Contents
(Higher tier only material appears bold)
How to use this book
6
1
Basic number
8
1.1 Solving real-life problems 9 1.2 Multiplication and division with decimals 12 1.3 Approximation of calculations 15 1.4 Multiples, factors, prime numbers, powers and roots 22 1.5 Prime factors, LCM and HCF 25 1.6 Negative numbers 30 Worked exemplars 34 Ready to progress? 36 Review questions 36
2 Fractions, ratio and proportion 2.1 One quantity as a fraction of another 2.2 Adding, subtracting and calculating with fractions 2.3 Multiplying and dividing fractions 2.4 Fractions on a calculator 2.5 Increasing and decreasing quantities by a percentage 2.6 Expressing one quantity as a percentage of another Worked exemplars Ready to progress? Review questions
38 39 40 42 44 48 51 54 56 56
3 Statistical diagrams and averages
58
3.1 3.2 3.3
Statistical representation Statistical measures Scatter diagrams Worked exemplars Ready to progress? Review questions
59 65 74 79 82 82
4
Number and sequences
86
4.1 Patterns in number 87 4.2 Number sequences 89 4.3 Finding the nth term of a linear sequence 92 4.4 Special sequences 95 4.5 General rules from given patterns 100 4.6 The nth term of a quadratic sequence 105 4.7 Finding the nth term for quadratic sequences 108 Worked exemplars 113
206745 GCSE Maths Higher SB_Contents_AQA.indd 3
Ready to progress? Review questions
114 114
5
Ratio and proportion
116
5.1 Ratio 5.2 Direct proportion problems 5.3 Best buys 5.4 Compound measures 5.5 Compound interest and repeated percentage change 5.6 Reverse percentage (working out the original amount) Worked exemplars Ready to progress? Review questions
117 125 128 132
6 Angles
150
6.1 6.2 6.3 6.4 6.5 6.6 6.7
151 154 157 160 163 166 168 174 176 176
Angle facts Triangles Angles in a polygon Regular polygons Angles in parallel lines Special quadrilaterals Scale drawings and bearings Worked exemplars Ready to progress? Review questions
140 143 146 148 148
7 Transformations, constructions and loci
178
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8
Congruent triangles Rotational symmetry Transformations Combinations of transformations Bisectors Defining a locus Loci problems Plans and elevations Worked exemplars Ready to progress? Review questions
179 181 183 195 198 201 203 208 212 214 214
8
Algebraic manipulation
216
8.1 Basic algebra 8.2 Factorisation 8.3 Quadratic expansion 8.4 Expanding squares 8.5 More than two binomials 8.6 Quadratic factorisation 8.7 Factorising ax2 + bx + c 8.8 Changing the subject of a formula
217 223 225 231 232 235 239 241
12/11/14 8:21 PM