IB Diploma Programme
IB Mathematics: Analysis and Approaches HL
AA HL is the most demanding IB Diploma maths course, with a strong emphasis on algebra, calculus and proof. It is the usual choice for students heading to mathematics, engineering, physics or economics.
- Paper 1
- 2 hours, no calculator, 110 marks, 30%
- Paper 2
- 2 hours, calculator, 110 marks, 30%
- Paper 3
- 1 hour 15 min, calculator, 55 marks, 20%
- Exploration (IA)
- 20 marks, 20%
Papers, marks and weightings
| Component | HL | SL |
|---|---|---|
| Paper 1 (no calculator) | 2 hours · 110 marks · 30% | 1 hour 30 min · 80 marks · 40% |
| Paper 2 (calculator) | 2 hours · 110 marks · 30% | 1 hour 30 min · 80 marks · 40% |
| Paper 3 (problem solving) | 1 hour 15 min · 55 marks · 20% | Not taken at SL |
| Exploration (IA) | 20 marks · 20% | 20 marks · 20% |
Papers 1 and 2 each have Section A (short questions) and Section B (long questions). Paper 3 has two compulsory extended problem-solving questions. Teaching time: 240 hours at HL, 150 at SL.
Syllabus: the five topics
| Topic | SL hours | HL hours |
|---|---|---|
| 1. Number and algebra | 19 | 39 |
| Sequences and series, logarithms, binomial theorem, proof; HL adds counting, complex numbers, induction and systems of equations. | ||
| 2. Functions | 21 | 32 |
| Graphs, composite and inverse functions, quadratics, rational and exponential functions, transformations; HL adds polynomials, inequalities and modulus. | ||
| 3. Geometry and trigonometry | 25 | 51 |
| 3D geometry, trig rules, radians, identities and equations; HL adds compound angles, reciprocal trig, vectors, lines and planes. | ||
| 4. Statistics and probability | 27 | 33 |
| Data, regression, probability, binomial and normal distributions; HL adds Bayes' theorem and continuous random variables. | ||
| 5. Calculus | 28 | 55 |
| Differentiation, integration, optimisation and kinematics; HL adds limits, L'Hôpital, implicit differentiation, integration by parts, differential equations and Maclaurin series. | ||
| Exploration | 30 | 30 |
| An individual written investigation into a mathematical topic of the student's choice. | ||
The EuclidCurve Road to 7
Our model for a 7 in Maths AA HL: live 1:1 online teaching, a question bank tagged to every syllabus point, and a data loop that decides what each student works on next.
- Every question is data: Each answer a student marks as Got it, Partly or Missed updates their mastery of that Maths AA HL syllabus point.
- Weakness × exam weight: The next lesson targets the syllabus points that are both weak and most often examined in past papers, so time goes where the marks are.
- Bank the IA: The internal assessment is 20% of the grade and is finished before exam revision, so a strong IA takes pressure off the final papers.
Diagnose (Week 1)
A diagnostic test and the EuclidCurve MindMap show which syllabus points are secure and which are costing marks.
Your tutor: Read the diagnostic and MindMap; set the three weakest, most-examined syllabus points as the first targets.
Learn the idea (DP1)
Each topic starts with EuclidCurve concept cards and interactive graph simulations, so the idea makes sense before the exam questions begin. No-calculator fluency is built from day one for Paper 1.
Your tutor: Teach the idea 1:1, then two straightforward questions before moving on.
Drill by syllabus point (DP1 – DP2)
Past-paper and EuclidCurve questions filtered to one syllabus point at a time, from straightforward to full exam level, each with a worked markscheme.
Your tutor: Set 8–10 questions on one syllabus point from the dashboard, easy to exam level.
Fix every gap (Every week)
Misses build a personal path of similar questions. The weekly 1:1 lesson and marked homework go straight to the biggest gaps.
Your tutor: Open the student's Missed list before each lesson; reteach, then set similar questions as homework.
Bank the IA (End DP1 – DP2 term 1)
The internal assessment is planned, drafted and finished early, aiming for the top band in every criterion.
Your tutor: Agree the topic by the end of DP1; review a plan, one full draft and the final version against the criteria.
Exam conditions (DP2)
Timed Paper 1, 2 and 3 practice under real exam conditions, marked against the official markscheme. Paper 3 problem solving is practised as full investigations, not short questions.
Your tutor: One timed paper every 2–3 weeks; mark it with the markscheme and log each lost mark as method, accuracy or time.
Final sprint (Last 8 weeks)
Mixed full papers, a review of where marks are lost (method, accuracy, time) and a day-by-day revision plan for the final weeks.
Your tutor: Weekly full papers; spend lesson time only on the syllabus points losing the most marks.
Internal assessment: 20% of the Maths AA HL grade
The mathematical exploration is a 12–20 page investigation of a topic the student chooses. It is marked by the teacher against fixed criteria, so every mark can be planned for.
- A. Presentation: 4 marks
- B. Mathematical communication: 4 marks
- C. Personal engagement: 3 marks
- D. Reflection: 3 marks
- E. Use of mathematics: 6 marks
Extended essay: the core points
The extended essay (4,000 words, about 40 hours) does not count towards the subject grade. It is graded A to E and, together with Theory of Knowledge, earns up to 3 of the 45 Diploma points. Students who write it in their strongest subject also deepen the understanding the exams reward.
- A Maths EE explores one question in depth, for example in number theory, geometry, probability or modelling.
- We help choose a focused research question and check the mathematics is at the right level.
AA HL on EuclidCurve
Enrolled students use an AA HL question bank organised by chapter, past-paper questions with markschemes, notes and one-to-one tutoring. Access is by invitation: contact us to discuss joining.
Frequently asked questions
How many papers are in IB Maths AA HL?
Three: Paper 1 (2 hours, no calculator, 110 marks), Paper 2 (2 hours, calculator, 110 marks) and Paper 3 (1 hour 15 minutes, 55 marks), plus the mathematical exploration (IA).
How much is each AA HL component worth?
Paper 1 is 30%, Paper 2 is 30%, Paper 3 is 20% and the exploration (IA) is 20% of the final grade.
How does EuclidCurve prepare students for a 7?
Through the EuclidCurve Road to 7: a diagnostic, concept cards, drills by syllabus point, weekly 1:1 online lessons targeting gaps, early IA guidance and timed full papers marked against the official markscheme.