Math does not need to be difficult. This book, complete with exercises and answers, forms a course which will take you from beginner or intermediate level to being a confident mathematician. This book includes: simple step-by-step explanations, to help you grasp new topics or those that have previously confused you; practice questions throughout, to help you embed your learning and improve your confidence; and end of chapter summaries, to help you remember the key points you've learned--all in one great-value book, so you don't need any separate workbooks or course books.
Chapters include: number, angles, fractions, two-dimensional shapes, decimals, statistics, directed numbers, graphs, measurement, perimeter and area, algebraic, three-dimensional shapes, ratio and proportion, pythagoras' theorem and trigonometry, indices and standard form.
Author(s): Hugh Neill; Trevor Johnson
Series: Teach Yourself
Publisher: Teach Yourself
Year: 2018
Language: English
Pages: 553
Title......Page 2
Contents......Page 3
Welcome to Mathematics: A complete introduction!......Page 10
Introduction......Page 11
1 Number......Page 14
1.1 Introduction – place value......Page 15
1.2 Arithmetic – the four operations......Page 17
1.3 Order of operations......Page 19
1.4 Problems which use arithmetic......Page 22
1.5 Special numbers......Page 24
1.6 Multiples, factors and primes......Page 27
2 Angles......Page 31
2.2 Angles......Page 32
2.3 Measuring and drawing angles......Page 36
2.4 Using angle facts......Page 38
2.5 Parallel lines......Page 41
2.6 Bearings......Page 45
3 Fractions......Page 50
3.2 What is a fraction?......Page 51
3.3 Which fraction is bigger?......Page 52
3.4 Simplifying fractions......Page 53
3.5 Improper fractions......Page 55
3.6 Adding and subtracting fractions......Page 58
3.7 Multiplication of fractions......Page 61
3.8 Fractions of quantities......Page 62
3.9 Division of fractions......Page 63
3.10 A number as a fraction of another number......Page 65
4 Two-dimensional shapes......Page 69
4.2 Triangles......Page 70
4.3 Constructing triangles......Page 77
4.4 Quadrilaterals......Page 79
4.5 Polygons......Page 84
4.6 Interior and exterior angles......Page 85
4.7 Symmetries of regular polygons......Page 88
4.8 Congruent shapes......Page 89
4.9 Tessellations......Page 90
5 Decimals......Page 97
5.2 Place value......Page 98
5.4 Converting fractions to decimals 1......Page 102
5.5 Addition and subtraction......Page 104
5.6 Multiplication of decimals......Page 106
5.7 Division of decimals......Page 110
5.8 Converting fractions to decimals 2......Page 114
6 Statistics 1......Page 119
6.2 Collection of data......Page 120
6.3 Pictograms......Page 121
6.4 Bar charts......Page 122
6.5 Pie charts......Page 126
6.6 Line graphs......Page 129
6.7 Scatter graphs......Page 133
6.8 Discrete and continuous data......Page 138
6.9 Grouping data......Page 139
7 Directed numbers......Page 147
7.2 Ordering directed numbers......Page 148
7.3 Addition and subtraction......Page 150
7.4 Multiplication and division......Page 153
7.5 Using a calculator......Page 157
8 Graphs 1......Page 159
8.1 Coordinates......Page 160
8.2 Straight-line graphs......Page 163
8.3 Lines parallel to the axes......Page 169
9 Measurement......Page 175
9.1 The metric system......Page 176
9.2 Imperial units......Page 178
9.3 Converting between metric and imperial units......Page 180
9.4 Choosing suitable units......Page 182
10 Perimeter and area......Page 186
10.1 Perimeter......Page 187
10.2 Area......Page 190
10.3 Area of a rectangle......Page 192
10.4 Area of a parallelogram......Page 195
10.5 Area of a triangle......Page 196
10.6 Area of a trapezium......Page 200
11 Algebraic expressions......Page 204
11.2 Writing expressions......Page 205
11.3 Simplifying expressions......Page 208
11.4 Evaluating expressions......Page 211
11.5 Squaring......Page 213
11.6 Brackets......Page 214
11.7 Factorizing expressions......Page 218
11.8 Indices......Page 220
11.9 Laws of indices......Page 222
11.10 Simplifying expressions with indices......Page 225
12 Approximation......Page 232
12.2 Rounding whole numbers......Page 233
12.3 Rounding with decimals......Page 235
12.4 Significant figures......Page 239
12.5 Estimates......Page 242
12.6 Rounding in practical problems......Page 244
12.7 Accuracy of measurements......Page 245
13 Equations 1......Page 249
13.2 Finding missing numbers......Page 250
13.3 Solving linear equations......Page 251
13.4 Equations with brackets......Page 258
13.5 Solving problems using equations......Page 260
13.6 Solving inequalities......Page 262
14 Percentages......Page 266
14.2 Percentages, decimals, fractions......Page 267
14.3 Percentages of quantities......Page 272
14.4 Increasing and decreasing quantities......Page 275
14.5 One quantity as a percentage of another quantity......Page 277
14.6 Percentage increases......Page 279
14.7 Using multipliers......Page 280
15 Formulae......Page 285
15.1 What is a formula?......Page 286
15.2 Evaluating terms other than the subject......Page 288
15.3 Changing the subject of a formula......Page 290
16 Circles......Page 294
16.1 Introduction......Page 295
16.2 Circumference of a circle......Page 297
16.3 Area of a circle......Page 300
16.4 Two properties of circles......Page 303
17 Probability......Page 309
17.1 Introduction......Page 310
17.2 Relative frequency......Page 311
17.3 Probability of a single event......Page 312
17.4 Two events......Page 316
17.5 Tree diagrams......Page 321
17.6 Expected frequency......Page 326
18 Three-dimensional shapes......Page 330
18.1 Introduction......Page 331
18.2 Nets and surface area......Page 334
18.3 Volume of a cuboid......Page 338
18.4 Volume of a prism......Page 340
18.5 Weight of a prism......Page 344
19 Ratio and proportion......Page 349
19.1 What is a ratio?......Page 350
19.2 Scales......Page 352
19.3 Using ratio......Page 355
19.4 Direct proportion......Page 358
19.5 Inverse proportion......Page 361
20 Pythagoras’ theorem and trigonometry......Page 365
20.1 Pythagoras’ theorem......Page 366
20.2 Using Pythagoras’ theorem......Page 367
20.3 Proof of Pythagoras’ theorem......Page 372
20.4 Pythagoras’ theorem problems......Page 373
20.6 The tangent ratio......Page 375
20.7 Values of the tangent......Page 377
20.8 Using tangents......Page 379
20.9 Sine and cosine......Page 382
21 Indices and standard form......Page 389
21.1 Indices......Page 390
21.2 Laws of indices......Page 391
21.3 Prime factors......Page 392
21.4 Highest common factor......Page 394
21.5 Lowest common multiple......Page 396
21.6 Standard form – large numbers......Page 398
21.7 Standard form – small numbers......Page 401
21.8 Standard form calculations......Page 403
22 Statistics 2......Page 407
22.2 The mode......Page 408
22.3 The median......Page 409
22.4 The mean......Page 410
22.5 The range......Page 414
22.6 Frequency tables......Page 415
22.7 Grouped frequency tables......Page 417
23 Graphs 2......Page 425
23.1 Equations of straight lines......Page 426
23.2 Drawing straight-line graphs......Page 429
23.3 The gradient of a straight line......Page 433
23.4 Curved graphs......Page 438
24 Equations 2......Page 445
24.1 Simultaneous equations......Page 446
24.2 Algebraic methods......Page 448
24.3 Quadratic expressions......Page 453
24.4 Factorizing quadratic expressions......Page 456
24.5 Quadratic equations......Page 459
24.6 Solution by factorizing......Page 461
24.7 Cubic equations......Page 464
Answers......Page 470
Taking it further......Page 548
Copyright......Page 553
