Mathematics
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study guide | mathematics
extension 2 | mathematics extension
1 | mathematics | general | year 10
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
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!
HSC (Year 12) and Preliminary (Year 11) resources
Mathematics Extension 2 (4-unit)
Mathematics Extension 1 (3-unit)
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 |
|
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 |
|
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 |
|
|
