Brighouse High Sixth Form College A-Level Maths & Further MathsInduction

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. Your 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.

Name ………………………………………………………………………….1. Arithmetic of Fractions

Number > Fractions > Adding Subtracting, Multiplying, Dividing

2. Rules and Manipulation of IndicesNumber > Powers and Roots > Indices 1, 2 and 3

3. Expanding Brackets and FactorisingAlgebra > Algebraic Manipulation > Single Brackets, Brackets,

Factorising Linear, Factorising Quadratics 1 and 2

3. Factorise

4. Factorise

4. SurdsNumber > Powers and Roots > Surds 1 and Surds 2

1. Write the following in their simplest forms

5. Linear EquationsAlgebra > Equations – Linear > Solving Equations, Equations with

FractionsSolve the equations below

6. Changing the Subject of a FormulaeAlgebra > Expressions and Formulae > Rearranging 1 and Rearranging

2

7. Solving Quadratic Equations - Factorising Algebra > Equations – Quadratic > Quadratic Equations,

8. Solving Quadratic Equations - Completing the Square and Using the Quadratic Formula

Completing the Square and Quadratic Formula

9. Solving Simultaneous Linear EquationsAlgebra > Equations – Simultaneous > Simultaneous 1, 2, 3 and

Negative

10. Algebraic FractionsAlgebra > Algebraic Manipulation > Cancelling, Adding and Multiplying

Algebraic Fractions

Further Maths Research TaskThis task concerns calendar dates of the form

d1d2 /m1m2/ y1 y2 y3 y4

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).]