Decimals, percentages and rounding

Contents

How to use this book Acknowledgements

1 Number and calculation

1.1 Irrational numbers 1.2 Standard form 1.3 Indices 5 6

7 9 11

2 Expressions and formulae

2.1 Substituting into expressions 13 2.2 Constructing expressions 16 2.3 Expressions and indices 23 2.4 Expanding the product of two linear expressions 26 2.5 Simplifying algebraic fractions 29 2.6 Deriving and using formulae 33

3 Decimals, percentages and rounding

3.1 Multiplying and dividing by powers of 10 37 3.2 Multiplying and dividing decimals 41 3.3 Understanding compound percentages 45 3.4 Understanding upper and lower bounds 50

4 Equations and inequalities

4.1 Constructing and solving equations 55 4.2 Simultaneous equations 59 4.3 Inequalities 63

5 Angles

5.1 Calculating angles 5.2 Interior angles of polygons 5.3 Exterior angles of polygons 5.4 Constructions 5.5 Pythagoras’ theorem 66 68 71 72 74

6 Statistical investigations

6.1 Data collection and sampling 77 6.2 Bias 78

7 Shapes and measurements

7.1 Circumference and area of a circle 81 7.2 Areas of compound shapes 86 7.3 Large and small units 92

8 Fractions

8.1 Fractions and recurring decimals 97 8.2 Fractions and the correct order of operations 100 8.3 Multiplying fractions 103 8.4 Dividing fractions 107 8.5 Making calculations easier 111

9 Sequences and functions

9.1 Generating sequences 9.2 Using the nth term 9.3 Representing functions 114 118 122

10 Graphs

10.1 Functions 10.2 Plotting graphs 10.3 Gradient and intercept 10.4 Interpreting graphs 127 129 131 133

11 Ratio and proportion

11.1 Using ratios 137 11.2 Direct and inverse proportion 141