This book is published as a companion to the Haese & Harris Publications Mathematics HL CORE textbook. It offers coverage of the Options set out in the Mathematics HL course (first examinations 2006). Details of the Topics and authors are as follows:
The accompanying CD includes many interactive features, and it also includes coverage of an additional Topic, for Further Mathematics students: Euclidean Geometry (by Peter Blythe, United World College of SE Asia, Singapore)
Note: HL Options does not have a separate book of worked solutions – detailed solutions are given at the back of the textbook.
| HL TOPIC 8 (Further mathematics SL Topic 2) | |||
| STATISTICS AND PROBABILITY | 9 | ||
| A | Expectation algebra | 10 | |
| B | Cumulative distribution functions | 19 | |
| C | Distributions of the sample mean | 45 | |
| D | Confidence intervals for means and proportions | 60 | |
| E | Significance and hypothesis testing | 73 | |
| F | The Chi-squared distribution | 88 | |
| Review set 8A | 101 | ||
| Review set 8B | 104 | ||
| HL TOPIC 9 (Further mathematics SL Topic 3) | |||
| SETS, RELATIONS AND GROUPS | 109 | ||
| A | Sets | 110 | |
| B | Ordered pairs | 119 | |
| C | Functions | 131 | |
| D | Binary operations | 136 | |
| E | Groups | 145 | |
| F | Further groups | 159 | |
| Review set 9A | 166 | ||
| Review set 9B | 169 | ||
| HL TOPIC 10 (Further mathematics SL Topic 4) | |||
| SERIES AND DIFFERENTIAL EQUATIONS | 171 | ||
| A | Some properties of functions | 174 | |
| B | Sequences | 190 | |
| C | Infinite series | 199 | |
| D | Taylor and Maclaurin series | 223 | |
| E | First order differential equations | 229 | |
| Review set 10A | 242 | ||
| Review set 10B | 242 | ||
| Review set 10C | 243 | ||
| Review set 10D | 244 | ||
| Review set 10E | 245 | ||
| HL TOPIC 11 (Further mathematics SL Topic 5) | |||
| DISCRETE MATHEMATICS | 247 | ||
| A | NUMBER THEORY | 248 | |
| A.1 | Number theory introduction | 248 | |
| A.2 | Order properties and axioms | 249 | |
| A.3 | Divisibility, primality and the division algorithm | 256 | |
| A.4 | Gcd, lcm and the Euclidean algorithm | 263 | |
| A.5 | The linear Diophantine equation ax + by = c | 270 | |
| A.6 | Prime numbers | 274 | |
| A.7 | Linear congruence | 278 | |
| A.8 | The Chinese remainder theorem | 286 | |
| A.9 | Divisibility tests | 289 | |
| A.10 | Fermat’s little theorem | 292 | |
| B | GRAPH THEORY | 296 | |
| B.1 | Preliminary problems involving graph theory | 296 | |
| B.2 | Terminology | 297 | |
| B.3 | Fundamental results of graph theory | 301 | |
| B.4 | Journeys on graphs and their implication | 310 | |
| B.5 | Planar graphs | 316 | |
| B.6 | Trees and algorithms | 319 | |
| B.7 | The Chinese postman problem | 332 | |
| B.8 | The travelling salesman problem (TSP) | 336 | |
| Review set 11A | 339 | ||
| Review set 11B | 340 | ||
| Review set 11C | 341 | ||
| Review set 11D | 342 | ||
| Review set 11E | 343 | ||
| APPENDIX (Methods of proof) | 345 | ||
| ANSWERS | 351 | ||
| INDEX | |||