FOR EDEXCEL
GCE Examinations
Advanced Subsidiary
Core Mathematics C1
Paper L
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 L – Marking Guide
1.
2.
3.
= 49 + ( 3 8 )2 = 7 + 22
= 11
5 +1
3
B1 M1
A1
(a)
u4 =
(b)
5=
M1 A1
14
A1
=2
B1
u2 + 1
, u2 = 14
3
u +1
= 1 , u1 = 41
3
(a)
b2 − 4ac = 122 − (4 × 4 × 9) = 0
∴ 1 real root
(b)
4x2 + 12x + 9 = 8
4x2 + 12x + 1 = 0
M1
8
= −12 ± 8 2
M1
= − 32 ±
A2
8
2
(a)
5x > 15
x>3
(b)
(x + 2)(x − 8) < 0
(c)
3<x<8
(a)
(2 −
−2
M1
M1
A1
8
B1
(b)
= (2 −
(c)
=
=
6.
(a)
(b)
(6)
x )2 = 0
x =2
x=4
∫
∫
(6)
M1
A1
−2 < x < 8
5.
(4)
M1
A1
x = −12 ± 144 − 16
4.
(3)
M1
A1
3 )2 = 4 − 4 3 + 3 = 7 − 4 3
M1 A1
x )2 dx
(2 −
(4 − 4 x + x) dx
3
2
= 4x −
8
3
grad =
−4 − 6
1 − (−3)
x +
1
2
B1
x2 + c
M1 A2
= − 52
M1 A1
∴ y − 6 = − 52 (x + 3)
M1
2y − 12 = −5x − 15
5x + 2y + 3 = 0
A1
2
k
m: y = − x −
7
k
∴ grad = −
l and m perp. ∴ − 52 × −
2
k
2
k
M1 A1
= −1
M1
k = −5
C1L MARKS page 2
(8)
A1
(8)
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© Science Exam Papers
7.
(a)
(b)
8.
(a)
f(x) =
∫
(5 +
4
x2
) dx
f(x) = 5x − 4x−1 + c
M1 A2
f(1) = 5 − 4 + c = 1 + c
f(2) = 10 − 2 + c = 8 + c
f(2) = 2f(1) ∴ 8 + c = 2(1 + c)
c=6
f(x) = 5x − 4x−1 + 6
f(4) = 20 − 1 + 6 = 25
M1
M1 A1
LHS = (x + 1)(x2 − 7x + 12)
= x3 − 7x2 + 12x + x2 − 7x + 12
= x3 − 6x2 + 5x + 12 = RHS
M1
M1
A1
(b)
M1
A1
(8)
y
(0, 12)
B3
(−1, 0) O
(c)
(3, 0)
(i)
(4, 0)
x
y
(ii)
y
(0, 12)
B2 B2
O
(0, 0) (1, 0)
(−4, 0)
x
(−4, 0) (−3, 0)
(1, 0)
O
x
(10)
9.
10.
= (t 2 − 5) − (t − 1) = t 2 − t − 4
= (t 2 − 5) + (t 2 − t − 4) = 2t 2 − t − 9
(a)
(i)
(ii)
(b)
2t 2 − t − 9 = 19
2t 2 − t − 28 = 0
(2t + 7)(t − 4) = 0
t>0 ∴t=4
M1
A1
(c)
a = 4 − 1 = 3, d = 16 − 4 − 4 = 8
u10 = 3 + (9 × 8) = 3 + 72 = 75
B1
M1 A1
(d)
=
(a)
A (0, 2)
B1
dy
= 3 − 2x
dx
M1 A1
grad = 3
∴ y = 3x + 2
M1
A1
(b)
40
2
M1 A1
M1 A1
[6 + (39 × 8)] = 20 × 318 = 6360
M1 A1
(11)
grad of m = 3
grad of curve at B =
−1
3
= − 13
M1 A1
at B: 3 − 2x = − 13
x=
5
3
M1 A1
5 2
y = 2 + 3( 53 ) − ( 3 ) = 4 29 ∴ B ( 1 23 , 4 29 )
 Solomon Press
M1 A1
(11)
Total
(75)
C1L MARKS page 3
© Science Exam Papers
Performance Record – C1 Paper L
Question no.
1
2
3
4
5
6
7
8
9
10
Topic(s)
indices
recur.
relation
quad.
formula
inequals
surds,
integr.
straight
lines
integr.
curve
sketch,
transform.
AP
diff.,
tangent
Marks
3
4
6
6
8
8
8
10
11
11
Total
Student
C1L MARKS page 4
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© Science Exam Papers
75