Support · Mathematics Advanced 11–12 – Year 12 · Integral calculus
Support Examine for a function f(x), which indicates the rate of change of a quantity, the meaning of ∑abf(x)Δx, where the interval a ≤ x ≤ b is divided into subintervals of length Δx, and describe ∑abf(x)Δx as an estimate of the total change in that quantity over the interval a ≤ x ≤ b
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
Recognise when modelling with a linear function that its gradient is the rate of change and determine the rate of change for linear functions in practical situations
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
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.
Estimate the instantaneous rate of change of a non-linear function at a given point from a given graph of a practical situation
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.