Mathematical Methods and Analysis

Prerequisites

It is recommended that an average of D or higher is achieved in Year 9 Mathematics.

Course Description

This course aligns with the Year 10 Victorian Curriculum 10/10A standards and strands and is the equivalent level to Mainstream Mathematics students have engaged in during the Middle School. This course is a prerequisite for Year 11 IB Mathematics Analysis and Approaches (MAA) – Standard Level and High Level or VCE Mathematical Methods Units 1 and 2.

Throughout the Year 10 Mathematics course, students build on skills obtained from previous study of Mathematics in the areas Number and Algebra, Measurement and Geometry, and Probability and Statistics. The course follows the standards set by the Victorian Curriculum for Year 10 and components of the 10A Mathematics to prepare students for VCE and IB MAA.

Year 10 Mathematics is a year-long course. Subject changes must abide by the Semester 1 subject change guidelines set by Senior School Curriculum with requests to change reviewed by the Leader of Learning Mathematics and availability. Students’ choice of mathematics is determined by their capability and potential to engage in the learning. Courses are designed to completed as a yearlong program.

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.

Essential Questions

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 factorisation and equation solving.
Manipulating and solving indicial, logarithmic, trigonometric and polynomial equations.

Measurement and Geometry

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