Topic 1 (Algebra)
Examination Practice Sets 1 and 2
Solutions to Topic 1 (Algebra)
Solutions to Examination Practice Sets 1 and 2
This aim of this Guide is to help you prepare for the Mathematics HL final examinations. The Guide has three distinct sections:
Good examination techniques come from good examination preparation and practice – and we hope this Guide will help you succeed.
| 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 |
