IB maths vocab: key terms for exam success
12 min readOliver Kidd (Co-founder)15 Jun 2026
IB Maths vocab is the specialised language of the IB Mathematics curriculum, and knowing it precisely is one of the clearest paths to higher exam marks. Every question paper uses command terms and technical language to signal exactly what examiners expect. Miss those signals, and you lose marks even when your mathematics is correct. The IBO curriculum is built around developing abstraction and generalisation through precise vocabulary, which means the words you use in your answers carry real weight.
1. what are IB maths command terms?
Command terms are the explicit instructions embedded in every IB exam question. They tell you how to answer, not just what to answer. Approximately 15 core command terms appear across DP Mathematics assessments, including Calculate, Show, Prove, Derive, Find, State, Sketch, Hence, and Justify.
Each term carries a different expectation. “State” means give a direct answer with no working. “Calculate” means show your method and reach a numerical result. “Prove” means construct a rigorous logical argument from first principles.
The most common student error is treating all command terms as interchangeable. Writing a full derivation when a question says “State” wastes time. Giving only an answer when a question says “Show” loses method marks.
Pro Tip: Underline the command term in every question before you write a single number. It takes three seconds and keeps your response focused.
2. the difference between “show,” “prove,” and “verify”
These three terms confuse students more than any others in the IB Mathematics lexicon. They look similar but demand very different responses.
“Show” means demonstrate a given result using clear mathematical steps. The answer is provided for you; your job is to produce the working that leads to it. “Prove” requires a formal logical argument, often from axioms or established results. “Verify” simply means substitute values and confirm a result holds numerically.
Using “Verify” logic when a question says “Prove” is a mark-losing mistake. Examiners are trained to spot the difference. Command terms dictate both the method and the presentation expected in your answer.
3. core algebra vocabulary you must know
Algebra forms the backbone of both Analysis and Approaches (AA) and Applications and Interpretation (AI) courses. Students must be fluent with terms including polynomial, quadratic, binomial expansion, arithmetic sequence, geometric sequence, and asymptote.
Knowing the word is not enough. You need to use it correctly in context. Writing “the curve approaches the asymptote” is far stronger than writing “the line gets close to the other line.” Examiners reward precise language because it signals genuine understanding.
Pro Tip: When you practise past paper questions, write out your reasoning in full sentences using correct terminology. This builds the habit of communicating mathematically, not just calculating.
4. calculus terms that appear in every paper
Calculus vocabulary is non-negotiable for AA HL and SL students. The key terms in IB Maths include derivative, integral, definite integral, indefinite integral, optimisation, inflection point, concavity, and differential equation.
Using terms like “integral” or “derivative” signals conceptual fluency to examiners. Writing “the area under the curve” when you mean “the definite integral” is technically acceptable, but precise terminology scores better in extended-response questions.
Optimisation questions are a particular area where vocabulary matters. You must state whether a point is a maximum or minimum and justify it using the second derivative test or a sign diagram. The words “hence” and “therefore” signal logical progression in your working.
5. statistics and probability: a vocabulary category students underestimate
Statistics and probability carry significant weight in both AA and AI courses, yet many students neglect the vocabulary. Key terms include normal distribution, probability density function, hypothesis testing, null hypothesis, significance level, correlation coefficient, and regression line.
Misusing these terms in Paper 2 or Paper 3 responses costs marks. Saying “the data is normal” instead of “the data follows a normal distribution” is imprecise. Examiners notice the difference between a student who understands the concept and one who is guessing at the language.
The IB Mathematics lexicon for statistics also includes terms like “unbiased estimator” and “confidence interval,” which appear in HL content and require exact usage.
6. geometry and vectors: terms that carry marks
Geometry vocabulary covers vectors, transformations, matrices, and coordinate geometry. Core terms include position vector, unit vector, scalar product, cross product, transformation matrix, translation, rotation, reflection, and enlargement.
Each transformation has a precise name. Writing “the shape moved” instead of “the shape underwent a translation” loses marks in a question asking you to describe a transformation fully. The word “describe” is itself a command term requiring you to name the transformation and state its key properties.
Vectors questions often use the term “hence” to link parts together. Recognising this connection is part of mastering IB Maths language at the level examiners expect.
7. paper 3 vocabulary: from calculation to generalisation
Paper 3 in AA HL is the most vocabulary-intensive component of the entire course. Paper 3 contains extended-response questions that progress from straightforward calculations through to generalisations and formal proofs, each requiring precise vocabulary at every stage.
The transition words matter enormously here. Terms like “conjecture,” “generalise,” “verify,” “comment,” and “hence” signal the type of reasoning required at each step. A conjecture is an educated mathematical guess that you then prove or disprove. Confusing it with a proof is a serious error.
Ignoring the command term “Hence” in Paper 3 is one of the most common causes of lost marks. It signals that you must use the result from the previous part, not start a fresh method. Starting fresh may produce the correct answer but earns zero marks.
The Paper 3 investigative format tests whether you can communicate mathematical reasoning, not just execute calculations. Vocabulary is the tool you use to do that.
8. how to build your IB maths word list effectively
Learning math vocabulary for IB exams works best when you connect terms to concepts rather than memorising definitions in isolation. The most successful students combine vocabulary knowledge with problem-solving practice and past paper review.
Here is a practical approach:
- Create a personal glossary organised by topic (Algebra, Calculus, Statistics, Geometry).
- Write a definition in your own words alongside the formal IB definition.
- Add an example question that uses the term.
- Use word banks in revision worksheets to test recall under timed conditions.
- Review command terms separately and practise identifying them in past papers.
Flashcards work well for command terms specifically. Write the term on one side and the expected response type on the other. Test yourself before each study session, not just before the exam.
Pro Tip: Read your answers aloud after writing them. If you cannot explain what you did using correct terminology, your written answer probably lacks clarity too.
Key takeaways
Mastering IB Maths terminology is not optional. It is the mechanism by which examiners distinguish students who understand mathematics from those who can only calculate it.
| Point | Details |
|---|---|
| Command terms direct your response | Identify the command term in every question before writing to match examiner expectations. |
| Precise vocabulary signals fluency | Using terms like “derivative” or “normal distribution” correctly earns marks beyond correct answers. |
| “Hence” is a critical signal | Ignoring “Hence” in Paper 3 means starting a fresh method, which earns zero marks even if correct. |
| Build a topic-organised glossary | Group terms by Algebra, Calculus, Statistics, and Geometry for structured revision. |
| Vocabulary enables generalisation | In Paper 3, terms like “conjecture” and “verify” guide the reasoning structure examiners reward. |
Why vocabulary is the skill most students ignore
Students often tell me they “know the maths” but cannot understand why their marks are lower than expected. When I look at their scripts, the pattern is almost always the same. The calculations are correct, but the communication is vague. They write “the graph goes up then down” instead of “the function has a local maximum at x = 3.” They answer “Show” questions as if they were “Find” questions.
The IB curriculum develops logical and creative thinking through abstraction and generalisation. That process requires language. Without the right vocabulary, you cannot fully express mathematical reasoning, and examiners cannot award the marks your thinking deserves.
My honest view is that vocabulary revision should start on day one of the course, not in the final weeks before exams. Treat command terms like a separate subject within Maths. Make a complete IB Maths guide part of your regular study toolkit. The students who score 6s and 7s are not always the fastest calculators. They are the clearest communicators.
— Oliver
How Tibertutor helps you master IB maths exam skills
Tibertutor is built by examiners and experienced educators who understand exactly what IB assessments demand. If you want structured support with command terms, core concepts, and exam technique, Tibertutor gives you the resources to build real confidence.
The platform offers exam-style questions, detailed notes, and flashcards designed specifically around IB curriculum vocabulary and marking expectations. You can track your progress by topic and identify precisely where your understanding needs strengthening. Whether you are preparing for Paper 1, Paper 2, or the demanding Paper 3, Tibertutor’s IB student resources give you the targeted practice that turns vocabulary knowledge into exam marks.
FAQ
What are command terms in IB maths?
Command terms are explicit instructions in IB exam questions that direct the type and depth of response required. There are approximately 15 core command terms used across DP Mathematics, including Calculate, State, Prove, and Hence.
Why does “hence” matter so much in IB maths exams?
“Hence” signals that you must use the result from the previous part of the question. Starting a fresh method, even if it produces the correct answer, earns zero marks.
Which topics have the most important IB maths terminology?
Calculus, statistics, and geometry carry the densest vocabulary demands. Key terms include derivative, integral, normal distribution, hypothesis testing, vector, and transformation.
How do i learn IB maths vocabulary efficiently?
Build a topic-organised glossary, use flashcards for command terms, and practise writing full explanations using correct terminology alongside past paper questions. Linking terms to worked examples is more effective than memorising definitions alone.
Does using correct terminology actually affect my IB maths marks?
Yes. Examiners reward precise language because it demonstrates conceptual fluency. Using terms like “inflection point” or “regression line” correctly signals understanding that vague descriptions cannot convey.