The course and the exams

⚖️AI or AA — what the split really is

Every Diploma student takes one mathematics subject, and there are two to choose from, each available at standard and higher level. They are not a hard course and an easy course. They are different mathematics, aimed at different appetites.

• Applications and Interpretation (AI) is for students who want mathematics pointed at the world — modelling, statistics, and using technology to explore problems that would be intractable by hand. It is unusually rich in statistics, and it contains material you will not meet anywhere else in the Diploma, such as Voronoi diagrams and, at HL, graph theory and Markov chains.
• Analysis and Approaches (AA) is for students who enjoy building and justifying mathematical arguments. It leans on algebraic fluency, keeps calculus at its centre, includes formal proof, and examines a whole paper without a calculator.

“AI is the easy one” is the single most damaging myth about this course. AI HL is a demanding qualification with an enormous statistics and modelling load; AI SL contains real calculus. The honest test is which mathematics you want to do. If fitting a model to messy real data and arguing about what it means appeals more than manipulating an identity until it yields, you are in the right place; if the reverse, look at AA.

Do check your university course requirements before committing. Some engineering, physics and mathematics degrees name AA specifically, and a few name HL. Most other subjects — economics, business, social sciences, medicine, design — accept either, and several actively value the statistical grounding AI gives.

📚The five topics

• 1 — Number and algebra. Sequences and series, financial mathematics, approximation and error; at HL complex numbers, matrices and eigenvalues.
• 2 — Functions. Lines, graphs and a library of models, plus the modelling cycle; at HL logistic, piecewise and logarithmic models and linearised data.
• 3 — Geometry and trigonometry. Solids, the sine and cosine rules, Voronoi diagrams; at HL matrix transformations, vectors and graph theory.
• 4 — Statistics and probability. The largest topic: sampling, summary statistics, regression, distributions and hypothesis testing; at HL confidence intervals, Poisson and Markov chains.
• 5 — Calculus. Differentiation, optimisation, integration and the trapezoidal rule; at HL further differentiation, kinematics and differential equations.

The first few sub-topics of each topic are shared word for word with AA, which is why a friend on the other course can genuinely help you with straight lines and the sine rule — and cannot help you at all with Voronoi diagrams or chi-squared tests.

🎓SL or HL

Standard level is 150 teaching hours; higher level is 240. The additional higher level material sits inside the same five topics rather than in separate units, and both levels are examined on the shared content in the same papers.

The two places the levels diverge most are worth knowing before you decide. Topic 3 goes from 18 hours at SL to 46 at HL — almost all of that being vectors, matrix transformations and graph theory, which SL students never see at all. And Topic 5 goes from 19 hours to 41, adding the differentiation rules, kinematics and differential equations. AI HL is not AI SL with extra statistics; it is a substantially wider course.

📝How you are assessed

Standard level — three hours of examinations plus the Exploration.

• Paper 1 — 40%, 90 minutes, 80 marks. Compulsory short-response questions across the whole syllabus. Technology required.
• Paper 2 — 40%, 90 minutes, 80 marks. Compulsory extended-response questions. Technology required.
• The Exploration — 20%, marked out of 20 across five criteria, internally marked and externally moderated.

Higher level — five hours of examinations plus the same Exploration.

• Paper 1 — 30%, 2 hours, 110 marks. Short-response.
• Paper 2 — 30%, 2 hours, 110 marks. Extended-response.
• Paper 3 — 20%, 1 hour, 55 marks. Two long problem-solving questions, each developing a single theme towards a generalisation or the interpretation of a context. This paper exists only at HL, and it is unlike anything in Papers 1 and 2 — practise it separately.
• The Exploration — 20%.

🔢The formula booklet

You are given a clean copy of the mathematics formula booklet in every paper. It carries the sequence and series formulae, the compound interest formula, the geometry and trigonometry formulae, the statistical formulae and the standard derivatives and integrals. Do not spend revision time memorising what is printed for you.

Spend it instead on knowing which formula applies and why, and on what the booklet does not give: the shapes of the standard models and what each parameter does to them, when a \(\chi^2\) test is appropriate rather than a \(t\)-test, and how to phrase a conclusion in context. Work with the booklet open from the first week so that finding a result in it under time pressure is automatic.

📝Command terms are instructions, not decoration

Examiners choose these words carefully and the markscheme follows them exactly. AI leans particularly hard on the interpretation terms.

• Write down — little or no working expected; you are extracting an answer.
• Find / Calculate — show the relevant stages of working.
• Show that — the answer is given; the marks are for the route to it.
• Hence — you must use the previous part. Hence or otherwise means you may start again if you prefer.
• Interpret — say what the number means for the situation, in words, with units. A bare value scores nothing here.
• Comment on — give a judgement based on the result, not a restatement of it.
• Justify — give the reason, not just the conclusion.
• Sketch — general shape with the important features labelled. Draw — accurate and to scale.

Marks are awarded for method, accuracy, answers and reasoning including interpretation. That last word is why AI candidates who write only numbers underperform candidates who understand less mathematics but write sentences.

✍️Accuracy conventions worth fixing now

Unless a question says otherwise, give final answers either exactly or to three significant figures. Keep full accuracy in your calculator through the middle of a question and round only at the end — rounding at every step is how a correct method produces an answer the markscheme will not accept. Never write calculator notation such as 5.2E30 in an answer, and give units and a context wherever the question involves a real quantity.