VCE Specialist Mathematics Units 1 and 2 – Graphs of Linear and Non-Linear Relations

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5.1 Motions in Straight Lines
5.2 Graphs
5.3 Applications of Differentiation

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Key knowledge
• the concepts of position, time, average and instantaneous speed, velocity and acceleration, displacement and distance travelled
• formulas for rectilinear motion involving constant acceleration
• central difference, step functions, numerical approximation and limiting value. Key skills
• construct continuous position-graphs, velocity-time and acceleration-time graphs based on empirical data, and interpret these and given graphs in context
• determine position, time, speed, displacement, distance travelled, velocity and acceleration in contexts involving rectilinear motion, and solve related problems
• apply the formulas for rectilinear motion involving constant acceleration to solve problems.

Non-linear relations and functions

Key knowledge
• the definition of relation and function, independent and dependent variables, domain, co-domain and range, graphs and their features
• reciprocal functions and their properties
• distance formula and locus definitions of curves in the plane
• cartesian, polar and parametric coordinate systems and graphs, including exact values for circular functions.

Key skills
• construct graphs from empirical data and form continuous interpolations and extrapolations, and identify and interpret key features of these graphs and given graphs
• construct the graph of a reciprocal function from the graph of the original function
• use the distance formula and locus definitions to obtain the rule of a relation and draw the corresponding curve
• graph non-linear relations in the plane from their cartesian, polar and parametric representations, and identify and interpret their key features.

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