Topic 1 (Algebra)
Examination Practice Sets 1 and 2
Solutions to Topic 1 (Algebra)
Solutions to Examination Practice Sets 1 and 2
The aim of this Guide is to help you prepare for the Mathematics SL final examinations. The Guide has three separate sections:
the first section covers all seven Topics in the course. For the main elements within each Topic, there is a succinct summary of key facts and concepts followed by two sets of Skill Builder Questions categorised as ‘no calculators’ and ‘calculators’. There is a total of 421 Skill Builder Questions in the first section.
the second section comprises six Examination Practice Sets: three ‘no calculators’ and three ‘calculators’. There are 20 questions in each set, a total of 120 questions altogether.
the third section provides fully worked solutions for all the Skill Builder Questions and the Examination Practice Sets, an overall total of 541 questions.
Good examination techniques come from good examination preparation and practice.
We hope this Guide will help you succeed.
| Mathematics SL – Exam Preparation & Practice Guide (2nd edition) | Page | No. of additional questions | |
| 1 | ALGEBRA | 5 | |
| Sequences and series | 5 | ||
| Exponentials and logarithms | 5 | ||
| The binomial theorem | 5 | ||
| Skill builder questions (no calculators) | 5 | 21 | |
| Skill builder questions (calculators) | 6 | 21 | |
| 2 | FUNCTIONS AND EQUATIONS | 7 | |
| Functions f : x → f(x) or y = f(x) | 7 | ||
| Graphs of functions | 7 | ||
| Linear functions | 7 | ||
| Quadratic functions | 7 | ||
| Quadratic equations | 8 | ||
| Exponential and logarithmic functions | 8 | ||
| Exponential equations | 8 | ||
| Skill builder questions (no calculators) | 8 | 23 | |
| Skill builder questions (calculators) | 9 | 14 | |
| 3 | CIRCULAR FUNCTIONS AND TRIGONOMETRY | 10 | |
| Non-right angled triangle trigonometry | 11 | ||
| Periodic Functions | 11 | ||
| Transforming y = sin x | 11 | ||
| The general sine function | 11 | ||
| The cosine function | 11 | ||
| The tangent function | 11 | ||
| Trigonometric identities | 11 | ||
| Trigonometric equations | 12 | ||
| Skill builder questions (no calculators) | 12 | 43 | |
| Skill builder questions (calculators) | 13 | 21 | |
| 4 | MATRICES | 14 | |
| Matrix operations | 14 | ||
| Matrix multiplication | 14 | ||
| Matrix determinants | 14 | ||
| Matrix inverses | 14 | ||
| Skill builder questions (no calculators) | 15 | 30 | |
| Skill builder questions (calculators) | 16 | 15 | |
| 5 | VECTORS | 17 | |
| Vectors in geometric form | 17 | ||
| Vectors in component form | 17 | ||
| Position vectors in 2-D | 17 | ||
| Position vectors in 3-D | 17 | ||
| Properties of vectors | 18 | ||
| Lines | 18 | ||
| Skill builder questions (no calculators) | 18 | 31 | |
| Skill builder questions (calculators) | 19 | 20 | |
| 6 | STATISTICS AND PROBABILITY | 20 | |
| Populations and samples | 20 | ||
| Types of data and its representation | 20 | ||
| Descriptive statistics | 21 | ||
| Probability | 21 | ||
| Discrete random variables | 21 | ||
| Continuous random variables | 22 | ||
| Skill builder questions (no calculators) | 22 | 15 | |
| Skill builder questions (calculators) | 23 | 36 | |
| 7 | CALCULUS | 26 | |
| Limits | 26 | ||
| Differentiation | 26 | ||
| Kinematic problems | 27 | ||
| Properties of curves | 27 | ||
| Optimisation problems | 27 | ||
| Integration | 28 | ||
| Solids of revolution | 28 | ||
| Skill builder questions (no calculators) | 29 | 90 | |
| Skill builder questions (calculators) | 33 | 41 | |
| EXAMINATION PRACTICE SETS | 36 | ||
| 1 No calculators | 36 | 20 | |
| 2 Calculators | 37 | 20 | |
| 3 No calculators | 39 | 20 | |
| 4 Calculators | 40 | 20 | |
| 5 No calculators | 42 | 20 | |
| 6 Calculators | 43 | 20 | |
| Total: 541 | |||
| SOLUTIONS | 46 | ||
| Topic 1 (Algebra) | |||
| No calculators | 46 | ||
| Calculators | 47 | ||
| Topic 2 (Functions and equations) | |||
| No calculators | 50 | ||
| Calculators | 53 | ||
| Topic 3 (Circular functions and trigonometry) | |||
| No calculators | 55 | ||
| Calculators | 59 | ||
| Topic 4 (Matrices) | |||
| No calculators | 61 | ||
| Calculators | 64 | ||
| Topic 5 (Vectors) | |||
| No calculators | 66 | ||
| Calculators | 69 | ||
| Topic 6 (Statistics and probability) | |||
| No calculators | 72 | ||
| Calculators | 74 | ||
| Topic 7 (Calculus) | |||
| No calculators | 77 | ||
| Calculators | 91 | ||
| Examination practice set 1 | 99 | ||
| Examination practice set 2 | 103 | ||
| Examination practice set 3 | 106 | ||
| Examination practice set 4 | 109 | ||
| Examination practice set 5 | 113 | ||
| Examination practice set 6 | 116 |
