Support · Mathematics Extension 2 11–12 – Year 12 · Applications of calculus to mechanics
Support Derive an expression for velocity as a function of time of a particle moving in a straight line and in the absence of external forces, except for a resistance oppositely directed to the motion and with a magnitude proportional to a power of the speed
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
Graph the function Q = P + Ae^(kt), where k > 0 and k and A > 0 and A, with and without graphing applications, and identify any asymptotes
Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Explain that if the rate of change of a quantity Q over time t is proportional to the difference Q - P at any instant, then this may be represented by the equation dQ/dt = k(Q - P), where k is a constant
Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Solve first order differential equations of the form dy/dx = g(y), where possible expressing the solution as a function with y as the subject
Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.