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Partial Fractions
Question Paper 1
Level
A Level
Subject
Maths
Exam Board
OCR
Module
Core 4
Topic
Algebra & Graphs
Sub Topic
Partial Fractions
Booklet
Question Paper - 1
60 minutes
Time Allowed:
Score:
/50
Percentage:
/100
Grade Boundaries:
A*
>85%
A
77.5%
B
C
D
E
U
70%
62.5%
57.5%
45%
<45%
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1
(i) Express
(ii)
2
3
+
as a single fraction in its simplest form.
3-x 1+x
Hence express c
2
Express x +
3
Express
4
Simplify
2
2
3
m # x + 8x - 233 as a single fraction in its lowest terms.
+
3-x 1+x
121 - x
1
2
+
as a single fraction, simplifying your answer.
1-x 1+x
(x - 7) (x - 2)
in partial fractions.
(x + 2) (x - 1) 2
[2]
[3]
[3]
[5]
(i)
1−x
,
x − 3x + 2
[2]
(ii)
(x + 1)
(x − 5)
.
−
(x − 1)(x − 3) (x − 3)(x − 4)
[4]
2
x4 − 10x2 + 9
.
(x2 − 2x − 3)(x2 + 8x + 15)
5
Simplify
6
Express
7
The equation of a curve is y = f(x), where f(x) =
[4]
x2
in partial fractions.
(x − 1)2 (x − 2)
(i) Express f(x) in partial fractions.
[5]
3x + 1
.
(x + 2)(x − 3)
[2]
(ii) Hence find f (x) and deduce that the gradient of the curve is negative at all points on the curve.
[3]
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8
(i) Express
7 − 2x
A
B
in the form
, where A and B are constants.
+
2
x − 2 (x − 2)2
(x − 2)
(ii) Hence find the exact value of ä
9
10
Simplify
5
4
7 − 2x
dx.
(x − 2)2
20 − 5x
.
6x2 − 24x
(i) Express
a, b and c are integers.
[4]
[3]
2x + 1
A
B
in the form
+
, where A and B are constants.
2
x − 3 (x − 3)2
(x − 3)
(ii) Hence find the exact value of [3]
10
4
[3]
2x + 1
dx, giving your answer in the form a + b ln c, where
(x − 3)2
[4]