Brighouse High Sixth Form College A-Level Maths & Further Maths
Induction
The material in this booklet has been designed to enable you to prepare for the
demands of A-Level maths. When your course starts in September you will find that
your ability to get the most from lessons, and to understand new material, depends
crucially upon both having a good facility with algebraic manipulation and
undertaking plenty of independent study.
It is vitally important that you spend some time working through the questions in
this booklet over the summer - you will need to have a good knowledge of these
topics before you commence the course in September. You will need to hand in your
completed booklet during your first maths lesson in September.
You will most-likely have met all the topics before at GCSE. At the start of each
section the relevant MyMaths lessons have been indicated; use these to help you if you
are stuck with anything or unsure of how to proceed. You should attempt every
question in each exercise. To log on to MyMaths go to www.mymaths.co.uk,
username: brighouse password: isosceles
Additionally, if you are taking Further Maths, you should also complete the research
task on the last page. Your Further Maths work should be handed in separately in
your first Further Maths lesson in Brighouse.
Name ………………………………………………………………………….
1. Arithmetic of Fractions
Number > Fractions > Adding Subtracting, Multiplying, Dividing
2. Rules and Manipulation of Indices
Number > Powers and Roots > Indices 1, 2 and 3
3. Expanding Brackets and Factorising
Algebra > Algebraic Manipulation > Single Brackets, Brackets, Factorising
Linear, Factorising Quadratics 1 and 2
3. Factorise
4. Factorise
4. Surds
Number > Powers and Roots > Surds 1 and Surds 2 1. Write the following in their simplest forms
5. Linear Equations
Algebra > Equations – Linear > Equations 1 to 5
Solve the equations below
6. Changing the Subject of a Formulae
Algebra > Expressions and Formulae > Rearranging 1 and Rearranging 2
7. Solving Quadratic Equations - Factorising
Algebra > Equations – Quadratic > Quadratic Equations 1 and 2
8. Solving Quadratic Equations - Completing the Square and
Using the Quadratic Formula
Algebra > Equations – Quadratic > Completing the Square and Quadratic
Formula
9. Solving Simultaneous Linear Equations
Algebra > Equations – Simultaneous > Simultaneous 1, 2, 3 and Negative
10. Algebraic Fractions
Algebra > Algebraic Manipulation > Cancelling, Adding and Multiplying
Algebraic Fractions
Further Maths Research Task
This task concerns calendar dates of the form
𝑑1𝑑2/𝑚1𝑚2/𝑦1𝑦2𝑦3𝑦4
in the order day/month/year.
The question specifically concerns those dates which contain no
repetitions of a digit. For example, the date 23/05/1967 is
such a date but 07/12/1974 is not such a date as both
1 = 𝑚1 = 𝑦1 and 7 = 𝑑2 = 𝑦3 are repeated digits.
We will use the Gregorian Calendar throughout (this is the calendar
system that is standard throughout most of the world; see below.)
i. Show that there is no date with no repetition of digits in the years
from 2000 to 2099.
ii. What was the last date before today, with no repetition of digits?
Explain your answer, including why I have not provided today’s date.
iii. When will the next such date be? Explain your answer.
iv. How many such dates were there in years from 1900 to 1999?
Explain your answer.
[The Gregorian Calendar uses 12 months, which have, respectively
31, 28 or 29, 31, 30, 31, 30, 31, 31, 30, 31, 30 and
31 days. The second month (February) has 28 days in years that are
not divisible by 4, or that are divisible by 100 but not 400 (such
as 1900); it has 29 days in the other years (leap years).]