Mathematics Department

AS and IB Preparation Booklet

Contents:

Introduction Page 2

1. Simplifying Algebraic Expressions Page 3

2. Factorisation Page 6

3. Algebraic Fractions Page 9

5. Indices and Surds Page 12

Page 17 B: Straight line (Co- ordinate Geometry)

Sixth Form Test – Topic List Page 24

Answers Page 25

Preparation Booklet for IB/A Level Mathematicians

Introduction

This booklet is intended to help you begin any Maths course in September with an awareness of what background knowledge we will expect from you. it is listed in the Summer Reading lists provided to you for every department.

It is not designed to deter you from studying Mathematics, but to help you become fluent in some of the prior knowledge required to be successful in the subject.

When you start the course in September you will be expected to use a lot of your (I)GCSE Maths skills, such as algebraic techniques, and to have a working knowledge of straight line graphs.

The chapters here have been extracted from a longer, older booklet produced by the Oakham Maths Department. Before the end of the summer term, you can collect a paper copy of this from the Maths office, if you’d like to.

We have reproduced 5 sections: 1 Simplifying Algebraic Expressions; 2 Algebraic Fractions, 3 Factorisation, 5 Indices and Surds, and B1/2/3 Straight Lines (Co-ordinate Geometry). Each section begins with some notes or theory. Then there are some examples to read and exercises to do. Check your answers at the back of the booklet. Don’t write in this booklet: you can use it first to see what you remember, then, after looking at some of the videos below, try the exercises again to see whether you’ve mastered the ideas.

Here are the interactive links that we recommended in the main Summer Reading list to help with active learning. The wider reading ideas are not included here.

http://www.cimt.plymouth.ac.uk/projects/mepres/step-up/default.htm

BE AWARE: in the first week of Maths lessons, you will sit a test based on the work in this booklet and more general GCSE knowledge. The range of topics is listed at the back of the book – and there are videos on all topics on the website above.

The test will help you to identify areas in which you are stronger and weaker; and to assess your suitability to pursue the level of Mathematics course which you have chosen. In other words, we have certain thresholds for Higher Level, Standard Level Maths and Maths Studies, Further Maths and A level Maths courses which we would expect you to obtain in the test. If you do not meet the relevant threshold, it flags up a discussion with you, your teacher and your tutor about your aspirations for the course.

Sixth-Form Test – Non-Calculator – Topic List September 2014

Length: 1 double lesson.

This list is indicative and not necessarily the complete range of topics covered.

GCSE numerical work – simple non-calculator arithmetic, including fractions and decimals.

Understanding rounding to significant figures.

GCSE Algebraic techniques – solving linear equations; simultaneous linear equations; expanding

brackets; factorising quadratic expressions; algebraic fractions; evaluating (without a calculator) and

simplifying indices and surds. Solving quadratic equations by factorisation*.

Straight line graphs – gradients and intercepts; finding the equation of a line from certain information;

Areas of triangles – perpendicular height and the general formula.

*Note: International students may not have covered this topic and this will be taken into account.