Mathematical Methods Unit 1 and 2

Prerequisites

An average performance of C or above in the Year 10 Mathematics Methods Analysis course.

Course Description

Mathematical Methods Units 1 and 2 are pre-requisites for Mathematical Methods Units 3 and 4, and for Specialist Mathematics Units 3 and 4.

Mathematical Methods is a course designed for students who have a solid understanding of Year 10 Mathematical content and who are interested in studying courses at a tertiary level which require a basis of mathematics. CAS technology is used throughout the course to support learning and in assessment. The mathematics explores complex concepts including Calculus. The course moves quickly through the concepts to complete the VCAA study design requirements requiring students to complete much of the consolidation of the concepts in their study and home learning time.

Areas of Study

Algebra, number and structure

Solution of equations of functions.
Review of algebraic processes.
Numeric approximations to solving equations.

Calculus

Average and instantaneous rates.
Gradient of the tangent function.
Derivative of simple functions including first principles.
Applications of differentiation, including stationary points, maximum and minimum problems.
Anti-differentiation.

Functions, Relations and Graphs

Definitions and properties of functions.
Graphs of polynomial and power functions, their transformations and inverses.
Circular functions, their properties and graphs.
Exponential functions, their properties and graphs.
Logarithmic functions and their properties and graphs.

Data Analysis, Probability and Statistics

Elementary and compound events and their representations.
Addition rule, conditional probability and independent events.
Addition and multiplication principles for counting.

Assessment

Outcomes	Assessment Tasks
Outcomes	(school-assessed coursework)
Define and explain the key concepts and be able to apply a range of related mathematical routines and procedures.	Assignments. Summaries. Tests.
Apply mathematical procedures in non-routine contexts and to analyse and discuss these applications of mathematics.	Modelling tasks. Problem-solving. Mathematical investigations.
Use numerical, graphical, symbolic and statistical technology to produce results and carry out analysis in situations involving problem-solving, modelling or investigative techniques.	Based on performance in a selection of tasks completed in achieving the outcomes above which incorporate the effective and appropriate use of technology.

Overall Final Assessment

End of Semester Examination – 1.5 hours.