VCE Mathematical Methods · Unit 3 & 4
Year 12 Methods
Topic lessons with hideable worked solutions, iteration tables, and Cambridge working-program references. More topics are added throughout the year.
Numerical methods
Available topic lessons
Bisection & Newton's method
Derive Newton's formula from a tangent, work through bisection iterations for $x^3+3x+1=0$, and learn the three classic failure modes of Newton's method.
Ch 11BAntiderivatives of $e^{kx}$ & trig
Examples 6–9 from the integration notes — exponential antiderivatives with initial conditions, trig antiderivatives, and the stationary-point method.
Ch 11E/F/GArea under a curve · the definite integral
The Fundamental Theorem of Calculus, the five properties of the definite integral, signed vs total area, and a VCAA-style application. Two video walkthroughs.
Ch 11IArea between two curves
The "top minus bottom" rule, four-step recipe for setting up the integral, and how to split when the upper curve swaps. Two video walkthroughs.
Ch 11HIntegration by recognition
Differentiate a given function and read off the integral — the standard "hence find" pattern, with chain-rule and product-rule examples. Three video walkthroughs.
Ch 11JAverage value of a function
Average value as the height of the balancing rectangle, with calculus and graphical period-shortcut examples. Includes a kinematics application. Three video walkthroughs.
Ch 11 reviewIntegration mixed practice
A decision-tree walkthrough and mixed worked examples covering definite integrals, areas under and between curves, recognition, and average value. Two recap video walkthroughs.
Exam preparation