## Mathematical Methods

### Unit 1 & 2

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 areas of study for Mathematical Methods Units 1 & 2 are:

Functions and graphs - graphical representation of simple algebraic functions and the key features of functions and their graphs

Algebra - algebra of polynomial functions of low degree, algebra of simple transcendental functions and transformations of the plane

Calculus - constant and average rates of change, instantaneous rate of change of a function, first principles approach to differentiation, differentiation and anti-differentiation by rule

Probability and statistics - the concepts of event, frequency, probability and representation of finite sample spaces and events; complementary, mutually exclusive, conditional and independent events, rules for computation of probabilities for compound events; counting principles and techniques and their application to probability and the law of total probability

In undertaking this unit, 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.

#### Outcomes

Students should be able to

• define and explain key concepts, and apply a range of related mathematical routines and procedures.
• 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.
• 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.

### Unit 3 & 4

These units are completely prescribed and extend the study of simple elementary functions to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts.

They also provide background for further study in, for example, science, humanities, economics and medicine.

Assumed knowledge and skills for Mathematical Methods Units 3 and 4 are contained in Mathematical Methods Units 1 and 2.

Areas of study for Mathematical Methods Units 3 & 4 are:

Functions and graphs - transformations of the plane; behaviour of elementary functions of a single real variable; key features of their graphs.

Algebra - algebra of functions, including composition of functions, simple functional relations, inverse functions and the solution of equations; the use of graphical and numerical approaches for problems involving equations

Calculus -  graphical treatment of limits, continuity and differentiability of functions, differentiation, anti-differentiation and integration of these functions

Probability and statistics - discrete and continuous random variables, their representation using tables, probability functions; the calculation and interpretation of central measures and measures of spread; statistical inference for sample proportions

#### 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