Extended-response questions in IB Mathematics: Analysis and Approaches reward more than a correct final value. To maximise marks, translate the command term, plan the mathematical route, show each important method, preserve exact values where appropriate, and finish with a clear answer that addresses the question.
This matters because IB markschemes award credit for method, accuracy and reasoning. A numerical slip does not necessarily destroy the whole response if the examiner can see a valid method and follow your subsequent work.
Where extended-response questions appear
Under the current Mathematics: Analysis and Approaches course, both SL and HL students encounter compulsory extended-response questions in Section B of Papers 1 and 2. HL students also take Paper 3, which consists of two compulsory extended-response problem-solving questions.
Paper 1 does not allow technology, while Papers 2 and 3 require appropriate technology. These differences change the tools available, but not the central expectation: your mathematics must be communicated clearly enough to be assessed.
The official IB subject brief identifies problem solving, communication, technology and reasoning as assessment objectives. Long questions often combine several of these objectives, which is why they may move through algebra, interpretation, proof and evaluation within one connected context.
How marks accumulate in a long Maths AA response
The official specimen markschemes use several important abbreviations:
| Mark type | Meaning | What your response must show |
|---|---|---|
| M | Method | An attempt to use an appropriate process, formula or technique |
| A | Answer or accuracy | Correct execution or a correct result, often dependent on a method mark |
| R | Reasoning | A valid explanation, justification or mathematical argument |
| AG | Answer given | The target is supplied in the question, so marks come from reaching it validly |
| FT | Follow-through | Credit for correctly continuing from an earlier incorrect result where applicable |
This system explains why unsupported calculator answers are risky. The IB explicitly states that full marks are not necessarily awarded for a correct answer without working and that answers should be supported by calculations, diagrams, graphs or explanations.
Suppose a question asks you to find the maximum volume of a container. A complete response may earn separate marks for forming the volume function, differentiating it, solving the stationary-point equation, verifying that the point is a maximum and stating the resulting volume with units. Writing only the final volume makes most of those mathematical decisions invisible.
Use a five-stage structure for every long question
1. Decode the task before calculating
Read the entire question, including later parts, before beginning. Underline the command term, identify the requested quantity and note restrictions such as an interval, exact form, specified accuracy or contextual units.
Then identify what earlier parts establish. Extended questions are usually designed as connected chains, so a derivative, identity or parameter found in one part may be intended for use later.
2. Establish the mathematical setup
Begin with the equation, theorem, diagram or model that controls the solution. Define variables if the question has not already done so, and label diagrams sufficiently to make your reasoning readable.
A strong opening is mathematically informative:
Let x be the radius of the cylinder in centimetres.Using conservation of area, 2πrh + 2πr² = 600.At a stationary point, V'(r) = 0.
Avoid spending time copying the full question. Your setup should reveal your strategy, not reproduce information already visible to the examiner.
3. Show the mark-bearing transitions
Write enough intermediate work to show how one expression leads to the next. For algebra, display substitutions, rearrangements, factorisation and rejected roots when they affect the answer.
For calculus, show the function being differentiated or integrated and identify the condition being used. For probability, state the distribution and its parameters before entering values. For vectors, identify the equation or geometric relationship before simplifying components.
You do not need to record every piece of mental arithmetic. The goal is to expose the decisions and transformations on which marks depend.
4. Justify and interpret
Many students stop when the calculation ends, even though the command term asks for more. If the question asks you to justify a maximum, use an appropriate argument such as a negative second derivative, a derivative sign change or a comparison with relevant endpoints.
In context, translate the result back into the problem. If a model gives t = 4.73, explain what 4.73 represents and whether rounding to a whole number is necessary. Check that probabilities lie between 0 and 1, lengths are positive and solutions belong to the stated domain.
5. Present the final answer clearly
End each part with an unmistakable conclusion. Include units, coordinates, an interval, exact form or required degree of accuracy as appropriate.
Unless a question states otherwise, the current IB examination convention is to give numerical answers exactly or correct to three significant figures. Keep unrounded calculator values during intermediate work so that premature rounding does not alter later answers.
Match your response to the command term
The command term determines what evidence the examiner needs. The same mathematical topic can require very different responses.
| Command term | Required response |
|---|---|
| Find / Calculate | Obtain the answer while showing the relevant stages of working |
| Show | Give the calculation or derivation steps |
| Show that | Reach the supplied result through valid working without assuming it |
| Hence | Use the preceding result to obtain the new answer |
| Hence or otherwise | The preceding result is suggested, but another valid method may earn credit |
| Prove | Give a formal sequence of logical steps leading to the required result |
| Justify | Supply valid mathematical reasons or evidence |
| Interpret | Use the result to identify a trend or conclusion in context |
| Sketch | Show the general shape with relevant features and labels |
In a show that question, reverse-engineering the printed answer is not enough. Begin from established information and transform it logically until the given result appears. Since the final answer is already supplied, the working is the substance of the response.
The word hence is equally important. It signals that you should use preceding work, often through a short substitution or deduction. Ignoring that link can create an unnecessarily long method and may fail to satisfy the intended instruction.
Adapt your working to each paper
Paper 1
Without a calculator, algebraic fluency and exact forms become especially important. Write identities, substitutions and transformations carefully, and avoid converting exact values such as radicals or multiples of π into decimals unless requested.
If you become stuck, write the relevant formula and make a meaningful substitution. This can expose a viable next step and may also earn method credit. The RevisionDojo guide to Maths AA Paper 1 provides additional paper-specific practice advice.
Papers 2 and 3
Technology can perform calculations, but it does not replace mathematical communication. Record the equation solved, the function analysed, the distribution used or the integral evaluated rather than writing only a calculator result.
For example, write P(X ≥ 14), where X ~ B(20, 0.6) before giving the numerical probability. For a numerical intersection, state the equations or define the function whose zero you found. Check angle mode, graph windows and statistical settings before trusting an output.
What to do when you are stuck
Do not leave an extended-response page blank. Long questions contain several possible entry points, and later parts may still be accessible.
Use this recovery sequence:
- Rewrite the known quantities and the requested quantity.
- Identify the relevant syllabus topic and formula.
- Draw or annotate a diagram if geometry, vectors or rates are involved.
- Attempt a substitution or define the necessary function.
- Move to the next part if progress stops, then return later.
If an earlier answer is wrong, use it consistently in later parts unless the result is impossible or the question supplies another value. Follow-through marks may be available when the later method remains valid. Clearly label the value you are carrying forward so the examiner can follow your reasoning.
Common mistakes that lose avoidable marks
- Giving a calculator answer without showing the mathematical setup
- Treating show that as permission to quote the required result
- Ignoring hence and repeating the problem by an unrelated route
- Rounding intermediate values too early
- Failing to reject solutions outside the domain or context
- Claiming a stationary point is a maximum without verification
- Omitting units or misreading significant figures
- Using calculator notation instead of standard mathematical notation
- Crossing out readable work before a replacement method is complete
- Continuing for several lines after obtaining a correct answer and introducing a contradiction
Readable layout also matters. Start each subpart on a new line, align equations where helpful and separate alternative attempts. Examiners can award only the marks supported by work they can understand.
Practise by studying how marks are built
Watching a model question being worked through is useful because it makes the hidden structure visible: where the method begins, which transition earns accuracy credit and where reasoning must be stated. Do not watch passively. Pause before each step, predict what should happen and then compare the model with your plan.
Use the RevisionDojo Maths AA hub and its question-level video resources to access Maths AA materials, including worked content and available per-question video support. The Maths AA video library is useful when you need to see a method performed rather than merely read the final markscheme.
Follow each model with a fresh question from the Maths AA Questionbank. After marking, use the guide to analysing IB Maths markschemes to classify each lost mark as a content, method, accuracy, command-term or communication error.
For timed preparation, combine targeted practice with Maths AA predicted papers. Jojo AI can help explain why a step was incomplete, but you should still compare your written solution line by line with the available markscheme or worked solution.
Conclusion
Successful IB Maths AA long answers follow a visible chain: decode the instruction, establish the model, show the important transitions, justify conclusions and present the final result in the required form. Full working protects method and follow-through marks while command-term alignment ensures that you answer the task actually set.
RevisionDojo can support this process through model videos, the Maths AA Questionbank, markscheme review and timed papers. Begin with the per-question video solutions, imitate the structure on a similar problem, and then test the method independently under timed conditions.
Sources and referenced URLs
- Official IB Mathematics: Analysis and Approaches guide
- Official IB Mathematics: Analysis and Approaches subject brief
- Official IB Mathematics: Analysis and Approaches specimen papers and markschemes
- RevisionDojo IB Mathematics AA resources
- RevisionDojo IB Mathematics AA Questionbank
- RevisionDojo Mathematics AA video library
- RevisionDojo Maths AA Paper 1 strategy
- RevisionDojo guide to analysing Maths markschemes
- RevisionDojo Mathematics AA predicted papers