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Endorsement of a resource does not mean that 19 18 17 16 the resource is required to achieve this Pearson qualification, nor does it mean 10 9 8 7 6 5 4 3 2 1 that it is the only suitable material available to support the qualification, and any resource lists produced by the awarding body shall include this and other British Library Cataloguing in Publication Data appropriate resources. A catalogue record for this book is available from the British Library ISBN 978 0 435 18144 4 Copyright notice All rights reserved. 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CONTENTS iii COURSE STRUCTURE IV PREFACE VI UNIT 1 2 UNIT 2 96 UNIT 3 174 UNIT 4 236 UNIT 5 298 FACT FINDERS 372 CHALLENGES 382 GLOSSARY 384 ANSWERS 388 INDEX 446 ACKNOWLEDGEMENTS 454 iv COURSE STRUCTURE UNIT 1 UNIT 2 UNIT 3 NUMBER 1 3 NUMBER 2 97 NUMBER 3 175 ◼ WORKING WITH FRACTIONS ◼ STANDARD FORM ◼ PRIME FACTORS ◼ ORDER OF OPERATIONS ◼ PERCENTAGES ◼ HCF AND LCM (BIDMAS) ◼ PERCENTAGE INCREASE ◼ RATIO ◼ SIGNIFICANT FIGURES AND DECREASE ◼ EXAM PRACTICE 183 AND DECIMAL PLACES ◼ EXAM PRACTICE 111 ◼ SUMMARY 184 ◼ EXAM PRACTICE 17 ◼ SUMMARY 112 ◼ SUMMARY 18 ALGEBRA 1 19 ALGEBRA 2 113 ALGEBRA 3 185 ◼ SIMPLIFYING ALGEBRAIC ◼ SIMPLIFYING ALGEBRAIC ◼ SIMPLE FACTORISING EXPRESSIONS FRACTIONS ◼ SIMPLIFYING FRACTIONS ◼ SIMPLIFYING ALGEBRAIC ◼ SOLVING EQUATIONS ◼ EQUATIONS WITH EXPRESSIONS WITH WITH ROOTS AND POWERS FRACTIONS BRACKETS ◼ POSITIVE INTEGER INDICES ◼ SIMULTANEOUS ◼ SOLVING EQUATIONS ◼ INEQUALITIES EQUATIONS ◼ EXAM PRACTICE 30 ◼ EXAM PRACTICE 124 ◼ EXAM PRACTICE 199 ◼ SUMMARY 31 ◼ SUMMARY 125 ◼ SUMMARY 200 GRAPHS 1 32 GRAPHS 2 126 GRAPHS 3 201 ◼ GRADIENT OF A ◼ STRAIGHT-LINE GRAPHS ◼ DISTANCE–TIME GRAPHS STRAIGHT LINE ◼ SKETCHING STRAIGHT-LINE ◼ SPEED–TIME GRAPHS ◼ PLOTTING STRAIGHT-LINE GRAPHS ◼ EXAM PRACTICE 211 GRAPHS ◼ SIMULTANEOUS EQUATIONS ◼ SUMMARY 212 ◼ STRAIGHT-LINE ◼ EXAM PRACTICE 135 CONVERSION GRAPHS ◼ SUMMARY 136 ◼ EXAM PRACTICE 48 ◼ SUMMARY 49 SHAPE AND SPACE 1 50 SHAPE AND SPACE 2 137 SHAPE AND SPACE 3 213 ◼ TRIANGLES ◼ PYTHAGORAS' THEOREM ◼ TANGENT RATIO ◼ QUADRILATERALS ◼ CIRCLE THEOREMS ◼ CALCULATING SIDES ◼ POLYGONS ◼ EXAM PRACTICE 148 ◼ CALCULATING ANGLES ◼ CONSTRUCTIONS ◼ SUMMARY 149 ◼ EXAM PRACTICE 222 ◼ SIMILAR TRIANGLES ◼ SUMMARY 223 ◼ EXAM PRACTICE 81 ◼ SUMMARY 82 SETS 84 HANDLING DATA 1 150 HANDLING DATA 2 224 ◼ SET NOTATION ◼ STATISTICAL INVESTIGATION ◼ FREQUENCY TABLES ◼ VENN DIAGRAMS ◼ PRESENTING DATA ◼ DISCRETE DATA ◼ EXAM PRACTICE 94 ◼ MISLEADING DATA PRESENTATION ◼ CONTINUOUS DATA ◼ SUMMARY 95 ◼ AVERAGES FOR DISCRETE DATA ◼ EXAM PRACTICE 234 ◼ EXAM PRACTICE 170 ◼ SUMMARY 235 ◼ SUMMARY 172 COURSE STRUCTURE v UNIT 4 UNIT 5 NUMBER 4 237 NUMBER 5 299 FACT FINDERS 372 ◼ COMPOUND ◼ CALCULATORS ◼ ANTS PERCENTAGES ◼ ESTIMATING ◼ FRAGILE EARTH ◼ INVERSE PERCENTAGES ◼ ROUNDING, UPPER AND ◼ GREAT WHITE SHARK ◼ EXAM PRACTICE 245 LOWER BOUNDS ◼ LONDON 2012 OLYMPIC ◼ SUMMARY 246 ◼ EXAM PRACTICE 309 GAMES ◼ SUMMARY 310 ◼ THE INCREDIBLE HUMAN BODY ALGEBRA 4 247 ALGEBRA 5 311 CHALLENGES 382 ◼ USING FORMULAE ◼ MULTIPLYING BRACKETS ◼ CHANGE OF SUBJECT ◼ FACTORISING QUADRATIC ◼ FURTHER FORMULAE EXPRESSIONS ◼ EXAM PRACTICE 257 ◼ SOLVING QUADRATIC EQUATIONS ◼ SUMMARY 258 BY FACTORISATION ◼ PROBLEMS LEADING TO QUADRATIC EQUATIONS ◼ EXAM PRACTICE 324 ◼ SUMMARY 325 GRAPHS 4 259 GRAPHS 5 326 ◼ QUADRATIC GRAPHS ◼ REPRESENTING y = ax ² + bx + c INEQUALITIES GRAPHICALLY ◼ SOLUTION OF 0 = ax ² + bx + c ◼ PERPENDICULAR LINES ◼ EXAM PRACTICE 269 ◼ MID-POINTS ◼ SUMMARY 270 ◼ USING PYTHAGORAS' THEOREM ◼ EXAM PRACTICE 336 ◼ SUMMARY 337 SHAPE AND SPACE 4 271 SHAPE AND SPACE 5 338 ◼ SINE AND COSINE RATIOS ◼ TRANSFORMATIONS ◼ CALCULATING SIDES ◼ TRANSLATIONS ◼ CALCULATING ANGLES ◼ REFLECTIONS AND ROTATIONS ◼ MIXED QUESTIONS ◼ ENLARGEMENTS ◼ EXAM PRACTICE 283 ◼ COMBINED TRANSFORMATIONS ◼ SUMMARY 284 ◼ EXAM PRACTICE 355 ◼ SUMMARY 356 HANDLING DATA 3 285 HANDLING DATA 4 357 ◼ MEASURES OF ◼ PROBABLILITY – DISPERSION SINGLE EVENTS ◼ QUARTILES ◼ EXPERIMENTAL ◼ CUMULATIVE FREQUENCY PROBABILITY ◼ EXAM PRACTICE 296 ◼ THEORETICAL ◼ SUMMARY 297 PROBABILITY ◼ EXAM PRACTICE 370 ◼ SUMMARY 371 vi PREFACE ABOUT THIS BOOK This two-book