Mathematics

Tutorials

• Animated graphs
  Part of a presentation on functions that review aspects of logarithmic and exponential functions with links to a slide show presentation on non-linear functions
• Derivative of exponents 
  A tutorial on the derivation of the exponential function, with links to MathView and Java demonstrations.
• Exponential decay  
  A presentation of an application of logarithms in modelling exponential decay.
• Exponential growth 
  A presentation of an application of logarithms in modelling exponential decay.
• Exponential review 
  A synopsis with links to exercises (no answers).
• Family of exponential functions 
  An animation of a family of exponential functions. (MathView)
• Family of log functions 
  An animation of a family of logarithmic functions. (MathView)
• Graphs in the Mathematics Course
  A synopsis of nine functions and their graphs, with links to an animated slide show.

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.
• Exponential exercises and graphs 
  A series of six questions at an advanced level with links to hints, answers and a synopsis.
• Indices and logs (T/F quiz) 
  A series of 20 true/false questions, with links to summary details.
• Interesting exponential growth question 
  One interesting question of moderate difficulty with links to hints, solutions and a synopsis.
• Natural logarithm exercises (some Extension 1 standard) 
  A series of four question of moderate difficulty with links to hints, solutions and a synopsis.

Resources

• Investigations with exponential and logarithmic functions 
  'Reflections' article by Mary Coupland & Jules Harnett, incorporating investigations of 'shakes, quakes, and stars'
• e as a limit 
  A synopsis and animation of the number e. (Java applet)
• Approximation of log function 
  An investigation of the exponential series and a power series. (MathView)
• Comparison of exponential and polynomial functions 
  An animated graphs demonstrating the difference between an exponential function and a polynomial. (MathView)
• Comparison of exponential and polynomial functions 
  A graphical comparison of an exponential and a polynomial, with links to animated presentations.
• Exponential fit 
  An investigation on using exponential functions to fit different data sets, with links to spreadsheet.
• Exponential graph 
  A graphical illustration of an exponential graph with links to an animation, and the Mathematica file.
• Exponential growth of bacteria 
  A question and answer from the pages of Dr Math.
• Exponential growth of compound interest 
  Worked examples on the application of simple and compound interest formulas.
• General exponential graph 
  A graph of an exponential function.
• General exponentials (with graphics caculator) 
  An investigation on Euler's number using a graphics calculator.
• Log/exponential graph (example) 
  A graphical illustraation of the difference between an exponential and logarithmic function.
• Read off e value (dynamic graph) 
  A snapshot of an exponential function, which has been zoomed in at the y-intercept.
• Tangent lines to log functions  
  Graphical illustration of a logarithmic function and the tangent to the curve, with links to presentations for simulation on graphics calculators.
• Various ways to introduce e 
  'Reflections' article by Mary Coupland, incorporating historical, graphical and practical perspectives.

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