Mathematics

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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!

Extension 2 Resources

Resource Type
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

Extension 1 Resources

Resource Type
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
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.
(old version)
Notes
Polynomials
Summarises remainder and factor theorems, relationship between the roots and approximation of roots.
(old version)
Notes
Trigonometric Equations
Discusses transformations, t-results and general solutions.
Notes

2-Unit Resources

Resource Type
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 and 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

Year 10 Resources

Resource Type
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

General Resources

Resource Type
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 an 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