Contents |
Introduction | 4 |
1. The language of algebra | 5 |
1.1 Key vocabulary | 5 |
1.2 Understanding the language of algebra | 6 |
2. Special expansions | 7 |
2.1 Expanding binomial products | 7 |
2.2 Expanding binomial products – challenge yourself! | 8 |
2.3 Special binomial products – a difference of two squares | 9 |
2.4 Special binomial products – a perfect square | 10 |
2.5 Binomial product review | 11 |
3. Special factorisations | 12 |
3.1 Factorisation summarised | 12 |
3.2 Factorising a difference of two squares | 13 |
3.3 Factorising a difference of two squares – challenge yourself! | 14 |
3.4 Factorising quadratic trinomials – getting ready | 15 |
3.5 How to factorise a monic quadratic trinomial using trial and error | 16 |
3.6 Factorising a monic quadratic trinomial – starting out | 17 |
3.7 Factorising a non-monic quadratic trinomial – next steps | 18 |
3.8 Factorising a non-monic quadratic trinomial – challenge yourself! | 19 |
3.9 Factorising a perfect square | 20 |
3.10 Factorising that involves grouping in pairs | 21 |
3.11 Review: Special factorisation dominoes | 22 |
3.12 Review: Recognising different types of factorisations | 23 |
3.13 Mixed factorising | 24 |
4. Algebraic fractions | 25 |
4.1 Revision: Adding and subtracting algebraic fractions | 25 |
4.2 Revision: Multiplying and dividing algebraic fractions | 26 |
4.3 Simplifying a single algebraic fraction using factorisation | 27 |
4.4 Adding and subtracting algebraic fractions – forming a common denominator | 28 |
4.5 Adding and subtracting algebraic fractions – next steps | 29 |
4.6 Compound fractions | 30 |
4.7 Multiplying and dividing algebraic fractions | 31 |
4.8 Algebraic fractions – factorising negative one | 32 |
4.9 Review: Algebraic fractions | 33 |
4.10 Review: Spot the error with algebraic fractions | 34 |
5. Indices | 35 |
5.1 "Powers of" table | 35 |
5.2 Arithmetic with negative indices | 36 |
5.3 Simplifying algebraic expressions with negative indices | 37 |
5.4 Fractions and negative powers | 38 |
5.5 Fractions and negative powers – challenge yourself! | 39 |
5.6 Arithmetic with fractional indices | 40 |
5.7 Review: Arithmetic involving negative and fractional indices | 41 |
5.8 Review: Arithmetic expressions with negative and fractional indices | 42 |
5.9 Review: Algebraic expressions with negative and fractional indices | 43 |
5.10 Review: Spot the error with index laws | 44 |
5.11 Indices – change of base | 45 |
5.12 Solving exponential equations | 46 |
5.13 Review: Indices dominoes | 47 |
5.14 Review: Match your Q&As | 48 |
5.15 Review: Match your Q&As – challenge yourself! | 49 |
6. Surds | 50 |
6.1 The real number system | 50 |
6.2 Simplifying surds | 51 |
6.3 Spot the error with surds | 52 |
6.4 Multiplying and powers of surds | 53 |
6.5 Review: Surds – dividing and rationalising the denominator | 54 |
6.6 Review: Application problems with surds | 55 |
6.7 Review: Four operations with surds | 56 |
6.8 Review: Rational or irrational? | 57 |
6.9 Surds and indices – the combined rules | 58 |
7. General review | 59 |
7.1 Legal or illegal? | 59 |
Answers | 60 |