Support · Mathematics Advanced 11–12 – Year 12 · Integral calculus
Support Conclude, for a continuous function y = f(x) on the interval a ≤ x ≤ b, that ∫abf(x)dx = (area of regions between curve and x -axis lying above the x -axis) - (area of regions between curve and the x -axis lying below the x -axis)
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
Examine and use the relationship between the angle of inclination of a line or tangent to a curve, θ, with the positive x -axis, and the gradient, m, of that line or tangent, and establish that tanθ = m
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
Describe a horizontal dilation as a stretch from the y -axis and a vertical dilation as a stretch from the x -axis
Mathematics Advanced 11–12 – Year 11 · Graph transformations Draft mapping
No checked resources on this prerequisite dot point yet.
Establish using graphing applications that replacing x by - x in the equation of a graph corresponds to the reflection of the graph in the y -axis, and that replacing y by - y corresponds to a reflection in the x -axis
Mathematics Advanced 11–12 – Year 11 · Graph transformations 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.