VCE | SPECIALIST MATHEMATICS

Specialist Mathematics Units 1–4 provide for the study of various mathematical structures, reasoning and proof. The areas of study in Units 3 and 4 extend content from Mathematical Methods Units 3 and 4 to include rational and other quotient functions as well as other advanced mathematics topics such as logic and proof, complex numbers, vectors, differential equations, kinematics, and statistical inference. They also provide background for advanced studies in mathematics and other STEM fields. Study of Specialist Mathematics Units 3 and 4 assumes concurrent study or previous completion of Mathematical Methods Units 3 and 4.

YEAR 11

SPECIALIST MATHEMATICS (Units 1 & 2)

This subject provides a course of study for students who wish to undertake an in-depth study of mathematics, with an emphasis on concepts, skills and processes related to mathematical structure, modelling, problem-solving, reasoning and proof. This study has a focus on interest in the discipline of mathematics and investigation of a broad range of applications, as well as development of a sound background for further studies in mathematics and mathematics (STEM) related fields. It is also designed as preparation for Specialist Mathematics Units 3 and 4 and contains assumed knowledge and skills for these units.

Areas of Study

• Algebra and number (notation, definitions, reasoning and proofs applied to number systems, networks, sets, logic and Boolean algebra, pseudocode and algorithms to describe a sequence of events leading to proofs in natural situations)

• Discrete mathematics (sequences and series, difference equations, combinatorics, permutations and combinations, matrices)

• Probability (sampling distributions, simulation of probability situations, description of data distributions)

• Measurement and space (circular functions, proofs and application of trigonometrical identities, transformations, vectors and their applications to displacement, velocity, statics and motion)

• Complex numbers (general solutions and calculations involving complex numbers)

• Functions and graphs (partial fractions, reciprocal and inverse circular functions, transformations of graphs)

In undertaking this unit, students are expected to be able to apply techniques, routines and processes with and without the use of technology. They are expected to be able to construct proofs and develop and interpret algorithms to solve problems. They should have the ability to work with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology is also developed throughout this subject.

Year 12

SPECIALIST MATHEMATICS (Units 3 & 4)

This subject focuses on mathematical structures, reasoning, proofs and algorithms across a range of modelling contexts.

Assumed knowledge and skills for Specialist Mathematics Units 3 and 4 are contained in Mathematical Methods Units 1 & 2, as well as Specialist Mathematics Units 1 and 2, and the concurrent study of Mathematical Methods Units 3 and 4. There will be a clear progression of skills from Unit 3 to Unit 4 across the year’s studies.

Areas of Study

• Discrete mathematics (logic, proof by deduction, implication, cases, contradiction, induction)

• Functions, graphs and relations (rational fractions, curve sketching, intercepts, asymptotes, stationary points, symmetry)

• Complex numbers (polar form, factorisation of polynomials, fundamental theorem of algebra)

• Calculus (differentiation, integration, combination of functions, curve sketching, differential equations, kinematics and modelling)

• Space and measurement (vectors, geometric proofs, vector kinematics in one, two and three dimensions, vector calculus)

• Probability (random variable distribution, statistical inference, confidence intervals, hypothesis testing for population statistics)

Students learn to apply computational thinking and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring investigative, modelling or problemsolving techniques or approaches. Students should also develop the ability to use relevant mental and by-hand approaches to estimation and computation. On completion of these units, students should be able to apply mathematical processes in non-routine contexts, including situations with some open-ended aspects requiring investigative, modelling or problem-solving techniques or approaches, and analyse and discuss these applications of mathematics.