IBDP Maths Class 11 and 12: Analysis and Approaches, Applications and Interpretation

Four courses, not one

IB Diploma mathematics is Analysis and Approaches or Applications and Interpretation, each at Higher or Standard Level. Those are four genuinely different syllabuses, not one subject at four difficulties, and a course page that treats them as interchangeable is no use to anyone choosing between them.

Analysis and Approaches develops mathematical analysis through functions and calculus, and rewards algebraic manipulation and proof. Applications and Interpretation is modelling, statistics and technology-oriented. Higher Level is 240 teaching hours against 150 at Standard Level, so HL is not simply harder — it is substantially more material at a faster pace.

One structural point that is useful later: each SL course is a complete subset of its HL course. Nothing an HL student learns is wasted if they move down.

What the examinations actually look like

At Standard Level: Paper 1 and Paper 2, each 1 hour 30 minutes, each worth 40 per cent, plus the Exploration at 20 per cent. Three hours of examinations in total.

At Higher Level: Paper 1 and Paper 2, each 2 hours, each worth 30 per cent; then Paper 3, one hour, 20 per cent, consisting of two compulsory extended-response problem-solving questions; plus the Exploration at 20 per cent. Five hours in total.

Paper 3 deserves separate mention because it exists only at HL and is a different task from the others. Instead of a spread of questions it asks a student to sustain work on a longer problem that develops in stages. Students who have practised only short questions find it genuinely uncomfortable, so we treat it as its own skill.

The choice is a university decision

Mathematics-heavy degrees — engineering, mathematics, physics, computer science, and economics at many universities — commonly ask for Analysis and Approaches, frequently at Higher Level. A student who takes AI because it looks more manageable may find a programme closed to them two years later.

Requirements are set per university and per programme, and they change. Check the entry requirements of the specific courses your child may apply to. No general statement, this one included, is a substitute for reading them.

The corollary matters too: a student heading for design, social sciences or business is often better served by AI, where the statistics and modelling are more relevant and the grade more achievable. Taking AA HL to look serious and finishing with a poor grade helps nobody.

The Exploration is a fifth of the grade

The internal assessment — the Exploration — carries 20 per cent of the final grade in both subjects at both levels, and it is compulsory. It is a piece of independent mathematical writing on a topic the student chooses, done without examination time pressure, and the assessment criteria are identical for SL and HL.

What it rewards is worth being precise about: mathematical communication — formulae, diagrams and graphs with accompanying commentary — together with good mathematical writing and genuine reflection. A correct result with no reflection scores poorly.

Students routinely treat it as a side project, start it late, and lose marks that were entirely available. The commonest failure is a question that is far too broad: the student picks something ambitious, cannot develop it in the space available, and the mathematics stays shallow throughout. A narrower question with real mathematical development scores better every time.

We timetable the Exploration into the course rather than leaving it to be discovered in Class 12, and supervise it individually against the published criteria.

The calculator rule differs between the two subjects

This is the sharpest practical difference between AA and AI, and families are routinely surprised by it.

In Analysis and Approaches, Paper 1 allows no technology at all; Paper 2 does. In Applications and Interpretation, every external assessment involves technology — there is no non-calculator paper.

So the two courses demand different disciplines. An AA student must keep real algebraic fluency alive, because on Paper 1 there is nothing to fall back on and no way to check a manipulation. An AI student must be genuinely fast and accurate with a graphical display calculator, because it is assumed throughout and a student who is slow with it loses time that cannot be recovered.

We practise accordingly rather than treating the calculator as a convenience.

The syllabus, and where HL students fall behind

Number and algebra: sequences and series, exponents and logarithms, the binomial theorem, with proof by induction and complex numbers at HL. Functions: domain and range, composite and inverse functions, transformations, quadratic, rational and exponential functions. Geometry and trigonometry: radians, trigonometric functions and identities, equations, and vectors at HL. Calculus: limits, differentiation and integration with their applications. Statistics and probability: binomial and normal distributions, correlation and regression, and the hypothesis testing that AI weights heavily.

HL students most often fall behind on the additional HL content specifically, because it arrives on top of a syllabus that is already full. We take it as it comes rather than deferring it to a revision block that never has enough room.

Both courses also include a 30-hour toolkit element for investigation, modelling and inquiry work and for completing the Exploration. It sits inside the 150 or 240 hours rather than being added on top, and teachers decide where to use it — which in practice means it is easy to let it quietly disappear into content teaching, and then the Exploration has no time of its own.

Changing level, honestly

If a student is struggling at Higher Level, that conversation belongs in Class 11, not Class 12. It is also less wasteful than families fear: because each SL course is a complete subset of its HL course, nothing already covered is thrown away.

For most university applications a strong SL grade is worth more than a poor HL grade — with the significant exception of programmes that explicitly require HL, which is exactly why the university plan has to be on the table.

We give a direct view rather than an encouraging one. The deadline for changing level is set by your school.

How the classes run

Live online group classes, a maximum of eight students, grouped by course and level so an AA HL student is never sitting through AI SL material. Exploration work is supervised individually, and past papers in the closing weeks are sat under time with calculator and non-calculator papers practised separately.

Who this suits

Students in Class 11 or 12 taking any of the four DP mathematics courses. Entry assumes MYP 5 extended, IGCSE Extended, CBSE Class 10 Standard or an equivalent background; HL entry is assessed before joining, because starting HL without the algebra it assumes is a decision that unravels in the second term.

A change coming in 2027

One thing every family choosing now should know. The IB reviews each DP subject on a seven-year cycle, and a revised mathematics curriculum has first teaching in August or September 2027, with first assessment in May 2029. It covers both AA and AI.

In practical terms, a student starting DP in 2026 and examined in 2028 follows the current syllabus. A student starting in 2027 follows the new one. Since most families reading this are choosing for a child who will enter DP in 2027, that is the relevant case.

What actually changes in content and assessment has not been published in full. We are not going to guess, and we would treat any page that claims to know the detail of the new courses with suspicion. Ask your school's DP coordinator which syllabus your child's cohort will be taught, and we will teach to that.

Session dates, grade boundaries and subject guide details are set by the IB and change between sessions. Check ibo.org and your school's coordinator for the current requirements.