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FOR EDEXCEL

GCE ExaminationsAdvanced Subsidiary

Core Mathematics C2

Paper D

MARKING GUIDE

This guide is intended to be as helpful as possible to teachers by providingconcise solutions and indicating how marks could be awarded. There are

obviously alternative methods that would also gain full marks.

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

Accuracy marks (A) can only be awarded when a correct method has been used.

(B) marks are independent of method marks.

Written by Shaun Armstrong

Solomon Press

These sheets may be copied for use solely by the purchasers institute.

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Solomon PressC2D MARKS page 3

7. (a) Sn = a + ar+ ar2

+ ... + arn 1

B1

rSn = ar+ ar2

+ ar3

+ ... + arn

M1

subtracting, SnrSn = aarn

(1 r)Sn = a(1 rn) M1

Sn =(1 )

1

na r

r

A1

(b) GP: a = 10, r= 2 B2

S12 =12

10(2 1)

2 1

M1 A1

= 40950 A1 (9)

8. (a)d

d

y

x= 1 2x M1

grad = 1 2 = 1 A1

grad of normal =1

1

= 1 M1

y 5 = 1(x 1) M1y =x + 4 A1

(b) 5 +xx2 =x + 4x

2 1 = 0 M1

x = 1 (atP) or 1 Q (1, 3) A1

(c) area under curve =1

1 (5 +xx2) dx

= [5x + 12x

2 1

3x

3]

11 M1 A1

= (5 + 12

13

) (5 + 12

+ 13

) = 13

9 M1

area of trapezium = 12

(3 + 5) 2 = 8 B1

shaded area = 13

9 8 = 43

M1 A1 (13)

9. (a) (x 4)2 16 + (y 5)2 25 + 16 = 0 M1(x 4)2 + (y 5)2 = 25 centre (4, 5), radius = 5 A2

(b) x = 0 y2 10y + 16 = 0 M1(y 2)(y 8) = 0 M1

y = 2, 8 (0, 2), (0, 8) A1

(c) 62

= 52

+ 52 (2 5 5 cos ) M2 A1

cos =25 25 36

50

+ = 7

25A1

(d) = cos1

725

= 1.287, sin = 0.96

area = 12

52 12

52 sin = 252

(1.287 0.96) M2 A1

= 4.09 (3sf) A1 (14)

Total (75)

3

4

5

6

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Solomon PressC2D MARKS page 4

Performance Record C2 Paper D

Question no. 1 2 3 4 5 6 7 8 9 Total

Topic(s) binomial cosinerule

SP trig. eqn exponential

graph,logs

remain.

theorem,alg. div.

GP area by

integr.

circle,

sectorof a

circle

Marks 4 4 6 8 8 9 9 13 14 75

Student