Area of Study: Rates of change: This area of study covers constant and average rates of change and an informal treatment of instantaneous rate of change of a function in familiar contexts, including graphical and numerical approaches to the measurement of constant, average and instantaneous rates of change.

Outcome 1
On completion of this unit the student will be able to define and apply a range of related mathematical routines and procedures including:

• constant rate of change (linear functions), use of gradient as a measure of rate of change;
• average rate of change, practical examples of average rates of change such as average speed;
• use of gradient of a tangent at a point on the curve to describe instantaneous rate of change of y = ƒ(x) with respect to x, practical examples of instantaneous rates of change, such as speedometer readings
• motion graphs, construction and interpretation of displacement–time and velocity–time graphs and informal treatment of the relationship between displacement–time and velocity–time graphs.

Outcome 2
On the completion of this unit the student will be able to apply mathematical processes in non-routine contexts, and analyse and discuss these applications of mathematics including the ability to:

• specify the relevance of key mathematical content from Rates of Change area of study relating to motion of an F1 car on the Australian Grand Prix track in the investigation of the curriculum framing questions;
• make inferences from analysis and use these to draw valid conclusions related to this investigation;
• communicate conclusions using both mathematical expression and everyday language, in particular, interpretation of mathematics with respect to this investigation.

© State of Victoria 2008  
Alan Thwaites is involved in the Intel Teach Program and developed this portfolio, in collaboration with other teachers.
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