Updates to VCE Mathematical Methods and Specialist Mathematics overviews (v0.2.0)
Changes ahoy!
The first major update to my VCE Mathematics overviews is here for Methods and Specialist!1
Below I’ll highlight some of the bigger changes I’ve made, but there are changelogs included in the pdfs for a list of the more granular changes.
If you have thoughts or questions or just want to chat about them, reach out on Substack, on socials (Twitter/X, Bluesky, LinkedIn), or via email.
Some changes have been applied across the board, so I’ll go through them first.
To improve navigation, I’ve added links to topics and sections within the document, including a proper front cover.
Given the detail these “overviews” have spiralled into, I’ve added some more summary-esque pages including a major themes page to highlight what the foci are for the study and topic-by-topic core ideas of what should be the major takeaways from them so that they don’t get drowned out by the minutia.
To keep track of what changes, I’ve included changelogs by version to track changes.
A number of corrections have been made as they were found.
Mathematical Methods overview
The probability topics have been reworked to have a greater focus on the relationship between probability and functions, such as through the inclusion of ranges of transformed random variables, event spaces, probability measures, and probability mass functions in units 1 and 2. Unit 4 has seen updates related to random samples of independent and identically distributed (iid) discrete random variables, mainly for Bernoulli trials to introduce statistics as functions of random samples, in particular the sample proportion as the mean of a random sample of iid Bernoulli random variables. Expectations now have their own subsections to allow for more space, depth, and detail and standardisation of random variables has been introduced earlier.
Sensitivity and increments have been included throughout as an additional application for rates of change and differentiation from linear functions in unit 1 to relate content to change easier.
Composite functions have been added at the start of linear functions in unit 1 to relate to transformations and inverse functions. This is only intended to be for algebraic manipulation of rules and to make it easier to discuss transformations of the forms f(ax) and f(x + b) (and their variations and combinations), not the full discussion of domains and ranges for them to be defined which remains in unit 4.
Integration has been restructured somewhat. Trapezium rule approximations have been grouped with modelling at the end. This allowed for fleshing it out more and comparing to exact integrals easier. Rectangle approximations are used more explicitly at the start to lead better into the definition of the definite integral via step function approximations. The fundamental theorems of integral and differential calculus have been clarified and content moved around them.
Click here to see the latest Mathematical Methods overview.
Specialist Mathematics overview
The unit 1 matrices topic has been moved after sequences in unit 1 so that it can take advantage of recurrence relations and nth term rules, especially in relation to powers of matrices. The matrices topic has also been significantly fleshed out and split into three subtopics to be a more cohesive topic relative to the others. The study design is very short on it, but there is a large amount that can be considered, especially for a heavier linear algebra study. Additionally, more connections between matrices and graph theory have been included.
The unit 2 probability topic has seen a significant overhaul to focus on random samples and random vectors, independent and identically distributed (iid) random variables, and statistics as functions of random samples. This is to help relate the topic better with the rest of the study and future learning. Some changes have been made in unit 4 to align with these changes.
Lengths, areas, and volumes using integration has been moved around and made into a full sub-topic near the start of unit 4. This has allowed for more depth to be included on them (including further extension content in red), being able to introduce the length integral prior to the surface area integral, and have them ready for applications of differential equations.
The unit 4 differential equations topic has been significantly reworked to remove the large clunky lists of applications so that they can be treated in more depth. The set up of the differential equations in specific scenarios has been separated from the solving of them so that they can still take place in context from early on, but only where the ODE is given. Financial ODEs to model loans and investments (in particular reducing-balance loans and annuities) have been included to fit with the financial recurrence relations that have also been added in unit 1 for financial literacy that is otherwise absent from the calculus-based studies. This also creates a nice connection between discrete and continuous modelling.
Click here to see the latest Specialist Mathematics overview.
For the future
After I’ve brought General Mathematics’ overview in line for its v0.2.0, I’m thinking about fleshing out the assessment details as proper sections with ideas of what that needs to or could include, especially for the required SACs in units 3&4 and the mathematical investigations.
I’ll also look into spinning it out into state specific versions starting with the closer variants of the AC v8.4 and VCE (QLD, WA, Tas) given their broad similarity to each other.
Note: updates to the VCE General Mathematics overview are coming but will take a bit as I’m rewriting most of it to sit more in line with the Methods and Specialist ones as well as doing further deep diving on some topics to flesh them out more.