Write Down Your Answers in the Spaces Provided

/ Centre Number / Paper Reference / Surname / Other Names
Candidate Number / Candidate Signature
1387 / For Examiner’s use only
Edexcel GCSE / For Team Leader’s use only
Mathematics A
Paper 3
INTERMEDIATE TIER
Specimen Paper
Time: 2 hours / N0000
Materials required for the examination / Items included with these question papers
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser.
Tracing paper may be used. / Formulae sheets
Instructions to Candidates
In the boxes above, write your centre number, candidate number, the paper reference, your surname and other names and your signature. The paper reference is shown in the top left hand corner.
Answer all questions in the spaces provided in this book.
Supplementary answer sheets may be used.
Information for Candidates
The total mark for this paper is 100.
The marks for the various parts of questions are shown in round brackets: e.g. (2).
Tracing paper may be used.
Calculators must not be used.
This question paper has 23 questions. There are 3 blank pages.
Advice to Candidates
Work steadily through the paper.
Do not spend too long on one question.
Show all stages in any calculations.
If you cannot answer a question, leave it and attempt the next one.
Return at the end to those you have left out.
N0000
© 2000 Edexcel
This publication may only be reproduced in accordance with Edexcel copyright policy.
Edexcel Foundation is a registered charity. /

Turn over

Answer ALL TWENTY ONE questions.

Write down your answers in the spaces provided.

Do NOT use a calculator. You must write down all stages in your working.

1.Work out

(a)2.56 × 4.5NA3a

Grade E

…………………….

(3)

(b)3.45 ÷ 2.5NA3a

Grade E

………………………..

(3)

(c)Work out

NA3b

Grade E

…………………..

(2)

(Total 8 marks)

The ages of everyone attending a youth club disco are recorded.

The results are shown in the pie charts for two separate weeks.

Mark suggests that there were more 15 year olds attending in week A than week B.

(a) Explain whether you think Mark was correct.HD1c

Give a reason for your answer.Grade E

………………………………………………………………………………………………

(2)

(b) Suggest how these diagrams could be improved.HD1c Grade E

………………………………………………………………………………………………

(2)

(Total 4 marks)

3.Jim said “I’ve got three quarters of a tin of paint”.

Mary said “I’ve got four sixths of a tin of paint and my tin of paint is the same size as yours”.

Who has got the most paint, Mary or Jim?

Explain your answer.

NA2c Grade E

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

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

(Total 1 mark)

(a)(i) Work out the value of x.SSM2b Grade E

x = ………….

(ii)Explain how you worked out your answer.

……………………………………………...………………………………………….

…………………………………………………………………………………………

(2)

(b)(i) Work out the value of y.SSM2a Grade E

y = ………….

(ii)Explain how you worked out your answer.

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

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

(2)

(Total 4 marks)

(Total 5 marks)

5.Marlene and Roy travelled from London to Edinburgh by car.

The distance from London to Edinburgh is 400 miles.

(a) Estimate the number of kilometres in 400 miles.

SSM4a

Grade E

…………. km

(2)

The car used 45 litres of petrol on the journey.

(b)Estimate the number of gallons in 45 litres.SSM4a Grade E

…………. gallons

(2)

(Total 4 marks)

6.The AOL postal company has a logo.SSM3c

The logo is to be made into a watermark which is three times as large.Grade E

Draw your answer on the grid below.

(Total 2 marks)

7.Draw the graph of y = 2x – 15 on the grid below.NA6b

Grade D

(Total 3 marks)

8.A maths test has two parts, A and B.

Part A is out of 30.

Part B is out of 50.

Zuleya scored 64 marks for the two parts.

Susie scored 90% in part A and 72% in part B.

Who scored the higher marks?NA3e

Explain your answer.Grade D

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

(Total 4 marks)

9.A cube has surface area 24 cm².

Work out the volume of the volume.SSM4d

Grade D

…………………………..

(Total 4 marks)

10.Farmer Giles makes his sheep pens in the shape of hexagons.

He uses straight hurdles to make the sides of the pens.

26 hurdles will be needed to make a row of 5 pens.

How many hurdles will be needed for a row of n pens?NA6a

Grade C

………………………….

(Total 2 marks)

11.Bill is carrying out a survey into the flavours of crisps that people like best.

He also wants to divide the results into those from males and those from females.

Design a suitable data collection sheet, in the form of a two-way table, that they could use to

collect this information.HD3c

Grade D

(Total 3 marks)

12.The cost of 15 pens is £2.45.

(a)Work out be the cost of 9 pens.

NA4a

Grade D

£ …………….

(2)

The probability that a pen will be faulty is 0.2.

(b)Work out the probability that a pen picked at random will not be faulty.HD4d

Grade E

…………………..

(1)

(c)A pen is of length 10 cm, measured to the nearest centimetre.

A pen case is of length 10.1 cm, measured to the nearest millimetre.

Explain why it might not be possible for the pencil to fit in the pencil case.SSM4a

Grade B

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

(3)

(Total 6 marks)

13.The exterior angle of a regular polygon is 45.

(a) Write down the interior angle of this regular polygon.SSM2d

Grade D

……………………

(1)

The exterior angle of a different regular polygon is 30º.

(b)Work out the number of sides in this regular polygon.SSM2d

Grade C

30º

……………………… sides

(2)

(Total 3 marks)

14.Here are the equations of 5 straight lines.

They are labelled from A to E.

A

/ y = 2x + 1
B / y = 1 – 2x
C / 2y = x – 1
D / 2x – y = 1
E / x + 2y = 1

Put ticks in the table to show the two lines that are parallel.NA6c

Grade C

(Total 2 marks)

15.

Two rods are fastened together.

The total length is inches.

The length of rod B is inches.

Find the length of rod A.NA3c

Grade C

……………..…. inches

(Total 3 marks)

16.(a)(i)Express 72 and 96 as a product of their prime factors. NA3a

Grade C

72 = ……………………….……..

96 = ……………………….……..

(4)

(ii)Use your answer to (i) to work out the Highest Common Factor of 72 and 96.NA2a

Grade C

…………………

(2)

2.56 × 720 = 1843.2

(b)Write down the answer toNA3a

Grade C

(i) 0.256 × 72 000

………………….….

(ii) 25.6 × 0.72

………………..……

(2)

(Total 8 marks)

17.Simplify

(a)7t + 3s – 5t + sNA5b

Grade E

………………..

(1)

Expand and simplify

(b)3(2m + 2) – 2(m – 3)NA5b

Grade C

..……………………….

(2)

Solve the equations

Grade D

q = …………….

(2)

(d)12a + 2 = 2a – 6 NA5f

Grade D

a = …………….

(2)

(e)Solve the equation

NA5f

Grade B

h = ………………..

(4)

(Total 11 marks)

18.Shade in the region that satisfies all three of these conditions.

(i)Closer to A than to B,

(ii)closer to the line AC than to the line AB,

(iii)more than 2 cm from A.SSM4e

Grade C

(Total 4 marks)

19.The manager at “Fixit Exhausts” records the time, to the nearest minute, to repair the exhaust on 20 cars.

Here are his results.

32, / 29, / 34, / 28, / 22, / 41, / 57, / 43, / 28, / 33,
35, / 25, / 52, / 47, / 39, / 27, / 36, / 48, / 53, / 44.

Draw a stem and leaf diagram to show this information.HD4a

Grade D

(Total 4 marks)

20.(a)SimplifyNA5d

Grade C

(i)

……………………

(ii)

……………………

(iii)

……………………

(3)

(b)Expand and simplifyNA5b

Grade B

(i)(2x + 3)(x – 2)

……………………………..

(ii)(3x – 2)²

……………………………

(4)

(c)Solve the equationNA5k

Grade B

…………………………………….

(3)

(Total 10 marks)

21.(a)The mass of an atom of Uranium is kg.

Calculate the mass of 3 000 000 atoms of Uranium.NA3h

Give your answer in standard form.Grade B

………………………………..kg

(2)

(b)Evaluate .NA2b

Grade B

……………………………..

(1)

(Total 3 marks)

22. D

(a)Work out the length of AD.SSM2g

Grade B

…………….. cm

(2)

(b)Work out the length of BC.SSM2g

Grade B

………… cm

(2)

(Total 4 marks)

23.There are 12 boys and 15 girls in a class.

In a test the mean mark for the boys was n.

In the same test the mean mark for the girls was m.

Find an expression for the mean mark of the whole class of 27 students.HD4e

Grade B

………………………………

(Total 3 marks)

TOTAL FOR PAPER: 100 MARKS

BLANK PAGE

Turn over

Centre Number / Paper Reference / Surname / Other Names
Candidate Number / Candidate Signature
1387 / For Examiner’s use only
Edexcel GCSE / For Team Leader’s use only
Mathematics A
Paper 4
INTERMEDIATE TIER
Specimen Paper
Time: 2 hours / N0000
Materials required for the examination / Items included with these question papers
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator.
Tracing paper may be used. / Formulae sheets.
Instructions to Candidates
In the boxes above, write your centre number, candidate number, the paper reference, your surname and other names and your signature. The paper reference is shown in the top left hand corner.
Answer all questions in the spaces provided in this book.
Supplementary answer sheets may be used
Information for Candidates
The total mark for this paper is 100.
The marks for the various parts of questions are shown in round brackets: e.g. (2).
Tracing paper may be used.
Calculators may be used.
This question paper has 22 questions. There is 1 blank page.
Advice to Candidates
Work steadily through the paper.
Do not spend too long on one question.
Show all stages in any calculations.
If you cannot answer a question, leave it and attempt the next one.
Return at the end to those you have left out.
N0000
© 2000 Edexcel
This publication may only be reproduced in accordance with Edexcel copyright policy.
Edexcel Foundation is a registered charity. /

Turn over

Leave

blank

Answer ALL TWENTY ONE questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1.Janet goes on holiday to Spain.

The exchange rate is £1 = 230.6 pesetas.

She changes £250 into pesetas.

(a)How many pesetas should Janet get?Grade E

NA4a

……………… pesetas

(2)

Janet comes back home.

She changes 650 pesetas back into pounds.

The exchange rate is the same.

(b)How much money should she get?Grade E

NA4a

£………………

(2)

(Total 4 marks)

2.In a survey, the eye colours of the 540 students in a school were recorded.

The table shows the information

Eye colour / Number of students
Green
Blue / 123
Grey
Brown / 243
540

This information can be shown in a pie chart.

The pie chart below is incomplete.

Complete the pie chart.Grade E

HD4a

(Total 3 marks)

3.Mark drives 90 miles to his friend’s house.

This travel graph shows Mark’s journey.

(a)Explain what might have happened to Mark when he was 50 miles from home.Grade E

NA6d

………………………………………………………………………………………………

(1)

Mark stays at his friend’s house for an hour.

He then travels home at a steady speed in 3 hours.

(b)Complete the graph to show this information.Grade E

NA6d

(2)

(Total 3 marks)

The diagram is part of a map showing the positions of several towns.

Measure and write down the bearing of

(a)Nottingham from Gloucester,Grade E

SSM4a



…..…….

(1)

(b)Ipswich from Nottingham,Grade E

SSM4a



…..…….

(1)

(Total 2 marks)

The diagram shows a kite

(a)(i)Write down the value of x.Grade E

SSM3b

x = …………

(ii)Give a reason for your answer.

……………….………………………………………………………………………..

(2)

(b)(i)Work out the value of y.Grade E

SSM2d

y = …………

(ii) Give a reason for your answer.

……………………………………...…………………………………………………..(2)

(Total 4 marks)

6.Whilst doing a science experiment, Sam is told to use the equation

v = 9.81t – 5.27

to work out the values of v.

She uses her calculator to work out the value of v when t = 6.23.

(a) Work out the correct value of v when t = 6.23.NA3o

Grade E

…………………….

(1)

When t = 7.28, Sam worked out her answer for v to be 66.1468.

Sam’s answer is correct.

Sam’s friend Jo worked out v to be 19.7181 when t = 7.28.

(b) Explain fully what is the most likely error made by Jo.NA3o

Grade E

………………………………………………………………………………………………

(2)

(Total 3 marks)

7.y = 2x + c

(a)Work out the value of y when x = –3 and c = 4.Grade E

NA5g

y = ……………

(2)

(b)Work out the value of c when y = 10 and x = 3. Grade E

NA5e

c = ……………

(2)

(c)Solve

6p – 5 = 2p + 7Grade D

NA5f

p = ……………

(2)

(d)Solve

5(q +3) = 40Grade D

NA5e

q = ……………

(2)

(e)Solve

7r + 3 = 3(r – 1)Grade D

NA5f

r = ……………

(2)

(Total 10 marks)

8.The table shows the engine size and the maximum speed of each of ten cars.

Engine Size
(cc) / Maximum speed (mph)
1600 / 111
1800 / 121
2000 / 129
2500 / 130
2900 / 140
1400 / 105
1300 / 95
1100 / 89
1000 / 80
2700 / 136

The information for the first six cars has been plotted on the scatter graph opposite.

(a)Complete the scatter graph opposite to show the information in the table.Grade D

HD4a

(2)

(b)Describe the relationship between a car’s engine size and its maximum speed.Grade D

HD5f

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

(1)

(Total 3 marks)

The diagram shows a shape.

Work out the area of the shape.Grade D

SSM4d

…………………… cm²

(Total 5 marks)

10.Sam wants to buy a Hooper washing machine.

Hooper washing machines are sold in four different shops.

(a)Find the difference between the maximum and minimum prices Sam could pay for aGrade D

washing machine.NA3j

£ …………..……

(7)

The price of the washing machine in the Homeworld shop is £293.75.

This includes VAT at %.

(b)Work out the cost of the washing machine before VAT is added.Grade B

NA3s

£ …………..……

(3)

(Total 10 marks)

11.

The diagram shows a rectangle with length x + 4 and width x 1.

All measurements are given in centimetres.

The perimeter of the rectangle is P centimetres.

The area of the rectangle is A square centimetres.

(a)Show that .Grade C

NA5g

(2)

The perimeter is 46 cm.

(b) Calculate the length of the diagonal of the rectangle.Grade C

SSM2f

………………………. cm

(5)

(Total 7 marks)

12.Circular fish ponds can be built to size.

The order form asks for the required diameter.

Ramana wants a circular fish pond with an area of 10 m².

What diameter should she put on the order form?SSM4h

Grade D

………………………. m

(Total 4 marks)

13.Calculate

NA3o

Grade C

……………………….

(Total 3 marks)

14.Wayne shares £360 between his children, Sharon and Liam, in the ratio of their ages.

Sharon is 13 years old and Liam is 7 years old.

(a)Work out how much each child receives.Grade C

NA3f

Sharon £ …………

Liam £ …………

(3)

(b)What percentage of the £360 does Sharon receiveGrade C

NA3f

……………%

(2)

(Total 5 marks)

15.n is an integer.

(a)Write down the values of n which satisfy the inequalityNA5j

Grade C

–2 < n ≤ 3

……………….

(2)

(b)Solve the inequalityNA5j

Grade C

3x + 2 ≤ 4

……………….

(2)

(Total 4 marks)

16.(a)ExpandGrade C

NA5d

……………….…..

(2)

(b)SimplifyGrade B

NA5b

……………….…..

(2)

(c)Factorise completelyGrade B

NA5b

ax + ay – by – bx

……………….…..

(2)

(Total 6 marks)

17.

A, B and C are points on the circumference of a circle, with centre O.

(i) Find angle AOC.Grade B

SSM2h

……………………….

(ii)Give a reason for your answer.

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

(Total 2 marks)

18.

The triangle P has been drawn on the grid.

(a)Reflect the triangle P in the line x = 2.Grade C

Label the image Q.SSM3b

(2)

(b)Rotate triangle Q through 180 about (2, 1).Grade C

Label this image R.SSM3b

(2)

(Total 4 marks)

19.The cumulative frequency graph gives information about the examination marks of a group of students.

(a)How many students were in the group?Grade B

HD5d

…………

(1)

(b)Use the graph to estimate the median mark.Grade B

HD5d

………...

(1)

The pass mark for the examination was 56.

(c)Use the graph to estimate the number of students who passed the examination.Grade B

HD5d

………...

(2)

(Total 4 marks)

20.The Andromeda Galaxy is 21 900 000 000 000 000 000 km from the Earth.

(a)Write 21 900 000 000 000 000 000 in standard form.Grade B

NA3h

………………………

(1)

Light travels km in one year.

(b)Calculate the number of years that light takes to travel from the Andromeda Galaxy to Grade B

Earth.NA3m

Give your answer in standard form correct to 2 significant figures.

………………………

(2)

(Total 3 marks)

21.Solve the simultaneous equationsGrade B

NA5i

x = …………

y = …………

(Total 3 marks)

22.

The diagram shows a triangle ABC.

The line CD is perpendicular to the line AB.

AC = 7.3 cm, BD = 6.4 cm and angle BAC = 51.

Calculate the size of the angle marked x.Grade B

Give your answer correct to 1 decimal place.SSM2g



………………

(Total 5 marks)

23.Tony carries out a survey about the words in a book.

He chooses a page at random.

He then counts the number of letters in each of the first hundred words on the page.

The table shows Tony’s results.

Number of letters in a word / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Frequency / 6 / 9 / 31 / 24 / 16 / 9 / 4 / 1

The book has 25000 words.

Estimate the number of 5 letter words in the book.HD4b

Grade C

……………………….

(Total 3 marks)

TOTAL FOR PAPER: 100 MARKS

Turn over

GCSE MATHEMATICS MARK SCHEME – PAPER 3

No /

NC Ref

Grade

Working

/ Answer / Mark / Notes
1 / (a)
(b) / NA3a
NA3a / E
E / 256
45
1280
10240
11520

95
75
200
200 / 11.52
1.38 / 3
3 / B1 for 1280 and 10240
B1 for 11520
B1 for 11.52
B1 for 34.5  25
B1 for 1 rem 9 and 3 rem 20
B1 for 1.38
(c) / NA3b / E / / 5 / 2 / M1 for 9 + 16 or 25
A1 cao
2 / (a)
(b) / HD1c
HD1c / E
E / 2
2 / B1 not correct
B1 need to know total attendance
B1 pie charts of a different size
B1 labels improved
3 / NA2c / E / 1 / B1 for explanation dep on Jim most
4 / (a)(i)
(ii)
(b)(i)
(ii) / SSM2b
SSM2b
SSM2a
SSM2a / E
E
E
E / (180 – 50)  2
180 – (35 + 115) / 65
30 / 2
2 / B1 cao
B1 for 180 degrees in a triangle and base angle of an isosceles triangle are equal
B1 ft for 180 –(35 + 115) = 30
B1 for 180 degrees in a straight line, 180 in a triangle
5 / (a)
(b) / SSM4a
SSM4a / E
E / 400  5  8
45  4.5 / 640 km
10 gallons / 2
2 / M1 for 400  5  8
A1
M1 for 45  4.5
A1
6 / SSM3c / E / 2 / B2 for whole shape correctly enlarged
(B1 for 1 length correct)
7 / NA6b / D / 3 / B1 for axes correct
B1 for at least 3 points plotted or calculated
B1 cao for straight line
8 / NA3e / D /

63
Therefore Zuleya did better than Susie / 4 / M1 for
M1 for
A1 for 63
A1 (dep) for writing Zuleya did better than Susie
9 / SSM4f / D / 6x² = 24
x = 2 / 8 cm³ / 4 / M1 for 6x² = 24
A1 for x = 2
A1 for volume = 8
B1 (indep) for cm³
10 / NA6a / C / 5n +1 / 2 / B1 for 5n
B1 for kn + 1, k 0
11 / HD3c / D / Flavour of packet of crisp
Male/female
Table structure / 3 / B1 for identifying different flavours
B1 for male/female
B1 for two-way table
12 / (a) / NA3n / D / 2.45  5 or 49p seen
3  49 / £1.47 / 2 / M1 for 2.45  5 or 49p seen
A1 cao for £1.47 or 147p
(b) / HD4d / E / 1 – 0.2 / 0.8 / 1 / B1 cao
(c) / SSM4a / B / 3 / M1 for realising 10 cm to 1 cm = 10.5 cm
M1 for realising 10.1 cm to 1 mm = 10.15 cm
A1 therefore pen might be too big
13 / (a) / SSM2d / D / 180 – 45 / 135 / 1 / B1 cao
(b) / SSM2d / C / 360  30 = 12 / 12 sides / 2 / M1 for 360  30
A1 cao
14 / NA6c / C / A and D selected / A & D / 2 / M1 for rearranging into y = mx + c
A1 cao
15 / NA3c / C / / / 3 / M1 for using 12 as denominator
M1 for decomposing 2 wholes
A1 cao
16 / (a)(i)
(ii) / NA3a
NA2a / C
C / 72 = 2  2  2  3  3 or 2³3²
96 = 2  2  2  2  2  3 or
2  2  2  3 = / 24 / 4
2 / M1 for dividing through by 2 then 3
A1 cao
M1 for dividing through by 2 then 3
A1 cao
M1 for selecting 2 and 3 as common prime factors
A1 cao
(b)(i)
(ii) / NA3a
NA3a / C
C / 18432
18.432 / 2 / B1 cao
B1 cao
17 / (a)
(b) / NA5b
NA5b / E
C / 2t + 4s
4m + 12 / 1
2 / B1 cao
B1 for 4m
B1 for +12
(c)
(d) / NA5f
NA5f / D
D / 2q + 7 = –1
2q = –8
12a – 2a = –6 – 2
10a = -8 / q = –4
a = –0.8 / 2
2 / M1 for –7 or 2
A1 cao
M1 for 12a – 2a = –6 – 2
A1 cao
(e) / NA5f / B / / – / 4 / M1 for 6
M1 for collecting terms
M1 for 7h + 16 = 5
A1 cao
18 / SSM4e / C / 4 / B1 for perpendicular bisector shaded correctly
B1 for angle bisector shaded correctly
B1 for circle radius 2 cm shaded
B1 cao all correct
19 / HD4a / D / Repair times 2 2 means 22
2257889
3234569
413478
5237 / 4 / B1 for using 20, 30 etc as stem
B1 for key
B1 for using units as leaves
B1 for complete accuracy
20 / (a)(i) / NA5d / C / / 3 / B1 cao
(ii) / NA5d / C / / B1 cao
(iii) / NA5d / C / / B1 cao
(b)(i) / NA5b / B / 2x² – x – 6 / 2 / B1 for x² – 6
B1 for –x
(ii) / NA5b / B / (3x – 2)(3x – 2) / 9x²–12x + 4 / 2 / B1 for 9x² + 4
B1 for –12x
(c) / NA5k / B / (x – 5)(x + 2) / x = 5 or
x = –2 / 3 / M1 for factorisation
A1 cao for correct factors
B1 cao for x
21 / (a) / NA3h / B / / 1.2  1018 / 2 / M1 for multiplying numbers
A1 cao for
(b) / NA2b / B / 4 / 1 / B1 cao
22 / (a)
(b) / SSM2g
SSM2g / B
B / 3 : 5 = 4.5 : 7.5
5 : 3 / 7.5
3 / 2
2 / M1 for realising ratio is 3 : 5
A1 for 7.5 cm
M1 for realising ratio is 3 : 5
A1 for 3
23 / HD4e / B / Total of boys marks = 12n
Total of girls marks = 15m
Total marks for whole class = 12 n + 15m
/ / 3 / B1 for 12n or 15m
M1 for 12 n + 15m
A1 cao

GCSE MATHEMATICS MARK SCHEME– PAPER 4

No /

NC Ref

Grade

Working

/ Answer / Mark / Notes
1 / (a)
(b) / NA4a
NA4a / E
E / 250  230.6
650  230.6 / 57650
2.81 or 2.82 / 2
2 / M1 for 250  230.6
A1 cao
M1 for 650  230.6
A1 cao
2 / HD4a / E / 360o 540 seen / Sector angles of 82 o, 68 o, 162 o / 3 / M1 or implied by one correct sector angle
A2 for all 3 sectors correct. Labels not essential
(A1 for 2 sectors correct)
3 / (a)
(b) / NA6d
NA6d / E
E / Explanation
Graph completed / 1
2 / B1 realises he is stationary
B1 horiz line from (2, 90) to (3, 90)
B1 for line from (3, 90) to (6, 0) or horiz translation of it
4 / (a)
(b) / SSM4a
SSM4a / E
E / (0)35
122 / 2 / B1 angle  2 o
B1 angle  2 o
5 / (a)(i)
(ii)
(b)(i)
(ii) / SSM3b
SSM3b
SSM2d
SSM2d / E
E
E
E / 117
symmetry
48
angle sum of quadrilateral
= 360 o / 2
2 / B1 cao
B1 for symmetry or congruent triangles
B1 cao
B1 for angle sum of quadrilateral = 360 o
6 / (a)
(b) / NA3o
NA3o / E
E / 55.8463 / 1
2 / B1 cao
B1 for subtracted 7.28 – 5.27
B1 for multiplied answer by 9.81
7 / (a)
(b) / NA5g
NA5e / E
E / (2 3) + 4
10 = 6 + c / 2
4 / 2
2 / M1 for (2 3) + 4
A1 cao
M1 for 10 = 6 + c
A1 cao
(c)
(d)
(e) / NA5f
NA5e
NA5f / D
D
D / 6p – 2p = 7 + 5
5q + 15 seen
5q = 25
3r – 3 seen
7r – 3r = 3 3 / 3
5
/ 2
2
2 / M1 for 6p – 2p = 7 + 5
A1 cao
M1 for 5q + 15 seen or 5q = 25
A1 cao
M1 for 3r – 3 seen or 7r – 3r = 3 3
A1 cao
8 / (a)
(b) / HD4a
HD5f / D
D / 4 points correct / 2
1 / B2 Allow ½ sq
(B1 for 2 or 3 correct)
B1 e.g. “As one goes up, the other goes up”, “positive correlation”
9 / SSM4d / D / Splits shape up e.g. into rect 
10  7 or 70

10 / 80
cm2 / 5 / M1 splits up shape
M1 for 10  7 or 70
M1 for
A1 for 10
A1cao
10 / (a) / NA3j / D / 370  4 or 92.5 / £37 / 7 / M1 for 370  4 or 92.5
A1cao for 277.5
0.15  370 or or 55.5
370 – “55.5” / M1 for 0.15  370 oe
A1 ft “314.50”
0.175  240 or 42 / M1 for 0.175  240 oe
A1 cao 282
A1 cao 37
(b) / NA3s / B / 1.175 seen
293.75  1.175 / 250 / 3 / M1 for 1.175 seen
M1 for 293.75  1.175
A1 cao
11 / (a)
(b) / NA5g
NA5g / D
C /
/ 4x + 6 / 2
2 / M1 for summation
A1 cao
B1 for
B1 cao
(c) / SSM2f / C / / 16.64 / 3 / M1 for
M1 for
A1 cao
12 / SSM4b / D /
/ 3.5 or 3.6 / 4 / M1 for
M1 for
A1 for 1.784
A1 cao for 3.5 m or 3.6 m oe
13 / NA3o / C / 10.2 / 3 / M1 for 4.33 or 29.57 or better seen
M1 for 2.90 or better seen
A1 cao
14 / (a)
(b) / NA3f
NA3f / C
C / 360  20 or 18
or 0.65 / 234, 126
65 / 3
2 / M1 for 360  20 or 18
A1 + 1
M1 for
A1 ft from “234”
15 / (a)
(b) / Na5j
NA5j / C
C / 3x ≤ 2 / –1, 0, 1, 2, 3
/ 2
2 / B2 (–1 eeoo)
M1 for 3x ≤ 2 oe
A1 cao
16 / (a) / NA5d / C / 3x³ + 4x / 2 / B1 for 3x³ (indep)
B1 for 4x (indep)
(b) / NA5b / B / / 2 / B2
(B1 if one error)
(c) / NA5b / B / (a – b)(x + y) / 2 / B2
(B1 for a(x + y) – b(y + x) or
y(a – b) + x(a – b) oe)
17 / SSM2h / B / 116
Angle at centre / 2 / B1 for 116
B1 for angle at centre = twice angle at circumference
18 / (a)
(b) / SSM3b
SSM3b / C
C / Q correct
R correct / 2
2 / B2
(B1 for horizontal translation of Q)
B2
(B1 for 180 o rotation of their Q)
19 / (a)
(b)
(c) / HD5d
HD5d
HD5d / B
B
B / 38 stated or indicated
on diagram / 52
42
14 / 1
1
2 / B1 cao
B1 cao to tolerance of  1
M1 for line drawn on graph
A1 ft line
19 / (a)
(b) / NA3h
NA3m / B
B /
/
/ 1
2 / B1 cao
M1 for
A1 for or better
20 / NA5i / B /
/ / 3 / M1 for attempt to double second equation
M1 for attempt to add
A1 cao
21 / SSM2g / B / 7.3 sin 51 o
5.673 …
tan x o =
/ 41.6 / 5 / M1 for 7.3 sin 51 o
A1 for 5.673
M1 for use of tan
M1 for tan x o =
A1 for 41.6 or better
22 / HD4b / C / / 4000 / 3 / M1 for
M1 for
A1 cao