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

Ch 10H

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 11B

Antiderivatives 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/G

Area 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 11I

Area 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 11I · Examples

Area between curves — extra worked examples

Two more fully-worked examples with sketches: a line and a parabola, and a "show that" question where the curves cross inside the region so you split the integral.

Ch 11H

Integration 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 11J

Average 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 review

Integration 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.

Probability & statistics

Discrete random variables

Ch 13D

Expected value, variance & standard deviation

The mean $E(X)=\sum x\,p(x)$ as a long-run average, variance via $E(X^2)-[E(X)]^2$, and standard deviation — with a "is the game worth playing?" casino/roulette angle. Two video walkthroughs.

Exam preparation

Revision & assessor feedback

VCAA · Exam 2

Differentiation & Integration mega quiz — solutions

Full worked solutions to the calculus mega quiz: eight past Exam 2 multiple-choice questions plus three extended-response questions (2016–2021), all answers CAS-checked.

VCAA 2024

What the markers actually wanted

The 2024 Exam 1 & Exam 2 assessor feedback, written for you — the small habits that cost most students marks and the quick fixes that get them back.