Mathematics: Core Topics HL-Textbook

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 ??/?6 and ??/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