One of the quiet but consistent themes running through the Specialist Mathematics Examiner’s Reports is that many students lose marks not because they cannot do the mathematics, but because they misunderstand what the question is actually asking them to do. This almost always comes down to command words. In Specialist Mathematics, command words are not decorative. They tell students exactly how their response will be assessed.
Why command words matter more in Specialist Mathematics than students expect
In many earlier mathematics subjects, students can often get away with focusing on the calculation and letting the final answer do most of the work. Specialist Mathematics does not operate that way. The Study Design makes it clear that reasoning, justification and interpretation are core skills, and command words are how those skills are activated in exam questions.
The Examiner’s Reports repeatedly note that students provide mathematically valid working that does not align with the instruction given. When this happens, marks are either restricted or not awarded at all, even if parts of the mathematics are correct.
“Show that” is not the same as “find”
Questions that use “show that” are among the most misunderstood in Specialist Mathematics. Students often treat them as discovery questions, attempting to derive a result without structure, or worse, simply writing down the given expression with minimal working.
The Examiner’s Reports make it clear that “show that” questions assess logical progression. Students are expected to start from known or established expressions and demonstrate, step by step, how the required result follows. Writing down the final expression without a clear chain of reasoning is not sufficient. Even if the final line matches what is asked, marks are lost when the logical bridge is missing.
By contrast, “find” questions assess outcome. In these cases, the final answer matters more, but appropriate working is still required for full marks. Confusing these two command words is one of the most common causes of unnecessary mark loss.
“Hence” signals dependency, not repetition
“Hence” is another command word that students frequently misinterpret. When a question says “hence”, it is explicitly telling the student to use the result from the previous part. The Examiner’s Reports highlight that students often redo the entire problem using a different method, which may be mathematically valid but ignores the structure of the question.
When students fail to use the earlier result, they often lose marks for efficiency and relevance. In some cases, marks are not awarded at all because the response does not demonstrate the intended connection between parts. Specialist Mathematics values coherence across a question, and “hence” is one of the main signals that such coherence is being assessed.
“Determine” requires reasoning, not just a number
“Determine” is often mistaken for a simple calculation instruction. In Specialist Mathematics, it almost always implies decision-making. Students are expected to select an appropriate method, apply it correctly, and present a justified conclusion.
The Examiner’s Reports note that students frequently provide correct numerical answers to “determine” questions but fail to explain how that result was obtained or why it is valid in the given context. In these cases, students may receive partial credit at best. The full allocation of marks depends on showing that the determination was reasoned, not guessed or assumed.
“Explain” and “justify” are mathematical tasks, not English ones
When students see “explain” or “justify”, many assume that a brief verbal statement will suffice. In Specialist Mathematics, these command words require mathematical explanation. That explanation must reference relevant definitions, properties, or results and show how they apply to the situation.
The Examiner’s Reports consistently point out that vague statements such as “because it is increasing” or “by symmetry” are not enough unless they are supported by mathematical reasoning. Explanation without mathematics is treated as incomplete.
Why misreading command words keeps happening
These errors persist because students are rarely penalised for them earlier in their mathematical education. Many students have been rewarded for getting the right answer, even if their reasoning was implicit or poorly expressed. Specialist Mathematics changes that expectation.
The Study Design positions mathematical communication as part of the skill set being assessed. Command words are the mechanism through which that communication is tested.
How students can respond more effectively
Improving performance with command words does not require learning new content. It requires changing how questions are read. Students need to pause before starting, identify the command word, and decide what kind of response is being demanded. Is the question asking for a result, a demonstration, a connection, or a justification?
Students who annotate command words during reading time and plan their response accordingly are far less likely to lose easy marks.
An ATAR STAR perspective
At ATAR STAR, we explicitly train students to recognise and respond to command words in Specialist Mathematics. We use past exam questions and Examiner’s Report commentary to show how small shifts in interpretation can dramatically change outcomes. This approach supports students who are capable but inconsistent, as well as high-performing students who want to refine their exam technique.
In Specialist Mathematics, understanding the mathematics is essential, but understanding the language of assessment is what allows that understanding to be rewarded.