Home › Mathematics Advanced 11–12 – Year 11 › Introduction to differentiation › Dot point

Support · Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation

Support Define f'(x), for any function f(x) and any value x, to be the gradient of the tangent to the curve y = f(x) at the point P(x,f(x)) if the tangent exists and is not vertical

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.

← Back to core resources

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 toolStarter
    Maths Is Fun: Point-slope form
    Maths Is Fun · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Point-gradient form of a line explained.
  • SimulationStarterDrill
    PhET Graphing Lines
    PhET Interactive Simulations · Interactive (browser) · Free · Link checked 2026-10-15 · Hands-on, No prep
    Use 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 toolStarter
    Maths Is Fun: Gradient (slope)
    Maths Is Fun · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Interactive line showing rise over run.
  • SimulationStarterDrill
    PhET Graphing Lines
    PhET Interactive Simulations · Interactive (browser) · Free · Link checked 2026-10-15 · Hands-on, No prep
    Use it for: Explore gradient and intercept; the Line Game screen gives quick practice.

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