## Edexcel GCSE (9-1) Mathematics: Higher Practice, Reasoning and Problem-solving Book

(2017)

### 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.

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
6.7: 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
16.2: 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