Mathematical Methods

Unit 1-2

Entry

It is required that students successfully complete the Pre VCE Math Methods course to a high standard before entering VCE Mathematical Methods Unit 1 and 2. It is ESSENTIAL THAT A STUDENT IS RECOMMENDED FOR THE SUBJECT BY THEIR TEACHER. This is a prerequisite in order for students to demonstrate the expected knowledge, skills and applications of VCE Mathematical Methods Units 1 and 2.  

Subject Overview

Mathematical Methods Units 1 and 2 provide an introductory study of simple elementary functions of a single real variable - algebra, calculus, probability and statistics, and their applications - in a variety of practical and theoretical contexts. They are designed as preparation for Mathematical Methods Units 3 and 4 and contain assumed knowledge and skills for these units. The focus of Unit 1 is the study of simple algebraic functions and the areas of study are ‘Functions and graphs’, ‘Algebra’, ‘Calculus’ and ‘Probability and statistics’. At the end of Unit 1, students are expected to have covered the content outlined in each Unit 1 area of study - with the exception of ‘Algebra’, which extends across Units 1 and 2. This content should be presented so there is a balanced and progressive development of skills and knowledge from each of the four areas of study, with connections between and across the areas of study being developed consistently throughout both Units 1 and 2.

In Unit 2, students focus on the study of simple transcendental functions and the calculus of simple algebraic functions. The areas of study are ‘Functions and graphs’, ‘Algebra’, ‘Calculus’ and ‘Probability and statistics’. At the end of Unit 2, students are expected to have covered the material outlined in each Unit 2 area of study. Material from the ‘Functions and graphs’, ‘Algebra’, ‘Calculus’ and ‘Probability and statistics’ areas of study should be organised so there is a clear progression of skills and knowledge from Unit 1 to Unit 2 in each area of study.

In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs and differentiation - 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 the unit as applicable.

Assessment

Satisfactory completion:

The award of satisfactory completion for a unit is based on whether the student has demonstrated the set of three outcomes specified for the unit. Teachers use a variety of learning activities and assessment tasks that provide a range of opportunities for students to demonstrate the key knowledge and key skills in the outcomes.

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

Outcome 1:

On completion of this 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.

Demonstration of achievement of Outcome 1 should be based on the student's performance on a selection of the following assessment tasks:

  • Assignments

  • Tests

  • Summary or review notes

Outcome 2:

On completion of this unit, the student should be able to apply mathematical processes in non-routine contexts, including situations requiring problem-solving, modelling or investigative techniques or approaches, 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.

Demonstration of achievement of Outcome 2 should be based on the student's performance on a selection of the following assessment tasks:

  • Modelling tasks

  • Problem-solving tasks

  • Mathematical investigations

Outcome 3:

On completion of this unit, the student should be able to 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 skills outlined in all the areas of study.

Demonstration of achievement of Outcome 3 should be based on the student’s performance on aspects of tasks completed in demonstrating achievement of Outcomes 1 and 2 that incorporate opportunity for the effective and appropriate use of technology.

Learning activities

Textbook and worksheet exercises, classroom-based exercises, online revision activities, application tasks

Key skills required

Mathematical skills and understanding, graphing calculator (CAS) technology, application of mathematical skills and knowledge