FOR EDEXCEL
GCE Examinations
Advanced Subsidiary
Core Mathematics C2
Paper A
MARKING GUIDE
This guide is intended to be as helpful as possible to teachers by providing
concise 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 purchaser’s institute.
C2 Paper A – Marking Guide
1.
(a)
f(−2) = −35
(b)
= f( 23 )
∴ −24 − 8 − 2k + 9 = −35
k=6
B1
8
= 3( 27
) − 2( 49 ) + 6( 23 ) + 9 =
2.
x
2x
−2
−1
1
4
1
2
area ≈
1
2
=
3.
tan2 θ =
π
6
,
(a)
(b)
5.
(a)
π
6
(5)
B1
B1 M1 A1
A1
(5)
M1
A1
π
6
− π or π −
π
6
, − π6
B1 M1
5π
6
,
A2
8
8
M1 A1
x = 0.001
(1.003)8 ≈ 1 + 0.024 + 0.000 252 + 0.000 001 512
= 1.024 253 5 (8sf)
B1
M1
A1
(i)
M1 A1
= 2 log3 x = 2t
=
1
2
2t −
log3 x
log 3 9
=
log3 x
2
=
1
2
t
M1 A1
(7)
M1 A1
8
3
M1
8
3
radius =
8
3
x = 3 = 18.7
,
25 + 1 =
M1 A1
26
M1
A1
(b)
(−4, 7), LHS = (−4 + 3)2 + (7 − 2)2 = 1 + 25 = 26 ∴ lies on circle
B1
(c)
grad of radius =
7−2
−4 − ( −3)
∴ grad of tangent =
∴ y−7=
1
5
−1
−5
(7)
M1 A1
∴ (x + 3)2 + (y − 2)2 = ( 26 )2
(x + 3)2 + (y − 2)2 = 26
= −5
=
M1
1
5
M1 A1
(x + 4)
M1
5y − 35 = x + 4
x − 5y + 39 = 0
C2A MARKS page 2
(6)
t=4
log3 x =
(a)
2
4
M1 A1
= 1 + 8(3x) +   (3x)2 +   (3x)3 + ...
2
 3
= 1 + 24x + 252x2 + 1512x3 + ...
t=
6.
+ 4 + 9 = 13
1
3
(ii)
(b)
8
9
or 5.63 (3sf)
θ = − 5π6 , − π6 ,
4.
1
2
−
1
3
tan θ = ±
θ =
0
1
8
9
× 1 × [ 14 + 4 + 2( 12 + 1 + 2)]
5 85
M1
A1
A1
 Solomon Press
(10)
7.
(a)
(b)
2x2 + 6x + 7 = 2x + 13
x2 + 2x − 3 = 0
(x + 3)(x − 1) = 0
x = −3, 1
∴ (−3, 7), (1, 15)
area under curve =
M1
M1
A1
A1
1
∫ −3
(2x2 + 6x + 7) dx
= [ 23 x3 + 3x2 + 7x] −13
M1 A2
= ( 23 + 3 + 7) − (−18 + 27 − 21) = 22 23
M1
area of trapezium =
1
2
× (7 + 15) × 4 = 44
shaded area = 44 − 22 23 = 21 13
8.
(a)
a(r 4 − 1)
r −1
M1 A1
2
= 10 × a(r − 1)
9.
A1
M1
M1
A1
a(33 − 1)
= 26
3 −1
26
a=
=2
13
M1 A1
A1
(c)
6
S6 = 2(3 − 1) = 728
(a)
area = 2xy + ( 12 × x2 × 0.5) = 2xy +
M1 A1
3 −1
∴ y=
50 − 14 x 2
2x
=
25
x
−
1
8
P = 2x + 4y + (x × 0.5) =
(b)
(c)
25
− 18 x)
x
100
− 12 x = 2x
x
=
5
2
x + 4(
=
5
2
x+
dx 2
x 2 = 50
x
5
2
= 2( 5 2 ) +
100
5 2
(11)
M1
A1
x + 4y
M1
M1
+
100
x
A1
M1 A1
M1
A1
= 200x−3
when x = 5 2 ,
(d)
1
4
dP
= 2 − 100x−2
dx
for minimum,
2 − 100x−2 = 0
x2 = 50
x = 50 or 5 2
d2 P
(11)
B1 M1
r −1
r4 − 1 = 10(r2 − 1)
r4 − 10r2 + 9 = 0
(r2 − 1)(r2 − 9) = 0
r2 = 1, 9
r = ± 1, ± 3
r>1 ∴r=3
(b)
B1
M1
d2 P
dx 2
=
2
5
2,
d2 P
dx 2
> 0 ∴ minimum
= 10 2 + 10 2 = 20 2
 Solomon Press
A1
M1 A1
(13)
Total
(75)
C2A MARKS page 3
Performance Record – C2 Paper A
Question no.
Topic(s)
Marks
1
2
3
4
remain. trapezium trig. eqn binomial
theorem
rule
5
5
6
5
6
7
8
9
logs
circle
area by
integr.
GP
circular
sector,
max./min.
problem
7
10
11
11
13
7
Student
C2A MARKS page 4
 Solomon Press
Total
75