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IB Mathematics: Applications and Interpretation HL

IB Math AI HL, topic by topic

Applications and Interpretation HL is the IB's technology-first mathematics course at higher level: all of AI SL, plus complex numbers, matrices, vectors, graph theory, further statistics and differential equations. This page maps the course — how it is assessed and what each topic contains — and links to a guide for every topic showing how its marks are awarded.

The course at a glance

The structure of the course as the IB publishes it.

Written papers

Paper 1, Paper 2 and Paper 3

Papers 1 and 2 are 2 hours, 110 marks and 30% each. Paper 3 is an hour of extended problem-solving, 55 marks and 20%. Technology is allowed on all three.

Internal assessment

Mathematical exploration

A piece of independent mathematical writing, worth 20% of the grade.

Syllabus

5 topics · 78 sections

The 39 sections of AI SL (numbered SL) plus 39 HL-only sections (numbered AHL).

Teaching time

240 hours

As recommended by the IB for a higher-level course, including the toolkit and the exploration.

How AI HL differs from AI SL

HL is not a different course; it is the same course taken further, with an extra paper. These are the differences that change what you practise.

  • AI HL contains every AI SL section. They are examined at HL too, usually inside longer and more connected questions.

  • HL adds 39 sections of its own: complex numbers, matrices and eigenvalues, vectors in three dimensions, graph theory, further statistics and differential equations.

  • HL students sit Paper 3, an hour of extended problem-solving that follows one situation through a sequence of linked parts. SL students do not.

  • HL calculus goes beyond polynomials — chain, product and quotient rules, substitution and volumes of revolution. SL calculus stays with polynomials and the trapezoidal rule.

  • Both courses are technology-first, with a calculator on every paper.

See the Math AI SL topic guides →

How AscentIQ covers AI HL

Every exercise is generated fresh, marked mark by mark against the IB scheme, with a reason for each M1, A1 and R1. For AI HL that comes with some course-specific behaviour.

  • 157 exam archetypes: everything in AI SL, plus 64 written for the HL-only sections.

  • Paper 3 practice: eight extended-investigation families, each following one situation through many linked parts.

  • Paper 2 long questions: twelve families that mix SL and HL sections the way the extended questions do.

  • Answers in the forms a mark scheme accepts — a matrix, a complex number, a vector or a line can each be written in more than one correct way.

  • Graph-theory questions have exactly one right answer: the engine rejects any graph where two correct runs of an algorithm could differ.

  • Radians from AHL 3.7, with the unit stated, and answers kept to the figures asked for — a three-significant-figure answer is written with all its figures, 6.40 and not 6.4.

  • Honest limits: a few sections — including SL 2.3 (sketching graphs), AHL 1.10 (rational exponents) and AHL 3.8 (the unit circle and identities) — do not have a dedicated exercise yet, and a question whose whole answer is a sketch is asked through values instead.

Questions

Questions about IB Math AI HL

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