Mathematical Methods Unit 3 and 4
Prerequisites
Successful completion of Mathematical Methods Units 1 and 2. Course Description
These units develop and extend the material listed for Mathematical Methods Units 1 and 2, and familiarity with this material is assumed. Students study material in the area of functions and graphs, algebra, calculus and probability and statistics. They make effective and appropriate use of CAS calculators during the course to enhance the learning of mathematics. Areas of Study
Algebra
 Review of polynomial algebra and properties such as symmetry.
 Inverse, composite and sums, differences and products of functions.
 Solution of equations including numeric, graphic and algebraic methods.
 Literal and simultaneous equations.
Calculus
 Review of the tangent and derivative function.
 Graphs of the derivative and antiderivative function.
 Derivative and antiderivatives of polynomial, power, circular and exponential and logarithmic functions.
 The chain, product and quotient rules for differentiation.
 informal treatment of the fundamental theorem of integral calculus.
 Application to curve sketching.
 Calculation of rates of change, equations of tangents, areas beneath and between curves, distance travelled and average function and maximumminimum problems.
Functions and Graphs
 Graphical representation of functions including polynomial, power, circular and exponential and logarithmic functions.
 Graphs of transformations of the above functions.
Statistics and Probability
 Discrete and continuous random variables including binomial and normal distributions.
 Means, variance and standard deviation.
 Probability density functions.
 Statistical inference including population parameters and sample statistics.
 Sample proportions and sample proportions as a random variable.
 Confidence intervals.
Assessment
Outcomes 
Assessment Tasks 
Marks Allocated 
(schoolassessed coursework) 
Students demonstrate satisfactory completion of all three outcomes in each assessment task.

 Define and explain key terms and concepts as specified in the content of the areas of study and apply a range of related mathematical routines and procedures.
 Apply processes in nonroutine contexts and analyse and discuss these applications.
 Select and appropriately use numeric, graphic and symbolic and statistical technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problemsolving, modelling or investigative techniques or approaches.

Application task (Unit 3).

50 
Modelling or problem solving task 1 (Unit 4).

25 
Statistical and probability modelling or problem solving task 2 (Unit 4). 
25 
Total Marks 
100 
Overall Final Assessment
Graded Assessment 
Title 
Assessment 
Exam Duration 
Contribution to Study Score (%) 
1 
Units 3 & 4 Coursework 
Schoolassessed 

34 
2 
Written Examination 1 
November 
1 hour 
22 
3 
Written Examination 2 
November 
2 hours 
44 
Reproduced by permission of the Victorian Curriculum and Assessment Authority, Victoria, Australia: www.vcaa.vic.edu.au
