“Show that” and “verify” questions appear regularly in VCE Mathematical Methods, yet they account for a surprisingly large amount of lost marks. This is not because the mathematics is unusually difficult. It is because many students misunderstand what these command terms require and, as a result, write answers that do not meet the marking criteria.
The Examiner’s Reports make it clear that these questions are not testing whether students can arrive at a result. They are testing whether students can justify a result using logically coherent mathematics.
What “show that” actually means in Methods
When a question asks students to “show that” a particular result holds, the result is not in doubt. Students are not being asked to discover it. They are being asked to demonstrate why it is true.
This distinction is critical.
A correct numerical answer on its own is worth little or nothing in these questions. Marks are awarded for the reasoning that leads from given information to the stated result. The endpoint is provided so that students can check their progress, not so that they can work backwards informally.
Examiner’s Reports repeatedly note that students lose marks by starting from the result they are meant to show and manipulating it until it resembles the given information. This approach does not demonstrate logical reasoning and is not rewarded.
Direction of working matters
In “show that” questions, the direction of reasoning matters.
VCAA expects students to begin with the information provided in the question and proceed step by step to the stated result. Each step must follow logically from the previous one. Working backwards, even if algebraically valid, does not demonstrate that the result follows from the given conditions.
This is a frequent source of confusion for capable students who are used to checking results informally during practice.
Common errors in algebraic justification
Many students lose marks in “show that” questions through incomplete algebraic justification.
For example, students may skip steps, combine multiple manipulations into one line, or rely on implied reasoning rather than explicit working. While this may be acceptable in other contexts, Mathematical Methods requires clarity.
Examiner’s Reports consistently highlight that steps must be shown clearly enough for the marker to follow the logic without inference.
What “verify” requires students to do
“Verify” questions are closely related but slightly different.
To verify a statement, students must substitute given values or conditions into an expression and demonstrate that the statement holds true under those conditions. This usually involves evaluation rather than derivation.
A common error is stating that the result is true without performing the verification explicitly. Another is performing the calculation but failing to state a clear conclusion.
Verification is not complete until the student explicitly confirms that the condition has been satisfied.
Why CAS use often undermines these questions
CAS can be used in some “verify” questions, but it often creates problems in “show that” questions.
Students may use CAS to jump directly to the final expression without demonstrating intermediate reasoning. Examiner’s Reports repeatedly note that unexplained CAS output is not sufficient evidence of reasoning.
Even when CAS is used, students are expected to translate output into conventional mathematical steps and explain how each step contributes to the result.
Why these questions are designed this way
“Show that” and “verify” questions exist to test a core expectation of Mathematical Methods: the ability to construct and communicate mathematical arguments.
The Study Design emphasises reasoning and logical structure. These questions make that emphasis explicit. They reward students who can write mathematics as an argument rather than as a sequence of calculations.
This is why marks are lost so quickly when structure is unclear.
How strong students approach these questions
Strong students treat these questions as writing tasks as much as calculation tasks.
They begin from the given information, write each algebraic step clearly, justify transformations where necessary, and aim to make their reasoning easy to follow. In verification questions, they conclude explicitly by stating that the condition has been met.
They do not rush. They use the given result as a guide, not as a shortcut.
How students can improve performance on these questions
Improvement comes from practising structure, not speed.
Students benefit from rewriting full solutions neatly, checking that each line follows logically, and asking whether a marker could follow the argument without explanation. Peer marking and self-marking against assessment guides are particularly effective for these questions.
Understanding the command term is often more important than understanding the mathematics.
An ATAR STAR perspective
ATAR STAR works closely with Mathematical Methods students to improve performance on “show that” and “verify” questions because they are a reliable source of mark leakage.
We train students to recognise what the command term is asking for and to structure their working accordingly. This supports students who understand the mathematics but struggle to communicate it under exam conditions, as well as high-performing students aiming to eliminate avoidable losses.
In Mathematical Methods, reasoning must be visible to be rewarded.