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SACE Stage 2 Mathematics

The Complete SACE Mathematical Methods Investigation Guide

The Mathematical Investigation is worth 20% of your SACE Methods school mark — yet most students treat it as an afterthought. This guide breaks down every section of the investigation report, what Performance Standard A actually requires, and the common mistakes that cost marks at each stage.

Assessment Overview

What the Investigation Requires

Understanding the assessment structure is the first step toward performing well in it.

Weight & Structure

Assessment Overview

The investigation folio is a formal mathematical inquiry — not an extended homework task. The marker expects a structured report demonstrating genuine mathematical reasoning.

  • ✓Worth 20% of school assessment (70% of total grade)
  • ✓Marked against SACE Board Performance Standards A–E
  • ✓Assessed on both mathematical rigour and written communication
  • ✓Typically 3–4 weeks allocated by the school
  • ✓Requires a formal written report with all sections
  • ✓Generalisation and verification are mandatory components
Why Students Underperform

Common Failure Modes

Most students who underperform on the investigation do so for reasons that are entirely preventable with the right preparation.

  • ✓Choosing a topic that runs out of mathematical content after two pages
  • ✓Presenting calculations without explaining the reasoning between steps
  • ✓Stating a generalisation without showing how the specific cases led to it
  • ✓Verifying with the same cases used to derive the generalisation
  • ✓Undefined variables and inconsistent notation throughout
  • ✓A conclusion that does not answer the opening research question
Report Structure

Section by Section Breakdown

Select a section to see exactly what it requires and the specific mistakes to avoid.

Introduction & Research Question

The introduction sets the standard for everything that follows. Its job is to establish a precise, answerable research question with clearly defined variables — and to signal to the marker that the investigation is mathematically purposeful, not exploratory in a vague sense.

Requirements & Common Mistakes
  • State your research question as a specific mathematical question — "How does [independent variable] affect [dependent variable]?" — not a topic heading
  • Define every variable algebraically before using it — do not assume the reader shares your notation
  • State the scope explicitly: what values are you investigating, and why those values
  • Justify the mathematical approach — why is this topic amenable to mathematical investigation?
  • A strong introduction is one paragraph: research question, variable definitions, scope, method overview
  • Common mistake: writing "I will investigate functions" — this is a topic, not a question
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Topic Selection

Choosing a Direction That Works

The investigation direction you choose within the given topic area significantly affects how achievable Performance Standard A is.

Strong Topic Characteristics

Topics That Work Well

Good investigation topics share common characteristics — they support depth, generalisation, and verification without running dry or becoming unmanageable.

  • ✓A clear independent variable whose effect on a dependent variable can be measured mathematically
  • ✓Multiple specific cases that build toward a visible pattern
  • ✓A generalisation that can be stated algebraically and verified
  • ✓Scope that is wide enough for 3–4 pages of genuine content
  • ✓Connection to calculus, functions, or statistics — the core Methods topics
Common Pitfalls

Topics to Avoid

Some topic directions consistently underperform — not because students are weak, but because the direction does not support the kind of mathematical investigation the assessment rewards.

  • ✓Topics that are purely computational with no discernible pattern
  • ✓Directions so broad that the investigation never goes deep into any single idea
  • ✓Topics whose generalisation is the starting formula, not a discovered result
  • ✓Directions that produce the same calculation type repeated with different numbers
  • ✓Real-world applications where the mathematics is secondary to the context
Frequently Asked Questions

SACE Methods Investigation — Questions from Adelaide Students

How much is the SACE Mathematical Methods investigation worth?
The Mathematical Investigation is worth 20% of your Stage 2 SACE Mathematical Methods school assessment mark, which contributes 70% of your final subject result. This makes the investigation worth approximately 14% of your total Methods grade — more than any single SAT.
How long should the SACE Methods investigation be?
There is no fixed length requirement, but most investigations that score Performance Standard A are 8 to 12 pages of mathematical content, including graphs, tables, and working. The key is depth rather than length — a 6-page investigation with rigorous reasoning scores higher than a 15-page investigation that is repetitive and shallow.
Can I choose my own investigation topic?
Schools typically provide a topic area and students choose a specific direction within that scope. The choice of direction significantly affects how easy it is to achieve depth — some directions run out of mathematical content quickly, while others support genuine generalisation. Choosing well is part of the task.
What is the difference between a conjecture and a proof in the investigation?
A conjecture is a general statement observed to hold in tested cases but not formally proved. A proof establishes it holds for all cases within the claimed scope. Both are valid in SACE Methods investigations — the important thing is to label which you are doing and be explicit about the distinction. Claiming a proof when you have only a conjecture costs marks.
How is the Mathematical Investigation marked?
The investigation is marked by your school against the SACE Board's Performance Standards (A–E). Performance Standard A requires systematic and thorough mathematical reasoning communicated clearly and concisely. The markers assess both the quality of the mathematics and the written communication — correct mathematics presented poorly will not score Performance Standard A.
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