Complete Mathematics: Teach Yourself

Cover......Page 1
Book title......Page 4
Contents......Page 6
Personal introduction......Page 12
Only got a minute?......Page 13
Only got five minutes?......Page 15
Only got ten minutes?......Page 17
1.1 Introduction – place value......Page 20
1.2 Arithmetic – the four operations......Page 22
1.3 Order of operations......Page 23
1.4 Problems which use arithmetic......Page 26
1.5 Special numbers......Page 27
1.6 Multiples, factors and primes......Page 29
2.1 Introduction......Page 34
2.2 Angles......Page 35
2.3 Measuring and drawing angles......Page 37
2.4 Using angle facts......Page 39
2.5 Parallel lines......Page 41
2.6 Bearings......Page 44
3.2 What is a fraction?......Page 48
3.4 Simplifying fractions......Page 50
3.5 Improper fractions......Page 52
3.6 Adding and subtracting fractions......Page 53
3.7 Multiplication of fractions......Page 55
3.8 Fractions of quantities......Page 56
3.9 Division of fractions......Page 57
3.10 A number as a fraction of another number......Page 59
4.2 Triangles......Page 63
4.3 Constructing triangles......Page 67
4.4 Quadrilaterals......Page 69
4.5 Polygons......Page 71
4.6 Interior and exterior angles......Page 72
4.8 Congruent shapes......Page 74
4.9 Tessellations......Page 76
5.1 Introduction......Page 82
5.2 Place value......Page 83
5.3 Converting decimals to fractions......Page 85
5.4 Converting fractions to decimals 1......Page 86
5.5 Addition and subtraction......Page 87
5.6 Multiplication of decimals......Page 88
5.7 Division of decimals......Page 91
5.8 Converting fractions to decimals 2......Page 93
6.1 Introduction......Page 99
6.2 Collection of data......Page 100
6.3 Pictograms......Page 101
6.4 Bar charts......Page 102
6.5 Pie charts......Page 106
6.6 Line graphs......Page 108
6.7 Scatter graphs......Page 112
6.8 Discrete and continuous data......Page 115
6.9 Grouping data......Page 116
7.1 Introduction......Page 123
7.2 Ordering directed numbers......Page 124
7.3 Addition and subtraction......Page 125
7.4 Multiplication and division......Page 127
7.5 Using a calculator......Page 130
8.1 Coordinates......Page 132
8.2 Straight-line graphs......Page 135
8.3 Lines parallel to the axes......Page 140
9.1 The metric system......Page 144
9.2 Imperial units......Page 146
9.3 Converting between metric and imperial units......Page 148
9.4 Choosing suitable units......Page 149
10.1 Perimeter......Page 153
10.2 Area......Page 155
10.3 Area of a rectangle......Page 157
10.5 Area of a triangle......Page 160
10.6 Area of a trapezium......Page 163
11.2 Writing expressions......Page 167
11.3 Simplifying expressions......Page 170
11.4 Evaluating expressions......Page 172
11.6 Brackets......Page 174
11.7 Factorizing expressions......Page 177
11.8 Indices......Page 178
11.9 Laws of indices......Page 179
11.10 Simplifying expressions with indices......Page 182
12.2 Rounding whole numbers......Page 188
12.3 Rounding with decimals......Page 190
12.4 Significant figures......Page 193
12.5 Estimates......Page 195
12.6 Rounding in practical problems......Page 197
12.7 Accuracy of measurements......Page 198
13.1 Introduction......Page 201
13.3 Solving linear equations......Page 202
13.4 Equations with brackets......Page 207
13.5 Solving problems using equations......Page 208
13.6 Solving inequalities......Page 210
14.2 Percentages, decimals, fractions......Page 214
14.3 Percentages of quantities......Page 218
14.4 Increasing and decreasing quantities......Page 220
14.5 One quantity as a percentage of another quantity......Page 221
14.6 Percentage increases......Page 222
14.7 Using multipliers......Page 224
15.1 What is a formula?......Page 228
15.2 Evaluating terms other than the subject......Page 230
15.3 Changing the subject of a formula......Page 232
16.1 Introduction......Page 235
16.2 Circumference of a circle......Page 237
16.3 Area of a circle......Page 240
16.4 Two properties of circles......Page 243
17.1 Introduction......Page 248
17.2 Relative frequency......Page 249
17.3 Probability of a single event......Page 250
17.4 Two events......Page 253
17.5 Tree diagrams......Page 258
17.6 Expected frequency......Page 262
18.1 Introduction......Page 265
18.2 Nets and surface area......Page 268
18.3 Volume of a cuboid......Page 270
18.4 Volume of a prism......Page 272
18.5 Weight of a prism......Page 275
19.1 What is a ratio?......Page 279
19.2 Scales......Page 281
19.3 Using ratio......Page 284
19.4 Direct proportion......Page 286
19.5 Inverse proportion......Page 288
20.1 Pythagoras’ theorem......Page 292
20.2 Using Pythagoras’ theorem......Page 293
20.3 Proof of Pythagoras’ theorem......Page 297
20.4 Pythagoras’ theorem problems......Page 298
20.5 Trigonometry......Page 299
20.6 The tangent ratio......Page 300
20.7 Values of the tangent......Page 301
20.8 Using tangents......Page 302
20.9 Sine and cosine......Page 304
21.1 Indices......Page 311
21.2 Laws of indices......Page 312
21.3 Prime factors......Page 313
21.4 Highest common factor......Page 314
21.5 Lowest common multiple......Page 316
21.6 Standard form – large numbers......Page 317
21.7 Standard form – small numbers......Page 320
21.8 Standard form calculations......Page 321
22.2 The mode......Page 325
22.3 The median......Page 326
22.4 The mean......Page 328
22.5 The range......Page 331
22.6 Frequency tables......Page 332
22.7 Grouped frequency tables......Page 334
23.1 Equations of straight lines......Page 341
23.2 Drawing straight-line graphs......Page 344
23.3 The gradient of a straight line......Page 347
23.4 Curved graphs......Page 350
24.1 Simultaneous equations......Page 356
24.2 Algebraic methods......Page 358
24.3 Quadratic expressions......Page 362
24.4 Factorizing quadratic expressions......Page 364
24.5 Quadratic equations......Page 367
24.6 Solution by factorizing......Page 368
24.7 Cubic equations......Page 371
Answers......Page 377
Taking it further......Page 407
C......Page 412
F......Page 413
M......Page 414
P......Page 415
S......Page 416
Z......Page 417