Mathematics

Tutorials

Definite integrals
A synopsis of the topic which includes the definition and properties of definite integrals, with links to further demonstrations (Java or Flash) and tutorials.
Definite integrals evaluation
A presentation on evaluating an integral using Riemann sums, with links to further information. (Flash)
Definite integrals evaluation by areas
A presentation of calculating the area under a curve using circumscribed rectangles, with links to further demonstrations (Java or Flash).
Demonstration of Riemann sums
An animated demonstration of approximation of the area under a sine curve using rectangles. (MathView)
Demonstration of disk method for volume
A graphical illustration of a volume by revolution, with animation and a table of values to determine the volume.
Fundamental theorem of calculus
An animated investigation on how well the animation application understands the fundamental theorem of calculus. (MathView)
Summation notation and examples
Review of summation and notation with links to Flash and Java presentations.

A set of HSC past papers & advice on the examination
Hints and answers from past exam papers (formerly '2 Unit'), and past articles from Sydney Morning Herald advice to students.
Integration (including log/exponential): T/F quiz
A series of 20 True/False questions, with links to summary details.

Approximation of areas
Approximation of the area under a curve using inscribed and circumscribed rectangles, with links to examples and approximation for the given function.
Area under curve applet (animated)
An animated demonstration of the calculation of the area under the curve. (Java)
Demonstration of Simpson's rule
Graphical animation of an approximation for an integral using Simpson's rule, with a table of values.
Demonstration of trapezoidal rule
Graphical animation of the approximation of an integral using trapezoids, with a table of values.
Evaluation of definite integral
A presentation of calculating the area under a curve using circumscribed rectangles, with links to further demonstrations (Java or Flash).
How Simpson's rule works
Graphical illustration of the approximation of an integral using Simpson's rule.
Table of integrals (with proofs)
Proofs and discussions of theorems
The integral
A synopsis of the Integral, with links to true / false quiz with answers.
Trapezoidal rule example
A visualisation of the use of trapeziums to approximate the area under a curve.
Upper & lower rectangles (animation)
A visualisation of the area of upper and lower rectangles in the calculation of the area within a sine curve.
Upper and lower rectangles
A presentation on using Riemann sums to approximate the area bounded by the graph and the axis.
Volume of revolution
An animated demonstration of volume of revolution of a triangle. (Java)