Specialist Mathematics Unit 3 and 4

Prerequisites

Successful completion of Mathematical Methods Units 1 and 2 and Specialist Mathematics Units 1 and 2. Mathematical Methods Units 3 and 4 must be studied concurrently or have been successfully completed.

Course Description

Specialist Mathematics is the most challenging of the VCE Mathematics courses with complex and sophisticated mathematical concepts taught. It expands on many topics that are covered in Mathematical Methods Units 3 and 4 and explores additional topics such as proof, vectors, mechanics, complex numbers, differential equations, Boolean algebra and statistical prediction.

The appropriate use of CAS technology to support and develop the learning process is incorporated throughout the course.

Areas of Study

Discrete Mathematics

Graphs of transformations of the above functions.

Functions Relations and Graphs

Rational Functions.
Simple quotient functions.
Sketching functions.

Algebra, number and structure

Complex Numbers.
Proofs.
Polynomials.

Calculus

Differential and integral calculas.
Differential equations.
Kinematics: rectilinear motion.

Space and Measurement

Vectors.
Vector and cartesian equations.
Vector Calculus.

Data Analysis, probability and statistics

Distribution of linear combinations of random variables.
Distribution of the sample mean.
Confidence intervals of the population mean.
Hypothesis testing.

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 and 4 Coursework	School-assessed		40
2	Written Examination 1	November	1 hour	20
3	Written Examination 2	November	2 hours	40