IB Math AI HL Paper 3 in 4 steps

Paper 3 is one hour long and worth 55 marks. It has two extended questions, each worth between 24 and 31 marks, and a GDC is allowed. It is 20% of your HL grade. Paper 1 is 30%, Paper 2 is 30% and the internal assessment is 20%.

Papers 1 and 2 test topics one at a time. Paper 3 gives one real-looking situation and takes you through it in 4 to 11 lettered parts, 7 on average. A study, a pair of lakes, a delivery network, a growth table: you model it, compute with the GDC and then say what the numbers mean.

Interpretation carries as many marks as arithmetic. A correct test statistic with no sentence in context loses marks. Each answer needs the model or test named, the value, and a sentence with units. Never write calculator keystrokes as your answer.

Notes alone do not train this. You need to sit a whole question against the clock, write full reasons and see where marks go. Every question follows the same six-stage pattern, and the nine types below cover all 40 questions we read. A statistical test appears in 15 of the 40 and a differential equation in 10.

Every question follows the same arc

1. OrientShort opening parts: a sketch, the first few terms, the name of a test. Later parts reuse these numbers, so do them carefully.
2. StructureThe derivation everything rests on, usually a show that. Write a chain from what you know to the printed line.
3. ExploreThe GDC earns the facts: vary a parameter, tabulate a sequence, run a regression or a test.
4. DeduceThe pattern is proved or explained. This is where the proof and reasoning marks sit.
5. GeneraliseThe longest parts. They repeat an earlier argument with letters, or add a twist such as a new starting value.
6. InterpretOne or two marks for a sentence: a meaning, a comparison or a limit of the model. Reach it even after a bad middle.

Done, next step →

We sorted all 40 questions in 20 papers, from the specimen paper to May 2026, into 9 types. Most common first. Open one at a time.

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Screen breaks at a call centre · 26 marks

This question asks you to judge whether short screen-free breaks improve the reaction times of call-centre staff. Priya manages a call centre. She measures the reaction time, in milliseconds (ms), of eight members of staff on a computer task, gives each of them a ten-minute screen-free break, and measures them again. $$\begin{array}{|l|r|r|r|r|r|r|r|r|}\hline \text{Staff member} & A & B & C & D & E & F & G & H\\\hline \text{Before (ms)} & 312 & 298 & 335 & 290 & 305 & 321 & 287 & 342\\\hline \text{After (ms)} & 301 & 296 & 318 & 285 & 299 & 309 & 290 & 326\\\hline\end{array}$$

Try each part yourself first, then open its solution. M is a method mark, A accuracy, R reasoning and AG a given answer.

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How to spend the hour

1. 0–3 minRead both questions. Note which has a test, a table or a diagram, and start with the one whose first parts you can do.
2. 3–8 minFirst question, opening parts: describe the data, set up the model or name the test. Write the context in a short phrase.
3. 8–18 minFirst question, structure and explore: the derivation, then the GDC work. Write what you entered and the value you read.
4. 18–30 minFirst question, deduce and interpret: the decision, the meaning in context, the limits of the model. Stop at 30 minutes.
5. 30–35 minSecond question, opening parts, with the same care.
6. 35–45 minSecond question, structure and explore.
7. 45–55 minSecond question, deduce, generalise and interpret. A sentence in context is worth a mark, so keep time for it.
8. 55–60 minGo back to the gaps. Check that each answer has units and a sentence, that hypotheses are about the population and that values are to 3 significant figures.

Five ways marks are lost

1. 1No sentence in context. After every number, write what it means in the story with its units. A decision with no context loses the reasoning mark.
2. 2Hypotheses about the sample. Write $\mathrm{H}_0$ and $\mathrm{H}_1$ about the population mean or proportion, and define the symbol. A hypothesis about $\bar{x}$ earns nothing.
3. 3Writing the calculator, not the model. Name the test or the model, then give the value. A line of menu commands is not an answer. Write what you entered, then the result.
4. 4Rounding early. Keep the full value on the GDC and round only the final answer to 3 significant figures, unless the question says otherwise.
5. 5Skipping the criticism parts. The last parts ask what the model leaves out or how the study could be improved. They are one or two marks each and answerable after a poor middle. Reach them.

The weeks before

1. Wk 1–2Repair the toolkit Paper 3 draws on: hypothesis tests, matrices, differential equations, regression and vectors. Use short exercises on the GDC.
2. Wk 3Learn the six stages and the mark codes. Read one worked investigation slowly, cover the solution and compare line by line.
3. Wk 4–5Work the statistics type in full, then vectors, motion and shape and networks. One question per sitting, untimed, writing every sentence.
4. Wk 6Cover the remaining types with one question each. Keep an error log of lost marks by type and stage.
5. Wk 7Sit full Paper 3s in one hour, with a GDC and no notes. Mark each against a written markscheme and rewrite the parts you lost.
6. Wk 8Redo your weakest type. Reread the error log, the mark codes and the hour plan. Sit one last paper two or three days before the exam, then stop.

Done