Notes/Mathematics
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Mathematics is "a group of related subjects, including Algebra, Geometry, Trigonometry and Calculus, concerned with the study of number, quantity, shape and space..." (Collins Dictionary of Mathematics).
Mathematics, often seen as a burden and an incomprehensible mountain of numbers, weird signs and strange language, is a subject that can open many doors to those who study it. Although its application and immediate use it not often visible at the outset, your mathematical study will develop your analytical and reasoning skills, as well as providing a foundation for further study in sciences and engineering. Many people wonder about how maths can ever be delightful — the answer is that the stimulation to further yourself comes from solving problems that before seemed insurmountable.
Note: I am slowly rewriting these notes, but the old versions will continue to be available by clicking the "old versions" link. The new notes are somewhat longer, but I hope that they remain useful as revision guides. The new documents are:
- Parametric Equations and the Parabola
- Polynomials
Contents |
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How to study maths: a quick guide
- Practise regularly and practise with commitment. Go over the work you did at school at night, and try to do the exercises set, and maybe find other challenging exercises to do as well.
- Make sure you know the basics before moving on to more advanced topics. In particular, make sure you can readily recall formulas and techniques.
- Before exams, do some past papers in the specified time limit. That will give you a feel as to what to expect in the real thing.
- Don't spend too much time on one question in the exam. If you can't do it, move on to the next question, and go back later.
- For Extension 2 students, don't worry if you can't do every question. At least give each question a go, and you should find that your success rate will gradually improve.
- Ask if you need help!
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HSC (Year 12) and Preliminary (Year 11) resources
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Mathematics Extension 2 (4-unit)
| Resource | Type | Versions |
|---|---|---|
| Fort Street High School 2003 Trial Contains questions and fully worked solutions. | Exam | |
| Fort Street High School Complex Numbers Assessment Task Contains questions on complex numbers and fully worked solutions. | Exam | |
| Integration (Extension 2) Contains notes and common examples on the topic of integration. | Notes | |
| Conics Contains notes and common examples in selected areas of conic sections. | Notes |
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Mathematics Extension 1 (3-unit)
| Resource | Type | Versions |
|---|---|---|
| Fort Street High School 2003 Trial Contains questions and fully worked solutions. | Exam | |
| Fundamental Limit Proves the fundamental limit, and provides examples of its use. | Notes | |
| Inequations (Extension 1) Shows step-by-step examples of how to solve more difficult inequalities. | Notes | |
| Parametric Equations and the Parabola NEW! Provides complete discussions and proofs of changing from parametric to cartesian equations, equations of tangents and normals, intersections of tangents and normals, focal chords, chord of contact, and commonly tested properties of parabolas. | Notes | old version |
| Polynomials NEW! Summarises remainder and factor theorems, relationship between the roots and approximation of roots. | Notes | old version |
| Trigonometric Equations Discusses transformations, t-results and general solutions. | Notes |
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Mathematics (2-unit)
| Resource | Type | Versions |
|---|---|---|
| Circle Geometry Provides definitions and common circle properties. Labelled diagrams included. | Notes | |
| Circular Functions Summarises radian measure, arcs, sectors, segments and simple sin and cos curves. | Notes | |
| Exponential and Logarithmic Functions Discusses differential and integral calculus involving exponential and logarithmic functions. | Notes | |
| Geometry Provides a complete summary of lines, types of angles, concurrent and parallel lines, properties of polygons, tests for congruency, intercept properties, similar triangles and the theorem of Pythagoras. | Notes | |
| Inequations Discusses axioms, square roots and absolute values. | Notes | |
| Integration Summarises approximation methods, and definite and indefinite integrals. | Notes | |
| Logarithms and Indices Outlines the laws of logarithms, indices, change of base and the conversion between index and logarithm forms. | Notes | |
| Basic Arithmetic and Algebra Discusses the real number system, factorisation, quadratics and surds. | Notes | |
| Probability Discusses terminology used in probability, mutually exclusive and independent events and the use of diagrams. | Notes | |
| Quadratic Equations Provides details of roots of quadratics, completing the square, quadratic formula and inequalities. | Notes | |
| Relations and Functions Defines commonly used functions terms, and summarises odd and even functions, graphs, straight lines, parabolas, circles, semi-circles, exponentials, hyperbolas and regions. | Notes | |
| Trigonometry Summarises ratios, special angles, elevation and depression, sine rule, cosine rule, area of a triangle, graphs of trignometric functions, identities and 3-D trignometry. | Notes |
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General resources
| Resource | Type | Versions |
|---|---|---|
| Areas and Volumes Outlines the formulas used to calculate the areas and volumes of common shapes and solids. Diagrams given. | Notes | |
| Maths Corner 1: Stick Tree Provides a complete analysis of the dimensions of a fractal tree, where each branch divides into two, each half the length of the parent branch. | Article | |
| Maths Corner 2: Infinity Explains the confounding and often bewildering concept of infinity, and briefly touches on the rules for operations with infinity and transfinite numbers. Just how many infinities are there? | Article |
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Year 10 resources
| Resource | Type | Versions |
|---|---|---|
| Circle Geometry Discusses properties of chords, angles and tangents, and lists several important proofs. | Notes | |
| Polynomials and Logarithms Summarises curve sketching, polynomial definitions, remainder and factor theorems, different graphs, function notation, inverse functions, logarithmic laws and graphs of logarithmic and exponential functions. | Notes | |
| Quadratics Discusses quadratic equations, parabolas, concavity, solutions to quadratics, factorisation, completing the square, quadratic formula, as well as different types of graphs, including straight lines, parabolas, expontentials, hyperbolas and circles. | Notes | |
| Yearly Exam Notes Provides notes on surds, rates and variations, surface area and volume and consumer arithmetic. | Notes |
