Support · Mathematics Advanced 11–12 – Year 12 · Integral calculus
Support Use a graphing application to compare different methods of approximating the area, A, of the region between the continuous function y = f(x) and the x -axis, where f(x) ≥ 0 on the interval a ≤ x ≤ b, by summing the areas of trapezia or rectangles each of width Δx = (b - a)/n and approximate height f(x) for any x lying in its base, and observe the effect on the precision of the approximation of A as the number n of subintervals of a ≤ x ≤ b increases, that is as Δx→0
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.
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Prerequisite dot points
Determine that the instantaneous speed of an object at time t can be approximated by the average speed between its position at time t and its position some time later, and explain how this approximation can be improved
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
Approximate the gradient of a curve f(x) = xⁿ at a point P(c,f(c)) by considering the gradient of the secant through P and Q(c + h,f(c + h)) as the magnitude of h approaches zero, using graphing applications or a spreadsheet
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation 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.