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VCE Mathematics

# 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 anti-derivative function.
• Derivative and anti-derivatives 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 maximum-minimum 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 (school-assessed 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 non-routine 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 problem-solving, 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 School-assessed 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