TERTIARY & CAREER PATHWAYS:
Actuary, Auditor, Building Contractor, Computer Programmer, Data Processing Operator, Laboratory Worker, Teacher, Mathematician, Pilot, Survey Assistant.
This unit extends on the ideas covered in the core Mathematics course. It is designed to give students a head start and a preview of the VCE Specialist Mathematics Course. There are five main areas of study considered. The study of Number Systems is extended to cover geometric and arithmetic sequences and series. In Trigonometry non-right angle triangles are investigated. Vectors, Matrices and Differential Calculus are three areas that will be studied for the first time.
Learning Standards:
- Definitions of sequences and series, arithmetic and geometric sequences and their partial sums
- Sequences generated by recursion
- Solution of first order linear recurrence relations of the form with constant coefficients and their application to financial problems and population modelling.
- Right-angled triangles and solutions to problems involving right-angled triangles using sine, cosine and tangent
- Exact values of sine, cosine and tangent for 30, 45 and 60 degrees
- Two-dimensional applications including angles of depression and elevation, navigation and surveying in simple contexts
- Solution of triangles by the sine and cosine rules
- Areas of triangles, including the formula for Heron’s Law
- Concept of the position vector of a point in the Cartesian plane
- The representation of plane vectors as ordered pairs and directed line segments
- Addition of plane vectors, using components or the parallelogram rule
- Simple vector algebra (addition, subtraction, multiplication by a scalar)
- The representation of a vector in the form ai + bj where i and j are the standard orthogonal unit vectors
- Diagrammatic and graphical representation of empirical position–time data for a single particle in rectilinear motion, examples with variable velocity
- Qualitative graphical analysis of the relationship between position–time, velocity–time and acceleration–time graphs for simple cases of rectilinear motion involving variable acceleration
- Matrix notation, dimension and the use of matrices to represent data
- Matrix operations and algebra, determinants and matrix equations, and simple applications.
Assessment:
Assessment will be based on the completion of a variety of tasks including:
- Workbook Activities
- Homework Tasks
- Problem Solving and Reasoning Activities
- Topic Tests
Contribution to class and completion of class work may also be considered.
Prerequisites:N/A
Recommendations:
It is recommended the student has an overall average score of 80% or above in Year 9 Mathematics.
.png)