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Contents MODULE 2 1 Scatter graphs 1. 1 Scatter graphs and relationships 1. 2 Lines of best fit and correlation 1. 3 Using lines of best fit Chapter summary Chapter review questions 1 1 5 6 10 10 4 Processing, representing and interpreting data 4. 1 Frequency polygons 4. 2 Cumulative frequency 4. 3 Box plots 4. 4 Comparing distributions 4. 5 Frequency density and histograms Chapter summary Chapter review questions 51 51 56 64 65 68 73 73 2 Collecting and recording data 14 2. 1 Introduction to statistics 2. 2 Data by observation and by experiment 2. 3 Grouping data 2. 4 Questionnaires 2. 5 Sampling 2. Databases Chapter summary Chapter review questions 14 14 16 18 20 23 27 28 5 Probability 5. 1 5. 2 5. 3 Writing probabilities as numbers Sample space diagrams Mutually exclusive outcomes and the probability that the outcome of an event will not happen 5. 4 Estimating probability from relative frequency 5. 5 Independent events 5. 6 Probability tree diagrams 5. 7 Conditional probability Ch apter summary Chapter review questions 77 77 79 81 84 86 88 89 92 93 3 Averages and range 3. 1 Mean, mode and median 3. 2 Using frequency tables to find averages 3. 3 Range and interquartile range 3. 4 Stem and leaf diagrams 3. Estimating the mean of grouped data 3. 6 Moving averages Chapter summary Chapter review questions 31 31 34 36 38 41 44 47 47 MODULE 3 6 Number 6. 1 6. 2 Properties of whole numbers Multiplication and division of directed numbers M4 6. 3 Squares, cubes 6. 4 Index laws 6. 5 Order of operations 6. 6 Using a calculator 6. 7 Prime factors, HCF and LCM Chapter summary Chapter review questions 97 97 98 100 101 102 104 106 110 110 Chapter summary Chapter review questions 124 124 8 Expressions and sequences 8. 1 8. 2 Expressions and collecting like terms Working with numbers and letters and using index notation M4 8. Index laws M4 8. 4 Sequences Chapter summary Chapter review questions 127 127 129 131 134 138 139 7 Angles (1) 7. 1 7. 2 7. 3 7. 4 7. 5 Triangles Equilat eral triangles and isosceles triangles Corresponding angles and alternate angles Proofs Bearings 113 113 114 116 119 120 9 Measure (1) 9. 1 9. 2 Compound measures – speed and density Converting between metric and imperial units Chapter summary Chapter review questions 141 141 144 145 145 ii 10 Decimals and fractions 10. 1 10. 2 10. 3 10. 4 Fractions revision Arithmetic of decimals Manipulation of decimals Conversion between decimals and fractions M4 10. Converting recurring decimals to fractions 10. 6 Rounding to significant figures Chapter summary Chapter review questions 147 147 149 151 154 157 159 161 161 14 Estimating and accuracy 14. 1 Significant figures 14. 2 Accuracy of measurements Chapter summary Chapter review questions 192 192 194 196 196 15 Three-dimensional shapes (1) 197 15. 1 Volume of three-dimensional shapes 15. 2 Surface area of three-dimensional shapes 15. 3 Coordinates in three dimensions Chapter summary Chapter review questions 197 202 204 205 206 11 Exp anding brackets and factorising 11. 1 11. 2 11. 3 11. 4 11. Expanding brackets Factorising by taking out common factors Expanding the product of two brackets Factorising by grouping Factorising expressions of the form 164 164 165 167 168 170 171 174 174 16 Indices and standard form 16. 1 Zero and negative powers 16. 2 Standard form M4 16. 3 Fractional indices Chapter summary Chapter review questions M4 207 207 208 215 217 217 x2 bx c 11. 6 Factorising the difference of two squares Chapter summary Chapter review questions 12 Two-dimensional shapes (1) 176 12. 1 Special quadrilaterals 12. 2 Perimeter and area of rectangles 12. 3 Area of a parallelogram 12. Area of a triangle 12. 5 Area of a trapezium 12. 6 Problems involving areas Chapter summary Chapter review questions 176 177 178 178 179 181 184 184 17 Further factorising, simplifying and algebraic proof 220 220 222 225 228 230 230 17. 1 Further factorising 17. 2 Simplifying rational expressions 17. 3 Adding and subtracting rationa l expressions 17. 4 Algebraic proof Chapter summary Chapter review questions 13 Graphs (1) 13. 1 Coordinates and line segments 13. 2 Straight line graphs Chapter summary Chapter review questions 186 186 187 191 191 18 Circle geometry (1) 18. 1 Parts of a circle 18. Isosceles triangles 18. 3 Tangents and chords Chapter summary Chapter review questions 232 232 232 233 236 237 MODULE 4 19 Angles (2) 19. 1 Quadrilaterals 19. 2 Polygons 19. 3 Exterior angles Chapter summary Chapter review questions 238 238 240 244 246 247 20 Fractions 20. 1 20. 2 20. 3 20. 4 248 248 249 251 253 Addition and subtraction of fractions Addition and subtraction of mixed numbers Multiplication of fractions and mixed numbers Division of fractions and mixed numbers iii CONTENTS 20. 5 Fractions of quantities 20. 6 Fraction problems Chapter summary Chapter review questions 255 256 258 258 7 Inequalities 27. 1 Inequalities on a number line 27. 2 Solving inequalities 27. 3 Integer solutions to inequalities 27. 4 Pro blems involving inequalities 27. 5 Solving inequalities graphically Chapter summary Chapter review questions 358 358 359 361 362 363 368 368 21 Scale drawings and dimensions 21. 1 Scale drawings and maps 21. 2 Dimensions Chapter summary Chapter review questions 260 260 262 263 264 28 Formulae 28. 1 28. 2 28. 3 28. 4 Using an algebraic formula Writing an algebraic formula Changing the subject of a formula Expressions, identities, equations and formulae 28. Further changing the subject of a formula Chapter summary Chapter review questions 372 372 374 376 378 379 381 382 22 Two-dimensional shapes (2) 266 22. 1 Drawing shapes 22. 2 Circumference of a circle 22. 3 Area of a circle 22. 4 Circumferences and areas in terms of 22. 5 Arc length and sector area 22. 6 Segment area 22. 7 Units of area Chapter summary Chapter review questions 266 268 270 272 273 274 276 277 277 29 Pythagoras’ theorem and trigonometry (1) 29. 1 Pythagoras’ theorem 29. 2 Finding lengths 29. 3 Applying Pythagoras’ theorem 29. 4 Line segments and Pythagoras’ theorem 29. Trigonometry – introduction 29. 6 Finding lengths using trigonometry 29. 7 Finding angles using trigonometry 29. 8 Trigonometry problems Chapter summary Chapter review questions 384 384 385 388 390 392 393 396 398 401 401 23 Linear equations 23. 1 The balance method for solving equations 23. 2 Setting up equations 23. 3 Solving equations with fractional terms 23. 4 Simultaneous linear equations 23. 5 Setting up simultaneous linear equations Chapter summary Chapter review questions 280 280 284 287 289 292 293 294 24 Percentages 24. 1 Percentages M3 24. 2 Increases and decreases 24. Use of multipliers 24. 4 Reverse percentages Chapter summary Chapter review questions 296 296 299 306 309 311 312 30 Ratio and proportion 30. 1 Introduction to ratio 30. 2 Problems 30. 3 Sharing a quantity in a given ratio 30. 4 Direct proportion 30. 5 Inverse proportion Chapter summary Chapter review questions 405 40 5 408 409 411 413 415 415 25 Graphs (2) 25. 1 Real life graphs 25. 2 Solving simultaneous equations graphically 25. 3 The equation y mx c 25. 4 Further uses of y mx c Chapter summary Chapter review questions 314 314 319 321 324 328 329 31 Three-dimensional shapes (2) 418 1. 1 Planes of symmetry 31. 2 Plans and elevations 31. 3 Volume of three-dimensional shapes 31. 4 Surface area of three-dimensional shapes Chapter summary Chapter review questions 418 420 422 427 430 431 26 Transformations 26. 1 Introduction 26. 2 Translations 26. 3 Rotations 26. 4 Reflections 26. 5 Enlargements 26. 6 Centre of enlargement 26. 7 Combinations of transformations Chapter summary Chapter review questions 332 332 332 336 338 343 346 351 354 354 32 Graphs (2) 32. 1 32. 2 Graphs of quadratic functions Using graphs of quadratic functions to solve equations 32. Using graphs of quadratic and linear functions to solve quadratic equations Chapter summary Chapter review questions 433 433 436 439 442 442 iv CONTE NTS 33 Further graphs and trial and improvement 33. 1 Graphs of cubic, reciprocal and exponential functions 33. 2 Trial and improvement Chapter summary Chapter review questions 445 445 449 453 453 40 Simultaneous linear and quadratic equations and loci 40. 1 40. 2 40. 3 Solving simultaneous equations Loci and equations Intersection of lines and circles – algebraic solutions Chapter summary Chapter review questions 30 530 532 536 538 538 34 Constructions, loci and congruence 34. 1 Constructions 34. 2 Loci 34. 3 Regions 34. 4 Drawing triangles 34. 5 Congruent triangles 34. 6 Proofs of standard constructions Chapter summary Chapter review questions 458 458 461 464 467 468 469 470 471 41 Similar shapes 540 540 544 547 550 552 554 555 41. 1 Similar triangles 41. 2 Similar polygons 41. 3 Areas of similar shapes 41. 4 Volumes of similar solids 41. 5 Lengths, areas and volumes of similar solids Chapter summary Chapter review questions 35 Bounds and surds 35. Lower bounds and upper bo unds 35. 2 Surds Chapter summary Chapter review questions 474 474 476 478 479 42 Direct and inverse proportion 42. 1 Direct proportion 42. 2 Further direct proportion 42. 3 Inverse proportion 42. 4 Proportion and square roots Chapter summary Chapter review questions 559 559 561 563 566 568 568 36 Circle geometry 36. 1 Circle theorems Chapter summary Chapter review questions 481 481 487 488 37 Completing the square 37. 1 Completing the square Chapter summary Chapter review questions 491 491 494 494 43 Vectors 43. 1 43. 2 43. 3 43. 4 43. 5 43. Vectors and vector notation Equal vectors The magnitude of a vector Addition of vectors Parallel vectors Solving geometric problems in two dimensions Chapter summary Chapter review questions 571 571 573 574 575 578 583 587 587 38 Quadratic equations 38. 1 Introduction to solving quadratic equations 38. 2 Solving by factorisation 38. 3 Solving by completing the square 38. 4 Solving using the quadratic formula 38. 5 Solving equations with algebrai c fractions 38. 6 Problems that involve quadratic equations Chapter summary Chapter review questions 496 496 496 498 499 501 502 505 505 44 Transformations of functions 4. 1 44. 2 44. 3 44. 4 44. 5 44. 6 Function notation Applying vertical translations Applying horizontal translations Applying reflections Applying stretches Transformations applied to the graphs of sin x and cos x Chapter summary Chapter review questions Index Licence 591 591 592 596 599 602 605 608 608 611 618 39 Pythagoras’ theorem and trigonometry (2) Problems in three dimensions Trigonometric ratios for any angle Area of a triangle The sine rule The cosine rule Solving problems using the sine rule, the cosine rule and 1 ab sin C 2 Chapter summary Chapter review questions 39. 1 39. 39. 3 39. 4 39. 5 39. 6 507 507 512 516 519 522 525 527 527 v Introduction Welcome to Edexcel GCSE Mathematics Modular Higher Student Book and ActiveBook. Written by Edexcel as an exact match to the new Edexcel GCSE Mathematics H igher Tier specification these materials give you more chances to succeed in your examinations The ActiveBook The ActiveBook CD-ROM is found in the back of this book. It is a digital version of this Student Book, with links to additional resources and extra support. Using the ActiveBook you can: ? Find out what you need to know before you can tackle the unit ?See what vocabulary you will learn in the unit ? See what the learning objectives are for the unit ? Easily access and display answers to the questions in the exercise sections (these do not appear in the printed Student Book) ? Click on glossary words to see and hear their definitions ? Access a complete glossary for the whole book ? Practice exam questions and improve your exam technique with Exam Tutor model questions and answers. Each question that has an Exam Tutor icon beside it links to a worked solution with audio and visual annotation to guide you through it The Student BookEach chapter has a number of units to work th rough, with full explanations of each topic, numerous worked examples and plenty of exercises, followed by a chapter summary and chapter review questions. There are some Module 3 topics that may also be assessed in Modules 2 or 4. These are identified in the contents list with the symbol: M4 These topics are also also assessed in highlighted within the Module 4 chapters themselves, using this flag by the relevant unit headings: The text and worked examples in each unit have been written to explain clearly the ideas and techniques you need to work through the subsequent exercises.The questions in these exercises have all been written to progress from easy to more difficult. At the end of each chapter, there is a Chapter Summary which will help you remember all the key points and concepts you need to know from the chapter and tell you what you should be able to do for the exam. Following the Chapter Summary is a Chapter Review which comprises further questions. These are either past e xam questions, or newly written exam-style questions – written by examiners for the new specifications.Like the questions in the exercise sections, these progress from easy to hard. In the exercise sections and Chapter Reviews Recommendation specification Pentium 3 500 Mhz processor 128MB RAM 8 speed CD-ROM 1GB free hard disc space 800 600 (or 1024 768) resolution screen at 16 bit colour sound card, speakers or headphones Windows 2000 or XP. This product has been designed for Windows 98, but will be unsupported in line with Microsoft’s Product Life-Cycle policy. Installation Insert the CD. If you have autorun enabled the program should start within a few seconds.Follow on-screen instructions. Should you experience difficulty, please locate and review the readme file on the CD.   vi by a question shows that you may use a calculator for this question or those that follow. by a question shows that you may NOT use a calculator for this question or those that follow. Tech nical support If after reviewing the readme you are unable to resolve your problem, contact customer support: ? telephone 0870 6073777 (between 8. 00 and 4. 00) ? email schools. [email  protected] com ? web http://centraal. uk. knowledgebox. com/kbase/