Contents Introduction Acknowledgements
5 6
1 Integers, powers and roots
7
1.1 Directed numbers 1.2 Square roots and cube roots 1.3 Indices 1.4 Working with indices End-of-unit review
8 10 11 12 14
2 Sequences and functions
15
2.1 Generating sequences 2.2 Finding the nth term 2.3 Finding the inverse of a function End-of-unit review
16 18 20 22
3 Place value, ordering and rounding
23
3.1 Multiplying and dividing decimals mentally 3.2 Multiplying and dividing by powers of 10 3.3 Rounding 3.4 Order of operations End-of-unit review
24 26 28 30 32
4 Length, mass, capacity and time
33
4.1 Solving problems involving measurements 4.2 Solving problems involving average speed 4.3 Using compound measures End-of-unit review
34 36 38 40
5 Shapes
41
5.1 Regular polygons 5.2 More polygons 5.3 Solving angle problems 5.4 Isometric drawings 5.5 Plans and elevations 5.6 Symmetry in three-dimensional shapes End-of-unit review
42 44 45 48 50 52 54
6 Planning and collecting data
55
6.1 Identifying data 6.2 Types of data 6.3 Designing data-collection sheets 6.4 Collecting data End-of-unit review
56 58 59 61 63
7 Fractions
64
7.1 Writing a fraction in its simplest form 7.2 Adding and subtracting fractions 7.3 Multiplying fractions 7.4 Dividing fractions 7.5 Working with fractions mentally End-of-unit review
65 66 68 70 72 74
8 Constructions and Pythagoras’ theorem
75
8.1 Constructing perpendicular lines 8.2 Inscribing shapes in circles 8.3 Using Pythagoras’ theorem End-of-unit review
76 78 81 83
9 Expressions and formulae
84
9.1 9.2 9.3 9.4 9.5 9.6 9.7
Simplifying algebraic expressions Constructing algebraic expressions Substituting into expressions Deriving and using formulae Factorising Adding and subtracting algebraic fractions Expanding the product of two linear expressions End-of-unit review
85 86 88 89 91 92
10 Processing and presenting data
97
10.1 Calculating statistics 10.2 Using statistics End-of-unit review
94 96
98 100 102
3