Brighouse High Sixth Form College A-Level Maths & Further ... · Linear, Factorising Quadratics 1 and 2 3. Factorise 4. Factorise . 4. Surds Number > Powers and Roots > Surds 1 and

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).]