The Rodillian Academy
Year 13
A-Level Maths
This booklet is for those students studying
A-Level Maths in year 13.
It should be completed over the summer
holidays in order to smooth the transition
between Year 12 and Year 13.
Introduction
Well done on getting to the end of Year 12, you have made the difficult transition from GCSE to Alevel!
While it’s tempting to switch off over the long summer holiday, the Maths Department is
committed to helping you to make good progress throughout the course, and we have put
together some work for you to complete over your summer break. This is to ensure that your hard
work is rewarded and that the Year 13 work you have started since your Year 12 exams is not
forgotten.
We have set you:
1. This booklet to work through;
2. Some questions on mymaths.co.uk.
This work will need to be completed before the start of the autumn term and you should be
aiming to get each question right and 100% in each mymaths homework.
You should bring your completed written work back with you after the holidays and there will be
an assessment on Algebraic Fractions and Functions when you return to school in September.
As well as using mymaths.co.uk, we would also like to point you in the direction of another
excellent online resource.
We hope you will find this useful and that you enjoy working through the various problems. The
more you practise applying your skills and the better you understand the concepts, the higher your
grades are likely to be.
Online Resource
A really great resource to use at
home is a website called Exam
Solutions. This will really help you if
you are getting stuck and is worth
looking at even if you aren’t.
Go to www.examsolutions.net
Select A-level Maths then Edexcel
from the menu
Here you will find the home page
for A-level maths and you should
take some time to explore this area
of the website but for help with the
work in this booklet, click on C3
The sections that will help you with
this booklet and to prepare for your
test are the algebra and series section
and the functions section. You will
find tutorials and example questions
on everything you need to know.
Summer holiday check list
Over the summer holidays you must ensure you:
1.
2.
3.
4.
Complete the questions in this booklet on Chapter 1 – Algebraic Fractions
Complete the questions in this booklet on Chapter 2 – Functions
Complete the mymaths.co.uk tasks
Familiarise yourself with the examsolutions.net website
If you don’t have computer access, please let a maths teacher know as soon as possible.
Useful Information
Mymaths
Website: www.mymaths.co.uk
Write your mymaths login here: ____________
School login: rodillian
School password: triangle
Write your password here: _____________
And Finally
It’s important that you have the support of people
at home to be as successful as possible so make
sure that a parent/guardian/carer reads this and
signs here to show they have done so:
______________________________________
C3 Algebraic Fractions Questions
June 2006
1.
3x 2  x  2
(a) Simplify
.
x2 1
(3)
(b) Hence, or otherwise, express
1
3x 2  x  2
–
as a single fraction in its simplest form.
2
x( x  1)
x 1
(3)
Jan 2008
1.
Given that
dx  e
2 x 4  3x 2  x  1
 (ax2 + bx + c) +
,
2
( x 2  1)
( x  1)
find the values of the constants a, b, c, d and e.
(4)
June 2009
7.
The function f is defined by
f(x) = 1 –
(a) Show that f (x) =
x 8
2
+
, x  ℝ, x ≠ −4, x ≠ 2.
( x  4) ( x  2)( x  4)
x3
.
x2
(5)
Jan 2007
2.
f(x) = 1 –
3
3
+
2 , x  –2.
x  2 ( x  2)
x2  x 1
(a) Show that f(x) =
, x  –2.
( x  2) 2
(4)
(b) Show that x2 + x + 1 > 0 for all values of x.
(3)
(c) Show that f(x) > 0 for all values of x, x  –2.
(1)
June 2007
2.
f(x) =
(a) Show that f (x) =
1
2x  3
9  2x
–
, x> 2.
2
x2
2 x  3x  2
4x  6
.
2x  1
(7)
C3 Functions Questions
June 2005
3.
The function f is defined by
f: x
(a) Show that f(x) =

5x  1
3
–
, x > 1.
x2
x  x2
2
2
, x > 1.
x 1
(4)
(b) Find f –1(x).
(3)
The function g is defined by
g: x
 x2 + 5,
x  ℝ.
1
(b) Solve fg(x) = 4 .
(3)
Jan 2008
8.
The functions f and g are defined by
f:x
 1 - 2x3,
g:x

x  ℝ.
3
 4, x > 0, x  ℝ.
x
(a) Find the inverse function f 1.
(2)
(b) Show that the composite function gf is
gf : x

8x 3  1 .
1  2x3
(4)
(c) Solve gf (x) = 0.
(2)
C3 Algebraic Fractions ANSWERS
June 2006
Jan 2008
June 2009
Jan 2007
June 2007
C3 Functions ANSWERS
June 2005
Jan 2008