Free Guide · IB Math
Command terms are the verbs IB examiners use to tell you exactly what to do. Misread one and you lose marks, even if your maths is correct. This guide covers every command term you'll encounter in IB Math AA and AI.
One of the most overlooked reasons students lose marks in IB Math exams is not a lack of mathematical knowledge, it's misreading what the question actually asks. The IB uses precise command terms to communicate the level of response required. A question saying "write down" expects no working. A question saying "show that" requires every logical step written out. These are not interchangeable.
Below you'll find every command term used in IB Mathematics (Analysis and Approaches AA and Applications and Interpretation AI), grouped by category, with a clear definition and exam-specific advice.
These terms ask for a direct answer. Writing extra working wastes time and gains nothing.
Write down
Obtain the answer without showing any working. The answer should follow directly from the information given.
Exam tip: Never write working for a "write down" question. You get the mark for the answer alone. Working cannot help you here.
State
Give a specific name, value, or brief answer without explanation or calculation. Usually a definition or identification.
Exam tip: One word or one short sentence is enough. "State the domain" → write the domain. Nothing more.
These terms require you to show the process, not just the result. Method marks are available.
Calculate
Obtain a numerical answer, showing all relevant stages in the working. A GDC result alone is not sufficient.
Exam tip: Always write intermediate steps. Even if your final answer is wrong, you can earn method marks (M marks).
Find
Obtain an answer, showing relevant stages in the working. Slightly less formal than "calculate" but still requires evidence of method.
Exam tip: Show at least one clear intermediate step. "Find the value of x" → show how you got there.
Determine
Obtain the only possible answer. There is a unique result; your working must lead to it clearly. Often used when the answer is not immediately obvious.
Exam tip: Full method expected. The word "determine" signals there's a definitive answer, show why.
Solve
Find the value(s) of a variable that satisfy an equation or system of equations. Show all steps leading to the solution(s).
Exam tip: For quadratics, show factorisation or quadratic formula. Don't just list the answers from your GDC without any working.
Obtain
Derive a result. Used similarly to "find", you need to show how you arrived at the answer.
Exam tip: Show the process clearly. "Obtain the equation of the line" → show the working, don't just write the equation.
The most misunderstood category. These terms have strict rules that many students get wrong.
Show that
Derive the given result. The answer is printed in the question, you must prove it through a clear, logical sequence of steps.
Exam tip: Never assume the answer is true and work backwards. Every step must follow from the previous one. Show more steps than you think necessary.
Prove
Use a sequence of logical steps to establish the truth of a statement in a formal way. More rigorous than "show that", often used in AA HL.
Exam tip: State what you are proving, show every step, state the conclusion. In AA HL, proof by induction or contradiction may be required.
Verify
Confirm that a given result is true by substituting specific values or using a specific method. Less formal than "prove".
Exam tip: Substitute the values and show that both sides are equal. Don't forget to write a conclusion: "Therefore [result] is verified."
These terms define how much freedom you have in choosing your method.
Hence
You must use the result from the previous part of the question. Using a different method will not earn full marks.
Exam tip: Always look at the previous part. If you couldn't do part (a), you can still use the given answer in part (b) for follow-through marks.
Hence or otherwise
Using the previous result is recommended but not required. You may use any valid method. The "hence" route is usually faster.
Exam tip: If you can see how to use the previous result, do so, it's usually more efficient. If not, use any method you know.
Deduce
Reach a conclusion by logical reasoning from information already given or established. The conclusion must follow necessarily from what precedes it.
Exam tip: Reference the information you're deducing from. Write: "From [previous result], it follows that..."
"Sketch" and "draw" are not the same thing. Getting this wrong costs marks.
Sketch
Produce a rough but clear diagram. No exact scale required, but key features must be clearly indicated: intercepts, asymptotes, turning points, general shape.
Exam tip: Label axes, label all key points with their coordinates, and show correct behaviour at extremes (e.g., asymptotic behaviour).
Draw
Produce an accurate diagram using a ruler and protractor where appropriate. Must be drawn to scale with labelled axes and correct values.
Exam tip: More marks for accuracy. Use a ruler for straight lines. Label every axis and key point. Scale must be consistent.
Plot
Mark the position of specific points on a given grid or set of axes. The grid is usually provided.
Exam tip: Plot each point as a small, clear dot or cross. Double-check your coordinates before plotting.
Construct
Draw with precision, typically using instruments (ruler, compass). Used for geometric constructions or accurate graphs.
Exam tip: Show all construction lines. Don't erase them, they're evidence of your method.
Label
Add identifying information (names, values, variables) to parts of a diagram or graph that already exists.
Exam tip: Use the exact notation from the question. If the question uses θ, label with θ, not "angle".
Annotate
Add brief explanatory notes or labels to a diagram to describe what is shown. More descriptive than "label".
Exam tip: Brief phrases are fine. The goal is to communicate what each part of the diagram represents.
These terms are worth Reasoning marks (R marks). You must communicate your thinking, not just calculate.
Justify
Give valid reasons or evidence to support an answer or conclusion. A numerical answer alone is not sufficient, explain why it is correct.
Exam tip: Refer to a theorem, rule, or tested condition. "Justify that x is a maximum" → reference the second derivative test or sign diagram.
Explain
Give a clear, detailed account including reasons or causes. More thorough than "state", you need to show understanding, not just recall.
Exam tip: Write in full sentences. Connect cause and effect. "Explain why..." → give the reason, not just the result.
Describe
Give a detailed account of characteristics, features, or behaviour. Often used for describing transformations or statistical results.
Exam tip: Include direction, magnitude, and type. "Describe the transformation" → say translation/rotation/reflection, the vector or angle, and any invariant points.
Comment
Give a judgment, observation, or comparison based on a result. Requires you to interpret what you see, not just repeat it.
Exam tip: State what the result means in context. "Comment on your answer" → say whether it's reasonable, what it implies, or how it compares.
Suggest
Propose a possible solution, hypothesis, or explanation. There may be more than one valid answer, you need a reasonable, justified one.
Exam tip: Give a specific, plausible answer. "Suggest a value of k" → any value that satisfies the condition, with a brief reason.
These terms specify the algebraic technique required. The method is part of the mark.
Simplify
Reduce an expression to its simplest form. What counts as "simplest" depends on context, usually means removing brackets, combining like terms, or rationalising denominators.
Exam tip: Keep going until no further simplification is possible. Leave surds in surd form unless told otherwise.
Factorize
Express an expression as a product of its factors. Show the factored form clearly.
Exam tip: Always check by expanding your answer. Don't leave partially factorized expressions.
Expand
Remove brackets and write the expression in its expanded form, collecting like terms.
Exam tip: Be careful with negative signs when expanding double brackets. Show the intermediate step before collecting terms.
Differentiate
Find the derivative of the given function. Specify with respect to which variable if not obvious.
Exam tip: Show the differentiation step before simplifying. If using the chain/product/quotient rule, write each part clearly.
Integrate
Find the integral of the given expression. Add the constant of integration (+C) for indefinite integrals. Show limits clearly for definite integrals.
Exam tip: Never forget +C for indefinite integrals. For definite integrals, substitute the limits and show the subtraction step.
Understanding how the IB markscheme works tells you where your marks come from, and how to avoid losing them even when you make arithmetic errors.
| Mark type | What it stands for | When you get it |
|---|---|---|
| M | Method mark | For demonstrating the correct method, even if the final answer is wrong. Writing the right formula or technique earns an M mark. |
| A | Accuracy mark | For a correct numerical answer, following correct working. You can only earn A marks if the corresponding M mark was awarded. |
| R | Reasoning mark | For a valid explanation or justification. Required for "justify", "explain", and "comment" questions. |
| ft | Follow-through mark | If you made an error in a previous part, you can still earn marks in subsequent parts by applying your wrong answer correctly. |
| AG | Answer given | The answer is printed in the question (used in "show that"). No marks are given for the answer itself, all marks are for the working. |
Before answering any question, ask yourself:
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