Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Use the product rule to prove that if P(x) has a zero, α, of multiplicity m > 1, then α is a zero of P'(x) of multiplicity m - 1, and use the result to determine the multiplicity of a discovered zero of P(x) and solve related polynomial problems
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
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.
Recognise that a function whose derivative is everywhere zero is a constant function
Mathematics Advanced 11–12 – Year 12 · Integral calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Add, subtract and multiply polynomials
Stage 5 · Polynomials (Path) Draft mapping
- VideoStarterEddie Woo (WooTube): Basic Polynomials playlistUse it for: Sydney teacher Eddie Woo's recorded lessons on polynomials; play a clip to model a method or for revision.