FOR EDEXCEL
GCE Examinations
Advanced Subsidiary
Core Mathematics C2
Paper H
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 H – Marking Guide
1.
2.
(a)
x2 + (y − 3)2 − 9 − 7 = 0
∴ centre (0, 3)
M1
A1
(b)
x2 + (y − 3)2 = 16
∴ radius = 4
M1
A1
(a)
9
2
P = 2r + (r × 2.5) =
r = 36
M1
OA = r = 8 cm
3.
× 8 × 2.5) − (
(b)
=(
(a)
7 − 2x − 3x2 =
(b)
A1
2
1
2
2
x
2
1
2
,
2
× 8 × sin 2.5) = 60.8 cm (3sf)
M2 A1
7x − 2x2 − 3x3 = 2
M1
3x3 + 2x2 − 7x + 2 = 0
A1
x = −2 is a solution ∴ (x + 2) is a factor
3x2 − 4x
x + 2 3x3 + 2x2
3x3 + 6x2
2
− 4x
2
− 4x
(a)
(b)
+ 1
− 7x + 2
− 7x
− 8x
x + 2
x + 2
M1 A1
(a)
(8)
M1 A1
2
3
= 1 + 4( 2 ) + 6( 2 ) + 4( 2 ) + ( 2 )
(ii)
5.
M1
A2
= 1 + 4x + 6x2 + 4x3 + x4
(i)
(5)
B1
∴ (x + 2)(3x2 − 4x + 1) = 0
(x + 2)(3x − 1)(x − 1) = 0
x = −2 (at P), 13 , 1 ∴ ( 13 , 6), (1, 2)
4.
(4)
4
M1
= 1 + 4 2 + 6(2) + 4( 2 2 ) + 4
M1
= 17 + 12 2
A1
4
(1 −
2 ) = 17 − 12 2
B1
(1 −
2 )8 = [(1 −
M1
2 )4]2 = (17 − 12 2 )2
= 289 − 408 2 + 288
M1
= 577 − 408 2
A1
reflection in the y-axis
y
B1
y = ( 13 )x
(b)
(9)
y = 2(3x)
B3
(0, 2)
(0, 1)
(c)
( 13 )x = 2(3x)
O
x 2
1 = 2 × (3 )
32x =
x=
1
2
2 lg 3
3x =
M1
, 2x =
lg 12
lg 12
M1
lg 3
= −0.32
1
2
×
y = 2(3x) = 2 ×
1
2
C2H MARKS page 2
1
2
=
x
A1
2
2
=
2 =
1
2
2
M1
2
A1
 Solomon Press
(9)
6.
(a)
(b)
7.
(a)
dy
= 3x2 + 2ax − 15
dx
SP when x = −1 ∴ 3 − 2a − 15 = 0
a = −6
y = x3 − 6x2 − 15x + b
(−1, 12) on curve ∴ 12 = −1 − 6 + 15 + b
b=4
M1
A1
M1
A1
3x2 − 12x − 15 = 0
3(x − 5)(x + 1) = 0
x = −1 [at (−1, 12)] or 5
∴ (5, −96)
1 − 8x3
M1
M1
A1
1 − 8x3 = 0
=0 ⇒
x2
x3 =
x=
(b)
M1 A1
M1
1
8
1
2
M1 A1
f(x) = x−2 − 8x
−2
∫ f(x) dx = ∫ (x − 8x) dx
= −x−1 − 4x2 + c
(c)
8.
(a)
M1 A2
2 2
−1
= −[−x − 4x ] 1
M1
= −{( − 12 − 16) − (−2 − 1)} = 13 12
M1 A1
sin2 θ = (2 −
M1
2
2 )2 = 4 − 4 2 + 2 = 6 − 4 2
2
cos θ = 1 − (6 − 4 2 ) = −5 + 4 2
(b)
2x −
π
6
2x =
π
2
,
,
11π
12
x=
9.
(a)
(9)
π
4
π
3
=
, 2π −
π
3
=
π
3
,
M1 A1
5π
3
B1 M1
11π
6
M1 A1
M1 A2
ar = −48, ar4 = 6
3
r =
6
−48
=
3
a=
−48
− 12
=
(c)
Sn =
M1
M1 A1
= 96
96
1 − (− 12 )
(b)
A1
= 64
96[1 − (− 12 )n ]
1 − (− 12 )
M1 A1
= 64[1 − ( − 12 )n]
M1 A1
S∞ − Sn = 64 − 64[1 − ( − 12 )n]
=
(10)
B1
− 18
− 18 = − 12
r=
(9)
64( − 12 )n
6
M1
−n
n
n
= 2 × (−1) × 2 = (−1) × 2
difference is magnitude, ∴ = 2
6−n
6−n
 Solomon Press
M1
A1
(12)
Total
(75)
C2H MARKS page 3
Performance Record – C2 Paper H
Question no.
1
2
Topic(s)
circle
sector
of a
circle
Marks
4
5
3
4
factor binomial exponential
graphs,
theorem,
logs
alg. div.
8
9
Student
C2H MARKS page 4
5
 Solomon Press
9
6
7
8
9
SP
area by
integr.
trig. eqn
GP
9
9
10
12
Total
75