Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Graph solutions to first order differential equations given a slope field and identify the unique solution curve that satisfies a set of initial conditions
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.
Prerequisite links are draft mappings generated from the syllabus structure (earlier stage, same strand, closest content). They are being reviewed by teachers. Spot a poor match? Tell us.
Prerequisite dot points
Verify by substitution that the function Q = Ae^(kt) satisfies the relationship dQ/dt = kQ with A being the initial value of Q
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Recognise that the equation dQ/dt = kQ where Q > 0, and its solution Q = Ae^(kt) represent exponential growth when k > 0 and exponential decay when k
Mathematics Advanced 11–12 – Year 12 · Applications of 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.