Sample chapters for download
Topic 1 (Algebra)
Examination Practice Sets 1 and 2
Solutions to Topic 1 (Algebra)
Solutions to Examination Practice Sets 1 and 2
About the book
This aim of this Guide is to help students prepare for the Mathematics HL final examinations. The Guide has three distinct sections:
- the first part covers all seven topics in the course. Each topic begins with a succinct summary of important concepts followed by a set of ‘skill builder’ questions. The number of ‘skill builder’ questions has been increased in this second edition.
- the second part comprises fifteen ‘exam practice’ sets, with about 26 questions in each. In this second edition, each exam practice set is categorised as ‘calculator’ or ‘no calculator’ in response to the introduction of a calculator-free examination paper.
- the third part provides the fully worked solutions to all the skill builder questions and examination practice sets, altogether a total of almost 700 questions.
Good examination techniques come from good examination preparation and practice – and we hope this Guide will help you succeed.
Table of contents
| Mathematics HL Core Exam Preparation & Practice Guide (2nd edition) |
Page | No. of additional questions | |
| 1 | ALGEBRA | 5 | |
| Sequences and series | 5 | ||
| Exponentials and logarithms | 5 | ||
| Complex numbers | 5 | ||
| Counting and the binomial theorem | 5 | ||
| Mathematical induction | 6 | ||
| Skill builder questions | 6 | 79 | |
| 2 | FUNCTIONS AND EQUATIONS | 8 | |
| Functions f : x → f(x) or y = f(x) | 8 | ||
| Graphs of functions | 9 | ||
| Quadratic functions | 9 | ||
| Quadratic equations | 9 | ||
| Inequalities in one variable | 9 | ||
| Real polynomials | 9 | ||
| Exponential and logarithmic functions | 10 | ||
| Skill builder questions | 10 | 54 | |
| 3 | CIRCULAR FUNCTIONS AND TRIGONOMETRY | 11 | |
| The general sine function | 12 | ||
| Other trigonometric functions | 12 | ||
| Trigonometric identities | 12 | ||
| Trigonometric equations | 12 | ||
| Skill builder questions | 12 | 42 | |
| 4 | MATRICES | 13 | |
| Skill builder questions | 14 | 26 | |
| 5 | VECTORS | 15 | |
| Lines | 15 | ||
| Planes | 16 | ||
| Intersection of planes | 16 | ||
| Skill builder questions | 16 | 24 | |
| 6 | STATISTICS AND PROBABILITY | 17 | |
| Descriptive statistics | 17 | ||
| Probability | 18 | ||
| Discrete random variables | 18 | ||
| Continuous random variables | 19 | ||
| Skill builder questions | 19 | 23 | |
| 7 | CALCULUS | 20 | |
| Limits | 20 | ||
| Differentiation | 21 | ||
| Implicit differentiation | 21 | ||
| Properties of curves | 21 | ||
| Kinematic problems | 21 | ||
| Optimisation problems | 21 | ||
| Integration | 21 | ||
| Solids of revolution | 22 | ||
| Differential equations | 22 | ||
| Skill builder questions | 22 | 39 | |
| EXAMINATION PRACTICE SETS | 23 | ||
| Exam Practice Set 1 No calculators | 23 | 26 | |
| Exam Practice Set 2 Calculators | 24 | 26 | |
| Exam Practice Set 3 No calculators | 26 | 26 | |
| Exam Practice Set 4 Calculators | 27 | 26 | |
| Exam Practice Set 5 No calculators | 29 | 26 | |
| Exam Practice Set 6 Calculators | 30 | 26 | |
| Exam Practice Set 7 No calculators | 31 | 26 | |
| Exam Practice Set 8 Calculators | 32 | 26 | |
| Exam Practice Set 9 No calculators | 33 | 26 | |
| Exam Practice Set 10 Calculators | 34 | 26 | |
| Exam Practice Set 11 No calculators | 35 | 26 | |
| Exam Practice Set 12 Calculators | 36 | 26 | |
| Exam Practice Set 13 No calculators | 38 | 26 | |
| Exam Practice Set 14 Calculators | 38 | 26 | |
| Exam Practice Set 15 Calculators | 40 | 26 | |
| Total: 677 | |||
| SOLUTIONS | 42 | ||
| Solutions to Topic 1 (Algebra) | 42 | ||
| Solutions to Topic 2 (Functions and equations) | 51 | ||
| Solutions to Topic 3 (Circular functions and trigonometry) | 57 | ||
| Solutions to Topic 4 (Matrices) | 61 | ||
| Solutions to Topic 5 (Vectors) | 64 | ||
| Solutions to Topic 6 (Statistics and probability) | 67 | ||
| Solutions to Topic 7 (Calculus) | 71 | ||
| Solutions to Examination Practice Set 1 | 76 | ||
| Solutions to Examination Practice Set 2 | 80 | ||
| Solutions to Examination Practice Set 3 | 83 | ||
| Solutions to Examination Practice Set 4 | 87 | ||
| Solutions to Examination Practice Set 5 | 92 | ||
| Solutions to Examination Practice Set 6 | 97 | ||
| Solutions to Examination Practice Set 7 | 100 | ||
| Solutions to Examination Practice Set 8 | 104 | ||
| Solutions to Examination Practice Set 9 | 109 | ||
| Solutions to Examination Practice Set 10 | 113 | ||
| Solutions to Examination Practice Set 11 | 117 | ||
| Solutions to Examination Practice Set 12 | 121 | ||
| Solutions to Examination Practice Set 13 | 125 | ||
| Solutions to Examination Practice Set 14 | 129 | ||
| Solutions to Examination Practice Set 15 | 133 |