## Description

Core Topics SL-Textbook

Mathematics: Core Topics SL has been written for the IB Diploma Programme courses Mathematics: Analysis and Approaches SL, and Mathematics: Applications and Interpretation SL, for first teaching in August 2019, and first assessment in May 2021.

The book contains the content that is common to both courses. This material can all be taught first, giving the potential to teach all the SL students together from this book at the start of the course.

A set of background knowledge chapters is accessible online for those who want to ensure that they have the prerequisite levels of understanding for the courses.

The material is presented in a clear, easy-to-follow style, free from unnecessary distractions, while effort has been made to contextualise questions so that students can relate concepts to everyday use.

Each chapter in this new Core Topics SL-Textbook begins with an Opening Problem, offering an insight into the application of the mathematics that will be studied in the chapter. Important information and key notes are highlighted, while worked examples provide step-by-step instructions with concise and relevant explanations. Discussions, Activities, Investigations, and Research exercises are used throughout the chapters to develop understanding, problem solving, and reasoning.

Discussion topics for Theory of Knowledge are included throughout the book.

Table of Contents

Mathematics: Core Topics SL

1 STRAIGHT LINES 19

A The equation of a line 20

B Graphing a straight line 26

C Perpendicular bisectors 28

D Simultaneous equations 30

E Problem solving with simultaneous equations 34

Review set 1A 36

Review set 1B 37

2 SETS AND VENN DIAGRAMS 39

A Sets 40

B Intersection and union 42

C Complement of a set 44

D Special number sets 45

E Interval notation 47

F Venn diagrams 51

G Venn diagram regions 54

H Problem solving with Venn diagrams 56

Review set 2A 59

Review set 2B 61

3 SURDS AND EXPONENTS 63

A Surds and other radicals 64

B Division by surds 68

C Exponents 70

D Laws of exponents 71

E Scientific notation 77

Review set 3A 80

Review set 3B 81

4 EQUATIONS 83

A Equations of the form x2 = k 84

B Power equations 85

C Equations in factored form 87

D Quadratic equations 88

E Solving polynomial equations using technology 95

F Solving other equations using technology 97

Review set 4A 98

Review set 4B 99

5 SEQUENCES AND SERIES 101

A Number sequences 102

B Arithmetic sequences 105

C Geometric sequences 110

D Growth and decay 113

E Financial mathematics 115

F Series 124

G Arithmetic series 127

H Finite geometric series 132

I Infinite geometric series 136

Review set 5A 139

Review set 5B 142

6 MEASUREMENT 145

A Circles, arcs, and sectors 146

B Surface area 149

C Volume 154

D Capacity 164

Review set 6A 167

Review set 6B 169

7 RIGHT ANGLED TRIANGLE TRIGONOMETRY 171

A The trigonometric ratios 173

B Finding side lengths 176

C Finding angles 178

D Right angles in geometric figures 180

E Problem solving with trigonometry 185

F True bearings 190

G The angle between a line and a plane 193

Review set 7A 196

Review set 7B 198

8 NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY 201

A The unit circle 202

B The area of a triangle 204

C The cosine rule 208

D The sine rule 212

E Problem solving with trigonometry 215

F The ambiguous case of the sine rule 219

Review set 8A 222

Review set 8B 224

9 POINTS IN SPACE 227

A Points in space 228

B Measurement 230

C Trigonometry 232

Review set 9A 235

Review set 9B 237

10 PROBABILITY 239

A Experimental probability 241

B Two-way tables 245

C Sample space and events 247

D Theoretical probability 250

E The addition law of probability 258

F Independent events 260

G Dependent events 264

H Conditional probability 268

I Formal definition of independence 272

J Making predictions using probability 273

Review set 10A 277

Review set 10B 279

11 SAMPLING AND DATA 281

A Errors in sampling 282

B Sampling methods 285

C Types of data 291

D Simple discrete data 293

E Grouped discrete data 296

F Continuous data 297

Review set 11A 301

Review set 11B 302

12 STATISTICS 305

A Measuring the centre of data 306

B Choosing the appropriate measure 311

C Using frequency tables 313

D Grouped data 316

E Measuring the spread of data 319

F Box and whisker diagrams 323

G Outliers 326

H Parallel box and whisker diagrams 329

I Cumulative frequency graphs 332

J Variance and standard deviation 336

Review set 12A 344

Review set 12B 347

ANSWERS 351

INDEX 387

Michael Haese, Mark Humphries, Chris Sangwin, Ngoc Vo – Haese Mathematics