Mathematical Methods and Analysis

Prerequisites

An average of C or higher in Year 9 Mathematics.

Course Description

This course is a prerequisite for Year 11 IB Mathematics MAA – Standard Level and High Level or VCE Mathematical Methods Units 1 and 2. Students who have achieved an average of C or above in Year 9 Mathematics are encouraged to select this subject.

Throughout the Year 10 Mathematics course, students build on skills obtained from previous study of extended Mathematics in the areas Number and Algebra, Measurement and Geometry, and Probability and Statistics.

The course follows the Victorian Curriculum for Year 10 and components of the 10A Mathematics to prepare students for the complexity of VCE Mathematical Methods, Specialist and IB MAA.

Students who have complete the Year 9A Mathematics course with an average of B or higher will continue to the Year 10A Mathematical Methods and Analysis course which will follow the Victorian 10A Mathematics curriculum. The course will continue to extend and challenge students with non-routine complex problems solving. The Year 10A Mathematical Methods and Analysis course is by invite only and with approval from the Leader of Learning Mathematics.

Problem-solving and modelling is developed progressively throughout the course using real life situations to improve the student's ability to think laterally and write coherently on a mathematical topic. CAS technology is used extensively in the course, both as an instructional aid and a computational tool, while notebook computers are an integral part of the course.

Essential Questions

What are the relationships between the angles and sides in polygons and circles?
What does the gradient of a straight line represent and how is this useful in the real world?
How is our number system structured to include surds and logarithms?
Where do quadratic relationships occur and how do we model these?
What is probability and how do we model the chance of events occurring?
What is the difference between a linear and quadratic equation and how do we solve them?

Areas of Study

Number and Algebra

Revision of fractions, decimals, percentage and ratios.
Surds, indices and logarithms.
Interpreting formulae, algebraic simplification and expansion.
Linear, quadratic and cubic factorisation and equation solving.
Manipulating and solving indicial, logarithmic, trigonometric and polynomial equations.

Measurement and Geometry

Spatial relations, geometric objects and mensuration (length, area, volume and capacity).
Pythagoras's Theorem.
Circle geometry theorems, arc length, congruence and similarity.
Graphs of linear, quadratic, cubic, exponential and logarithmic functions.
Finding lengths and angles in right angled and other triangles in two- and three-dimensions using formulae.
Applications, the unit circle and the graphical representation and trigonometric functions.

Probability and Statistics

Use of tree diagrams, Venn diagrams and two way tables to calculate theoretical probability.
Independent and mutually exclusive events.

Assessment