Support · Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation
Support Recognise when modelling with a non-linear function that the rate of change is not constant and is represented by the gradient of the tangent to the curve at each point on the curve
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 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.
Use graphing applications to graph a variety of equations of the form y = (kx)ⁿ, where n is an integer and n ≥ 2, and describe the effect on the shape of the curve where n is an odd or an even number
Stage 5 · Non-linear relationships C (Path) 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 gradient and the point–gradient form to find the equation of a line passing through 2 points
Stage 5 · Linear relationships C (Path) Draft mapping
- Interactive toolStarterMaths Is Fun: Point-slope formUse it for: Point-gradient form of a line explained.
- Corbettmaths practice questions: Linear graphs: y=mx+cUse it for: Free printable graded practice questions (with answers) on linear graphs: y=mx+c for drill or a quick check.
- VideoStarterCorbettmaths video: Linear graphs: equation through 2 pointsUse it for: Short worked-example video on linear graphs: equation through 2 points to model the method before practice or for flipped revision.