Unit 1 & 2

Specialist Mathematics Units 1 and 2 provide 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 and reasoning. This study has a focus on interest in the discipline of mathematics in its own right and investigation of a broad range of applications, as well as development of a sound background for further studies in mathematics and mathematics related fields.

Mathematical Methods Units 1 and 2 and Specialist Mathematics Units 1 and 2, taken in conjunction, provide a comprehensive preparation for Specialist Mathematics Units 3 and 4.

The areas of study for Units 1 and 2 of Specialist Mathematics come from:

Arithmetic and number 
- Number systems and recursion; principles of counting

Geometry, measurement and trigonometry 
- Geometry in the plane and proof 
     

Graphs of linear and non-linear relations - Graphs of non-linear relations; kinematics


Algebra and structure - Logic and algebra


Transformations, trigonometry and matrices - Linear transformations of the plane

Discrete mathematics - Graph theory


Statistics - Simulation, sampling and sampling distributions

Outcomes

Students should be able to:

• define and explain key concepts in relation to the topics from the selected areas of study, and apply a range of related mathematical routines and procedures.
• apply mathematical processes in non-routine contexts, and analyse and discuss these applications of mathematics in at least three areas of study.
• use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches in at least three areas of study.

Unit 3 & 4

Specialist Mathematics Units 3 and 4 assumes familiarity with the key knowledge and skills from Mathematical Methods Units 1 and 2, the key knowledge and skills from Specialist Mathematics Units 1 and 2 topics 'Number systems and recursion' and 'Geometry in the plane and proof', and concurrent or previous study of Mathematical Methods Units 3 and 4.

The areas of study 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 complex numbers, vectors, differential equations, mechanics and statistical inference.

Functions and graphs - inverse circular functions, reciprocal functions, rational functions and other simple quotient functions, the absolute value function

Algebra - partial fractions; the arithmetic and algebra of complex numbers, including polar form; points and curves in the complex plane;

Calculus - advanced calculus techniques for analytic and numeric differentiation and integration; curve sketching, evaluation of arc length, area and volume, differential equations and kinematics

Vectors - arithmetic and algebra of vectors, proof of geometric results using vectors, vector representation of curves in the plane and vector kinematics in one and two dimensions

Mechanics
- Newtonian mechanics, for both constant and variable acceleration

Probability and statistics
- statistical inference related to the definition and distribution of sample means, simulations and confidence intervals 


Outcomes

Students 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.
• apply mathematical processes, with an emphasis on general cases, in non-routine contexts, and analyse and discuss these applications of mathematics.
• select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Assessment

Contact Teacher - Glenys Kidd