For Edexcel

GCSE Mathematics

Higher Tier

Paper 1B (Non-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 Armstrong

Only to be copied for use in the purchaser's school or college

2012 EHB Paper 1 marks Page 1 © Churchill Maths Limited

Higher Tier Paper 1B Marking Guide

1 e.g. bus is cheaper than shared taxi B1staying: 2 × 25 + 4 × 2 + 39.99 M1

= 50 + 8 + 39.99 = £97.99 A1not staying: 4 × 20 + 8 × 2

= 80 + 16 = £96 M1cheapest by not staying and using bus, cost = £96 A1 Total 5

2 (a) ≈ 1.8 m [ accept 1.6 to 2.0 m ] B1

(b) e.g. height of man ≈ 6 feetheight of giraffe ≈ 2.5 × height of man M1[ accept 2 to 3 × height of man ]height of giraffe ≈ 15 feet A1 Total 3

3 (a) = 7 ÷ 20 = 35 ÷ 100 = 0.35 B1

* (b) e.g. repeating will probably give different results 20 rolls is too few to be sure that dice is biased C2 Total 3

[ valid explanation expressed clearly ]

4 5r – 3r < 9 + 1 M12r < 10r < 5 M1 A1 Total 3

5 (a) 3, 7, 11, 15 B2

(b) difference = 80th term = 11 – 8 = 3nth = 8n + 3 M1 A1

(c) (i) = 3 × (2, 5, 10, 17 …)nth = 3n2 + 3 B1

(ii) = (3, 7, 11, 15 …) + (11, 19, 27, 35 …)nth = 4n – 1 + 8n + 3 = 12n + 2 B1

(iii) = (3, 7, 11, 15 …) + (2, 5, 10, 17 …)nth = 4n – 1 + n2 + 1 = n2 + 4n B1 Total 7

2012 EHB Paper 1 marks Page 2 © Churchill Maths Limited

6 e.g. M1

Suitcase Holdall Rucksack Total

Boy 2 24

Girl 9

Total 15 45

leading to M1

Suitcase Holdall Rucksack Total

Boy 2 6 16 24

Girl 9 21

Total 15 45

Girl, not Holdall = 21 – 9 = 12Girl, rucksack = 12 ÷ 2 = 6 M1Total rucksacks = 16 + 6 = 22

P(Boy) = 1622 [ =

811 ] A1 Total 4

*7 XS area = 12 (18 + 22) × 20 M1

= 20 × 20 = 400 cm2 A1volume = 400 × 80 = 32 000 cm3 M1

= 32 litresvolume for 4 boxes = 4 × 32 = 128 litres A16 bags gives 120 litres, 7 bags gives 140 litresneed to buy 7 bagscost = 7 × 2.98 = 7 × 3 – 7 × 0.02 = 21 – 0.14 = £20.86 A1 C1 Total 6

[ showing method for finding area, volume, cost and stating conversion to litres ]

8 (a) = 2 × 32 × 7 = 126 M1 A1

(b) 23 × 33 × 72 × 11 B1 Total 3

9 let number sold at break be xat lunch he sold 4x B1after school he sold x + 2x + 4x + x + 2 = 20 M1 A16x + 2 = 206x = 18 M1x = 3 A1 Total 5

10 15 ÷ 10 = 1.5 M11.5 × 12 = 18 cm A1 Total 2

2012 EHB Paper 1 marks Page 3 © Churchill Maths Limited

11 (a) = p2 = p B1

(b) 2a(4a – 3b) M1 A1

(c) = y2 + y + 3y + 3 M1= y2 + 4y + 3 A1

(d) = 3m 3

m 3 = 3 B1

(e) (x + 5)(x – 2) M1 A1 Total 8

12 (a)2

15 B1

the other denominators have only 2 and 5 as prime factors B1

(b) let x = 0.0 2̇100x – 10x = 90x = 2. 2̇ – 0. 2̇ = 2 M1

x = 2

90 [ = 1

45 ] A1 Total 4

13 (a) = 5.7 × 107 + 1.07 × 108

= 0.57 × 108 + 1.07 × 108 M1= 1.64 × 108 A1

(b) = 7.77 × 108 ÷ (5.7 × 107)≈ 8 × 108 ÷ (6 × 107) M1

= 80 ÷ 6 = 1313 so 13 times [ accept 13 to 14 inc. ] A1 Total 4

14 (a) number of frames = 23

median = 12

(23 + 1)th = 12th value = 64 B1

quartiles = 6th, 18th = 54, 75 M1

A1

(b) e.g. the median is higher for the second match B1the interquartile range is slightly lower for thesecond match B1 Total 5

15 gradient = (e.g.) 6 − 22 − 0

= 2 M1

equation is y = 2x + c A1P (4, 2) so 2 = 8 + c

c = –6 M1y = 2x – 6 A1 Total 4

2012 EHB Paper 1 marks Page 4 © Churchill Maths Limited

Number of points30 40 6050 70 80 90

*16 let radius of smaller semicircles be xradius of larger semicircle = 3xx + 3x = 12 M14x = 12, x = 3 cm A1

area of smaller semicircle = 12 × π × 32 =

92 π cm2 M1

radius of larger semicircle = 9 cm

area of larger semicircle = 12 × π × 92 =

812 π cm2

area of shape = 3 × 92 π +

812 π =

272 π +

812 π =

1082 π = 54π cm2 M1 A1 C1 Total 6

[ showing how radii obtained and valid method leading to answer, allow arithmetic error ]

*17 84 – 67 = 17 M117º A1angles in the same segment are equal C1 Total 3

[ correct reason expressed clearly ]

18 area of A = (4x – 2)(x + 3) = 4x2 + 10x – 6 M1 A1area of B = (2x + 4)(2x + 1) = 4x2 + 10x + 4(4x2 + 10x + 4) – (4x2 + 10x – 6) = 10 M1rectangle B by 10 cm2 A1 Total 4

19 (a) E B1

(b) A B1

(c) D B1

(d) F B1 Total 4

20 (a) money in = £100

P(HH) = 12 ×

12 =

14 B1

expected no. of wins = 14 × 100 = 25 M1

expected profit = 100 – 25 × 3 = £25 M1 A1

(b) P(HHHH) = 12 ×

12 ×

12 ×

12 =

116

P(THHH) = P(HTHH) = P(HHTH) = P(HHHT) = 1

16 M1

P(3 or 4 heads) = 5 × 1

16 = 5

16 [ > 14 =

416 ] M1

yes, Lujain does have more chance of winning A1 Total 7

2012 EHB Paper 1 marks Page 5 © Churchill Maths Limited

21 (a) = 9×5 – 4×5= 35 – 25 = 5 M1 A1

(b) = 6 − 3

3 ×

3

3M1

= 63 − 3

3M1

= 23 – 1 A1 Total 5

22 (a) HJ B1

(b) BE B1

(c) JG B1

(d)

M1

EG A1 Total 5

TOTAL FOR PAPER: 100 MARKS

2012 EHB Paper 1 marks Page 6 © Churchill Maths Limited

A

B

C

D

E

F

G

H

I

J