Mathematics: Core Topics HL 1

Mathematics: Core Topics HL 1

Mathematics: Core Topics HL has been written for the IB Diploma Programme courses Mathematics: Analysis and Approaches HL, and Mathematics: Applications and Interpretation HL, 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 HL students together from this book at the start of the course.

This is the first of two books students will require for the completion of their HL Mathematics course. Upon the completion of this book, students progress to the particular HL textbook for their course: either Mathematics: Analysis and Approaches HL, or Mathematics: Applications and Interpretation HL. This is expected to occur approximately 6-7 months into the two-year course.

Table of Contents

Mathematics: Core Topics HL

1 STRAIGHT LINES 19
A Lines in the Cartesian plane 20
B Graphing a straight line 25
C Perpendicular bisectors 26
D Simultaneous equations 28
Review set 1A 30
Review set 1B 31

2 SETS AND VENN DIAGRAMS 33
A Sets 34
B Intersection and union 36
C Complement of a set 37
D Special number sets 38
E Interval notation 40
F Venn diagrams 43
G Venn diagram regions 46
H Problem solving with Venn diagrams 47
Review set 2A 50
Review set 2B 51

3 SURDS AND EXPONENTS 53
A Surds and other radicals 54
B Division by surds 58
C Exponents 59
D Laws of exponents 60
E Scientific notation 66
Review set 3A 69
Review set 3B 69

4 EQUATIONS 71
A Power equations 72
B Equations in factored form 74
C Quadratic equations 75
D Solving polynomial equations using technology 84
E Solving other equations using technology 86
Review set 4A 87
Review set 4B 88

5 SEQUENCES AND SERIES 89
A Number sequences 90
B Arithmetic sequences 92
C Geometric sequences 98
D Growth and decay 101
E Financial mathematics 103
F Series 111
G Arithmetic series 114
H Finite geometric series 119
I Infinite geometric series 123
Review set 5A 126
Review set 5B 128

6 MEASUREMENT 131
A Circles, arcs, and sectors 132
B Surface area 134
C Volume 140
D Capacity 150
Review set 6A 154
Review set 6B 155

7 RIGHT ANGLED TRIANGLE TRIGONOMETRY 157
A Trigonometric ratios 159
B Inverse trigonometric ratios 162
C Right angles in geometric figures 164
D Problem solving with trigonometry 169
E True bearings 174
F The angle between a line and a plane 176
Review set 7A 179
Review set 7B 181

8 THE UNIT CIRCLE AND RADIAN MEASURE 183
A Radian measure 184
B Arc length and sector area 186
C The unit circle 190
D Multiples of ​π/​6 and ​π/4​​ 196
E The Pythagorean identity 199
F Finding angles 201
G The equation of a straight line 203
Review set 8A 204
Review set 8B 205

9 NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY 207
A The area of a triangle 208
B The cosine rule 212
C The sine rule 216
D Problem solving with trigonometry 221
Review set 9A 228
Review set 9B 230

10 POINTS IN SPACE 233
A Points in space 234
B Measurement 236
C Trigonometry 240
Review set 10A 244
Review set 10B 245

11 PROBABILITY 247
A Experimental probability 249
B Two-way tables 253
C Sample space and events 255
D Theoretical probability 257
E Making predictions using probability 264
F The addition law of probability 265
G Independent events 267
H Dependent events 271
I Conditional probability 275
J Formal definition of independence 278
K Bayes’ theorem 280
Review set 11A 284
Review set 11B 286

12 SAMPLING AND DATA 289
A Errors in sampling and data collection 292
B Sampling methods 294
C Writing surveys 300
D Types of data 302
E Simple discrete data 304
F Grouped discrete data 308
G Continuous data 309
Review set 12A 312
Review set 12B 313

13 STATISTICS 315
A Measuring the centre of data 316
B Choosing the appropriate measure 321
C Using frequency tables 323
D Grouped data 326
E Measuring the spread of data 328
F Box and whisker diagrams 332
G Outliers 335
H Parallel box and whisker diagrams 337
I Cumulative frequency graphs 340
J Variance and standard deviation 344
Review set 13A 353
Review set 13B 356

14 QUADRATIC FUNCTIONS 359
A Quadratic functions 361
B Graphs of quadratic functions 362
C Using the discriminant 369
D Finding a quadratic from its graph 372
E The intersection of graphs 376
F Problem solving with quadratics 379
G Optimisation with quadratics 381
H Quadratic inequalities 385
Review set 14A 389
Review set 14B 390

15 FUNCTIONS 393
A Relations and functions 394
B Function notation 397
C Domain and range 400
D Rational functions 405
E Composite functions 410
F Inverse functions 414
Review set 15A 421
Review set 15B 423

16 TRANSFORMATIONS OF FUNCTIONS 425
A Translations 426
B Stretches 429
C Reflections 435
D Miscellaneous transformations 438
E The graph of y=1/​f(x)​​ 441
Review set 16A 443
Review set 16B 445

17 TRIGONOMETRIC FUNCTIONS 447
A Periodic behaviour 448
B The sine and cosine functions 452
C General sine and cosine functions 454
D Modelling periodic behaviour 459
E Fitting trigonometric models to data 461
F The tangent function 464
G Trigonometric equations 467
H Using trigonometric models 475
Review set 17A 477
Review set 17B 479

ANSWERS 483

INDEX 546

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