Algorithms in VCE Maths

Computation and Algorithms have always been a part of mathematics. Think about all of the methods you learnt for addition, multiplication, division you learnt in primary school; and before calculators, you'd learn algorithms for extracting square roots, how to use trig tables and slide rules etc. As digital computers have become more available, more mathematical computation is easily available; this makes algorithms more ubiquitous, but also more hidden!

VCAA have long had computational thinking as part of the VCE courses, but with the 2023 study design, it is now made explicit through the expectation that you can describe and run a computation described with pseudocode: see the notes from VCAA reproduced here.

VCAA states that pseudocode can be used in the following areas of Methods and Specialist Maths:

Maths Methods

• piecewise defined functions

• bisection method (and using the mean of the endpoints as a point estimate)

• numerical evaluation of limits for derivatives

• Newton’s method for polynomials (Units 1 and 2) and other functions (Units 3 and 4)

• Polynomial approximations to transcendental functions

• Optimisation of integer valued functions

• Counting in a probability context, and simple simulations for probability

• Simulations for sampling distributions, central limit theorem

• Numerical integration, left and right interval values, trapezium rule

Specialist Mathematics

• Investigation of number properties, sequences, partial sums and products

• Numerical integration – Reimann sums for areas, volumes and surface areas of solids of revolution, length of segments of a curve

• Vector operations including scalar product, cross product, projections

• Numerical solution of differential equations including Euler’s method

• Sums of random variables / Sample distributions for means

The bolded options are maybe more likely in a VCAA Exam...  Also seen is simple sequences like repeated addition/subtraction for multiplication/division, or things akin to decreasing balance sequences etc.