Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Solve differential equations of the form (dP)/(dt) = kP(1 - P/C) for some constants k and C, given the appropriate decomposition into partial fractions, to obtain the logistic function
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 = Ae^(kt), where k > 0 and k and A > 0 and A, with and without graphing applications, and identify any asymptotes
Mathematics Advanced 11–12 – Year 12 · 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.
Prove and use the formula d/dx(a^x) = (lna)a^x, where a is a constant and a > 0
Mathematics Advanced 11–12 – Year 12 · Differential calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Graph y = f'(x) and y = f''(x) for a function y = f(x), given only a graph of y = f(x)
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.