Table of Contents
Number and arithmetic
Introducing numbers 10
Decimals 11
Written addition and subtraction 12
Adding and subtracting decimals 13
Negative numbers 14
Multiplying and dividing by 10, 100, and 1,000 15
Methods of multiplication 16
Methods of division 18
Mental addition and subtraction 20
Mental multiplication and division 21
Powers of numbers 22
Factors and multiples 23
Prime numbers 24
Prime factorization 25
Common factors and multiples 26
Order of operations 28
Angles and shapes
Angles 30
Angle facts 31
Angles and parallel lines 32
Measuring and drawing angles 34
Symmetry 35
Properties of triangles 36
Properties of quadrilaterals 37
Properties of polygons 38
Angles in a triangle 39
Angles in a quadrilateral 40
Exterior angles of a polygon 41
Interior angles of a polygon 42
Properties of a circle 43
Practice question: Working with angles 44
Fractions, decimals, and percentages
Fractions 46
Improper fractions and mixed numbers 47
Comparing fractions 48
Adding and subtracting fractions 49
Fraction of an amount 50
Multiplying fractions 51
Dividing fractions 52
Percentages 54
Fractions, decimals, and percentages 55
Percentage of an amount 56
Mental percentage calculations 57
Finding the percentage change 58
Percentage increase and decrease 59
Reverse percentages 60
Growth and decay 61
Compound interest 62
Recurring decimals 63
Recurring decimals and fractions 64
Measure
Metric units of measure and time 66
Imperial units of measure 67
Converting units of measure 68
Converting units of area and volume 69
Compound units of measure 70
Practice questions: Working with compound units 72
Perimeter and area 73
Area formulas 74
How area formulas work 75
Circumference and area of a circle 76
Length of an arc and area of a sector 77
Practice questions: Compound 20 shapes 78
3D shapes 79
3D cross-sections 80
Plans and elevations 81
Volume of a rectangular prism 82
Surface area of a rectangular prism 83
Volume and surface area of a prism 84
Volume and surface area of a cylinder 85
Volume and surface area of a pyramid 86
Volume and surface area of a cone 87
Volume and surface area of a sphere 88
Practice questions: Compound 3D shapes 89
Rounding and estimating 90
Bounds of accuracy 92
Introducing algebra
Algebraic terms 95
Expressions 96
Substitution 97
Exponents in algebra 98
Expanding parentheses 99
Expanding quadratics 100
Factoring 101
Factoring quadratics 102
Factoring harder quadratic expressions 104
The difference of two squares 105
Algebraic fractions 106
Adding and subtracting algebraic fractions 107
Multiplying and dividing algebraic fractions 108
Formulas 109
Rearranging formulas 110
Functions 111
Inverse functions 112
Composite functions 113
Powers and calculations
Higher powers and estimating powers 115
Roots 116
Negative powers 117
Multiplying and dividing with powers 118
Raising a power to a power 119
Fractional powers and roots 120
Practice questions: Calculating with powers 121
Irrational square roots and irrational numbers 122
Simplifying square root expressions 123
Irrational square roots in fractions 124
Exact calculations 124
Scientific notation 126
Multiplying and dividing with scientific notation 127
Adding and subtracting with scientific notation 128
Equations and graphs
Equations 130
Solving simple equations 131
Solving harder equations 132
Equations with parentheses 133
Simultaneous equations 134
Practice question: Real-world simultaneous equations 136
Solving simple quadratic equations 137
Solving harder quadratic equations 138
Completing the square 139
How to complete the square 140
The quadratic formula 141
Practice question: Choosing a method for quadratic problems 142
Trial and error 143
The coordinate grid 144
Linear graphs 145
Equation of a line 146
Parallel and perpendicular lines 147
Length and midpoint of a line segment 148
Quadratic graphs 149
Quadratics in the real world 150
Solving simple equations using graphs 152
Solving harder equations using graphs 153
Inequaiities 154
Graphing linear inequalities 155
Quadratic inequaiities 156
Ratio and proportion
Ratios 158
Dividing in a given ratio 159
Direct proportion 160
Inverse proportion 161
Unitary method 162
Scaling method 163
Proportion 164
Comparing proportions 165
Proportion equations 166
Practice questions: Ratio and proportion 167
Geometry
Vectors 169
Working with vectors 170
Adding and subtracting vectors 171
Multiplying vectors 172
Practice question: Vectors and geometry 173
Translations 174
Reflections 175
Rotations 176
Constructing rotations 177
Dilations 178
Fractional and negative dilations 179
Scaling area and volume 180
Practice questions: Combinations of transformations 181
Scale drawings 182
Bearings 183
Constructing perpendicular lines 184
Constructing angles 185
Loci 186
Practice questions: Using loci 187
Congruent and similar shapes 188
Congruent triangles 189
Similar triangles 190
Practice questions: Similarity and congruence 191
Constructing triangles 192
Circle theorems 1 193
Circle theorems 2 194
Trigonometry
The Pythagorean theorem 196
Trigonometry 197
Sine, cosine, and tangent 198
Finding lengths and angles 199
Special angles 200
The law of sines 201
The law of cosines 202
Area of a triangle 203
Practice question: Using trigonometry 204
Angles of elevation and depression 205
Pythagoras in 3D 206
Practice question: 3D trigonometry 207
Probability
Probability scale 209
Calculating probability 210
Mutually exclusive events 211
Counting outcomes 212
Probability of two events 213
Tree diagrams 214
Conditional probability 215
Conditional probability tables 216
Venn diagrams 217
Venn diagrams and probability 218
Relative frequency 219
Frequency trees 220
Probability distributions 221
Statistics
Statistical inquiry 223
Types of data 224
Populations and samples 225
Frequency tables 226
Bar charts 227
Pictograms 228
Line graphs 229
Pie charts 230
Mean, median, mode, and range 231
Frequency tables and typical values 232
Standard deviation 234
Practice question: Using standard deviation 235
Cumulative frequency 236
Quartiles 237
Histograms 238
Drawing histograms 239
Time series 240
Box plots 241
Practice questions: Comparing distributions 242
Scatter graphs 243
Lines of best fit 244
Further graphs
Distance-time graphs 246
Speed-time graphs 247
Area under a curve 248
Slope of a curve 249
Linear real-life graphs 250
Nonlinear real-life graphs 251
Domain and range of a function 252
Cubic graphs 254
Reciprocal graphs 255
Exponential graphs 256
Trigonometric graphs 258
Transformations of graphs 260
Equation of a circle 262
Sequences
Number sequences 265
Term-to-term rule 266
Position-to-term rule 267
Finding the nth term 268
The nth term formula 269
Arithmetic pattern sequences 270
Arithmetic series 271
Square and cube number sequences 272
The triangular number sequence 273
Quadratic sequences 274
Geometric sequences 276
The Fibonacci sequence 278
Glossary 280
Index 284
Acknowledgments 288
