For Edexcel

GCSE Mathematics

Higher Tier

Paper 2A (Calculator)Marking Guide

Method marks (M) are awarded for knowing and using a correct method.

Accuracy marks (A) are awarded for correct answers, having used a correct method.

(B) marks are independent of method marks.

(C) marks are for communication.

Written by Shaun ArmstrongOnly to be copied for use in the purchaser's school or college

2012 EHA Paper 2 marks Page 1 Churchill Maths Limited

Higher Tier Paper 2A Marking Guide

1 one 5p coin weighs 26 8 = 3.25 g M1three 5p coins weigh 3 3.25 = 9.75 g A1 Total 2

2 (a) 2 2.2 = 4.4 pounds B1

(b) 3 inches 3 2.5 cm = 7.5 cm M182 mm = 8.2 cm82 millimetres is the largest A1 Total 3

3 (a) = (25 + 20) 30 = 45 30 = 15 M1 A1

(b) C = 30t B1

(c) approx. t = 2.5 B1

(d) if they think the job will take less than 2.5 hrs, Badri willbe cheaper, if more than 2.5 hrs, Martin will be cheaper B1 Total 5

*4 1st to 15th April = 15 days16th April to 11th May = 15 + 11 = 26 days M112th May to 18th June = 20 + 18 = 38 days15 0.50 + 26 0.80 + 38 1.20 M1

= 7.50 + 20.80 + 45.60 = 73.90 A1Fran has not reached her target C1 Total 4

[ use of correct number of days in months, valid method leading to consistent conclusion, allow arithmetic slip ]

5 radius = 40 cmvolume = 402 120 = 603186 cm3 M1 A11 cm3 = 1 ml so 1000 cm3 = 1 litre B1needs 603.2 litres to fill barreltime = 603.2 seconds = 10 minutes 3.2 seconds M1so 10 minutes to nearest minute A1 Total 5

2012 EHA Paper 2 marks Page 2 Churchill Maths Limited

Mean Maximum Temperature (C)0 2 64 8 10

Cost of Gas

Used()

20

30

25

35

40

6 e.g. M1 A1x 3 2 1 0 1 2 3y 12 7 4 3 4 7 12

M1 A1

Total 4

7 (a) negative B1

(b) e.g. B1

2012 EHA Paper 2 marks Page 3 Churchill Maths Limited

6

7

9

8

10

1 2 43 x34 2 1

1

2

4

3

5

O

11

y12

(c) e.g. 0.4 C is outside range of datarelationship may not be valid B1

* (d) 3 3 + 4 6 + 5 10 + 6 7 + 7 4 + 8 1 M1= 9 + 24 + 50 + 42 + 28 + 8 = 161mean max temp = 161 31 = 5.2 C (1dp) M1using line of best fit 30 (from graph) A1 C1 Total 7

[clear evidence of using data to find mean and line of best fit to estimate cost of gas]

8 (a) other angles in triangle = 12 (180 32) = 74 M1x = 360 (2 32 + 2 74) = 360 212 = 148 M1 A1

(b) interior angle = 180 2yexterior angle = 180 (180 2y) = 2y M1

no. of sides = 3602 y [ =

180y ] M1 A1 Total 6

9 one must = 78 (to be median) B1total = 7 81 = 567 M1other must = 567 (69 + 106 + 51 + 89 + 72 + 78)

= 567 465 = 102 A1 Total 3

10 (a) 23 B1

(b) 150 = 2

100 = 0.02 B1

(c) = 0.0125 0.008 = 0.0045 [ or 4.5 10 3 ] M1 A1 Total 4

11 (a) 0.7 B1

(b) = 0.3 0.4 = 0.12 M1 A1 Total 3

12 2 + 3 = 525000 5 = 5000 M1sales: first year = 10000, second year = 15000 A1

600 as % of 10000 = 60010000 100% = 6% M1

1200 as % of 15000 = 120015000

100% = 8%

ratio of profit as % of sales = 6 : 8 = 3 : 4 M1 A1 Total 5

2012 EHA Paper 2 marks Page 4 Churchill Maths Limited

13 (a) (i) 4p = 44 M1p = 11 A1

(ii) 3 6y = 15 4y M112 = 2y M1y = 6 A1

* (b) let c = cost of cup of coffee and t = cost of cup of tea4c + 2t = 11 (1) B12c + 4t = 10 (2)e.g. (2) 2 c + 2t = 5 (3) M1

(1) (3) 3c = 6 M1c = 2

sub (3) 2 + 2t = 52t = 3t = 1.5 A1

coffee 2, tea 1.50 C1 Total 10

[ appropriate mathematical method communicated and carried through to answer ]

14 (a) (i) (0, 6, 4) B1

(ii) B (5, 0, 8)D ( 552 ,

602 ,

082 ) = (5, 3, 4) M1 A1

(b) area of XS = (6 4) + ( 12 3 4) = 24 + 6 = 30 M1volume = 30 5 = 150 cm3 M1 A1 Total 6

15 (a) = 4 x 1 2 x 3 x 3x 1 M1 A1

= 4 x 4 2 x 6 x 3 x 1 =

6 x 10 x 3 x 1 A1

(b) = 22 x 3

2 x 32 x 3 = 2

2 x 3 M2 A1 Total 6

16 distance to airport < 37.5 miles B1cost per mile < 1.65total cost < 37.5 1.65 M1max cost = 61.87 A1 Total 3

17 * (a) e.g. the sample will represent each group fairly C1the manager can see how opinions vary betweenthe groups C1

[ any sensible advantages, expressed clearly ]

(b) = 283840 100 M1= 33.6... so 34 A1 Total 4

2012 EHA Paper 2 marks Page 5 Churchill Maths Limited

18 (a) = (1.05)3 2000 M2= 2315.25 A1

(b) 1 x100 3

400 [ left ] B1 Total 4

19 (a) 8q(p 2q2) B2

(b) x = 3 9 2010

M1

+ve soln = 3 2910

= 0.839 (3sf) M1 A1 Total 5

20 P(AA) = P(CC) = 210 19 M1

P(DD) = 310 29

P(2 same) = 2 210 19 +

310

29 M1 A1

= 490 + 6

90 = 1090 =

19 A1 Total 4

21

M1

AD = 100 cos 50 = 64.279 M1BD = 100 sin 50 = 76.604 A1CD = BD = 76.604 B1BC 2 = (76.604)2 + (76.604)2 M1BC 2 = 11736BC = 11736 = 108.335 A1total = 100 + 108.335 + 76.604 + 64.279

= 349 km (3sf) A1 Total 7

TOTAL FOR PAPER: 100 MARKS

2012 EHA Paper 2 marks Page 6 Churchill Maths Limited

A

100 kmQ

B

CD

50

45