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: Pythagorasâ€™ theorem 1 | 39 | ||

5.5: Pythagorasâ€™ 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 |