Mathematics: A Complete Introduction: Teach Yourself

Description

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. 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