IB Mathematics AA command terms 2026: What they mean and how to respond correctly

IB Mathematics AA command terms are the action words used in exam questions to tell students exactly what type of response, reasoning, and working is required. Terms such as calculate, find, show that, prove, sketch, draw, hence, state, and determine each carry different expectations for method, notation, and justification. Misreading a command term can lead to lost method marks even when the mathematics itself is correct.

This guide explains the most important IB Mathematics AA command terms and how students should respond to each one in exam conditions.

Why understanding command terms is essential for scoring high in IB Mathematics AA

The IB mark scheme is built around method marks (M marks) and accuracy marks (A marks). When a command term signals that working must be shown, each algebraic or calculus step carries its own mark allocation. A student who writes only a final answer, even a correct one, will collect the accuracy mark but forfeit every method mark attached to that step.

Drawing on years of experience at Times Edu supporting students through the IB Mathematics AA curriculum ^[1], one pattern is consistently clear: Students who treat command terms as background noise rather than as scoring instructions are the ones who score a 5 when their mathematical ability is comfortably at a 7.

The IB groups its command terms into functional categories based on the depth of response required. Understanding these categories is the single fastest way to raise your exam score without learning any new mathematics.

>>> Read more: IB Mathematics AA books 2026: Complete guide for students and teachers

Calculate and find in IB Mathematics AA: What level of working is expected

“Calculate” and “find” are the two most frequently appearing command terms in IB Mathematics AA, and they are broadly equivalent in what they ask for. Both require you to obtain a numerical value or algebraic expression as your answer.

The critical distinction lies not between these two terms but between the paper on which they appear. On Paper 1 (non-calculator), “calculate” or “find” requires you to show full algebraic working because there is no GDC to verify your steps. On Paper 2, you are permitted to use the GDC to perform the computation, but you must write down the mathematical setup before stating the answer.

A common mistake we see at Times Edu is students on Paper 2 writing only the final number with no supporting expression. If your GDC produces an incorrect output due to a miskeyed entry and there is no written setup, the examiner has no partial credit to award. Always write the integral, equation, or expression first, then state the calculator’s result.

>>> Read more: IB Maths AA : Syllabus, Exam Structure & Roadmap to an 7

IB

How to Achieve a 7 in the IB Diploma Programme

699.000đBuy →

Show that and prove in IB Mathematics AA: How to structure your response

These two command terms are the most demanding in the entire IB Mathematics AA command terms list, and they are also the most commonly mishandled by students who believe they understand what is being asked.

“Show that” gives you the final result in the question. Your job is to construct every algebraic or calculus step required to arrive at that printed result. The most dangerous trap here is working backward from the given answer, which examiners call “circular reasoning” and will award zero marks. You must begin from a defined starting point and progress forward, step by step, to land precisely on the stated result.

One critical detail often overlooked is that “show that” answers require complete notation at every stage. Skipping a line because it feels obvious, or writing an arrow between two expressions without showing the algebraic manipulation that connects them, will cost method marks even when your logic is sound.

“Prove” requires a formal mathematical argument. In IB Mathematics AA, this most commonly appears as proof by induction, proof by contradiction, or the verification of a trigonometric identity. Each of these proof types has a specific structure that the mark scheme expects.

For proof by mathematical induction, the required structure is:

1. State and verify the base case (typically n = 1).
2. Assume the statement is true for n = k (the inductive hypothesis).
3. Show the statement is true for n = k + 1 using the assumption from step 2.
4. Write a formal conclusion statement linking the three steps.

In our experience working with international students, the base case and the conclusion statement are the two steps most often omitted under exam pressure. Both carry marks. Neither can be skipped.

>>> Read more: IB Math AA HL Topic Priority List 2026: 10 Topics Worth 70% of Marks

Sketch and draw in IB Mathematics AA: What each term requires from you

Graph questions in IB Mathematics AA use two distinct command terms that carry very different marking expectations, yet students frequently treat them as interchangeable. This is a reliable source of avoidable mark loss.

“Sketch” asks you to produce a general representation of a curve’s shape. Precision of plotted coordinate points is not the priority. What the mark scheme checks for is the presence and accurate labelling of key graphical features: Axes intercepts with their coordinates, any asymptotes with their equations, and the coordinates of maximum or minimum turning points. A sketch drawn freehand is entirely acceptable, provided these features are visible and labelled.

“Draw” requires a geometrically accurate construction. This term appears in statistical contexts (drawing a box-and-whisker plot on a given scale) and in geometric contexts where a ruler and calculated coordinates are necessary. The difference in precision expected is significant. A “draw” response submitted freehand on a non-scaled axis would not satisfy the mark scheme.

A common mistake we see is students producing a beautiful, precisely plotted curve in response to a “sketch” question while omitting axis labels and intercept coordinates, and then losing marks despite the effort invested. The command term tells you where to focus your time.

>>> Read more: IB Math AA SL Daily Routine: 30-Min Habit That Builds Score 7

Hence and hence or otherwise in IB Mathematics AA explained

No pair of command terms in IB Mathematics AA causes more mark loss than “hence” and “hence or otherwise,” because the difference between them is not just stylistic. It is a direct instruction about which method the examiner will credit.

“Hence” means you must use the result from the immediately preceding part of the question to solve this part. The word “immediately” is not casual. If part (b) asks you to “hence” find a derivative and you obtained an expression in part (a), you must build on part (a)’s result. If you solve part (b) using an entirely independent method, and your answer is correct, you will still score zero marks for that part. The examiner is assessing your ability to make mathematical connections, not just to produce a correct number.

“Hence or otherwise” gives you a genuine choice. The examiners prefer that you use the previous result because that method is usually faster and more elegant, but an alternative valid mathematical method will receive full marks if correctly executed. In practice, “hence or otherwise” is the IB’s way of signalling that the question can be solved through multiple routes.

Drawing on years of experience at Times Edu reviewing past papers and mark schemes, the practical advice is this: When you see “hence or otherwise,” attempt the “hence” route first. If the connection to the previous answer is clear to you, it will be the faster route under timed conditions. If you cannot see how to apply the previous result, switch to an independent method immediately rather than spending time on an unproductive approach.

One critical detail often overlooked is that “hence” questions are deliberately structured in sequence. If a student leaves part (a) blank and then attempts part (b) with “hence,” they have no result to build from. In this situation, examiners will allow you to state an assumed value for part (a) and proceed. Always write something in part (a), even if it is incomplete.

>>> Read more: IB Math AA HL Paper 3 Tips 2026: How to Tackle Unfamiliar Questions with More Confidence

Write down, state and determine in IB Mathematics AA: Key distinctions

These three command terms sit at different points on the working-required spectrum and are worth distinguishing carefully.

“Write down” and “state” are functionally equivalent in IB Mathematics AA. Both signal that no working or justification is required. The answer is either read directly from a graph, extracted from the formula booklet, or follows so directly from a given result that intermediate steps carry no marks. These questions are typically worth one mark. Writing lengthy working in response to “write down” wastes exam time without gaining additional credit.

“Determine” sits between “find” and “state” in terms of expected response depth. It asks you to reach a conclusion, but crucially it expects that conclusion to be supported by a reasoned argument or by referencing relevant evidence. In statistics questions, “determine” might ask you to decide whether a result is statistically significant, requiring you to compare a calculated p-value to the significance level and then state your conclusion in context. The numerical output alone is insufficient.

In our experience working with international students preparing for the IB Mathematics AA Higher Level, the “determine” command term appears most frequently in hypothesis testing, optimization, and geometric proof contexts. The examiner is looking for a connection between your calculation and your conclusion, stated explicitly in your response.

>>> Read more: IB Math AA HL Revision for 2026: A High-Impact Study Plan for Papers 1, 2, and 3

Frequently asked questions

Conclusion

At Times Edu, our 1-on-1 IB Mathematics AA tutors work through past papers and mark schemes with students in a way that makes command term logic instinctive rather than something to recall under pressure. If your student is approaching their IB examinations and losing marks on questions they mathematically understand, a personalized academic roadmap session with our specialist consultants is the most direct path to closing that gap. Reach out to the Times Edu team to schedule a consultation and build a targeted preparation strategy around the specific papers and topics your student needs most.

Olivia