FOR EDEXCEL
GCE Examinations
Advanced Subsidiary
Core Mathematics C1
Paper E
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.
© Science Exam Papers
C1 Paper E – Marking Guide
1.
2.
3.
5.
3
3
×
=
(b)
= 4 − 2 3 − 4 3 + 6 = 10 − 6 3
= 6 3
M1 A1
M1 A1
3x2 − 5 = 2x
3x2 − 2x − 5 = 0
(3x − 5)(x + 1) = 0
x = −1, 53
x − 5y = 7
grad m =
4.
18
3
(a)
⇒
−1
1
5
M1
M1
A2
1
5
y=
x−
7
5
∴ grad =
1
5
(4)
B1
= −5
M1 A1
∴ y − 1 = −5(x + 4)
y = −5x − 19
M1
A1
(a)
1, 7, 25, 79
B2
(b)
7=a+b
25 = 7a + b
subtracting,
M1
A1
M1
A1
(a)
(4)
6a = 18
a = 3, b = 4
(5)
(6)
5
8x − x 2 = 0
3
x(8 − x 2 ) = 0
3
x = 0 (at O) or x 2 = 8
∴ x=( 8) =4
M1 A1
dy
=8−
dx
x2
M1 A1
grad = 8 − ( 52 × 8) = −12
M1 A1
(a)
f(x) = 2[x2 − 2x] + 1
= 2[(x − 1)2 − 1] + 1
a = 2, b = −1, c = −1
= 2(x − 1)2 − 1,
M1
M1
A2
(b)
x=1
B1
(b)
6.
(c)
7.
M1
2
3
(a)
5
2
3
(7)
2
2(x − 1) − 1 = 3
(x − 1)2 = 2
x=1± 2
M1
M1 A1
2
f(x) = x − 8 x1 + 16
M1
(8)
2x 2
f(x) =
(b)
f ′(x) =
f ′(x) =
f ′(x) =
C1E MARKS page 2
1
2
3
1
x 2 − 4x 2 + 8x
3
4
1
4
1
4
1
x 2 − 2x
− 12
− 12
− 4x
,
A=
1
2
, B = −4, C = 8
− 32
x
− 32
(3x2 − 8x − 16)
x
− 32
(3x + 4)(x − 4) =
A2
M1 A2
M1
(3x + 4)( x − 4)
M1 A1
3
(9)
4x 2
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© Science Exam Papers
8.
(a)
translation by 1 unit in the positive x-direction
(b)
B2
y
y=0
O
x
B3
(0, −1)
x=1
(c)
1
x −1
=2+
1
x
x = 2x(x − 1) + (x − 1)
2x2 − 2x − 1 = 0
9.
(a)
M1
A1
x=
2± 4+8
4
M1
x=
2±2 3
4
M1
x=
1
2
±
6
2
S6 =
1
2
3
A1
[3000 + (5 × −x)] = 8100
3000 − 5x = 2700,
M1 A1
x = 60
M1 A1
(b)
= 1500 − (7 × 60) = 1500 − 420 = £1080
(c)
Sn =
n
2
10.
(a)
(b)
M1 A1
[3000 − 60(n − 1)]
M1
= n[1500 − 30(n − 1)]
= 30n[50 − (n − 1)] = 30n(51 − n)
(d)
[ k = 30 ]
the value of sales in a month would become negative
which is not possible
y=
∫
(10)
M1 A1
B1
(10)
(3x2 + 4x + k) dx
y = x3 + 2x2 + kx + c
(0, −2) ∴ c = −2
(2, 18) ∴ 18 = 8 + 8 + 2k − 2
k=2
3
y = x + 2x2 + 2x − 2
M1 A2
B1
M1
A1
A1
x3 + 2x2 + 2x − 2 = x − 2
x3 + 2x2 + x = 0
x(x2 + 2x + 1) = 0
x(x + 1)2 = 0
repeated root ∴ tangent
point of contact where x = −1
∴ (−1, −3)
M1
M1
A1
M1
A1
(12)
Total
(75)
 Solomon Press
C1E MARKS page 3
© Science Exam Papers
Performance Record – C1 Paper E
Question no.
1
2
Topic(s)
surds
quad.
Marks
4
4
3
4
5
straight sequence, indices,
diff.
lines
recur.
relation
5
6
7
6
7
8
9
10
compl.
square
diff.
transform.,
quad.
formula
AP
integr.,
rep. root
8
9
10
10
12
Total
Student
C1E MARKS page 4
 Solomon Press
© Science Exam Papers
75