.
The bearing of Skenfrith Castle from White Castle is .................... °
The bearing of White Castle from Grosmont Castle is .................... °
[2]
(c)
Treasure has been buried at a position X.
X is the position that meets both the following criteria:


X is equidistant from Grosmont Castle and Skenfrith Castle.
X is equidistant from White Castle Castle and Skenfrith Castle.
Find the treasure by marking X on the map.
[2]
12. Yolanda and Emyr set up a gardening business together.
They decide to calculate the charge for the time that they spend on a gardening
job using the following method.
Gardening by Yolanda and Emyr





(a)
START with a standard charge of £15
ADD a fee of £10 for every complete hour worked
ADD an additional fee of 20p for every additional minute worked
MULTIPLY the total charge so far by 2
EQUALS the final charge
Calculate the charge for a gardening job that takes 2  hours.
[2]
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…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
………………………………………………………………………………………………….
(b) (i) The fourth bullet point in calculating the charge reads:

MULTIPLY the total charge so far by 2.
Why do you think this is included in Emyr and Yolanda’s method for
calculating a charge for gardening?
[1]
…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
………………………………………………………………………………………………….
(ii)
Write a formula for working out the final charge, £T, for gardening that takes h
hours and m minutes.
[3]
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(c)
Yolanda notices that there is a problem with the method for calculating the
charge.
They spent 2 hours on gardening for Mr Rees, and 1 hour 55 minutes
gardening for Ms Elmander.
Mr Rees paid less than Ms Elmander.
Explain why this happens.
[2]
…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
………………………………………………………………………………………………….
13. The information shown below was found in a holiday brochure for a small island.
The information shows monthly data about the rainfall in centimetres.
(a)
Looking at the rainfall, which month had the most changeable weather?
You must give a reason for your answer.
[1]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b)
Circle either TRUE or FALSE for each of the following statements.
[2]
If you don’t want much rain, the time to visit the island is in
June.
The greatest difference in rainfall is between the months of
February and March
The interquartile range for May is approximately equal to the
interquartile range for June.
The range of rainfall in February was approximately 15 cm.
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
During June, there were more days with greater than 7·5 cm of
rainfall than there were days with less than 7·5 cm of rainfall.
TRUE
FALSE
(c) In July 2014, the interquartile range for the rainfall was 10 cm and the range was
40 cm.
Is it possible to say whether July has more or less rainfall than June?
You must give a reason for your answer.
[1]
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14. Two different European Political Parties are proposing changing the rules for
income tax payments for the tax year April 2018 to April 2019.
Income Tax proposed by the Yellow
Party
April 2018 to April 2019
taxable income = gross income – personal allowance




personal allowance is €5000
basic rate of tax 10% on the first €10 000 of taxable income
middle rate of tax 25% is payable on all taxable income over €10 000
and up to €30 000
higher rate tax 50% is payable on all taxable income over €30 000
Income Tax proposed by the Orange
Party
April 2018 to April 2019
taxable income = gross income – personal allowance



(a)
personal allowance is €10 000
basic rate of tax 20% on the first €20 000 of taxable income
higher rate tax 40% is payable on all other taxable income
During the tax year 2018 to 2019, Janina’s gross income is likely to be
€55 000.
Which party’s tax proposal would result in Janina paying the least tax, and by
how much?
You must show all your working
[7]
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(b)
Samuli plays rugby for an international team.
He is likely to earn €200 000 during the tax year 2018 to 2019.
Without any calculations, explain why Samuli might favour the Orange Party’s
proposal for income tax.
[1]
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END OF PAPER
Candidate Name
Centre
Number
Candidate
Number
0
GCSE
MATHEMATICS - NUMERACY
UNIT 1: NON - CALCULATOR
HIGHER TIER
2nd SPECIMEN PAPER SUMMER 2017
1 HOUR 45 MINUTES
ADDITIONAL MATERIALS
The use of a calculator is not permitted in this examination..
A ruler, protractor and a pair of compasses may be
required.
INSTRUCTIONS TO CANDIDATES
Write your name, centre number and candidate number in
the spaces at the top of this page.
Answer all the questions in the spaces provided in this
booklet.
Take π as 3∙14.
INFORMATION FOR CANDIDATES
You should give details of your method of solution when
appropriate.
Unless stated, diagrams are not drawn to scale.
For Examiner’s use only
Question
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
TOTAL
Maximum
Mark
Mark
Awarded
5
8
1
4
5
8
4
8
6
6
6
4
11
4
80
Scale drawing solutions will not be acceptable where you
are asked to calculate.
The number of marks is given in brackets at the end of each
question or part-question.
The assessment will take into account the quality of your linguistic and mathematical
organisation, communication and accuracy in writing in question 1.
1. You will be assessed on the quality of your organisation, communication and
accuracy in writing in this question.
Ingredients to make 4 pancakes
55 g plain flour
1 egg
100 ml milk
37·5 ml water
25 g butter
Useful information: metric and imperial units
25 ml of milk or water is approximately 1 fluid ounce
Owen works in a school kitchen.
He uses the recipe information for pancakes shown above.
He has measured out the plain flour, milk and butter and placed them with the eggs
in a large bowl.
Owen measures out 150 fluid ounces of water to add to his other pancake
ingredients in the bowl.
How many pancakes is Owen making?
[3 + OCW 2]
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
…………………………………………………………………………………………………
2. Derek works for a company which designs and fits kitchen cupboards.
Kitchen cupboards and worktops are usually measured in mm.
(a) A rectangular worktop needs to be covered in a special varnish.
The worktop measures 3000 mm long by 700 mm wide.
Calculate the area of the top surface of the worktop in m2.
[2]
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
(b)
A kitchen cupboard is in the shape of a cuboid.
Its capacity is 420 000 cm3.
Internally, the cupboard measures 60 cm wide and 70 cm deep.
Calculate the internal height of the cupboard in cm.
[2]
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
(c)
A kitchen worktop measures 301 cm, correct to the nearest 1 cm.
Derek needs to fit two of these worktops together along a wall measuring
605 cm, correct to the nearest 5 cm.
Unfortunately, he finds that the worktops do not fit.
Explain why this might have happened, and state the greatest possible
difference between the lengths of the wall and the two worktops.
[4]
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
3.
Lucy has been given pie charts showing the number of computers sold by 2
different companies.
RG computers
LF computers
Lucy says
‘More men buy RG computers than LF computers.’
Explain how this could be true.
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
[1]
4.
Coffee is often sold in a carton.
The height of one coffee carton is 13·4 cm.
Diagram not drawn to scale
A stack of 4 empty coffee cartons is shown below.
Diagram not drawn to scale
(a)
What is the total height of a stack of 21 coffee cartons?
Circle your answer.
32 cm
(b)
33·34 cm
33·6 cm
45·4 cm
[1]
47 cm
The height of a stack of x coffee cartons is 61·4 cm.
By forming an equation, or otherwise, calculate the number of coffee cartons
in the stack.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
5. The three Welsh castles, shown below, are all within walking distance of each
other.
White Castle
Skenfrith Castle
Grosmont Castle
These castles are shown on the map below.
The black lines represent the footpaths between the castles.
N
(a)
By road, White Castle is 11 km from Skenfrith Castle.
Complete the sentence below.
The map scale is approximately 1 cm to represent …………. km.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b)
Treasure has been buried at a position X.
X is the position that meets both the following criteria:


X is equidistant from Grosmont Castle and Skenfrith Castle.
X is equidistant from White Castle Castle and Skenfrith Castle.
Find the treasure by marking X on the map.
[2]
6. Yolanda and Emyr set up a gardening business together.
They decide to calculate the charge for the time that they spend on a gardening
job using the following method.
Gardening by Yolanda and Emyr





(a)
START with a standard charge of £15
ADD a fee of £10 for every complete hour worked
ADD an additional fee of 20p for every additional minute worked
MULTIPLY the total charge so far by 2
EQUALS the final charge
Calculate the charge for a gardening job that takes 2  hours.
[2]
…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
…………………………………………………………………………..………………………
…………………………………………………………………………………………………..
…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
………………………………………………………………………………………………….
(b)(i) The fourth bullet point in calculating the charge reads:

MULTIPLY the total charge so far by 2.
Why do you think this is included in Emyr and Yolanda’s method for
calculating a charge for gardening?
[1]
…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
………………………………………………………………………………………………….
(ii)
Write a formula for working out the total charge, £T, for gardening that takes h
hours and m minutes.
[3]
…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
…………………………………………………………………………..………………………
…………………………………………………………………..………………………………
…………………………………………………………………………………………………..
(c)
Yolanda notices that there is a problem with the method for calculating the
charge.
They spent 2 hours gardening for Mr Rees, and they spent 1 hour 55 minutes
gardening for Ms Elmander.
Mr Rees paid less than Ms Elmander.
Explain why this happens.
[2]
…………………………………………………………………………………………..………
…………………………………………………………………………………..………………
………………………………………………………………………………………………….
7. The information shown below was found in a holiday brochure for a small island.
The information shows monthly data about the rainfall in centimetres.
(a)
Looking at the rainfall, which month had the most changeable weather?
You must give a reason for your answer.
[1]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
(b)
Circle either TRUE or FALSE for each of the following statements.
[2]
If you don’t want much rain, the time to visit the island is in
June.
The greatest difference in rainfall is between the months of
February and March
The interquartile range for May is approximately equal to the
interquartile range for June.
The range of rainfall in February was approximately 15 cm.
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
During June, there were more days with greater than 7·5 cm of
rainfall than there were days with less than 7·5 cm of rainfall.
TRUE
FALSE
(c) In July 2014, the interquartile range for the rainfall was 10 cm and the range was
40 cm.
Is it possible to say whether July has more or less rainfall than June?
You must give a reason for your answer.
[1]
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8. Two different European Political Parties are proposing changing the rules for
income tax payments for the tax year April 2018 to April 2019.
Income Tax proposed by the Yellow
Party
April 2018 to April 2019
taxable income = gross income – personal allowance




personal allowance is €5000
basic rate of tax 10% on the first €10 000 of taxable income
middle rate of tax 25% is payable on all taxable income over €10 000
and up to €30 000
higher rate tax 50% is payable on all taxable income over €30 000
Income Tax proposed by the Orange
Party
April 2018 to April 2019
taxable income = gross income – personal allowance



(a)
personal allowance is €10 000
basic rate of tax 20% on the first €20 000 of taxable income
higher rate tax 40% is payable on all other taxable income
During the tax year 2018 to 2019, Janina’s gross income is likely to be
€55 000.
Which party’s tax proposal would result in Janina paying the least tax, and by
how much?
You must show all your working
[7]
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(b)
Samuli plays rugby for an international team.
He is likely to earn €200 000 during the tax year 2018 to 2019.
Without any calculations, explain why Samuli might favour the Orange Party’s
proposal for income tax.
[1]
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9. A team of examiners has 64 000 examination papers to mark.
It takes each examiner 1 hour to mark approximately 10 papers.
(a) The chief examiner says that a team of 50 examiners could mark all 64 000
papers in 8 days.
What assumption has the chief examiner made?
You must show all your calculations to support your answer.
[4]
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.......................................................................................................................................
(b) Why is the chief examiner’s assumption unrealistic?
What effect will this have on the number of days the marking will take?
[2]
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.......................................................................................................................................
.......................................................................................................................................
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10. Greta has 50 empty jelly moulds which she plans to fill with layers of red and
green jelly. Each jelly mould is shaped as an inverted hollow cone of height 15 cm
and volume 540 cm3.
Greta begins by making 1 litre of red jelly. She then pours an equal amount into
each of the 50 jelly moulds.
Calculate the height of the red jelly in each jelly mould.
You must show all your working.
[6]
15 cm
Diagram not drawn to scale
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11. (a) At the National Eisteddfod in August each year, a concert is performed on the
opening night.
Of those performing this year:
 39 are primary school children,
 73 are secondary school children,
 128 are adults.
In order to gather opinions from the performers about the backstage facilities, the
organisers decide to question a stratified sample of 40 people.
Find how many secondary school children should be selected.
You must show all your working.
[3]
.......................................................................................................................................
.......................................................................................................................................
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.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
Number of secondary school children ........................................................
(b)
Rhodri calculates that 7 primary school children should be selected.
Rhodri selects the first 7 primary school children to get off the bus that brings
them to the concert.
Explain why this does not represent a random sample of the primary school
children.
[1]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
(c)
Of the 128 adult performers, 52 are male and 76 are female.
Gwen decides to interview a stratified sample of 16 adults and has exactly 16
copies of the questionnaire ready for them.
Using these numbers, she calculates that she should interview 7 male
performers and 10 female performers, making a total of 17 adults.
Explain how this has happened.
[2]
.......................................................................................................................................
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12. Anwen is designing an indoor play centre.
The cuboid ABCDEFGH represents a diagram of the room to be used for the play
centre.
A
B
F
C
D
H
E
G
Diagram not drawn to scale
Anwen measures the vertical height of the room to be 5 m.
She measures the distance along the floor from E to F to be 9 m.
The distance from E to G is 12 m.
Anwen is thinking of purchasing a long straight slide for the play centre.
The total length of the slide, including space to get on and off, is 12·5 m.
Would it be possible to fit the slide into the room?
You must show all your working.
[4]
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13. The histogram illustrates the floor areas of the offices available to let by Office
Space Wales letting agency.
Frequency density
8
6
4
2
0
Floor area (m2)
0
50
100
150
200
(a) Calculate the number of offices available that have a floor area greater than
75 m2.
[3]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
(b) Office Space Wales charges a £200 arrangement fee when any of the offices
with a floor area of up to 100 m2 are let.
Assuming that all of the offices under 100 m2 are let, how much will Office Space
Wales receive in arrangement fees for these offices?
[3]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
(c) Circle either TRUE or FALSE for each of the following statements.
[2]
There are definitely no offices available with less than 10 m2 of
space.
The modal class of office space is between 125 m2 and 150 m2.
TRUE
FALSE
TRUE
FALSE
The number of offices over 100 m2 is double the number under
100 m2.
There is enough information in the histogram to allow us to
calculate an exact value for the mean office space.
The number of offices under 50 m2 is definitely the same as the
number over 175 m2.
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
(d) It is reported that the median size of office space available to let is 80 m2.
Is this true for the offices that are available to let by Office Space Wales?
You must give a reason for your answer.
[2]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
14. Dafydd is an engineer working at the Welsh Science Research Centre.
During an experiment, Dafydd knows that a certain chemical particle loses half of
its mass every second.
The initial mass of the particle is 80 grams.
(a) The mass of the particle after 8 seconds is
0·15625 g
0·3125 g
0·625 g
5g
10 g
[1]
(b) Dafydd needs to write down a formula for finding the final mass, f grams, of
the particle after t seconds.
What formula should he write?
[3]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
(c) Comment on the mass of the particle after a long time, such as a whole day,
has passed.
[1]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
END OF PAPER
Candidate Name
Centre
Number
Candidate
Number
0
GCSE
MATHEMATICS - NUMERACY
UNIT 2: CALCULATOR - ALLOWED
FOUNDATION TIER
2nd SPECIMEN PAPER SUMMER 2017
1 HOUR 30 MINUTES
ADDITIONAL MATERIALS
A calculator will be required for this paper.
A ruler, protractor and a pair of compasses may be
required.
INSTRUCTIONS TO CANDIDATES
Write your name, centre number and candidate number in
the spaces at the top of this page.
Answer all the questions in the spaces provided in this
booklet.
Take π as 3∙14 or use the π button on your calculator.
INFORMATION FOR CANDIDATES
You should give details of your method of solution when
appropriate.
For Examiner’s use only
Question
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
TOTAL
Maximum
Mark
Mark
Awarded
9
4
8
4
4
5
2
4
9
6
4
8
65
Unless stated, diagrams are not drawn to scale.
Scale drawing solutions will not be acceptable where you
are asked to calculate.
The number of marks is given in brackets at the end of each
question or part-question.
The assessment will take into account the quality of your linguistic and mathematical
organisation, communication and accuracy in writing in question 3.
Formula list
Area of a trapezium =
1
( a  b) h
2
1. Alys carried out a survey of 30 people to find out which vegetable, from a choice of
cabbage, peas, broccoli and sprouts, they liked the most.
Her results are as follows.
Cabbage
Peas
Broccoli
Peas
Cabbage
Cabbage
Cabbage
Sprouts
Peas
Peas
Peas
Peas
Cabbage
Peas
Cabbage
Peas
Sprouts
Sprouts
Cabbage
Broccoli
Sprouts
Peas
Peas
Sprouts
Broccoli
Sprouts
Peas
Peas
Cabbage
Peas
(a) Use the data to draw a vertical line graph on the squared paper below.
[6]
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(b) Why would Alys collect her data in a frequency table using a tallying method?
[1]
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(c) Alys wanted to compare the popularity of different vegetables.
What is the modal vegetable?
Put a tick next to your answer.
[1]
Cabbage
Peas
There is no modal vegetable
Broccoli
Sprouts
(d) Alys chose one person at random from the people that she had surveyed.
What is the probability that the person chosen said that broccoli was the vegetable
that they liked the most?
[1]
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…………………………………………………………………………………………………
2.
Amelia is organising her 16th birthday party and decides to
make the invitations for the party herself.
Each invitation is a rectangle measuring 6 cm by 8 cm.
She makes the invitations from coloured card measuring
18 cm by 16 cm.
(a) What is the maximum number of invitations that Amelia can cut from one piece of
coloured card?
[2]
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Maximum number of invitations is …………………………….
(b) Amelia wishes to invite 120 people to her birthday party.
What is the least number of pieces of coloured card, measuring 18cm by 16cm, that
Amelia needs to buy?
[2]
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3. You will be assessed on the quality of your organisation, communication and
accuracy in writing in this question.
Ashley usually works 32 hours a week at £6.50 per hour.
She pays one tenth of her earnings in tax and national insurance.
She gives £50 of her weekly earnings to her family for her room and food.
She spends £60 a week on socialising, clothing and other things.
She saves the rest of her earnings.
Ashley wants to book a week’s holiday in Portugal costing £419.
How many weeks will it take her to save for her holiday?
You must show all your working.
[6 + OCW 2]
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4.
A local fitness centre wishes to build an outdoor 5-a-side football pitch of length
45 metres and width 25 metres.
25 metres
45 metres
The cost of building the outdoor 5-a-side football pitch is £85 per square metre.
Calculate the total cost of building the outdoor 5-a-side football pitch.
You must show your working.
[4]
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5.
A chef needs to cook a 4 kilogram
turkey.
The following rule is used to calculate
the cooking time:
“Cook for 40 minutes per kilogram
and then add an extra 25 minutes.”
The chef wants the turkey to be ready at
1:30pm.
What is the latest time that the chef
should begin cooking the turkey?
[4]
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6. Teabags are on offer.
Offer A
Offer B
Which is the better buy?
Show all your calculations.
[5]
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7. A pair of trainers is sold in a box.
The number of pairs of trainers sold each month from January to April is shown in
the pictogram.
The symbol
represents 100 pairs of trainers
January
February
March
April
(a)
What is the approximate range of the numbers of pairs of trainers sold each
month?
Circle your answer.
[1]
100
(b)
150
200
250
300
The total number of trainers sold from January to April is 1300.
What is the mean of the number of pairs of trainers sold each month?
Circle your answer.
[1]
250
300
325
380
400
8. Bikes are built around a frame.
The diagram below is a scale drawing of a bike frame.
It is drawn to a scale of 1: 8.
(a)
Write down an approximate length of the cross bar AB.
Give you answer in metres.
[2]
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(b)
Is AE parallel to BD?
Use angle facts to explain your answer.
[2]
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9. Boat owners are charged to keep their boats in a harbour.
Charges for a North Wales harbour are given in the table below.
Period
Price per metre
(£ per metre)
exclusive of VAT
Notes
Annual
320
Minimum length of boat 9 m
Six monthly
180
Minimum length of boat 7 m
Monthly
40
No minimum length
Notes



(a)
VAT is charged at a rate of 20%.
All charges are per metre; any part metre is charged as a
complete metre.
Combinations of the periods are allowed.
For example, for exactly 7 months, pay for 6 months then pay
for an extra month, or pay monthly for each of the 7 months.
Including VAT, how much would the monthly charge be for a 10 m boat?
Circle your answer.
[1]
£40
(b)
£48
£400
£480
£4800
Excluding VAT, how much would the six monthly charge be for an
8·2 m boat?
[1]
£180
£1440
£1620
£1944
£1728
(c)(i) Lars owns a 9·3 m boat.
He wants to keep his boat in the harbour for 11 months.
Which option should he choose?
You should consider all possibilities, including VAT.
Show all your working.
[6]
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(ii)
What is the greatest saving that Lars could make by selecting your option?
[1]
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Greatest possible saving is £ ……………
10. A container is used to collect the liquid produced by a factory.
As soon as the container is full, it starts to empty the liquid into a tanker.
As soon as the container is empty, it starts to fill again.
The graph shows the process of the container being filled and emptied into the
tanker.
Volume of liquid in the container (m3)
Time (hours)
(a)
What is the volume of the liquid in the container 2  hours into the process?
…………… m3
[1]
(b)
How long does it take to half fill the container?
Give your answer in minutes.
[2]
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(c)
The container is empty at 8:36 a.m.
At what other times is the container empty between 9 a.m. and 9 p.m.?
[2]
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…………………………………………………………………………………………………
(d)
Put a tick in the box next to the correct statement.
[1]
The container fills at a constant rate from when it is empty to when it is full.
The container fills at a constant rate to start with, then slows down.
After starting to fill, the rate at which the container fills up increases.
The container starts to fill quickly, then slows down to a constant rate.
It is not possible to tell whether or not the rate at which the tank fills up
remains the same.
11. Newspapers often give temperatures in both degrees Fahrenheit (°F) and
degrees Celsius (°C).
In the formula below, c represents a temperature in Celsius and f represents a
temperature in Fahrenheit.
9c + 160 = 5f
(a) Complete the following statement.
10°C is the same as …….. °F.
[2]
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(b) Make c the subject of the formula.
9c + 160 = 5f
[2]
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12. A construction company is working on plans to lay a new gas pipeline.
The gas pipeline is to run from Abermor to Brentor to Cantefore then continue on to
another town.
(a) The above diagram shows the section of gas pipeline from Abermor to Cantefore.
(i) The bearing of Brentor from Cantefore is
073°
107°
163°
253°
287°
(ii) Write down the bearing of Abermor from Brentor.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b) As the gas pipeline continues towards the next town, it has to make a 30° turn so
that it follows the road, as shown in the sketch.
Using a pair of compasses and a ruler, construct a line that shows the
direction of the gas pipeline as it follows the road after the 30° turn.
You must show all of your construction lines and arcs.
[3]
END OF PAPER
Candidate Name
Centre
Number
Candidate
Number
0
GCSE
MATHEMATICS - NUMERACY
UNIT 2: CALCULATOR - ALLOWED
INTERMEDIATE TIER
2nd SPECIMEN PAPER SUMMER 2017
1 HOUR 45 MINUTES
ADDITIONAL MATERIALS
A calculator will be required for this paper.
A ruler, protractor and a pair of compasses may be
required.
INSTRUCTIONS TO CANDIDATES
Write your name, centre number and candidate number in
the spaces at the top of this page.
Answer all the questions in the spaces provided in this
booklet.
Take π as 3∙14 or use the π button on your calculator.
INFORMATION FOR CANDIDATES
You should give details of your method of solution when
appropriate.
Unless stated, diagrams are not drawn to scale.
For Examiner’s use only
Question
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
TOTAL
Maximum
Mark
Mark
Awarded
5
2
4
11
6
3
7
5
8
3
7
8
6
5
80
Scale drawing solutions will not be acceptable where you
are asked to calculate.
The number of marks is given in brackets at the end of each
question or part-question.
The assessment will take into account the quality of your linguistic and mathematical
organisation, communication and accuracy in writing in question 4(c)(i).
Formula list
Area of a trapezium =
1
( a  b) h
2
Volume of a prism = area of cross section  length
1. Teabags are on offer.
Offer A
Offer B
Which is the better buy?
Show all your calculations.
[5]
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
…………………………………………………………………………………………………
2. A pair of trainers is sold in a box.
The number of pairs of trainers sold each month from January to April is shown in
the pictogram.
The symbol
represents 100 pairs of trainers
January
February
March
April
(a)
What is the approximate range of the numbers of pairs of trainers sold each
month?
Circle your answer.
[1]
100
(b)
150
200
250
300
The total number of trainers sold from January to April is 1300.
What is the mean of the number of pairs of trainers sold each month?
Circle your answer.
[1]
250
300
325
380
400
3. Bikes are built around a frame.
The diagram below is a scale drawing of a bike frame.
It is drawn to a scale of 1: 8.
(a)
Write down an approximate length of the cross bar AB.
Give you answer in metres.
[2]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(b)
Is AE parallel to BD?
Use angle facts to explain your answer.
[2]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
4. Boat owners are charged to keep their boats in a harbour.
Charges for a North Wales harbour are given in the table below.
Period
Price per metre
(£ per metre)
exclusive of VAT
Notes
Annual
320
Minimum length of boat 9 m
Six monthly
180
Minimum length of boat 7 m
Monthly
40
No minimum length
Notes



(a)
VAT is charged at a rate of 20%.
All charges are per metre; any part metre is charged as a
complete metre.
Combinations of the periods are allowed.
For example, for exactly 7 months, pay for 6 months then pay
for an extra month, or pay monthly for each of the 7 months.
Including VAT, how much would the monthly charge be for a 10 m boat?
Circle your answer.
[1]
£40
(b)
£48
£400
£480
£4800
Excluding VAT, how much would the six monthly charge be for an
8·2 m boat?
[1]
£180
£1440
£1620
£1944
£1728
(c) (i) You will be assessed on the quality of your organisation, communication and
accuracy in writing in this part of the question.
Lars owns a 9·3 m boat.
He wants to keep his boat in the harbour for 11 months.
Which option should he choose?
You should consider all possibilities, including VAT.
Show all your working.
[6 + OCW 2]
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…………………………………………………………………………………………………
(ii)
What is the greatest saving that Lars could make by selecting your option?
[1]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
Greatest possible saving is £ ……………
5. A container is used to collect the liquid produced by a factory.
As soon as the container is full, it starts to empty the liquid into a tanker.
As soon as the container is empty, it starts to fill again.
The graph shows the process of the container being filled and emptied into the
tanker.
Volume of liquid in the container (m3)
Time (hours)
(a)
What is the volume of the liquid in the container 2  hours into the process?
…………… m3
[1]
(b)
How long does it take to half fill the container?
Give your answer in minutes.
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(c)
The container is empty at 8:36 a.m.
At what other times is the container empty between 9 a.m. and 9 p.m.?
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(d)
Put a tick in the box next to the correct statement.
[1]
The container fills at a constant rate from when it is empty to when it is full.
The container fills at a constant rate to start with, then slows down.
After starting to fill, the rate at which the container fills up increases.
The container starts to fill quickly, then slows down to a constant rate.
It is not possible to tell whether or not the rate at which the tank fills up
remains the same.
6. Newspapers often give temperatures in both degrees Fahrenheit (°F) and degrees
Celsius (°C).
In the formula below, c represents a temperature in Celsius and f represents a
temperature in Fahrenheit.
9c + 160 = 5f
(a) Complete the following statement.
10°C is the same as …….. °F.
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b) Make c the subject of the formula.
9c + 160 = 5f
[2]
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
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7. A construction company is working on plans to lay a new gas pipeline.
The gas pipeline is to run from Abermor to Brentor to Cantefore then continue on to
another town.
(a) The above diagram shows the section of gas pipeline from Abermor to Cantefore.
(i) The bearing of Cantefore from Brentor is
073°
107°
163°
253°
287°
(ii) Write down the bearing of Abermor from Brentor.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b) As the gas pipeline continues towards the next town, it has to make a 30° turn
so that it follows the road, as shown in the sketch.
Using a pair of compasses and a ruler, construct a line that shows the
direction of the gas pipeline as it follows the road after the 30° turn.
You must show all of your construction lines and arcs.
[3]
8.
A ribbon is tied around all the faces of a box, as shown in the picture.
The ribbon is placed across each face of the box and meets all the edges of the box
at right angles.
A bow is tied on top of the box.
(a)
A box has length 8·5 cm, width 4·6 cm and height 2·2 cm.
The bow is made using 18 cm of ribbon.
Calculate the total length of ribbon required.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
………………………………………………………………………………………………...
(b)
A different box is to be decorated with ribbon in the same way.
The box has length l cm, width w cm and height h cm.
The bow is made using 18 cm of ribbon.
Write down an expression for the total length of ribbon needed to decorate
this box.
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
9. Lech went on holiday from his home in Wales to Poland.
Before going, he went into his local money exchange shop to buy some Polish
zloty.
Lech only had £250 to spend on buying zloty.
He wanted to buy as many zloty as possible.
Unfortunately, the money exchange shop only had 50 zloty notes.
The exchange rate to buy zloty was £1 = 4.37 zloty.
(a)
How much did Lech pay for the zloty?
[5]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b)
While in Poland, Lech spent 340.40 zloty.
On returning to Wales from his holiday, Lech changed his zloty back to
pounds.
Unfortunately, the money exchange shop would only buy back a whole
number of zloty.
The exchange rate used for changing zloty back to pounds was
£1 = 4.43 zloty.
Calculate how much Lech received back from the money exchange shop.
Give your answer correct to the nearest penny.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
10.
Sabrina sees the following advertisement.
Money Today
Borrow today – why wait until payday?
Costs 1% per day compound interest
Sabrina knows that she will be paid in 2 weeks’ time.
She decides to borrow £400 for a period of 2 weeks.
How much will Sabrina have to pay back after 2 weeks?
Show all your working.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
11.(a) The North Hoyle Offshore Wind Farm is located approximately 7·5 km off the
coast of North Wales.
When this wind farm opened, it was working at 35% of its full capacity, and it
produced enough annual electricity for 50 000 homes.
For how many homes would the wind farm have been able to produce electricity
each year if it had worked at full capacity?
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b) There are many offshore wind farms off the coast of Wales, Scotland and
England.
The full power of the individual wind turbines is different in
the various wind farms.
The table shows information for 4 wind farms.
Wind farm
Full power of each turbine
in Mega Watts (MW)
Number of wind turbines
North Hoyle
2·0
30
Lynn and Inner Dowsing
3·5
54
Rhyl Flats
3·6
25
Robin Rigg
3·0
60
If each of these 4 wind farms worked at 45% of full power, what would be the mean
power of a single wind turbine?
Give your answer correct to 2 decimal places.
You must show all your working.
[5]
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
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12. In Aberfar, a group of local people took part in a challenge to learn how to tie a
Celtic knot.
The frequency diagram shows the times taken by the local people to tie a Celtic
knot for the first time.
(a)
Complete the cumulative frequency table for the times taken by the local
people to tie a Celtic knot for the first time.
[2]
Time, t in
minutes
t ≤ 2·5
t≤ 5
t ≤ 7·5
t ≤ 10
t ≤ 12·5
t ≤ 15
t ≤ 17·5
Cumulative
frequency
(b) The graph paper opposite shows a cumulative frequency diagram of the times
taken by 140 visitors to Wales to tie a Celtic knot for the first time.
On the same graph, draw a cumulative frequency diagram for the times taken by
the local people to tie a Celtic knot for the first time.
[2]
(c)
The visitors had been set a target that 100 of the group would finish within 17 minutes.
By how many minutes did they miss or beat their target?
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………......................
Did they miss the target or beat the target?
By how many minutes?
(d)
…………………..
…………………
Circle either TRUE or FALSE for each of the following statements.
[2]
The tenth percentile reading for the local people is between 5
minutes and 7 minutes.
40% of the visitors took less than 12  minutes.
TRUE
FALSE
TRUE
FALSE
The estimated median time taken by the visitors is 13·75
minutes.
The difference between the estimated median times of the two
groups of people is about 3 minutes.
If there had been only 120 visitors, they would certainly all have
finished within 18 minutes.
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
13. Luis has a large dog which lives in a kennel.
In order to design a similar kennel for a smaller dog, Luis wants to calculate the
angle of elevation of the roof of his dog’s kennel.
He has noticed that the front of his dog’s kennel is symmetrical.
He has measured a number of lengths and recorded them on a diagram of the
kennel, as shown below.
Diagram not drawn to scale
Luis has marked the angle of elevation with an x on the diagram.
(a)
Calculate the size of angle x to an appropriate degree of accuracy.
[5]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
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…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(b)
Explain why, in practice, this angle may not be as accurate as you have
calculated.
[1]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
14. The length of the flag shown is twice its width.
Diagram not drawn to scale
The diagonal of the flag measures 2·5 metres.
Calculate the width of the flag.
[5]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
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…………………………………………………………………………………………..
Width of the flag is ……………….
END OF PAPER
,
Candidate Name
Centre
Number
Candidate
Number
0
GCSE
MATHEMATICS - NUMERACY
UNIT 2: CALCULATOR - ALLOWED
HIGHER TIER
2nd SPECIMEN PAPER SUMMER 2017
1 HOUR 45 MINUTES
ADDITIONAL MATERIALS
A calculator will be required for this paper.
A ruler, protractor and a pair of compasses may be
required.
INSTRUCTIONS TO CANDIDATES
Write your name, centre number and candidate number in
the spaces at the top of this page.
Answer all the questions in the spaces provided in this
booklet.
Take π as 3∙14 or use the π button on your calculator.
INFORMATION FOR CANDIDATES
You should give details of your method of solution when
appropriate.
Unless stated, diagrams are not drawn to scale.
For Examiner’s use only
Question
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14
TOTAL
Maximum
Mark
Mark
Awarded
2
10
3
7
8
6
5
4
5
8
5
7
5
5
80
Scale drawing solutions will not be acceptable where you
are asked to calculate.
The number of marks is given in brackets at the end of each
question or part-question.
The assessment will take into account the quality of your linguistic and mathematical
organisation, communication and accuracy in writing in question 2(a).
1.
A ribbon is tied around all the faces of a box, as shown in the picture.
The ribbon is placed across each face of the box and meets all the edges of the box
at right angles.
A bow is tied on top of the box. The bow is made using 18 cm of ribbon.
The box has length l cm, width w cm and height h cm.
Write down an expression for the total length of ribbon needed to decorate this box.
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
2. Lech went on holiday from his home in Wales to Poland.
Before going, he went into his local money exchange shop to buy some Polish
zloty.
Lech only had £250 to spend on buying zloty.
He wanted to buy as many zloty as possible.
Unfortunately, the money exchange shop only had 50 zloty notes.
The exchange rate to buy zloty was £1 = 4.37 zloty.
(a)
You will be assessed on the quality of your organisation, communication and
accuracy in writing in this part of the question.
How much did Lech pay for the zloty?
[5 + OCW 2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b)
While in Poland, Lech spent 340.40 zloty.
On returning to Wales from his holiday, Lech changed his zloty back to
pounds.
Unfortunately, the money exchange shop would only buy back a whole
number of zloty.
The exchange rate used for changing zloty back to pounds was
£1 = 4.43 zloty.
Calculate how much Lech received back from the money exchange shop.
Give your answer correct to the nearest penny.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
3.
Sabrina sees the following advertisement.
Money Today
Borrow today – why wait until payday?
Costs 1% per day compound interest
Sabrina knows that she will be paid in 2 weeks’ time.
She decides to borrow £400 for a period of 2 weeks.
How much will Sabrina have to pay back after 2 weeks?
Show all your working.
[3]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
4. (a) The North Hoyle Offshore Wind Farm is located approximately 7·5 km off the
coast of North Wales.
When this wind farm opened, it was working at 35% of its full capacity, and it
produced enough annual electricity for 50 000 homes.
For how many homes would the wind farm have been able to produce
electricity each year if it had worked at full capacity?
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(b) There are many offshore wind farms off the coast of Wales, Scotland and
England.
The full power of the individual wind turbines is different in
the various wind farms.
The table shows information for 4 wind farms.
Wind farm
Full power of each turbine
in Mega Watts (MW)
Number of wind turbines
North Hoyle
2·0
30
Lynn and Inner Dowsing
3·5
54
Rhyl Flats
3·6
25
Robin Rigg
3·0
60
If each of these 4 wind farms worked at 45% of full power, what would be the mean
power of a single wind turbine?
Give your answer correct to 2 decimal places.
You must show all your working.
[5]
…………………………………………………………………………………………………
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…………………………………………………………………………………………………
5.
In Aberfar, a group of local people took part in a challenge to learn how to tie a
Celtic knot.
The frequency diagram shows the times taken by the local people to tie a Celtic
knot for the first time.
(a)
Complete the cumulative frequency table for the times taken by the local
people to tie a Celtic knot for the first time.
[2]
Time, t in
minutes
t ≤ 2·5
t≤ 5
t ≤ 7·5
t ≤ 10
t ≤ 12·5
t ≤ 15
t ≤ 17·5
Cumulative
frequency
(b) The graph paper opposite shows a cumulative frequency diagram of the times
taken by 140 visitors to Wales to tie a Celtic knot for the first time.
On the same graph, draw a cumulative frequency diagram for the times taken by
the local people to tie a Celtic knot for the first time.
[2]
(c)
The visitors had been set a target that 100 of the group would finish within 17 minutes.
By how many minutes did they miss or beat their target?
[2]
…………………………………………………………………………………………………
…………………………………………………………………………………......................
Did they miss the target or beat the target?
By how many minutes?
(d)
…………………..
…………………
Circle either TRUE or FALSE for each of the following statements.
[2]
The tenth percentile reading for the local people is between 5
minutes and 7 minutes.
40% of the visitors took less than 12  minutes.
TRUE
FALSE
TRUE
FALSE
The estimated median time taken by the visitors is 13·75
minutes.
The difference between the estimated median times of the two
groups of people is about 3 minutes.
If there had been only 120 visitors, they would certainly all have
finished within 18 minutes.
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
6. Luis has a large dog which lives in a kennel.
In order to design a similar kennel for a smaller dog, Luis wants to calculate the
angle of elevation of the roof of his dog’s kennel.
He has noticed that the front of his dog’s kennel is symmetrical.
He has measured a number of lengths and recorded them on a diagram of the
kennel, as shown below.
Diagram not drawn to scale
Luis has marked the angle of elevation with an x on the diagram.
(a)
Calculate the size of angle x to an appropriate degree of accuracy.
[5]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(b)
Explain why, in practice, this angle may not be as accurate as you have
calculated.
[1]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
7. The length of the flag shown is twice its width.
Diagram not drawn to scale
The diagonal of the flag measures 2·5 metres.
Calculate the width of the flag.
[5]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
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…………………………………………………………………………………………..
…………………………………………………………………………………………..
Width of the flag is ……………….
8. On holiday, Ffion sees a necklace priced at 168 euros in a shop.
The shopkeeper tells her there is an error in the marked price. The rate of value
added tax (VAT) included in the price has been calculated as 15%, but it should be
20%.
As Ffion is disappointed, the shopkeeper offers her an additional reduction of 12%
after the VAT is corrected.
If she accepts the shopkeeper’s offer, how much does Ffion eventually pay for the
necklace?
[4]
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9. An engineer needs to check the density of steel produced by the factory where he
works.
He collects a sample of 1000 ball bearings, each with a radius of 0·8 cm.
The total mass of the ball bearings is 16·935 kg.
Calculate the density of the steel.
Give your answer in kg / m3.
[5]
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10. Ceri is a jewellery designer and is making a brooch.
The brooch is in the shape of a sector of a circle of radius 2·8 cm, as shown in the
diagram.
110°
Diagram not drawn to scale
(a) Ceri is planning to cover the brooch in gold leaf.
Ceri buys gold leaf in square sheets of side length 80 mm. The cost of one sheet of
gold leaf is £48.00.
Assuming that no gold leaf is wasted, find the cost of the gold leaf that is required to
cover the brooch.
[5]
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(b) (i) The cost of the metal Ceri uses for the base of her first brooch should be
£2.28.
She decides to produce a larger brooch in a similar shape, but with a base of the
same thickness. The radius of the sector of the circle she uses this time is 4·2 cm.
The cost of the metal needed for the base of the second brooch should be
£3.19
£3.42
£4.47
£5.13
£9.58
[1]
(ii) Ceri finds that when she makes the base of a brooch, she wastes  of the
metal that she buys.
Including the waste, the actual cost of the metal for the base of the smaller
brooch is
£0.57
£1.71
£2.85
£3.04
£9.12
[1]
11. Dragon Nation Bank is advertising a savings account.
Account
Nominal interest rate
AER
Annual Equivalent Rate,
correct to 2 decimal
places
Dragon Saver
7·6% p.a., paid quarterly
.................... %
(a) Complete the AER entry in the table.
[4]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(b) Explain why AER is used by the bank.
[1]
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
12. A cylinder is made of bendable plastic.
Part of a child’s toy is made by bending the cylinder to form a ring.
The two circular ends of the cylinder are joined to form the ring.
The inner radius of the ring is 9 cm.
The outer radius of the ring is 10 cm.
9 cm
Diagram not drawn to scale
Calculate an approximate value for the volume of the ring.
State and justify what assumptions you have made in your calculations and the
impact they have had on your results.
[7]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
13. Dewi was a cyclist.
He travelled along a straight flat road to the bottom a hill and cycled up the hill.
The gradient of the hill was constant at first, then decreased near the top, where
Dewi stopped for a rest.
Dewi maintained the same level of effort throughout his journey.
(a) Which of the following velocity-time graphs represents Dewi’s journey?
[1]
Velocity
(m/s)
Velocity
(m/s)
A
B
Time (s)
Time (s)
Velocity
(m/s)
C
Time (s)
Velocity
(m/s)
Velocity
(m/s)
E
D
Time (s)
The graph which represents Dewi’s journey is graph ..........................
Time (s)
(b) Later in the day, Dewi’s greatest velocity was 22 metres per second, measured to
the nearest metre per second.
In that location, the speed limit on the road was 80 kilometres per hour.
Is it possible that Dewi exceeded the speed limit?
You must show all your working.
[4]
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
14. A solid concrete base for a garden statue is to be made in the shape of a
frustum of a pyramid. The frustum is formed by removing a small pyramid from a
large pyramid, as shown in the diagram.
Calculate the volume of concrete required to make the base for the garden statue.
Give your answer in litres.
[6]
Diagram not drawn to scale
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
END OF PAPER
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Foundation Tier
1.
Item
Orange juice
Mushrooms
A bag of sugar
Quantity
2 litres
50 kilograms
1 kilogram
X or 
()
X

Tomato sauce
Potatoes
Chocolate bar
350 litres
5 grams
100 grams
X
Bottle of vinegar
Butter
Milk
250 millilitres
500 grams
4 litres



Washing-up liquid
500 litres
X
Mark
B4
MARK SCHEME
Comments (Page 1)
Award B4 for all 8 correct responses
Award B3 for 7 correct responses
Award B2 for 6 correct responses
Award B1 for 5 correct responses
(X)

4
M1
A1
B1
2. 7345 + 6339 + 4991 + 1093
= 19768
19800
Attempt to add 3 or 4 numbers
CAO
FT their total
3
3.
(a) Two numbers less than or equal to 4 AND two
numbers greater than 4.
(b) Four numbers less than 3
B1
B1
4. (a) Correct net circled or clearly indicated
2
B1
(b)
(c) A
B1
B1
Triangular prism
For both parts accept use of appropriate
decimal, fractional and/or negative values.
e.g. 1, 2, 5, 6 OR 3, 4, 5, 6 OR 4, 4, 7, 7
etc
e.g. 0, 0, 0, 0 OR 2, 1, 0, -1 etc
Accept answers either circled or clearly
indicated.
3
5. (a)
Position
st
1
Name
F. Loxley
Score
-7
A. Jenkins
G. Francis
-2
-1
H. Smith
8
B3
B2 for 3 correct
B1 for 2 correct.
nd
2
rd
3
th
4
th
5
th
6
th
7
B1
B1
(b) 8 circled or clearly indicated
(c) 16
Accept 15 (for jointly winning)
OR Accept 17, 18, 19. ……..
5
6.
Identifying/sight of when Chloe can(/cannot) go
Identifying/sight of when Gethin can go
B1
B1
Identifying / sight of when Martyn can(/cannot) go
B1
th
Identifying common dates – (25 Jan), 22
th
th
March, 26 April & 28 June
th
Latest date = 28 June
nd
B1
Look at calendar for indication throughout
the question
e.g. Sept, Oct, Nov, Dec crossed out
Look for focus on Sundays
th
nd
nd
th
(25 Jan), (22 Feb), 22 (& 29 )
th
th
st
th
March, 26 April, (24 & 31 May), 28
th
rd
th
th
June, (26 July, 23 & 30 Aug, 27
th
nd
th
th
Sept, 25 Oct, 22 & 29 Nov & 27
Dec)
st
Sight of common dates triggers 1 4
marks
B1
Award full marks for an unsupported
correct answer
5
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Foundation Tier
7. (Cost for the Jones and Williams families =)
3 × 16 + 1× 15
= (£)63
(Cost for the Phillips family =) (99 – 63) = 36
(Number of nights =) (36 ÷ 12 =) 3 nights
Mark
MARK SCHEME
Comments
(Page 2)
M1
A1
B1
B1
Organisation and communication
Accuracy of writing
FT ‘their 63’ if M1 awarded
FT ‘their 36’. Not dependent on
M1
OC1
W1
6
8.
Reading at the end of the period
Reading at the beginning of the period
65197
64947
Number of units used
250
Cost of the units, in £
75.00
Standing charge for the 3 months
25.34
Total cost
100.34
9. (a) (Total wage for 10 people) 10 × 280
(Wage of each of the other 9 people =)
(2800 – 1000) ÷ 9
(£)200
Median AND modal wage (£)200
(b) Inserts £200 and gives a reason relating to ‘median’ or
‘mode’ including a related statement such as ‘the most
common’ or ‘the middle value’
B1
B2
FT their numbers of units in £.
B1 for answer in pence.
B1
FT their cost of units + 25.34.
If any entry is blank, look in the
work area.
4
M1
(£2800)
m1
A1
B1
FT ‘their 2800’
E1
Needs sight of intention of
reference to the median and / or
mode
FT ‘their derived 200’
Only award if clearly linked to
evidence of understanding of the
average selected. Accept a
reason justifying the selection of
‘mode or median’ or ‘not the
mean’.
10.(a)
11:30
5
B1
(b) 17:37 train selected at Blaenau Ffestiniog,
(Arrives 18:35 Llandudno Junction,) and
Departs Llandudno Junction at 18:39
M1
Needs sight of 17:37 train and
18:39 train
Arrives in Rhyl at 18:55
A1
May be implied
17:37  23 (minutes) + 55 (minutes)  18:55 or
78 (minutes)
M1
Or alternative method to find the
time difference e.g. using the
durations given in the timetables,
58 + 4 + 16 (= 78 mins) etc
1 hour 18 minutes
11. Correct rooms allocated to
(Sasha and Mia), (Mr & Mrs Jones), (Flavia),
(Mr & Mrs Evans), (Morys & Ifan), (Heledd) and
(Mr & Mrs Igorson).
A1
5
B4
4
There are several acceptable
combinations.
B4 for all 7.
B3 for 6.
B2 for 5.
B1 for 4.
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Foundation Tier
Mark
12.
MARK SCHEME
Comments (Page 3)
Accept equivalent simple methods
involving compensation from rounding
with multiplication or any valid
multiplication method throughout, but not
repeated addition
(a) 7 × 99p worked as 7×£1 – 7×1p
5 × £3.95 worked as 5×£4 – 5×5p
3×£7.50 – 3×1p or 3×£7 + 3×50p – 3×1p
Total (£)49.15 or 4915p
B1
B1
B1
B1
(b)
B1
Wrong change, should be 85p
13.(a) Reason e.g. ‘fair comparison’, ‘doing
survey the same way’
(b) (i) Name: Shaun
Length in range 10.3 to
10.5(cm)
(ii) Shaun with a reason, e.g. ‘Shaun because
(positive) correlation’, ‘Shaun because leaves are
similar’, ‘Shaun as there is a connection between
length and width’
(iii) Reasonable straight line of best fit
(iv) Width in the range 6.8 to 7.5 cm
14. Use of × 48 ÷ 4 or × 12 OR realising 55g is
2oz
(12 × 55) ÷ 110 × 4 OR 2 × 12 OR equivalent
24 (ounces)
15. Attempt at unit cost e.g. for 100ml or 1ml,
OR 1(.)28 / 8(00) with 45 / 3(00) or similar,
OR looking to equate volumes,
OR looking to almost equate volumes no more
than 100ml difference, e.g. by looking at 3300ml
with 800ml, or 2800ml with 5300ml
Allow £49.15p. Answer in (a) or (b)
FT provided less than £50 and of
equivalent difficulty.
5
B1
B1
B1
B1
Points above and below following trend
B1
OR correct reading from their line of best
fit
5
B1
M1
A1
3
S1
(2 oz for 4 pancakes, so 2 × 12)
e.g. Idea of doubling or halving to equate,
each done more than once. Method that
would lead to a correct equate or
comparison, e.g. for 300ml, 1200ml,
2400ml, …
Large bottle 16(p) per 100ml or 0.16(p) per 1ml
Small bottle 15(p) per 100ml or 0.15(p) per 1ml
B1
B1
OR 2.4l costs (£)3.84 or 1.2l costs (£)1.92
OR 2.4l costs (£)3.60 or 1.2l costs (£)1.80
Better value statement, conclusion small bottle
E1
E mark is dependent on conditions:
EITHER
Award provided B1 and B1 awarded,
OR
Award as FT from their logical conclusion
provided at least B1 awarded, ignoring
further incorrect processing within a final
statement,
OR
Award provided S1 awarded for
conclusion from comparison with correct
calculations and correct difference in price
for stated extra volume, e.g. ‘(900ml in) 3
small bottles (is £1.35) which is better
value because you get 100ml more (than
a large bottle) for 7p more’
16.
4
B1
B1
065 °
197 °
2
Allow a tolerance of ±2°.
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Intermediate Tier
Mark
MARK SCHEME
Comments (Page 1)
1. (a) (Total wage for 10 people) 10 × 280
(Wage of each of the other 9 people =)
(2800 – 1000) ÷ 9
(£)200
Median AND modal wage (£)200
M1
(£2800)
m1
A1
B1
FT ‘their 2800’
(b) Inserts £200 and gives a reason relating to
‘median’ or ‘mode’ including a related statement
such as ‘the most common’ or ‘the middle value’
E1
Needs sight of intention of reference to
the median and / or mode
FT ‘their derived 200’
Only award if clearly linked to evidence of
understanding of the average selected.
Accept a reason justifying the selection of
‘mode or median’ or ‘not the mean’.
5
B1
B1
M1
Needs sight of 17:37 train and 18:39 train
Arrives in Rhyl at 18:55
A1
May be implied
17:37  23 (minutes) + 55 (minutes)  18:55 or
78 (minutes)
M1
Or alternative method to find the time
difference e.g. using the durations given
in the timetables, 58 + 4 + 16 (= 78 mins)
etc
2.(a)
11:30
(b) 12 minutes
(c)(i) 17:37 train selected at Blaenau Ffestiniog,
(Arrives 18:35 Llandudno Junction,) and
Departs Llandudno Junction at 18:39
1 hour 18 minutes
Organisation and communication
Accuracy of writing
(ii) 19:12 AND reason e.g. catches the next train
(at Llandudno Junction at 18:53)
3. Correct rooms allocated to
(Sasha and Mia), (Mr & Mrs Jones), (Flavia),
(Mr & Mrs Evans), (Morys & Ifan), (Heledd) and
(Mr & Mrs Igorson).
A1
OC1
W1
E1
9
B4
There are several acceptable
combinations.
B4 for all 7.
B3 for 6.
B2 for 5.
B1 for 4.
4
4.
Accept equivalent simple methods
involving compensation from rounding
with multiplication or any valid
multiplication method throughout, but not
repeated addition
(a) 7 × 99p worked as 7×£1 – 7×1p
5 × £3.95 worked as 5×£4 – 5×5p
3×£7.50 – 3×1p or 3×£7 + 3×50p – 3×1p
Total (£)49.15 or 4915p
B1
B1
B1
B1
(b)
B1
Wrong change, should be 85p
5
Allow £49.15p. Answer in (a) or (b)
FT provided less than £50 and of
equivalent difficulty.
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Intermediate Tier
Mark
5.(a) Reason e.g. ‘fair comparison’, ‘doing survey
the same way’
(b) (i) Name: Shaun
Length in range 10.3 to
10.5(cm)
(ii) Shaun with a reason, e.g. ‘Shaun because
(positive) correlation’, ‘Shaun because leaves are
similar’, ‘Shaun as there is a connection between
length and width’
(iii) Reasonable straight line of best fit
B1
B1
Points above and below following trend
(iv) Width in the range 6.8 to 7.5 cm
B1
OR correct reading from their line of best
fit
6.(a) Use of × 48 ÷ 4 or × 12 OR realising 55g is
2oz
(12 × 55) ÷ 110 × 4 OR 2 × 12 OR equivalent
24 (ounces)
(b) 150 fl oz = 150 × 25 (ml) (=3750 ml)
1 pancake 37.5 / 4 (= 9.375) ml water, or
notices 3750 is 100 × ‘amount given in recipe’
(3750 / 9.375 OR 100 × 4 =)
400 (pancakes)
7. Attempt at unit cost e.g. for 100ml or 1ml,
OR 1(.)28 / 8(00) with 45 / 3(00) or similar,
OR looking to equate volumes,
OR looking to almost equate volumes no more
than 100ml difference, e.g. by looking at 3300ml
with 800ml, or 2800ml with 5300ml.
MARK SCHEME
Comments (Page 2)
B1
B1
5
B1
M1
A1
M1
M1
(2 oz for 4 pancakes, so 2 × 12)
OR 3750 ÷ 37.5 = 100
A1
6
S1
e.g. Idea of doubling or halving to equate,
each done more than once. Method that
would lead to a correct equate or
comparison, e.g. for 300ml, 1200ml,
2400ml, …
Large bottle 16(p) per 100ml or 0.16(p) per 1ml.
Small bottle 15(p) per 100ml or 0.15(p) per 1ml.
B1
B1
OR 2.4l costs (£)3.84 or 1.2l costs (£)1.92
OR 2.4l costs (£)3.60 or 1.2l costs (£)1.80
Better value statement, conclusion small bottle.
E1
E mark is dependent on conditions:
EITHER
Award provided B1 and B1 awarded,
OR
Award as FT from their logical conclusion
provided at least B1 awarded, ignoring
further incorrect processing within a final
statement,
OR
Award provided S1 awarded for
conclusion from comparison with correct
calculations and correct difference in price
for stated extra volume, e.g. ‘(900ml in) 3
small bottles (is £1.35) which is better
value because you get 100ml more (than
a large bottle) for 7p more’
4
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Intermediate Tier
Mark
8.(a)(i) 4.5(00 m)
B1
(ii) 3000  700 with an attempt to change units
M1
2
(b) 60  70  .... = 420 000
100 (cm)
(c) Sight of maximum length of worktop(s)
301.5(cm) or 603 (cm)
Sight of minimum length of wall 602.5(cm)
Problem caused by 603(cm) worktop along wall
(only) 602.5(cm) long
Difference in measurement is 0.5 cm
9.(a) Shows understanding that the pie charts
don’t show how many computers were sold
(b) Top right graph
(b)
Attempt to change units needs evidence
n
of ÷10 where n≥3
A1
2.1 (m )
10.(a)
MARK SCHEME
Comments (Page 3)
M1
A1
Or equivalent method
B1
B1
E1
.
B1
9
E1
B1
45.4 cm
(x – 1)  1.6 + 13.4 = 61.4
OR
x = 61.4 – 13.4 + 1
1.6
31 (cartons)
2
B1
M2
Accept equation where x is the number of
stacked cups (excluding the bottom one),
provided 1 is added at the end.
M1 for 1.6  x + 13.4 = 61.4 (omitting +1),
or x = (61.4 – 13.4) / 1.6, or
M1 for an equation that would be correct
apart from missing brackets, or
M1 for correct equation expressed in
words.
Accept missing brackets if implied by a
correct response.
A1
If no marks allow SC1 for 31 (cartons).
Alternative method (using answer to (a)):
(x – 21)  1.6 = 61.4 – 45.4 = 16
M1
x – 21 = 10
M1
x = 31
A1
11.(a) Measuring a distance slightly greater than
the direct distance between White Castle and
Skenfrith Castle.
Approximate answer for 11 ÷ ‘their measured
distance’.
4
M1
M1
FT their measured distance in cm.
Reasonable answer from appropriate calculation
A1
FT from M0, M1
(b) 065 °
197 °
B1
B1
Allow a tolerance of ±2°.
(c) One of the appropriate perpendicular bisectors
±2° shown
X indicated, with both correct perpendicular
bisectors ±2°
M1
A1
7
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Intermediate Tier
12.(a) [15 + 10 × 2 + 15 × 0.20 ] × 2
Mark
M1
MARK SCHEME
Comments (Page 4)
Intention to × 2, however brackets may be
missing
(£)76
A1
(b)(i) e.g. x 2 to account for 2 people working
E1
(ii) Sight of 10 × h
B1
Or equivalent in pence throughout
T = 2(15 + 10 h + 0.2m) or equivalent
B2
B1 for (T =) 15 + 10 × h + (0).2 × m (× 2),
i.e. missing brackets or partially in
brackets
OR (15 + 10 × h + (0).2 × m) × 2 with any
2 of the 3 terms within the brackets
correct
(c) Explanation, e.g. ‘60×20p is more than the
cost per hour’, or ‘£12 paying for an hour charged
by the minute, but £10 for the hour’, ‘55×20p
(=£11) is more than the cost per hour’, or
‘between 51 and 60 minutes cost more than an
hour’, or similar
E2
E1 for an attempt to calculate the charge
for 1 hour 55 minutes
OR
(0).2 × m OR
m/5
8
13.(a) April
Reason, e.g. greatest range, or greatest
interquartile range
E1
(b) TRUE
B2
FALSE
TRUE
TRUE
FALSE
(c) States or implies ‘not possible to tell’ with a
reason, e.g. ‘ can’t tell as it doesn’t give any
information about how much rain fell’, or ‘just the
difference between maximum and minimum not
how much rain fell’, or ‘don’t know as the
difference between UQ & LQ doesn’t give the
actual amount of rain, just a range for the middle
50%’
B1
4
B1 for any 4 correct
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Intermediate Tier
14.(a) Yellow Party
Taxable income (55000 – 5000=)
AND
(10% tax to be paid on (€)10000 =)
(25% tax to be paid on (€)20000=)
AND
(50% tax to be paid on (€)20000=)
Mark
MARK SCHEME
Comments (Page 5)
(€)50000
(€)1000
B1
(€)5000
(€)10000
B1
FT 50% of (‘their 50000’ – 30000)
Yellow Party Tax to pay (€)16000
B1
CAO
Orange Party
Taxable income (55000 – 10000=)
AND
(20% tax to be paid on (€)20000 =)
(€)45000
(€)4000
B1
(€)10000
B1
FT 40% of (‘their 45000’ – 20000)
Orange Party Tax to pay (€)14000
B1
CAO
Orange Party (€)2000 (less to pay)
B1
FT their subtraction provided at least B2
awarded in each tax calculation.
E1
The reason must focus on the 40% and
50% comparison.
Do not accept ‘pays less tax’ without an
explanation.
(40% tax to be paid on (€)25000=)
(b) Reason, e.g. ‘most of his earnings taxed at
40% rather than at 50%’
8
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Higher Tier
1.
150 fl oz = 150 × 25 (ml) (=3750 ml)
1 pancake 37.5 / 4 (= 9.375) ml water, or
notices 3750 is 100 × ‘amount given in recipe’
(3750 / 9.375 OR 100 × 4 =)
400 (pancakes)
Organisation and communication
Accuracy of writing
Mark
M1
M1
MARK SCHEME
Comments (Page 1)
OR 3750 ÷ 37.5 = 100
A1
OC1
W1
5
2.
(a) 3000  700 with an attempt to change units
2
(b) 60  70  .... = 420 000
100 (cm)
(c) Sight of maximum length of worktop(s)
301.5(cm) or 603 (cm)
Sight of minimum length of wall 602.5(cm)
Problem caused by 603(cm) worktop along wall
(only) 602.5(cm) long
Difference in measurement is 0.5 cm
Shows understanding that the pie charts
don’t show how many computers were sold.
4.(a)
(b)
45.4 cm
(x – 1)  1.6 + 13.4 = 61.4
OR
x = 61.4 – 13.4 + 1
1.6
31 (cartons)
Attempt to change units needs evidence
n
of ÷10 where n≥3
A1
2.1 (m )
3.
M1
M1
A1
Or equivalent method
B1
B1
E1
B1
8
E1
1
B1
M2
Accept equation where x is the number of
stacked cups (excluding the bottom one),
provided 1 is added at the end.
M1 for 1.6  x + 13.4 = 61.4 (omitting +1),
or x = (61.4 – 13.4) / 1.6, or
M1 for equation that would be correct
apart from missing brackets, or
M1 for correct equation expressed in
words.
Accept missing brackets if implied by a
correct response.
A1
If no marks allow SC1 for 31 (cartons).
4
Alternative method (using answer to (a)):
(x – 21)  1.6 = 61.4 – 45.4 = 16
M1
x – 21 = 10
M1
x = 31
A1
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Higher Tier
Mark
MARK SCHEME
Comments (Page 2)
5. (a) Measuring a distance slightly greater than
the direct distance between White Castle and
Skenfrith Castle
Approximate answer for 11 ÷ ‘their measured
distance’
M1
M1
FT their measured distance in cm
Reasonable answer from appropriate calculation
A1
FT from M0, M1
(b) One of the appropriate perpendicular bisectors
±2° shown
X indicated, with both correct perpendicular
bisectors ±2°
M1
A1
5
M1
6. (a) [15 + 10 × 2 + 15 × 0.20 ] × 2
Intention to × 2, however brackets may be
missing
(£)76
A1
(b)(i) e.g. x 2 to account for 2 people working
E1
(ii) Sight of 10 × h
B1
Or equivalent in pence throughout
T = 2(15 + 10 h + 0.2m) or equivalent
B2
B1 for (T =) 15 + 10 × h + (0).2 × m (×2),
i.e. missing brackets or partially in
brackets
OR (15 + 10 × h + (0).2 × m) × 2 with any
2 of the 3 terms within the brackets
correct
(c) Explanation, e.g. ‘60×20p is more than the
cost per hour’, or ‘£12 paying for an hour charged
by the minute, but £10 for the hour’, ‘55×20p
(=£11) is more than the cost per hour’, or
‘between 51 and 60 minutes cost more than an
hour’, or similar.
E2
E1 for an attempt to calculate the charge
for 1 hour 55 minutes.
OR
(0).2 × m OR
m/5
8
7. .(a) April
Reason, e.g. greatest range, or greatest
interquartile range
E1
(b) TRUE
B2
FALSE
TRUE
TRUE
FALSE
(c) States or implies ‘not possible to tell’ with a
reason, e.g. ‘can’t tell as it doesn’t give any
information about how much rain fell’, or ‘just the
difference between maximum and minimum not
how much rain fell’, or ‘don’t know as the
difference between UQ & LQ doesn’t give the
actual amount of rain, just a range for the middle
50%’.
B1
4
B1 for any 4 correct.
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Higher Tier
8. (a) Yellow Party
Taxable income (55000 – 5000=)
AND
(10% tax to be paid on (€)10000 =)
Mark
MARK SCHEME
Comments (Page 3)
(€)50000
(€)1000
(25% tax to be paid on (€)20000=)
AND
(50% tax to be paid on (€)20000=)
B1
(€)5000
(€)10000
B1
FT 50% of (‘their 50000’ – 30000)
Yellow Party Tax to pay (€)16000
B1
CAO
Orange Party
Taxable income (55000 – 10000=)
AND
(20% tax to be paid on (€)20000 =)
(€)45000
(€)4000
B1
(€)10000
B1
FT 40% of (‘their 45000’ – 20000)
Orange Party Tax to pay (€)14000
B1
CAO
Orange Party (€)2000 (less to pay)
B1
FT their subtraction provided at least B2
awarded in each tax calculation.
E1
The reason must focus on the 40% and
50% comparison.
Do not accept ‘pays less tax’ without an
explanation.
(40% tax to be paid on (€)25000=)
(b) Reason, e.g. ‘most of his earnings taxed at
40% rather than at 50%’
8
9. (a) 64 000 ÷ 10
÷ 50
M2
M1 for dividing 64 000 by two of 10, 50 or
8.
Accept alternative method involving
multiplication e.g.
50 × 10 = 500
64 000 / 500 (= 128)
128 / 8 (M1 for 2 of the 3 steps)
A1
CAO
÷8
= 16 (hours per examiner per day)
Correct interpretation of the answer e.g.
assumption that each examiner works for a total
of 16 hours per day.
E1
(b) Reason e.g. it is unlikely that all examiners will
work for as long as 16 hours in one day
OR it is unlikely that the examiners will be able to
work at the same rate for 16 hours
AND effect e.g. 8 days is too short a time to
complete the marking.
E2
6
FT ‘their 16’ if appropriate.
E1 for reason only.
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Higher Tier
10. Amount of jelly per mould = 1000 / 50
3
= 20 (cm )
Mark
MARK SCHEME
Comments (Page 4)
M1
A1
Volume scale factor = 540 / 20
= 27
Length scale factor = 3
M1
A1
M1
Height of water = 15 / 3 = 5 (cm)
A1
3
FT ‘their 20 cm ’.
FT cube root of ‘their 27’ provided M1
awarded.
Alternative for final 4 marks:
3
3
M2 for h =15 × 20 / 540.
3
M1 for (h/15) = 20 / 540 or equivalent.
3
m1 for h = √153 ×
20
540
. A1 for 5(cm).
6
11. (a)
(Number of secondary school children =)
73 / (39 + 73 + 128)
73 / 240 × 40
( = 2920 / 240 or 73 / 6 or 12(.1666...) or 12 (1/6))
M1
m1
Intention to find proportion of 40
A1
Must be given as a whole number.
(b) Valid reason e.g. ‘all the children are not
equally likely to be selected’ or ‘the children
selected are likely to be in a friendship group’.
E1
Showing understanding of the definition of
a random sample.
(c) 6.5 (male performers)
OR 9.5 (female performers)
Explanation that both numbers have been
rounded up.
B1
= 12
12. Identifying a suitable right-angled triangle
e.g. AEG
2
2
2
AG = 5 + 12
AG = 13 (m)
Conclusion e.g. ‘Yes, because 12·5 m < 13 m’
E1
6
S1
M1
A1
B1
4
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 1 (Non-calculator) Higher Tier
13. (a) Method of finding 1 correct area.
2 correct areas AND intention to add all areas.
525
M1
M1
A1
(b) 1×75 + 4×25 (= 175)
MARK SCHEME
Comments (Page 5)
Areas are 4×25 + 6×25 + 7×25 + 2×50
= 100 + 150 + 175 + 100
CAO
For an answer of 600 by considering full
area, award M1, SC1
M1
× 200
m1
(£) 35 000
(c)
Mark
FALSE
A1
If no marks, then SC1 for ‘their 175’ × 200
correctly evaluated.
B2
B1 for any 4 correct
E2
E1 for an answer that implies no with a
statement implying that the median is
2
greater than 80m but without giving a
reason why , OR
E1 for NO with an incorrect median stated
in the range 100<median<125 without
further statement.
Do not accept reference to mode.
TRUE
FALSE
FALSE
FALSE
(d)
No, stated or implied with a reason, e.g.
2
‘skew to offices greater than 80m ’, ‘the median
th
(300 value) lies within the 100-125 interval’, ‘No,
2
2
the majority are greater than 80m (or 100m )’
10
14. (a) 0·3125 g
t
B1
t
(b) f = 80 / 2 or f = 80 × 0·5 .
B3
(c) Valid explanation e.g. ‘tends to zero’ or
‘becomes negligibly small’.
E1
5
t
t
B2 for expression 80 / 2 or 80 × 0·5
OR B1 for evidence of 80 repeatedly
being divided by 2 or multiplied by 0·5 i.e.
t
t
more than once, or sight of 2 or 0·5 .
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 2 (Calculator allowed) Foundation Tier
1. (a) Cabbage 8, Peas 13, Sprouts 6, Broccoli 3
Mark
MARK SCHEME
Comments (Page 1)
B2
May be inferred from their bar chart.
B1 for any two/three correct frequencies.
If frequencies score 0, then give B1 for all
4 correct tallies.
Both axes labelled, e.g. frequency or number of
people along one axis and Cabbage, Peas,
Sprouts, Broccoli along the other axis (or on the
bars), anywhere within the base (inc) of the
corres. bar AND uniform scale for the frequency
axis starting at 0.
B2
Four bars at correct heights (bars must be of
equal width). Can be in any order.
B2
B1 if no scale but allow one square to
represent 1
OR B1 if not labelled as ‘frequency’ or
similar.
If frequency scale starts with 1 at the top
of the first square the starting at 0 will be
implied for this axis.
Condone frequency values alongside
square instead of at the top of the
squares.
FT their frequencies throughout. FT their
scale.
B1 for any 2 or 3 correct bars on FT.
(b) Suitable reason given linked to organising
and/or collecting her data in a methodical way.
E1
(c) Peas
B1
(d) 3/30 or equivalent
B1
9
B2
ISW
M1
A1
FT their number of rectangles.
2. (a) 6 rectangles, measuring 6cm by 8cm,
correctly drawn or stated.
(b) 120 ÷ 6
20 (pieces of card)
3. (earnings) (32 × 6.50=) (£)208
(Tax &NI )(1/10 of 208=) (£)20.8(0)
(Total outgoings) (20.8(0) + 50 + 60=) (£)130.8(0)
(Has left) (208 – 130.8(0)=) (£)77.2(0)
(Number of weeks) (419 ÷ 77.2(0)= 5.427...) 6
Organisation and communication
Accuracy of writing
4. (a) (area =) 45 × 25
2
1125(m )
(Cost =) 1125 × (£)85
(£) 95625
4
B1
B1
B1
B1
B2
OC1
W1
8
M1
A1
M1
A1
Award B1 for 2, 3, 4 or 5 rectangles
correctly drawn.
CAO
FT ‘their 208’
FT ‘their 20.8(0)’
FT ‘their 130.8(0)’
B1 for 5(.427) weeks.
FT ‘their 77.2(0)’ for equivalent difficulty
Alternative method
Earnings = 208
B1
Tax = 20.80
B1
(208 – 20.80 = )187.20
B1
Has left 77.20 B1
FT ‘their 187.20’
– 50 – 60
Number of weeks = 6 weeks B2 FT
their 77.2(0) B1 for 5(.427) weeks
FT ‘their area’
If no marks awarded, award SC2 for sight
of (£)11900
OR award SC1 for  85 correctly
5. 4 ½ × 40 = 180
(Cooking time =) 180 mins (or 3 hrs) + 25 mins
= 205 mins or 3 hours 25 mins
(Chef begins cooking at) 10.05 (am)
4
B1
M1
A1
B1
4
FT ‘their 180’
FT their cooking time
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 2 (Calculator allowed) Foundation Tier
6. Use of 30 teabags (for £1.80)
Method to compare, e.g. multiples of 30 & 40:
30, 60, 90, 120 & 40, 80, 120
4 × 1.8(0) and 3 × 2.60
(£)7.2(0) and (£)7.8(0) or equivalent
B1
M1
m1
MARK SCHEME
Comments (Page 2)
OR equivalent, e.g. 1 or 10 teabags
considered for both bags of 30 & 40
OR 1(.)80 ÷ 3(0) and 2(.)60 ÷ 4(0) with
consistent place value to compare
OR 60(p for 10) and 65(p for 10) with
consistent place value to compare
OR 60(p for 10) and (£) 2(.)60 – (£)1(.)80
= 80p for extra 10
OR 2.40 for 40 OR 1.80 ÷ 30 × 40
OR 1.80 ÷ 3 × 4 OR 60(p) for 10 and
80(p) for extra 10.
A1
Offer A (20 teabags + 50% free) is better value
7.(a)
(b)
Mark
E1
5
B1
B1
150
325
2
M1
8.(a) 7cm (± 0.2cm) × 8 (÷ 100)
0.56 (m)
Depends on M1, m1 awarded with
appropriate FT
Accept answers suggesting ‘depends if
you need 40 teabags exactly’ etc.
provided M1, m1, A1 previously awarded.
SC1 for an answer based on comparison
of 20 teabags for £1.80 with 40 teabags
for £2.60, appropriate working with
conclusion of 40 teabags
Award M1 only for answers 56cm or 56m
or 56 or similar from ± 0.2cm tolerance
A1
(b) Measuring 2 appropriate angles (±2°) to check
interior (allied), or appropriate corresponding or
alternate angles
B1
The size of angles may not actually be
recorded, e.g. on diagram equal angles
marked x and y.
Conclusion based on the angles measured and
accurate knowledge of parallel line angle facts.
E1
Accept references to the angles which are
equal or sum to 180°
Do not accept ‘travelling in the same
direction so won’t meet’
4
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Mark
MARK SCHEME
Comments (Page 3)
Unit 2 (Calculator allowed) Foundation Tier
9.(a)
£480
(b)
£1620
B1
B1
(c)(i) Paying for 10m
B1
If not awarded, FT use of 9m throughout
B2
B1 for either correct, or if neither correct
award for excluding VAT charges of
(£)4400 and (£)3200 respectively
M1
A1
Accept excluding VAT (£3800)
E1
FT appropriate conclusion depending on
the sight of any two of the 3 correct
charges given including VAT
11×1mth (11×10×40×1.2 =)
(£)5280
AND
12mth charge (320×10×1.2 =)
(£)3840
6mth + 5×1mth
180×10 + 5×40×10 (×1.2)
(£)4560
Conclusion to pay annual charge based on the
calculation of all 3 possibilities
If misread not using ‘per metre’
consistently, hence MR-1, then B0, then
FT throughout
(ii) Greatest saving (£5280 - £3840 =) (£)1440
B1
10.(a) 5·5 (metres)
9
B1
(b) Intention to read horizontal scale for depth of
3m filling
36 (minutes)
M1
(c) 13(:)36 or 1 36 pm
B2
AND 18(:)36 or 6 36 pm
th
B1
11.(a) 9 × 10 + 160 = 250 or equivalent
50(°F)
6
M1
A1
c = 5f – 160 or c = 5(f – 32)
9
9
Accept answers in the range 5.4 to 5.6
inclusive
Accept sight of 0.6 (hours)
A1
(d) 4 statement identified
(b) 9c =5f – 160
FT their least of 3 possibilities subtracted
correctly from their greatest of 3
possibilities
B1
B1
B1 for either correct, or B1 if both given
with incorrect time notation
or B1 for two times given that are 5 hours
apart e.g. 14:36 and 19:36, i.e. FT 'their
first time' + 5 hours for second B1.
B0 if more than one statement identified.
nd
FT until 2
error
4
B1
12. (a)(i) 253(°)
(ii) 360 – 42
= 318(°)
M1
A1
(b) 60° with construction arcs
M1
(30° by) bisecting ‘their angle’, with arcs shown
Correct 30° from appropriate construction with
line shown at the right hand end of the given line
M1
A1
6
SC1 for answers of 073(°) and 138(°) in (i)
and (ii)
Accept anywhere on the line
Allow sight of construction arcs for 60°
Line (road) may not be shown
Depends on both M marks
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 2 (Calculator allowed) Intermediate Tier
1. Use of 30 teabags (for £1.80)
Method to compare, e.g. multiples of 30 & 40:
30, 60, 90, 120 & 40, 80, 120
4 × 1.8(0) and 3 × 2.60
(£)7.2(0) and (£)7.8(0) or equivalent
Offer A (20 teabags + 50% free) is better value
2.(a)
(b)
Mark
B1
M1
m1
325
E1
2
M1
3.(a) 7cm (± 0.2cm) × 8 (÷ 100)
0.56 (m)
OR equivalent, e.g. 1 or 10 teabags
considered for both bags of 30 & 40
OR 1(.)80 ÷ 3(0) and 2(.)60 ÷ 4(0) with
consistent place value to compare
OR 60(p for 10) and 65(p for 10) with
consistent place value to compare
OR 60(p for 10) and (£) 2(.)60 – (£)1(.)80
= 80p for extra 10
OR 2.40 for 40 OR 1.80 ÷ 30 × 40
OR 1.80 ÷ 3 × 4 OR 60(p) for 10 and
80(p) for extra 10.
A1
5
B1
B1
150
MARK SCHEME
Comments (Page 1)
Depends on M1, m1 awarded with
appropriate FT
Accept answers suggesting ‘depends if
you need 40 teabags exactly’ etc.
provided M1, m1, A1 previously awarded.
SC1 for an answer based on comparison
of 20 teabags for £1.80 with 40 teabags
for £2.60, appropriate working with
conclusion of 40 teabags
Award M1 only for answers 56cm or 56m
or 56 or similar from ± 0.2cm tolerance
A1
(b) Measuring 2 appropriate angles (±2°) to check
interior (allied), or appropriate corresponding or
alternate angles
B1
The size of angles may not actually be
recorded, e.g. on diagram equal angles
marked x and y.
Conclusion based on the angles measured and
accurate knowledge of parallel line angle facts.
E1
Accept references to the angles which are
equal or sum to 180°
Do not accept ‘travelling in the same
direction so won’t meet’
4
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Mark
MARK SCHEME
Comments (Page 2)
Unit 2 (Calculator allowed) Intermediate Tier
4.(a)
£480
(b)
£1620
B1
B1
(c)(i) Paying for 10m
B1
If not awarded, FT use of 9m throughout
B2
B1 for either correct, or if neither correct
award for excluding VAT charges of
(£)4400 and (£)3200 respectively
M1
A1
Accept excluding VAT (£3800)
E1
FT appropriate conclusion depending on
the sight of any two of the 3 correct
charges given including VAT
11×1mth (11×10×40×1.2 =)
(£)5280
AND
12mth charge (320×10×1.2 =)
(£)3840
6mth + 5×1mth
180×10 + 5×40×10 (×1.2)
(£)4560
Conclusion to pay annual charge based on the
calculation of all 3 possibilities
If misread not using ‘per metre’
consistently, hence MR-1, then B0, then
FT throughout
Organisation and communication
Accuracy of writing
OC1
W1
(ii) Greatest saving (£5280 - £3840 =) (£)1440
B1
5.(a) 5·5 (metres)
11
B1
(b) Intention to read horizontal scale for depth of
3m filling
36 (minutes)
M1
(c) 13(:)36 or 1 36 pm
B2
AND 18(:)36 or 6 36 pm
th
Accept answers in the range 5.4 to 5.6
inclusive
Accept sight of 0.6 (hours)
A1
(d) 4 statement identified
B1
6.(a) 9 × 10 + 160 = 250 or equivalent
50(°F)
6
M1
A1
(b) 9c = 5f – 160
c = 5f – 160 or c = 5(f – 32)
9
9
FT their least of 3 possibilities subtracted
correctly from their greatest of 3
possibilities
B1
B1
B1 for either correct, or B1 if both given
with incorrect time notation
or B1 for two times given that are 5 hours
apart e.g. 14:36 and 19:36, i.e. FT 'their
first time' + 5 hours for second B1.
B0 if more than one statement identified.
nd
FT until 2
error
4
B1
7. (a)(i) 253(°)
(ii) 360 – 42
= 318(°)
M1
A1
(b) 60° with construction arcs
M1
(30° by) bisecting ‘their angle’, with arcs shown
Correct 30° from appropriate construction with
line shown at the right hand end of the given line
M1
A1
6
SC1 for answers of 073(°) and 138(°) in (i)
and (ii)
Accept anywhere on the line
Allow sight of construction arcs for 60°
Line (road) may not be shown
Depends on both M marks
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 2 (Calculator allowed) Intermediate Tier
8.(a) 2(8.5 + 4.6) + 42.2 ( + 18) and no others
= 53 (cm)
(b) 2l + 2w + 4h + 18 (cm) or equivalent
(and no extras)
Mark
MARK SCHEME
Comments (Page 3)
M2
Or equivalent.
Attempt to consider all 6 faces or all 8
lengths (+ 18)
M1 for omitting one dimension OR for
adding all three dimensions with at least
one multiplied by 2 or 4.
A1
CAO. An answer of 35 implies M2A0.
B2
B1 for 1 error or 1 slip in notation.
Treat an answer of l + w + 4  h + 18 as 1
error (omitting bottom), hence award B1.
If B2 penalise extra incorrect working -1
5
M1
A1
A1
FT provided M1 awarded
= (£)240.27(46)
M1
A1
FT ‘their 1050 zloty’ provided rounded to
the nearest 50. Must be in zloty not £s.
(b) (1050 – 340.40 =) 709.6(0)
709  4.43
B1
M1
FT ‘their (a)’ provided >340.40
FT rounding down their 709.60 to whole
number
Accept (£)160.04 but not (£)160.045
An answer of (£)160.18 (omitting to round
down) should be awarded B1 then SC1 in
(b).
An answer of (£)160.27 (rounding up
instead of down) should be awarded SC1,
with B1 if 709.6(0) seen.
9.(a) 250  4.37
= 1092.5(0)
(Buys )1050 (zloty)
1050  4.37
(£) 160.05
10.
400 × 1.01
14
A1
or equivalent full method
(£)459.79
8
M2
A1
M1 for correctly multiplying by 1.01
where n is a positive integer.
Award M2A0 for (£)459.789(685...)
n
3
M1
A1
11.(a) 50 000 ÷ 0.35 =
142857
(b) (Total power in MW is)
2.0×30 + 3.5×54 + 3.6×25 + 3.0×60
(Total number of turbines 30+54+25+60 = 169)
(Mean full power of a turbine is)
519 ÷ 169
3.07(1…. MW)
(At 45% power) 0.45 × 3.07(….) or equivalent
1.38 (MW)
M1
(Σfx = 60+189+90+180 = 519)
m1
A1
FT ‘their Σfx’ ÷ ‘their 517’
CAO. Do not accept 3.1 or 3 (MW)
m1
FT ‘their 3.07(…)’ provided M1, m1
previously awarded
Their answer must be given correct to 2
decimal places, i.e. award M1A0 for
1.381(95...) or 1.3815 or 1.382.
A1
Alternative:
(45% power) 0.45×2, 0.45×3.5, 0.45×3.6,
0.45×3
M1
0.9×30 + 1.575×54 + 1.62×25 + 1.35×60
m1
233.55 (MW)
CAO A1
÷169
m1
1.38 (MW)
A1
7
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Mark
Unit 2 (Calculator allowed) Intermediate Tier
12. (a) 0, 5, 25, 49, 83, 113, 120
B2
(b) 3 unique vertical plots correct at upper bounds
All plots correct and joined, including to 0 at t=2.5
M1
A1
(c) Use of 15 minutes
M1
A1
Conclusion: Target beaten by 2 minutes
(d) TRUE
FALSE
B2
TRUE
TRUE
FALSE
13.(a) Form and use a right-angled triangle with
base 55cm and height 50 cm.
Tan x = 50/55
42(°) or 42.3(°)
(a) Reason, e.g. ‘original measurements may not
have been accurate’, or ‘doesn’t consider the
thickness of the wood’, …
14. Attempt to use Pythagoras’ Theorem, e.g.
2
2
2
length + width = 2.5
Use of length = 2 × width
2
2
2
(2 × width) + width = 2.5 or equivalent
2
width = 1.25 or width = √1.25
Width 1.1(2 metres) or 1.118(03… metres)
MARK SCHEME
Comments (Page 4)
B1 for any three correct values, OR FT
from 1 error for finding 3 further
cumulative values accurately
Only FT their cumulative table to (c)
Accuracy of plotting: time on the grid line,
cumulative frequency within the
st
appropriate square with 1 & last plots on
the grid lines
B1 for any 4 correct
FT their cumulative frequency diagram
CAO
CAO
FT their cumulative frequency diagram
CAO
8
S1
M1
A3
Or alternative FULL method.
A2 for 42.27….(°)
-1
-1
A1 for tan 0.909… or tan (50/55)
E1
6
M1
M1
m1
m1
A1
OR equivalent. If units are given they
must be correct.
Alternative:
Attempt to use Pythagoras’ Theorem,
2
2
2
e.g. length + width = 2.5
M1
Use of length = 2 × width
M1
Trial of a pair of values(< 2.5), one double
the other in Pythagoras’ Theorem
m1
Trial of a pair of values(< 2.5), one
double the other in Pythagoras’ Theorem
with improvement, closer to 2.5m
m1
Width 1.1 metres or equivalent
A1
5
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 2 (Calculator allowed) Higher Tier
1.
2l + 2w + 4h + 18 (cm) or equivalent (and
no extras)
2.(a) 250  4.37
= 1092.5(0)
(Buys )1050 (zloty)
1050  4.37
= (£)240.27(46)
(b) (1050 – 340.40 =) 709.6(0)
709  4.43
B1 for 1 error or 1 slip in notation.
Treat an answer of l + w + 4  h + 18 as 1
error (omitting bottom), hence award B1.
If B2 penalise extra incorrect working -1.
2
M1
A1
A1
FT provided M1 awarded
M1
A1
FT ‘their 1050 zloty’ provided rounded to
the nearest 50. Must be in zloty not £s.
B1
M1
(£) 160.05
14
B2
MARK SCHEME
Comments (Page 1)
OC1
W1
Organisation and communication
Accuracy of writing
3. 400 × 1.01
Mark
A1
or equivalent full method
(£)459.79
10
M2
A1
FT ‘their (a)’ provided >340.40
FT rounding down their 709.60 to whole
number
Accept (£)160.04 but not (£)160.045
An answer of (£)160.18 (omitting to round
down) should be awarded B1 then SC1 in
(b).
An answer of (£)160.27 (rounding up
instead of down) should be awarded SC1,
with B1 if 709.6(0) seen.
M1 for correctly multiplying by 1.01
where n is a positive integer.
Award M2A0 for (£)459.789(685...)
n
3
M1
A1
4. (a) 50 000 ÷ 0.35 =
142857
(b) (Total power in MW is)
2.0×30 + 3.5×54 + 3.6×25 + 3.0×60
(Total number of turbines 30+54+25+60 = 169)
(Mean full power of a turbine is)
519 ÷ 169
3.07(1…. MW)
(At 45% power) 0.45 × 3.07(….) or equivalent
1.38 (MW)
M1
(Σfx = 60+189+90+180 = 519)
m1
A1
FT ‘their Σfx’ ÷ ‘their 517’
CAO. Do not accept 3.1 or 3 (MW)
m1
FT ‘their 3.07(…)’ provided M1, m1
previously awarded
Their answer must be given correct to 2
decimal places, i.e. award M1A0 for
1.381(95...) or 1.3815 or 1.382.
A1
Alternative:
(45% power) 0.45×2, 0.45×3.5, 0.45×3.6,
0.45×3
M1
0.9×30 + 1.575×54 + 1.62×25 + 1.35×60
m1
233.55 (MW)
CAO A1
÷169
m1
1.38 (MW)
A1
7
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Mark
Unit 2 (Calculator allowed) Higher Tier
5. (a) 0, 5, 25, 49, 83, 113, 120
B2
(b) 3 unique vertical plots correct at upper bounds
All plots correct and joined, including to 0 at t=2.5
M1
A1
(c) Use of 15 minutes.
M1
Conclusion: Target beaten by 2 minutes.
A1
(d)
B2
TRUE
FALSE
TRUE
TRUE
FALSE
6. (a) Form and use a right-angled triangle with
base 55 cm and height 50 cm.
Tan x = 50/55
42(°) or 42.3(°)
(b) Reason, e.g. ‘original measurements may not
have been accurate’, or ‘doesn’t consider the
thickness of the wood’, …
7. Attempt to use Pythagoras’ Theorem, e.g.
2
2
2
length + width = 2.5
Use of length = 2 × width
2
2
2
(2 × width) + width = 2.5 or equivalent
2
width = 1.25 or width = √1.25
Width 1.1(2 metres) or 1.118(03… metres)
MARK SCHEME
Comments (Page 2)
B1 for any three correct values, OR FT
from 1 error for finding 3 further
cumulative values accurately.
Only FT their cumulative table to (c)
Accuracy of plotting: time on the grid line,
cumulative frequency within the
st
appropriate square with 1 & last plots on
the grid lines.
B1 for any 4 correct.
FT their cumulative frequency diagram.
CAO
CAO
FT their cumulative frequency diagram.
CAO
8
S1
M1
A3
Or alternative FULL method.
A2 for 42.27….(°)
-1
-1
A1 for tan 0.909… or tan (50/55)
E1
6
M1
M1
m1
m1
A1
OR equivalent. If units are given they
must be correct.
Alternative:
Attempt to use Pythagoras’ Theorem,
2
2
2
e.g. length + width = 2.5
M1
Use of length = 2 × width
M1
Trial of a pair of values (< 2.5), one
double the other in Pythagoras’ Theorem
m1
Trial of a pair of values (< 2.5), one
double the other in Pythagoras’ Theorem
with improvement, closer to 2.5m
m1
Width 1.1 metres or equivalent .
A1
8.
((€)168) ÷ 1.15
× 1.2(0)
× 0.88
= 154.27 (euros)
5
M1
M1
M1
A1
4
Or equivalent e.g. × 120 / 115
CAO
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Mark
Unit 2 (Calculator allowed) Higher Tier
3
9. Volume = 4/3 × π × 0.8 (× 1000)
3
[OR 4/3 × π × 0.008 (× 1000)]
MARK SCHEME
Comments (Page 3)
M1
Accept incorrect place value for digit 8 for
M1.
A1
Accept answers in range 2143 to 2146
Or 2048 π / 3
Use of conversion 1 m = 1 000 000 cm .
B1
FT ‘their derived volume’ from
dimensionally correct use of formula.
Use of mass / volume e.g. 16.935 ÷ 0.002144
M1
3
= 2144(.6605...) cm
3
[OR 0.002144(6605...) m ].
3
3
3
A1
7896 (kg / m )
Accept answers in the range 7893 to
7901.
5
10. (Area of brooch =)
2
2
110 / 360 × π × 2.8 OR 110 / 360 × π × 28
2
M1
2
= 7.52(5...) (cm ) or 752.58(5...) (mm )
or equivalent
2
2
e.g. 539π / 225 (cm ) or 2156 π / 9 (mm )
A1
(Cost of gold leaf per unit =)
2
(£)48 ÷ (8 × 8) (per cm ) or (£)48 ÷ (80 × 80) (per
2
mm )
2
2
= (£)0.75 (per cm ) or (£)0.0075 (per mm )
or equivalent in pence
Accept answers in range 7.52 to 7.53
2
(cm )
M1
A1
(Cost of gold leaf for brooch =
7.52(5...) × 0.75 or 752(.585...) × 0.0075)
= (£)5.64
which is rounded UP to give (£)5.65
A1
(b) (i)
£5.13
B1
(ii)
£3.04
B1
Accept (£)5.64 (rounded down) or (£)5.65
(directly from rounded area)
9.
7
10. 11. (a)
Use of i = 0·076 AND n = 4
4
(1 + 0·076 / 4) – 1
AER 7·82(%)
(b) Explanation, based on need for fair
comparison of interest rates.
Check table.
B1
M1
A2
E1
5
Correct substitution in the formula.
A1 for 0·078(19...) or incorrect rounding or
truncation of the AER percentage.
Accept ‘percentage of interest paid
annually’. Must mention ‘year’ or ‘annual’.
MATHEMATICS - NUMERACY
nd
2 SAMs 2017
Unit 2 (Calculator allowed) Higher Tier
11. 12. Radius of the cylinder = 0.5 cm
12.
OR diameter = 1 cm
13.
Idea that height of cylinder is approximately the
circumference of the ring.
Circumference of ring = 2 × π × value between 9
and 10 inclusive
2
Volume = π × 0.5 × circumference of ring
3
Mark
MARK SCHEME
Comments (Page 4)
B1
May be shown on the diagram
S1
May be internal, external or somewhere in
between.
Accept sight of 9 × π or 10 × π for S1.
M1
M1
Volume in the range 44.3 to 49.4 (cm )
inclusive.
A1
Statement about assumption, e.g. volume of
cylinder used to calculate volume of toy, use of
mid-value for radius of ring.
E1
Justification, e.g. used smaller radius so actual
volume will be greater,
or used larger radius so actual volume will be
less,
or used 9.5 cm as height of cylinder is clearly
between 9 cm and 10 cm.
E1
13. (a) D
7
B1
(b) 22.5
× 60 × 60
÷ 1000
‘Yes’ AND 81 (km / h)
B1
M1
M1
A1
FT ‘their 22.5’
CAO
5
14. (Ratio of lengths 45 : 60 = )
3:4
B1
90 (cm)
B1
 × 452 × 90
M2
M1 for one correct product attempted for a
volume (or sight of 144 000 or 60 750)
A2
A1 for 83 250 (cm )
3
FT their answer in cm for conversion to
litres for final A1.
(Height of small pyramid =)
(Volume of frustum =)
 × 60 × 120 –
2
= 83·25 (litres)
3
Alternative solution:
Ratio of lengths = 3 : 4
B1
Ratio of volumes = 27 : 64
B1
3
Volume of large pyramid = 144 000 cm B1
Volume of frustum = 64 – 27 × 144 000 M1
64
83·25 (litres)
A2
3
Award A1 for 83 250 (cm )
3
FT their answer in cm for conversion to
litres for final A1.
6
GCSE Mathematics - Numeracy
Foundation Unit 1
Qu.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
AOs
Max
Common
AO1 AO2 AO3
mark
(Interm)
Topic
Sarah's shopping
Liberty stadium rounding
Jay and Alex fair spinner
Jewellery boxes
Golf Negative numbers
Mountain walk
Marine Bay Caravan park
Electricity bill
Dragon fitness centre wages average
Rhyl to Blaenau Ffestiniog
Gwesty Traeth accommodation
Market stall addition method reflection
Leaf comparison scatter diagram
Pancake recipe with change of units
Best buy shampoo
Three castles
Totals
4
3
2
3
5
5
6
4
5
5
4
5
5
3
4
2
4
65
12
OCW
3
2
3
1
4
5
6
4
4
5
2
1
1
3
4

1
4
4
2
2
35
18
5(Q1)
5(Q2)
4(Q3)
5(Q4)
5(Q5)
3(Q6)
4(Q7)
2(Q11)
33
GCSE Mathematics - Numeracy
Intermediate Unit 1
Qu.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
AOs
Max
Common Common
AO1 AO2 AO3
mark
(Found) (Higher)
Topic
Dragon fitness centre wages average
Rhyl to Blaenau Ffestiniog
Gwesty Traeth accommodation
Market stall addition method reflection
Leaf comparison scatter diagram
Pancake recipe with change of units
Best buy shampoo
Kitchen cupboards
Computer misleading piecharts and headline graph
Stacking coffee cartons equation
Three castles
Yolanda and Emyr gardening business
Box and whisker rainfall graph
European Tax political party proposals
5
9
4
5
5
6
4
9
2
4
7
8
4
8
Totals
80
4
9
2
1
1
6
4
5
4
2
1
4
3
4
2
7
13
46
1
4
4
2
5(Q9)
5(Q10)
4(Q11)
5(Q12)
5(Q13)
3(Q14)
4(Q15)
4
1
21

3(Q1)
2(Q16)
8(Q2)
1(Q3)
4(Q4)
5(Q5)
8(Q6)
4(Q7)
8(Q8)
33
41
2
2
1
OCW
GCSE Mathematics - Numeracy
Higher Unit 1
Qu.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
AOs
N
Max
Common
uAO1 AO2 AO3
mark
(Interm)
m
5
5
3(Q6)
8
4
4
8(Q8)
1
1
1(Q9)
4
4
4(Q10)
5
2
3
5(Q11)
8
2
4
2
8(Q12)
4
3
1
4(Q13)
8
7
1
8(Q14)
6
6
6
6
6
1
3
2
4
4
10
3
5
2
5
4
1
Topic
Pancake recipe with change of units
Kitchen cupboards
Computer misleading piecharts
Stacking coffee cartons equation
Three castles
Yolanda and Emyr gardening business
Box and whisker rainfall graph
European Tax political party proposals
Marking exam papers (proportions)
Jelly moulds (similar cone volumes)
Eisteddfod performers
Slide (3D Pythagoras)
Office Space Wales (histogram)
Particle mass formula
Totals
80
16
40
24
41
OCW

GCSE Mathematics - Numeracy
Foundation Unit 2
Qu.
1
2
3
4
5
6
7
8
9
10
11
12
AOs
Max
Common
AO1 AO2 AO3
mark
(Interm)
Topic
Alys's survey on vegetables
Amelia's 16th birthday party invitations
Ashley's holiday savings
Local fitness centre football pitch
Cooking a turkey
Teabag best value multiples with 50% extra free
Pictogram trainers mean and range
Bike frame parallel
Harbour boat charges
Filling and emptying a tank
Celsius to Fahrenheit rearrange formula
Laying a gas pipe
Totals
9
4
8
4
4
5
2
4
9
6
4
6
8
65
16
OCW
1
4

8
4
4
5
2
2
2
9
5
1
4
6
33
16
5(Q1)
2(Q2)
4(Q3)
9(Q4)
6(Q5)
4(Q6)
6(Q7)
36
GCSE Mathematics - Numeracy
Intermediate Unit 2
Qu.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
AOs
Max
Common Common
AO1 AO2 AO3
mark
(Found) (Higher)
Topic
Teabag best value multiples with 50% extra free
Pictogram trainers mean and range
Bike frame parallel
Harbour boat charges
Filling and emptying a tank
Celsius to Fahrenheit rearrange formula
Laying a gas pipe
Package with a ribbon
Holiday to Poland (zloty)
Pay Day loan
Off shore wind farm
Celtic knot frequency cumulative frequency
Dog kennel angle of elevation
Width of a flag Pythagoras' Theorem
5
2
4
11
6
4
6
5
8
3
7
8
6
5
Totals
80
5
2
2
2
11
5
1
4
6
5(Q6)
2(Q7)
4(Q8)
9(Q9)
6(Q10)
4(Q11)
6(Q12)
5
8
3
2
4
2
5
5
2
1
5
19
45
16

2(Q1)
8(Q2)
3(Q3)
7(Q4)
8(Q5)
6(Q6)
5(Q7)
36
OCW
39
GCSE Mathematics - Numeracy
Higher Unit 2
Qu.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
AOs
N
Max
uAO1
mark
m
2
2
10
3
7
8
4
6
5
4
5
5
7
5
4
7
5
6
Topic
Package with a ribbon
Holiday to Poland (zloty)
Pay Day loan
Off shore wind farm
Celtic knot frequency cumulative frequency
Dog kennel angle of elevation
Width of a flag Pythagoras' Theorem
Necklace VAT error
Density of steel (volume of a sphere)
Gold leaf for brooch
Dragon Nation Bank AER
Child's toy
Dewi's bicycle journey
Concrete base for garden statue
Totals
80
17
AO2
10
3
2
2
5
AO3
5
2
1
5
Common
(Interm)
2(Q8)
8(Q9)
3(Q10)
7(Q11)
8(Q12)
6(Q13)
5(Q14)
OCW

4
7
1
7
5
6
42
.
21
39