IB Maths command terms: your guide to exam success
12 min readOliver Kidd (Co-founder)1 Jul 2026
IB Maths command terms are the specific instruction verbs embedded in exam questions that tell you exactly how to respond. Each term signals the type of answer required, from a brief numerical result to a full logical proof. Command terms like ‘show that’, ‘hence’, and ‘justify’ are placed deliberately by examiners to specify both the depth and style of your response. Misreading a single term can cost you marks even when your mathematics is correct. Understanding IB Maths assessment vocabulary is one of the most direct ways to improve your exam performance.
1. What are IB Maths command terms?
IB Maths command terms are the official instruction words used across all IB Mathematics papers. They appear at the start of a question or sub-part and define what a correct response looks like. Common terms include Calculate, Find, Solve, State, Describe, Sketch, Draw, Justify, Explain, and Show that. Each one corresponds to a specific type of mathematical response and a particular level of detail.
The IB uses these terms consistently across papers and mark schemes. That consistency is deliberate. When you recognise the term, you know immediately what the examiner is looking for, which saves time and reduces errors in your answer structure.
2. Calculate and Find: when working must be shown
Both “Calculate” and “Find” ask you to produce a numerical or algebraic result. The key difference is that “Calculate” typically implies a multi-step process where intermediate working is expected. “Find” is slightly broader and may involve fewer steps, but showing your method still earns method marks.
Never write only a final answer for either term. Examiners award marks at each stage of working. A correct answer with no working shown can receive zero marks if the method is not visible.
3. State and Write down: direct answers only
When a question uses ‘write down’ or ‘state’, you give a direct answer without calculations or explanations. These terms signal that the answer should be immediately obvious from the context, a formula, or a previous result.
Students often over-explain here and waste time. If the question says “state the value of k”, write the value. One line is enough. Spending three lines justifying a “state” answer gains no extra marks and costs you time elsewhere.
4. How to interpret ‘show that’ in IB Maths
‘Show that’ means the result is already given and you must prove it step by step. You cannot work backwards from the answer. Your response must move logically from the starting point to the given result using clear, sequential steps.
A common mistake is to assume the result and then manipulate both sides of an equation simultaneously. Examiners reject this approach. Write each line of working as a consequence of the line before it.
Key rule for ‘show that’ questions: Every line must follow logically from the previous one. State any formula or rule you apply. Do not skip steps, even if they feel obvious.
Pro Tip: In ‘show that’ questions, write more steps than you think you need. Examiners award marks for visible reasoning, not just the final line.
5. How ‘hence’ links your answer to previous work
‘Hence’ is a direct instruction to use the result from a previous part of the question. You must build on what you already established. Using a completely different method, even if it produces the correct answer, will not receive full marks.
Experienced examiners include ‘hence’ to check logical continuity in your reasoning. Recognising this term quickly during a timed exam tells you exactly where to look for your starting point. It also tells you that the previous part was not just a standalone question but a building block.
When you see “hence or otherwise”, you may choose your method. However, using the previous result is almost always faster and aligns more closely with the mark scheme.
6. Justify: prove your reasoning, not just your answer
‘Justify’ requires clear, logical mathematical reasoning rather than a bare statement. Writing “the function is increasing because the gradient is positive” is not enough. You must show the gradient calculation and explain why it confirms your conclusion.
Think of “justify” as a mini-proof. The examiner wants to see the chain of logic that leads to your claim. One or two well-constructed sentences backed by mathematical evidence will score full marks. Vague statements will not.
7. Explain and Describe: words matter as much as numbers
“Explain” asks you to give reasons for a mathematical result or behaviour. “Describe” asks you to give a clear account of features or behaviour, often using information from graphs or tables. Both terms require written responses, not just numerical values.
For “describe”, name the feature you are addressing. For a graph, say whether a function is increasing or decreasing, identify any turning points, and note the behaviour at the boundaries. Vague phrases like “it goes up then down” lose marks. Precise language like “the function increases for x greater than 2 and has a local minimum at (2, 3)” earns them.
8. Sketch and Draw: know the difference
“Sketch” asks for a clear diagram showing key features without requiring precise accuracy. A sketch must show intercepts, turning points, and asymptotes, but exact coordinates are not always needed unless stated. The focus is on the shape and behaviour of the curve.
“Draw” is more demanding. It requires accuracy, often to scale, and may require you to plot specific points. Treating a “draw” question like a sketch will cost you marks.
- For sketches: label intercepts, turning points, and asymptotes clearly.
- For draw questions: use a ruler where appropriate and plot key coordinates accurately.
- For both: label axes and include units where relevant.
Pro Tip: Always label your sketch with at least the x and y intercepts and any asymptotes. An unlabelled sketch rarely receives full marks, even if the shape is correct.
9. Tips for mastering IB Maths exam language
Recognising command terms quickly under exam conditions is a skill you build through practice. These strategies will help you use them confidently.
- Learn the full list. The IB publishes its official list of command terms in the Mathematics subject guide. Read it before your first mock exam.
- Practise with past papers. Identify the command term in every question before you start answering. This builds the habit of reading the instruction first.
- Check your IB Maths vocabulary. Command terms sit alongside mathematical vocabulary. Knowing both gives you full clarity on what each question demands.
- Match your response to the term. Before writing, ask yourself: does this term need working, reasoning, a diagram, or a direct answer?
- Review mark schemes. The IB mark scheme shows exactly how examiners award marks for each command term. Seeing this pattern once changes how you answer permanently.
Pro Tip: Underline the command term as soon as you read a question. This single habit stops you from answering the wrong type of question under pressure.
Key takeaways
Mastering IB Maths command terms is the single most direct way to align your answers with examiner expectations and stop losing marks on questions you understand.
| Point | Details |
|---|---|
| Command terms define response type | Each term tells you whether to calculate, prove, sketch, or explain. |
| ‘Show that’ requires step-by-step proof | Work forward from the given information; never assume the result. |
| ‘Hence’ links to a previous part | Always use the result from the preceding sub-question when you see this term. |
| ‘State’ and ‘Write down’ need no working | Give a direct answer only; over-explaining wastes time and gains no marks. |
| Sketches need labelled key features | Mark intercepts, turning points, and asymptotes on every sketch. |
Why command terms are the most underrated exam skill
Students spend months mastering calculus and statistics, then drop marks because they wrote a sketch when the question said “draw”. I have seen this pattern repeatedly, and it is genuinely frustrating to watch, because the mathematics was correct.
The IB exam is not just a test of mathematical ability. It is a test of your ability to communicate mathematics in a specific way. Command terms are the code. Once you learn to read them fluently, you stop second-guessing your answers and start writing with real confidence.
The students who struggle most with command terms are usually those who read the numbers in a question before they read the instruction. Flip that habit. Read the command term first. Let it shape your entire approach before you write a single symbol.
Quick recognition also matters in timed conditions. Spotting “hence” in five seconds and knowing it means “use part (a)” is worth more than any shortcut formula. It keeps your reasoning on track and your answer aligned with the mark scheme from the first line.
— Oliver
Tibertutor: exam-focused support for IB Maths students
Building confidence with IB Maths assessment vocabulary takes consistent, targeted practice. Tibertutor is built by examiners and experienced educators who understand exactly how command terms appear in real exam questions and what responses earn full marks.
The platform offers exam-style questions and resources designed around the IB syllabus, giving you repeated exposure to command terms in context. You can also explore the IB Maths exam breakdown guide to see how command terms fit into the broader structure of each paper. Whether you are preparing for your first mock or your final exams, Tibertutor gives you the tools to practise with purpose and approach every question with clarity.
FAQ
What are IB Maths command terms?
IB Maths command terms are the official instruction words used in exam questions to specify the type and depth of response required. Terms like Calculate, Justify, Sketch, and Show that each demand a different style of answer.
What is the difference between ‘sketch’ and ‘draw’ in IB Maths?
‘Sketch’ requires key features such as intercepts and asymptotes without precise accuracy, while ‘draw’ demands a more accurate, often scaled, diagram with specific points plotted.
What does ‘hence’ mean in an IB Maths question?
‘Hence’ instructs you to use the result from a previous part of the question. Using a different method, even if correct, will not receive full marks.
When should I show working in IB Maths?
Show working for any term that implies a process, such as Calculate, Find, Solve, or Show that. Reserve direct answers for ‘State’ and ‘Write down’ questions only.
How do I learn all the IB Maths command terms?
Read the official IB Mathematics subject guide for the complete list, then practise identifying terms in past papers. Reviewing mark schemes alongside your answers reinforces exactly what each term expects.