Specialist Mathematics
Unit 3-4
Entry
Specialist Mathematics Units 3 and 4 assumes successful completion of Mathematical Methods Units 1 and 2, successful completion of Specialist Mathematics Units 1 and 2 and concurrent or previous study of Mathematical Methods Units 3 and 4. Together, these cover the assumed knowledge and skills for Specialist Mathematics, which are drawn on as applicable in the development of content from the areas of study and key knowledge and skills for the outcomes.
Subject Overview
Specialist Mathematics Units 3 and 4 consist of the areas of study ‘Functions and graphs’, ‘Algebra’, ‘Calculus’, ‘Vectors’, ‘Mechanics’ and ‘Probability and statistics’. The development of course content should highlight mathematical structure, reasoning and applications across a range of modelling contexts, with an appropriate selection of content for each of Unit 3 and Unit 4. The selection of content for Unit 3 and Unit 4 should be constructed so there is a balanced and progressive development of knowledge and skills, with connections among the areas of study being developed as appropriate across Unit 3 and Unit 4.
In Unit 3, a study of Specialist Mathematics would typically include content from ‘Functions and graphs’ and a selection of material from the ‘Algebra’, ‘Calculus’ and ‘Vectors’ areas of study. In Unit 4, this selection would typically consist of the remaining content from the ‘Algebra’, ‘Calculus’, and ‘Vectors’ areas of study and the content from the ‘Mechanics’ and ‘Probability and statistics’ areas of study.
In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational, real and complex arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs, differentiation, anti-differentiation and integration and inference - with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.
Outcomes
For each unit, the student is required to demonstrate achievement of three outcomes. As a set, these outcomes encompass all the areas of study for each unit. For each of Unit 3 and Unit 4, the outcomes apply to the content from the areas of study selected for that unit.
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. To achieve this outcome, the student will draw on knowledge and skills outlined in all the areas of study.
Outcome 2:
On completion of each unit, the student should be able to apply mathematical processes - with an emphasis on general cases and in non-routine contexts - and analyse and discuss these applications of mathematics. To achieve this outcome, the student will draw on knowledge and skills outlined in one or more areas of study.
Outcome 3:
On completion of each unit, the student should be able to 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. To achieve this outcome, the student will draw on knowledge and related skills outlined in all the areas of study.
Assessment
Satisfactory completion
The award of satisfactory completion for a unit is based on a decision that the student has demonstrated achievement of the set of outcomes specified for the unit. This decision will be based on the teacher’s assessment of the student’s performance on assessment tasks designated for the unit. Students are also required to meet the minimum work requirements for each unit as well as the TC VCE minimum attendance requirement of 80 per cent.
A non-satisfactory outcome for Unit 3 or Unit 4 implies that the student will not receive a study score for this subject.
Assessment
The Victorian Curriculum and Assessment Authority will supervise the assessment of all students undertaking Units 3 and 4. In the study of VCE Mathematics, students’ level of achievement will be determined by School-assessed Coursework (SACs) and two end-of-year examinations.
Unit 3 School-assessed Coursework: 20 %
Unit 4 School-assessed Coursework: 20 %
Examination 1: 20 %
Examination 2: 40 %
School-based assessment
UNIT 3
UNIT 4
External assessment
Examination 1:
Description
This examination comprises short-answer and some extended-answer questions covering all areas of study in relation to Outcome 1. It is designed to assess students’ knowledge of mathematical concepts, their skills in carrying out mathematical algorithms without the use of technology and their ability to apply concepts and skills.
Conditions
The examination will be one hour in duration and no technology (calculators or software) or notes of any kind are permitted. A sheet of formulas will be provided with the examination. VCAA examination rules will apply.
Contribution to final assessment
The examination will contribute 20%.
Examination 2:
Description
This examination comprises multiple-choice questions and extended-answer questions covering all areas of study in relation to all three outcomes, with an emphasis on Outcome 2. The examination is designed to assess students’ ability to understand and communicate mathematical ideas and to interpret, analyse and solve both routine and non-routine problems.
Conditions
The examination will be two hours in duration and student access to an approved technology with numerical, graphical, symbolic and statistical functionality will be assumed. One bound reference - text (which may be annotated) or lecture pad - may be brought into the examination. VCAA examination rules will apply.
Contribution to final assessment
The examination will contribute 40 %