Mathematical Methods Units 1 & 2

Mathematical Methods incorporates a range of skill areas including, but not limited to, algebra, trigonometry, probability and calculus. Skills developed in Mathematical Methods are applied to a range of practical contexts. The motion of a pendulum can be modeled using periodic functions. The relationship between the pendulum’s position and speed can be understood through a study of calculus. Radioactive decay can be modeled using exponential functions, rates of decay understood through a study of calculus. Games of chance, including those found in gaming venues are examined from a theoretical probability perspective. Students studying Mathematical Methods need to have a strong mathematical background and a commitment to study.

Structure

It is expected that students will have successfully completed ‘Advanced Mathematics’ in year 10 and study General Mathematics (Methods) Units 1 & 2 concurrently with Mathematical Methods Units 1 and 2. Students that do not study General Mathematics (Methods) may be required to undertake additional course work as prescribed by their teacher.

Students attempting Mathematical Methods are expected to have a sound background in number, algebra, function, and probability. Mathematical Methods Units 1 and 2 contain assumed knowledge and skills for Mathematical Methods Units 3 and 4.

Unit 1

The areas of study for Unit 1 are ‘Functions and graphs’, ‘Algebra’, ‘Rates of change and calculus’ and ‘Probability’. At the end of Unit 1, students will be expected to have covered the material outlined in each area of study, with the exception of ‘Algebra’ which should be seen as extending across Units 1 and 2.

Students are expected to be able to apply techniques, routines and processes involving arithmetic, algebraic manipulation, equation solving, graph sketching, differentiation and integration with and without the use of technology, as applicable. Students should have facility with relevant mental and by hand approaches in simple cases.

Students are encouraged to use graphics calculators, spreadsheets, statistical software, graphing packages or computer algebra systems as applicable across the areas of study, both in the learning of new material and the application of this material in a variety of different contexts.

Familiarity with determining the equation of a straight line from combinations of sufficient information about points on the line or the gradient of the line and familiarity with Pythagoras theorem and its application to finding the distance between two points is assumed. Students should also be familiar with quadratic and exponential functions, algebra and graphs, and basic concepts of probability.

Unit 2

The areas of study for Unit 2 are ‘Functions and graphs’, ‘Algebra’, ‘Rates of change and calculus’, and ‘Probability’. At the end of Unit 2, students will be expected to have covered the material outlined in each area of study.
Students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, algebraic manipulation, equation solving, graph sketching, differentiation and integration with and without the use of technology, as applicable. Students should be familiar with relevant mental and by hand approaches in simple cases.
Students are encouraged to use graphics calculators, spreadsheets, statistical software, graphing packages or computer algebra systems as applicable across the areas of study both in the learning of new material and the application of this material in a variety of different contexts.

Assessment

Outcome 1

On completion of each unit the student should be able to define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures.

Outcome 2

On completion of each unit the student should be able to apply mathematical processes in non-routine contexts, and analyse and discuss these applications of mathematics.

Outcome 3

On completion of each unit the student should be able to use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Note: Students undertaking Mathematical Methods Units 1 and 2 in 2008 will be expected to have access to a TI-84Plus graphics calculator. From 2009 students will be expected to have access to a TI-Nspire(CAS+) calculator. These calculators will be available for purchase through the school as applicable.

Pathways

• VCE Further Mathematics (Units 3 and 4)
• VCE Mathematical Methods (Units 3 and 4)
• VCE Specialist Mathematics (Units 3 and 4)

Students successfully completing both year 11 General Mathematics (Methods) and Mathematical Methods are recommended to study any one of the following combinations:

• Further Mathematics & Mathematical Methods
• Mathematical Methods only
• Mathematical Methods & Specialist Mathematics