BOOK
Edexcel GCSE (9-1) Mathematics: Higher Practice, Reasoning and Problem-solving Book
Bola Abiloye | Gemma Batty | Phil Boor | Catherine Murphy | Claire Powis
(2017)
Additional Information
Book Details
Abstract
Exam Board: Edexcel
Level: GCSE
Subject: Maths
First teaching: September 2015
First exams: June 2017
- Problem solving and reasoning questions included throughout.
- Exam style questions give students exposure to the sort of questions they will need to answer in their exam.
- Problem Solving lessons build up strategies from the Student Book so that students need to choose the most appropriate strategy.
- Mixed problem solving questions drawing on knowledge from this and previous chapters in the book give students the opportunity to practice using this strategy.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Acknowledgement | ii | ||
| Contents | iii | ||
| Chapter 1: Number | 1 | ||
| 1.1: Number problems and reasoning | 1 | ||
| 1.2: Place value and estimating | 1 | ||
| 1.3: HCF and LCM | 2 | ||
| 1.4: Calculating with powers (indices) | 3 | ||
| 1.5: Zero, negative and fractional indices | 4 | ||
| 1.6: Powers of 10 and standard form | 5 | ||
| 1.7: Surds | 6 | ||
| Problem-solving | 7 | ||
| Chapter 2: Algebra | 9 | ||
| 2.1: Algebraic indices | 9 | ||
| 2.2: Expanding and factorising | 9 | ||
| 2.3: Equations | 10 | ||
| 2.4: Formulae | 11 | ||
| 2.5: Linear sequences | 12 | ||
| 2.6: Non-linear sequences | 13 | ||
| 2.7: More expanding and factorising | 15 | ||
| Problem-solving | 15 | ||
| Chapter 3: Interpreting and representing data | 17 | ||
| 3.1: Statistical diagrams 1 | 17 | ||
| 3.2: Time series | 19 | ||
| 3.3: Scatter graphs | 20 | ||
| 3.4: Line of best fit | 21 | ||
| 3.5: Averages and range | 23 | ||
| 3.6: Statistical diagrams 2 | 25 | ||
| Problem-solving | 26 | ||
| Chapter 4: Fractions, ratio and percentages | 29 | ||
| 4.1: Fractions | 29 | ||
| 4.2: Ratios | 30 | ||
| 4.3: Ratio and proportion | 31 | ||
| 4.4: Percentages | 32 | ||
| 4.5: Fractions, decimals and percentages | 33 | ||
| Problem-solving | 34 | ||
| Chapter 5: Angles and trigonometry | 35 | ||
| 5.1: Angle properties of triangles and quadrilaterals | 35 | ||
| 5.2: Interior angles of a polygon | 37 | ||
| 5.3: Exterior angles of a polygon | 38 | ||
| 5.4: Pythagoras’ theorem 1 | 39 | ||
| 5.5: Pythagoras’ theorem 2 | 40 | ||
| 5.6: Trigonometry 1 | 41 | ||
| 5.7: Trigonometry 2 | 42 | ||
| Problem-solving | 44 | ||
| Chapter 6: Graphs | 45 | ||
| 6.1: Linear graphs | 45 | ||
| 6.2: More linear graphs | 46 | ||
| 6.3: Graphing rates of change | 47 | ||
| 6.4: Real-life graphs | 49 | ||
| 6.5: Line segments | 51 | ||
| 6.6: Quadratic graphs | 52 | ||
| 6.7: Cubic and reciprocal graphs | 53 | ||
| 6.8: More graphs | 54 | ||
| Problem-solving | 56 | ||
| Chapter 7: Area and volume | 58 | ||
| 7.1: Perimeter and area | 58 | ||
| 7.2: Units and accuracy | 59 | ||
| 7.3: Prisms | 60 | ||
| 7.4: Circles | 61 | ||
| 7.5: Sectors of circles | 63 | ||
| 7.6: Cylinders and spheres | 64 | ||
| 7.7: Pyramids and cones | 65 | ||
| Problem-solving | 66 | ||
| Chapter 8: Transformations and constructions | 68 | ||
| 8.1: 3D solids | 68 | ||
| 8.2: Reflection and rotation | 68 | ||
| 8.3: Enlargement | 70 | ||
| 8.4: Translations and combinations of transformations | 72 | ||
| 8.5: Bearings and scale drawings | 73 | ||
| 8.6: Constructions 1 | 74 | ||
| 8.7: Constructions 2 | 75 | ||
| 8.8: Loci | 77 | ||
| Problem-solving | 78 | ||
| Chapter 9: Equations and inequalities | 80 | ||
| 9.1: Solving quadratic equations 1 | 80 | ||
| 9.2: Solving quadratic equations 2 | 81 | ||
| 9.3: Completing the square | 81 | ||
| 9.4: Solving simple simultaneous equations | 82 | ||
| 9.5: More simultaneous equations | 83 | ||
| 9.6: Solving linear and quadratic simultaneous equations | 84 | ||
| 9.7: Solving linear inequalities | 85 | ||
| Problem-solving | 86 | ||
| Chapter 10: Probability | 88 | ||
| 10.1: Combined events | 88 | ||
| 10.2: Mutually exclusive events | 89 | ||
| 10.3: Experimental probability | 90 | ||
| 10.4: Independent events and tree diagrams | 91 | ||
| 10.5: Conditional probability | 92 | ||
| 10.6: Venn diagrams and set notation | 94 | ||
| Problem-solving | 95 | ||
| Chapter 11: Multiplicative reasoning | 97 | ||
| 11.1: Growth and decay | 97 | ||
| 11.2: Compound measures | 98 | ||
| 11.3: More compound measures | 99 | ||
| 11.4: Ratio and proportion | 100 | ||
| Problem-solving | 101 | ||
| Chapter 12: Similarity and congruence | 102 | ||
| 12.1: Congruence | 102 | ||
| 12.2: Geometric proof and congruence | 103 | ||
| 12.3: Similarity | 104 | ||
| 12.4: More similarity | 106 | ||
| 12.5: Similarity in 3D solids | 107 | ||
| Problem-solving | 108 | ||
| Chapter 13: More trigonometry | 110 | ||
| 13.1: Accuracy | 110 | ||
| 13.2: Graph of the sine function | 110 | ||
| 13.3: Graph of the cosine function | 112 | ||
| 13.4: The tangent function | 113 | ||
| 13.5: Calculating areas and the sine rule | 115 | ||
| 13.6: The cosine rule and 2D trigonometric problems | 116 | ||
| 13.7: Solving problems in 3D | 117 | ||
| 13.8: Transforming trigonometric graphs 1 | 118 | ||
| 13.9: Transforming trigonometric graphs 2 | 119 | ||
| Problem-solving | 121 | ||
| Chapter 14: Further statistics | 123 | ||
| 14.1: Sampling | 123 | ||
| 14.2: Cumulative frequency | 124 | ||
| 14.3: Box plots | 125 | ||
| 14.4: Drawing histograms | 127 | ||
| 14.5: Interpreting histograms | 127 | ||
| 14.6: Comparing and describing populations | 129 | ||
| Problem-solving | 130 | ||
| Chapter 15: Equations and graphs | 131 | ||
| 15.1: Solving simultaneous equations graphically | 131 | ||
| 15.2: Representing inequalities graphically | 132 | ||
| 15.3: Graphs of quadratic functions | 134 | ||
| 15.4: Solving quadratic equations graphically | 136 | ||
| 15.5: Graphs of cubic functions | 137 | ||
| Problem-solving | 139 | ||
| Chapter 16: Circle theorems | 141 | ||
| 16.1: Radii and chords | 141 | ||
| 16.2: Tangents | 142 | ||
| 16.3: Angles in circles 1 | 143 | ||
| 16.4: Angles in circles 2 | 144 | ||
| 16.5: Applying circle theorems | 146 | ||
| Problem-solving | 147 | ||
| Chapter 17: More algebra | 148 | ||
| 17.1: Rearranging formulae | 148 | ||
| 17.2: Algebraic fractions | 149 | ||
| 17.3: Simplifying algebraic fractions | 149 | ||
| 17.4: More algebraic fractions | 150 | ||
| 17.5: Surds | 151 | ||
| 17.6: Solving algebraic fraction equations | 152 | ||
| 17.7: Functions | 152 | ||
| 17.8: Proof | 153 | ||
| Problem-solving | 154 | ||
| Chapter 18: Vectors and geometric proof | 155 | ||
| 18.1: Vectors and vector notation | 155 | ||
| 18.2: Vector arithmetic | 155 | ||
| 18.3: More vector arithmetic | 156 | ||
| 18.4: Parallel vectors and collinear points | 158 | ||
| 18.5: Solving geometric problems | 159 | ||
| Problem-solving | 160 | ||
| Chapter 19: Proportion and graphs | 162 | ||
| 19.1: Direct proportion | 162 | ||
| 19.2: More direct proportion | 162 | ||
| 19.3: Inverse proportion | 163 | ||
| 19.4: Exponential functions | 165 | ||
| 19.5: Non-linear graphs | 166 | ||
| 19.6: Translating graphs of functions | 168 | ||
| 19.7: Reflecting and stretching graphs of functions | 169 | ||
| Problem-solving | 171 |