Support · Mathematics Advanced 11–12 – Year 12 · Integral calculus
Support Use definite integrals to solve problems involving the areas of regions bounded by the graph of the continuous function y = f(x), the x -axis and the lines x = a and x = b, in cases where f(x) ≥ 0 throughout a ≤ x ≤ b, f(x) ≤ 0 throughout a ≤ x ≤ b or where f(x) changes sign in the interval a ≤ x ≤ b, with or without the graph provided
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
Define the average rate of change of y with respect to x for a function y = f(x) over the domain [a,b] as (Δy)/(Δx) = (change iny)/(change inx), that is (Δy)/(Δx) = (f(b) - f(a))/(b - a), and recognise (f(b) - f(a))/(b - a) as the gradient of the secant through (a,f(a)) and (b,f(b)) on the graph of y = f(x)
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
Determine the equation of a straight line passing through two points (x_1,y_1) and (x_2,y_2) by calculating its gradient m using the formula m = (y_2 - y_1)/(x_2 - x_1)
Mathematics Advanced 11–12 – Year 11 · Working with functions 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.