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.
The five topics
Each topic has its own guide: the sections it covers, how they are examined, a marked example and the mistakes that cost marks.
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.
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
Yes. A graphic display calculator is allowed on all three papers. Where a question asks for an exact value or a stated form, the answer is exact and the calculator only checks it.
Three written papers and an internal assessment. Papers 1 and 2 are 2 hours and 110 marks each, worth 30% of the grade each; Paper 3 is an hour and 55 marks, worth 20%; the mathematical exploration is worth the remaining 20%.
The third paper, taken only by HL students: an hour of extended problem-solving questions that follow one situation through a sequence of linked parts, often in a context you have not seen before. AscentIQ has eight Paper 3 practice families.
AI HL contains all of AI SL and adds 39 HL-only sections — complex numbers, matrices, vectors, graph theory, further statistics and differential equations — plus Paper 3. Both are technology-first, with a calculator on every paper.
Nearly all of it: exercises for the large majority of the 78 sections, Paper 2-style long questions and Paper 3 practice. A few sections do not have a dedicated exercise yet, and AA HL is not covered.
Try AI HL practice, marked like the real thing
Seven days of full access, no card required. Every exercise is generated fresh and every mark comes with a reason.
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