Mathematics
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Tutorials | Assessment | Resources
Tutorials
- Continuity of functions
A page with links to summaries related to continuity of functions. - Definition of tangent (Java)
A synopsis of the derivative of a function with links to discussions and visual examples. - Demonstation of tangent by zooming in
An animated presentation of approximating the slope of a tangent by zooming in at the point of contact. - Differentiation using function of a function
A synopsis of the chain rule with some worked examples. - Explore definition of continuity (piecewise function) with MathView
An animated demonstration of determining continuity of a function with links to explanations. - Formal definition of limits
A page with links to summaries related to formal definition of functions. - Limits
A page with links to summaries related to limits. - Limits to infinity
A page with links to summaries related to limits to infinity. - Problems with graphing piecewise functions
An animated investigation of continuity of a point by using a MathView tool. (MathView) - Rules of differentiation
A page with links to summaries related to rules for differentiation. - Tangent as the limit of secants
An animated investigation of the construction of a tangent line. (MathView) - Tangent lines and the derivative
A page with links to summaries related to tangent lines and the derivative. - Tangents as introduction to derivatives
A synopsis of the topic with links to other demonstrations and discussion pages. - Using the definition of tangent for fractional indices
An algebraic and graphical demonstration of function which is not differentiable at a point. (MathView) - Using the definition of tangent for quotient rule
A demonstration of finding a derivative from first principles. (MathView) - Using the definition of tangent for radicals
A demonstration of finding a derivative from first principles. (MathView)
Assessment
- 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. - Drill questions for the chain rule (various functions)
A synopsis with a set of examples with links to discussion and drill questions. - Drill questions for the product rule (various functions)
A synopsis with a set of examples with links to discussion and drill questions. - Drill questions for the quotient rule (various functions)
A synopsis with a set of examples with links to discussion and drill questions. - Evaluating limits
A quiz on limits with links to check the answer. - Introductory calculus (T/F quiz)
A series of twenty true/false questions with answers provided, - Quiz on mixed derivative of functions (various functions)
A series of sixty questions on differentiation with a score provided at the end. - Quiz using definition of continuity
A series of seventy five questions on definition of continuity with a score provided at the end.
Resources
- Approximation for tangent at a point
An animated presentation of the tangent line to a function. (MathView) - Definition of derivatives (Visicalc)
A synopsis with links to examples and discussion on the definition of derivatives. - Derivative surfer (applet)
Brilliant applet demonstrating the effect of 'surfing the waves' of a curve to generate derivative values and the resultant graph. - Differentials and differences
A synopsis with links to an animation presenting a tangent to a curve, - Differentiation formulae
A synopsis of the rules of differentiation with links to discussion pages and examples. - Dynamic examination of slope
A graphical illustration of the approximation of the tangent of a function. - Example of application of chain rule
An interactive presentation of differentiation from first principles. (MathView) - Example of application of product rule
An interactive presentation of differentiation from first principles. (MathView) - Example of application of quotient rule
An interactive presentation of differentiation from first principles. (MathView) - Example of derivative of a sum
An interactive presentation of differentiation from first principles. (MathView) - Example of derivative of power rule
An interactive presentation of differentiation from first principles. (MathView) - Example of derivative of quadratic
An interactive presentation of differentiation from first principles. (MathView) - Example of derivative of quotient
An interactive presentation of differentiation from first principles. (MathView) - Example of derivative of radical
An interactive presentation of differentiation from first principles. (MathView) - Gathering evidence of horizontal asymptote
A tabulated illustration of determining the horizontal asymptote with links to instructions for graphics calculators. - Horizontal asymptote
A graphical investigation of the limit of a function for varying values of coefficients. (MathView) - How the ball bounces
Three brilliant animations exploring the graphical representation of a bouncing ball (consider continuity & differentiability). - Introduction to limits
A synopsis with examples and links to exercises, drill questions and instructions for graphics calculators. - Limits of x, sin x, tan x
Applet which explores visually and numerically the relationship between x in radians, sin x and tan x as x-> 0. - Secants and tangents
A synopsis of tangents and the curve with a link to an animation illustrating the similarity of the two lines. - Summary of the derivative
A synopsis of Introductory Calculus with links to a tutorial. - The limit of sinx/x
A synopsis of the topic with links to graphical demonstration of the limit. - Vertical asymptote
An animated presentation of the limiting value of a function as the value approaches the vertical aymptote. (MathView) - Visually finding a tangent
An animated presentation of instructions to find the tangent lines on a graphics calculator. (Flash) - Zooming in on a tangent (dynamic)
An animated demonstration of zooming in on a tangent at the point of contact.