Support · Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation
Support Infer that nx^(n - 1) is the gradient of f(x) = xⁿ and verify the result using graphing applications
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
Use graphing applications to find the midpoint and gradient/slope of an interval
Stage 5 · Linear relationships A 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.
Use the point–gradient form (y - y_1 = m(x - x_1)) or the gradient–intercept form (y = mx + c) to find the equation of a line passing through a point (x_1,y_1), with a given gradient m
Stage 5 · Linear relationships C (Path) Draft mapping
- Interactive toolStarterMaths Is Fun: Point-slope formUse it for: Point-gradient form of a line explained.
- PhET Graphing LinesUse it for: Explore gradient and intercept; the Line Game screen gives quick practice.
Explain why horizontal intervals have a gradient of 0 and vertical intervals have undefined gradients using the gradient relationship
Stage 5 · Linear relationships A Draft mapping
- Interactive toolStarterMaths Is Fun: Gradient (slope)Use it for: Interactive line showing rise over run.
- PhET Graphing LinesUse it for: Explore gradient and intercept; the Line Game screen gives quick practice.