## Specialist Mathematics

### 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

#### Units 1 and 2

The award of satisfactory completion for a unit is based on the teacher’s decision that the student has demonstrated achievement of the set of outcomes specified for the unit; determined by evidence gained through the assessment of a range of learning activities and tasks.

These tasks may include assignments; tests; summary or review notes; modelling tasks; problem-solving tasks and mathematical investigations.

Assessment tasks will include components to be completed with and without the use of technology as applicable to the outcomes.

#### Units 3 and 4

The award of satisfactory completion for a unit is based on the teacher’s decision that the student has demonstrated achievement of the set of outcomes specified for the unit; determined by evidence gained through the assessment of a range of learning activities and tasks.

A student’s level of achievement in Units 3 and 4 will be determined by a combination of School-Assessed Coursework (SACs) and external assessment.

- Unit 3 School-assessed Coursework: 17 per cent - one application task
- Unit 4 School-assessed Coursework: 17 per cent - two modelling tasks
- Units 3 and 4 Examination 1: 22 per cent - technology free examination
- Units 3 and 4 Examination 2: 44 per cent - access to approved technology

Contact Teacher - Glenys Kidd