Write Down Your Answers in the Spaces Provided

Centre Number Paper Reference Surname Other Names

Candidate Number Candidate Signature

For Examiner’s 1387 use only

For Team Leader’s Edexcel GCSE use only Mathematics A Paper 3 INTERMEDIATE TIER Specimen Paper

Time: 2 hours N0000

BLANK PAGE Materials required for the examination Items included with these question papers Ruler graduated in centimetres and Formulae sheets millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

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.

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.

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 × 4.5 NA3a Grade E

……………………. (3) (b) 3.45 ÷ 2.5 NA3a Grade E

……………………….. (3)

(32  42 ) NA3b Grade E

………………….. (2) (Total 8 marks)

2 Leave blank

2. 18 15 18 15

17 16 17 16

Week A Week B 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

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

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

3 Turn over Leave blank

…………………………………………………………………...……………………………… (Total 1 mark)

4 Leave blank

4. Diagram NOT accurately drawn 50 35

y (a) (i) Work out the value of x. 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 Turn over Leave blank

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

6 Leave blank

Grade D

(Total 3 marks)

7 Turn over Leave blank

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)

8 Leave blank

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)

9 Turn over Leave blank

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)

10 Leave blank

(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

45

…………………… (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 30

30º

……………………… sides (2) (Total 3 marks)

11 Turn over Leave blank

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)

12 Leave blank 1 3 15. 4

A B

1 3 3 Two rods are fastened together. 1 The total length is 3 3 inches. 3 The length of rod B is 1 4 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)

13 Turn over Leave blank

2.56 × 720 = 1843.2

(b) Write down the answer to NA3a Grade C (i) 0.256 × 72 000

………………….…. (ii) 25.6 × 0.72

………………..…… (2) (Total 8 marks)

14 Leave blank

17. Simplify

(a) 7t + 3s – 5t + s NA5b Grade E

……………….. (1)

Expand and simplify

(b) 3(2m + 2) – 2(m – 3) NA5b Grade C

..………………………. (2) Solve the equations

q = ……………. (2) (d) 12a + 2 = 2a – 6 NA5f Grade D

a = ……………. (2)

15 Turn over Leave blank

(e) Solve the equation

2h 1 h  6 5   NA5f 3 2 6 Grade B

h = ……………….. (4) (Total 11 marks)

16 Leave blank

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

 C

A   B

(Total 4 marks)

17 Turn over Leave blank

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)

18 Leave blank

20. (a) Simplify NA5d Grade C (i) t 3  t 5

…………………… m 2 (ii) m5

……………………

h 2  h3 (iii) h

…………………… (3) (b) Expand and simplify NA5b Grade B (i) (2x + 3)(x – 2)

…………………………….. (ii) (3x – 2)²

…………………………… (4) (c) Solve the equation NA5k Grade B x 2  3x 10  0

……………………………………. (3) (Total 10 marks)

21. (a) The mass of an atom of Uranium is 41025 kg.

19 Turn over Leave blank

Calculate the mass of 3 000 000 atoms of Uranium. NA3h Give your answer in standard form. Grade B

………………………………..kg (2) 1 (b) Evaluate 16 2 . NA2b Grade B

…………………………….. (1) (Total 3 marks)

20 Leave blank

22. D D Diagram NOT accurately B drawn

4.5 cm 5 cm

A 6 cm C 4 cm E

(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)

21 Turn over Leave blank

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

22 Leave blank

BLANK PAGE

23 Turn over Leave blank

BLANK PAGE

24 Leave blank

BLANK PAGE

25 Turn over Centre Number Paper Reference Surname Other Names

Candidate Number Candidate Signature

For Examiner’s 1387 use only

For Team Leader’s Edexcel GCSE 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 Formulae sheets. millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper 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.

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)

27 Turn over Leave blank

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

Green

48

(Total 3 marks)

28 Leave blank

3. Mark drives 90 miles to his friend’s house. This travel graph shows Mark’s journey.

60 Distance from home in miles 50

O 1 2 3 4 5 6 7 8 Time in hours (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)

29 Turn over Leave blank

 N Manchester

 Nottingham

Ipswich  Gloucester Luton  

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)

30 Leave blank

5. Diagram NOT D accurately drawn. 117

A 78 y C

x B

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)

31 Turn over Leave blank

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)

32 Leave blank

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)

6p – 5 = 2p + 7 Grade D NA5f

p = …………… (2) (d) Solve

5(q +3) = 40 Grade 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.

33 Turn over Leave blank

Engine Size Maximum speed (cc) (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)

34 Leave blank

150

140 

130  

120  Maximum speed (mph) 110   100

70 1000 1250 1500 1750 2000 2250 2500 2750 3000

Engine size (cc)

(Total 3 marks)

35 Turn over Leave blank

7 cm

Diagram NOT accurately drawn 6 cm

10 cm

12 cm

The diagram shows a shape.

Work out the area of the shape. Grade D SSM4d

…………………… cm²

36 Leave blank

(Total 5 marks)

37 Turn over Leave blank

10. Sam wants to buy a Hooper washing machine. Hooper washing machines are sold in four different shops.

Washing Power Whytes Clean Up

OFF 15% OFF £240 usual price plus VAT of £370 usual price at 17½ % of £370

(a) Find the difference between the maximum and minimum prices Sam could pay for a Grade D washing machine. NA3j

£ …………..…… (7)

38 Leave blank

Homeworld

£293.75

including VAT

The price of the washing machine in the Homeworld shop is £293.75. 1 This includes VAT at 17 2 %.

(b) Work out the cost of the washing machine before VAT is added. Grade B NA3s

£ …………..…… (3) (Total 10 marks)

39 Turn over Leave blank

x + 4 11.

x – 1

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 A  x 2  3x  4 . 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)

40 Leave blank

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

3.87  2.962  4.61cos20 . NA3o 7.83  0.593 Grade C

………………………. (Total 3 marks)

41 Turn over Leave blank

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 receive Grade C NA3f

……………% (2) (Total 5 marks)

15. n is an integer.

(a) Write down the values of n which satisfy the inequality NA5j Grade C –2 < n ≤ 3

………………. (2) (b) Solve the inequality NA5j Grade C 3x + 2 ≤ 4

………………. (2) (Total 4 marks)

42 Leave blank

16. (a) Expand Grade C NA5d x3x 2  4.

……………….….. (2)

(b) Simplify Grade B NA5b 2x2 y3 5x3 y

……………….….. (2)

……………….….. (2) (Total 6 marks)

43 Turn over Leave blank

17. B

58 Diagram NOT accurately drawn

A C

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)

44 Leave blank

18. y

P P 2

-6 -4 -2 O 2 4 6 8 x

-2

-4

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)

45 Turn over Leave blank

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

Cumulative frequency 40

0 20 40 60 80 100 Mark HD5d ………… (1) (b) Use the graph to estimate the median mark. Grade B HD5d ………... (1) The pass mark for the examination was 56.

46 Leave blank

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 9.461012 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 equations Grade B NA5i 3x  4y  5 5x  2y 17

x = …………

y = ………… (Total 3 marks)

47 Turn over Leave blank

22.

Diagram NOT 7.3 cm accurately drawn

51 x A B D 6.4 cm

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)

48 Leave blank

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

49 Turn over Leave blank

BLANK PAGE

50 GCSE MATHEMATICS MARK SCHEME – PAPER 3

No NC Grade Working Answer Mark Notes Ref 1 (a) NA3a E 256 11.52 3 B1 for 1280 and 10240 45  B1 for 11520 1280 B1 for 11.52 10240 11520

(b) NA3a E 1.38 1.38 3 B1 for 34.5  25 25 34.50 B1 for 1 rem 9 and 3 rem 20 B1 for 1.38 25 95 75 200 200

(c) NA3b E 9 16  25 5 2 M1 for 9 + 16 or 25 A1 cao 2 (a) HD1c E 2 B1 not correct B1 need to know total attendance (b) HD1c E 2 B1 pie charts of a different size B1 labels improved 3 NA2c E 1 B1 for explanation dep on Jim most 4 (a)(i) SSM2b E (180 – 50)  2 65 2 B1 cao B1 for 180 degrees in a triangle and base (ii) SSM2b E angle of an isosceles triangle are equal (b)(i) SSM2a E 180 – (35 + 115) 30 2 B1 ft for 180 –(35 + 115) = 30 (ii) SSM2a E B1 for 180 degrees in a straight line, 180 in a triangle 5 (a) SSM4a E 400  5  8 640 km 2 M1 for 400  5  8 A1 (b) SSM4a E 45  4.5 10 gallons 2 M1 for 45  4.5 A1 6 SSM3c E 2 B2 for whole shape correctly enlarged

51 GCSE MATHEMATICS MARK SCHEME – PAPER 3

No NC Grade Working Answer Mark Notes Ref (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 90 4 90 100 30 M1 for 100 30 72 72 100 50 M1 for 100 50 63 A1 for 63 Therefore Zuleya did better than Susie A1 (dep) for writing Zuleya did better than Susie 9 SSM4f D 6x² = 24 8 cm³ 4 M1 for 6x² = 24 x = 2 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 3 B1 for identifying different flavours Male/female B1 for male/female Table structure B1 for two-way table 12 (a) NA3n D 2.45  5 or 49p seen £1.47 2 M1 for 2.45  5 or 49p seen 3  49 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

52 GCSE MATHEMATICS MARK SCHEME – PAPER 3

No NC Grade Working Answer Mark Notes Ref 15 NA3c C 4  9 16  9 1 7 3 M1 for using 12 as denominator 2 1 12 12 12 M1 for decomposing 2 wholes A1 cao 16 (a)(i) NA3a C 72 = 2  2  2  3  3 or 2³3² 4 M1 for dividing through by 2 then 3 A1 cao 96 = 2  2  2  2  2  3 or 253 M1 for dividing through by 2 then 3 A1 cao (ii) NA2a C 2  2  2  3 = 24 2 M1 for selecting 2 and 3 as common prime factors A1 cao (b)(i) NA3a C 18432 2 B1 cao (ii) NA3a C 18.432 B1 cao 17 (a) NA5b E 2t + 4s 1 B1 cao (b) NA5b C 4m + 12 2 B1 for 4m B1 for +12 (c) NA5f D 2q + 7 = –1 q = –4 2 M1 for –7 or 2 2q = –8 A1 cao (d) NA5f D 12a – 2a = –6 – 2 a = –0.8 2 M1 for 12a – 2a = –6 – 2 10a = -8 A1 cao (e) NA5f B 2 2h 1  3 h  6  5 4 4 M1 for 6     –1 7 4h  2  3h  18  5 M1 for collecting terms 7h  16  5 M1 for 7h + 16 = 5 A1 cao 7h  11

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 4 B1 for using 20, 30 etc as stem Repair times 2 2 means 22 B1 for key B1 for using units as leaves 2 2 5 7 8 8 9

53 GCSE MATHEMATICS MARK SCHEME – PAPER 3

No NC Grade Working Answer Mark Notes Ref 3 2 3 4 5 6 9 B1 for complete accuracy 4 1 3 4 7 8 5 2 3 7

20 (a)(i) NA5d C t8 3 B1 cao (ii) NA5d C m3 B1 cao (iii) NA5d C h4 B1 cao (b)(i) NA5b B 2x² – x – 6 2 B1 for x² – 6 B1 for –x (ii) NA5b B (3x – 2)(3x – 2) 2 B1 for 9x² + 4 9x²–12x + 4 B1 for –12x (c) NA5k B (x – 5)(x + 2) x = 5 or 3 M1 for factorisation x = –2 A1 cao for correct factors B1 cao for x 21 (a) NA3h B 3106  41025 2 M1 for multiplying numbers 1.2  1018 A1 cao for 1.21018 (b) NA2b B 4 1 B1 cao 22 (a) SSM2g B 3 : 5 = 4.5 : 7.5 7.5 2 M1 for realising ratio is 3 : 5 A1 for 7.5 cm (b) SSM2g B 5 : 3 3 2 M1 for realising ratio is 3 : 5 A1 for 3 23 HD4e B Total of boys marks = 12n 12n 15m 3 B1 for 12n or 15m Total of girls marks = 15m 27 M1 for 12 n + 15m Total marks for whole class = 12 n + 15m A1 cao 12n 15m Mean  27

54 GCSE MATHEMATICS MARK SCHEME– PAPER 4

No NC Grade Working Answer Mark Notes Ref 1 (a) NA4a E 250  230.6 57650 2 M1 for 250  230.6 A1 cao (b) NA4a E 650  230.6 2.81 or 2.82 2 M1 for 650  230.6 A1 cao 2 HD4a E 360o  540 seen Sector angles 3 M1 or implied by one correct sector angle of 82 o, 68 o, A2 for all 3 sectors correct. Labels not 162 o essential (A1 for 2 sectors correct) 3 (a) NA6d E Explanation 1 B1 realises he is stationary (b) NA6d E Graph 2 B1 horiz line from (2, 90) to (3, 90) completed B1 for line from (3, 90) to (6, 0) or horiz translation of it 4 (a) SSM4a E (0)35 2 B1 angle  2 o (b) SSM4a E 122 B1 angle  2 o 5 (a)(i) SSM3b E 117 2 B1 cao (ii) SSM3b E symmetry B1 for symmetry or congruent triangles (b)(i) SSM2d E 48 2 B1 cao (ii) SSM2d E angle sum of B1 for angle sum of quadrilateral = 360 o quadrilateral = 360 o 6 (a) NA3o E 55.8463 1 B1 cao (b) NA3o E 2 B1 for subtracted 7.28 – 5.27 B1 for multiplied answer by 9.81

7 (a) NA5g E (2  3) + 4 2 2 M1 for (2  3) + 4 A1 cao (b) NA5e E 4 2

55 GCSE MATHEMATICS MARK SCHEME – PAPER 4

No NC Grade Working Answer Mark Notes Ref 10 = 6 + c M1 for 10 = 6 + c A1 cao (c) NA5f D 6p – 2p = 7 + 5 3 2 M1 for 6p – 2p = 7 + 5 A1 cao (d) NA5e D 5q + 15 seen 5 2 M1 for 5q + 15 seen or 5q = 25 5q = 25 A1 cao (e) NA5f D 3r – 3 seen 1 2 M1 for 3r – 3 seen or 7r – 3r = 3 3 1 7r – 3r = 3 3 2 A1 cao 8 (a) HD4a D 4 points 2 B2 Allow ½ sq correct (B1 for 2 or 3 correct) (b) HD5f D 1 B1 e.g. “As one goes up, the other goes up”, “positive correlation” 9 SSM4d D Splits shape up e.g. into rect  &  80 5 M1 splits up shape 10  7 or 70 cm2 M1 for 10  7 or 70 1 1 "5""4" M1 for "5""4" 2 2 10 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

56 GCSE MATHEMATICS MARK SCHEME– PAPER 4

No NC Grade Working Answer Mark Notes Ref 15 M1 for 0.15  370 oe 0.15  370 or 370 or 55.5 100 A1 ft “314.50”

370 – “55.5” 0.175  240 or 42 M1 for 0.175  240 oe A1 cao 282 A1 cao 37 (b) NA3s B 1.175 seen 250 3 M1 for 1.175 seen 293.75  1.175 M1 for 293.75  1.175 A1 cao 11 (a) NA5g D x  4  x  4  x 1 x 1 4x + 6 2 M1 for summation A1 cao (b) NA5g C x  4x 1 2 B1 for x2  x  4x  4 x2  x  4x  4 B1 cao 2 2 (c) SSM2f C 142  92 16.64 3 M1 for 14  9 M1 for 142  92 A1 cao 12 SSM4b D r 2  10 3.5 or 3.6 4 M1 for r 2  10 r  10 M1 for 10   1.784 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) NA3f C 360  20 or 18 234, 126 3 M1 for 360  20 or 18 A1 + 1 (b) NA3f C " 234" 65 2 " 234" or 0.65 M1 for 360 360 A1 ft from “234”

57 GCSE MATHEMATICS MARK SCHEME – PAPER 4

No NC Grade Working Answer Mark Notes Ref 15 (a) Na5j C –1, 0, 1, 2, 3 2 B2 (–1 eeoo) (b) NA5j C 3x ≤ 2 2 2 M1 for 3x ≤ 2 oe x  3 A1 cao 16 (a) NA5d C 3x³ + 4x 2 B1 for 3x³ (indep) B1 for 4x (indep) (b) NA5b B 10x5 y 4 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 2 B1 for 116 Angle at B1 for angle at centre = twice angle at centre circumference 18 (a) SSM3b C Q correct 2 B2 (B1 for horizontal translation of Q) (b) SSM3b C R correct 2 B2 (B1 for 180 o rotation of their Q) 19 (a) HD5d B 52 1 B1 cao (b) HD5d B 42 1 B1 cao to tolerance of  1 (c) HD5d B 38 stated or indicated 2 M1 for line drawn on graph on diagram 14 A1 ft line 19 (a) NA3h B 2. 19 1019 1 B1 cao 19 19 12 (b) NA3m B " 2. 19 10 "  2. 3106 2 M1 for " 2. 19 10 "  9. 46 10 9. 46 1012 A1 for 2. 3106 or better 20 NA5i B 10x  4y  34 x  3, y  1 3 M1 for attempt to double second equation 13x  39 M1 for attempt to add A1 cao 21 SSM2g B 7.3 sin 51 o 41.6 5 M1 for 7.3 sin 51 o 5.673 … A1 for 5.673 tan x o = M1 for use of tan

58 GCSE MATHEMATICS MARK SCHEME– PAPER 4

No NC Grade Working Answer Mark Notes Ref " 5. 673. . . " "5.673" M1 for tan x o = 6. 4 6.4 A1 for 41.6 or better 22 HD4b C 16 4000 3 16  25000 M1 for  100 100 16 M1 for " "25000 100 A1 cao

59 GCSE MATHEMATICS MARK SCHEME – PAPER 6