HSC tutorials and examples by syllabus topic

The aim of this section of the site is to collect resources from around the web and organise them by syllabus topic so that it can provide a useful reference for your study. If you have any resources that you would like to add, please e-mail me your suggestions.

Please note that Phoenix Mathematics does not endorse the content of these sites nor does the content reflect the way that Phoenix teaches. We have simply compiled a list of links which you may find useful in your study.

Mathematics course

Topic 1 - Basic arithmetic and algebra

• Absolute values
• Inequalities
• Simultaneous equations
• Quadratic equations

Topic 2 - Plane geometry

• Congruent triangles

Topic 3 - Probability

• Random experiments, probability of a given result
• Sum and product of results

Topic 7 - Series and Applications

• Arithmetic series
• Geometric series

Topic 10 - Geometrical Application of Differentiation

• Second derivative
• Sketching of simple curves (towards the bottom)
• Stationary points on curves

Topic 13 - The Trigonometric functions

• Radian measure of angles

Extension 1

Topic 7 - Series and Application

• Mathematical induction

Topic 14 - Application of Calculus to the Physical World

• Projectile motion (skip the notes on relative velocity)
• Projectile motion applet (play around and find the maximum range)
• Rates of change

Topic 15 - Inverse Functions and the Inverse Trigonometric Functions

• The inverse trigonometric functions
• Derivatives of inverse trigonometric functions

Topic 16 - Polynomials

• Newton's method

Extension 2

Topic 2 - Complex numbers

• Arithmetic of complex numbers
• Complex numbers summary
• Quiz on complex numbers

Topic 3 - Conics

• Ellipse
• Descriptive properties of conics
• Hyperbola

Topic 4 - Integration

• Integration by parts
• Integration of rational functions