IB Mathematics AA HL Syllabus & Study Guide
Analysis and Approaches HL for DP students at SJI International, UWCSEA, Tanglin, ACS Independent and more
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IB Math AA HL in brief
IB Mathematics Analysis and Approaches Higher Level (Math AA HL) is the more theoretical, calculus-heavy of the two IB Diploma Programme mathematics courses. It is often required for quantitative university courses in the UK, Australia, US and Asia, and NUS, NTU and SMU commonly expect it for courses that list H2 Math 9758 as a prerequisite. The syllabus covers number and algebra, functions (including transformations and rational functions), geometry and trigonometry (vectors, complex numbers), statistics and probability (binomial, normal distribution, sampling), and calculus (limits, differentiation, integration, differential equations).
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HL students study the same five topics in more depth, with HL-only content such as proof by induction, complex numbers and further calculus. Math AA HL has no optional topic. Assessment is three external papers (Paper 1 no calculator, Paper 2 graphical calculator, Paper 3 problem-solving) plus the Internal Assessment (a 12 to 20 page exploration worth 20 percent of the final grade).
Our IB Math AA HL tutors run a structured DP1 to DP2 programme. The DP1 syllabus covers algebra, functions, trigonometry foundations, calculus introduction and the IA exploration planning. The DP2 syllabus then layers calculus advanced techniques, vectors, complex numbers, statistics and Paper 3 problem-solving practice, with intensive past-paper drilling from January of DP2 onwards. Each tutor's own qualifications and teaching experience are shown on the shortlist.
A practical note on the Internal Assessment: it counts for 20 percent of the final grade and is built over months rather than written in an exam hall. The criteria reward a focused mathematical exploration with personal engagement, a clear research question, mathematical content above the standard curriculum (calculus, modelling, statistical inference) and reflection on limitations. Common topic mistakes include picking a topic too broad to bound (game theory of cricket), too narrow to develop (one specific integral identity), or too computational to show genuine mathematical reasoning.
Our tutors start IA scoping in DP1 to settle a workable topic, then use IA-coaching lessons through DP2 to build out the analysis with proper rigour. The same approach applies to Paper 3, the HL problem-solving paper, where long unfamiliar questions reward regular practice.
IB Math AA HL tuition rates
Real ranges by level and tutor tier. We re-match free if the fit is wrong.
| Level | Part-time / undergrad | Full-time | Ex-MOE or NIE-trained |
|---|---|---|---|
| IB Diploma (DP1-DP2) / IGCSE | S$60-80/hr | S$75-110/hr | S$95-150/hr |
Final rate is set on tutor match and depends on tutor tier, level and lesson frequency. See full pricing page.
Full rate guide · IB Math AA HL tuition: rates and tutors
Official syllabus: IB, Mathematics: Analysis and Approaches
Common IB Math AA HL Struggles We Fix
Math AA HL marks at the 6 and 7 grade levels are decided on Paper 3 problem-solving and Internal Assessment quality. The patterns we see most often:
Paper 1 (no calculator) computational fluency is below the demands of the syllabus.
Paper 3 (problem-solving) questions are unfamiliar in style and the student does not have a structured approach.
Calculus integration and differential equations are confused under multi-step pressure.
Vector geometry and complex number geometry questions lose marks because the diagram is not drawn.
2 more
Internal Assessment exploration choice is unsuitable (too narrow, too broad, no clear math content) leading to a low IA mark.
Paper 3 extended problem-solving questions get too little timed practice at school.
These are the gaps our IB Math AA HL tutors fix with structured DP1 to DP2 sequencing, dedicated IA coaching, and weekly past-paper drilling.
IB Math AA HL Programme Structure
A full-syllabus programme spanning DP1 and DP2, with dedicated IA coaching:
Algebra and Functions (DP1)
Foundational topics for everything downstream.
Topics covered
- Sequences and series (arithmetic, geometric)
- Logarithms and exponentials
- Functions (one-one, inverse, composite)
- Polynomial functions and their graphs
- Rational functions and asymptotes
- Transformations of functions
Trigonometry, Vectors, Complex Numbers
Geometric and algebraic Pure Math topics.
Topics covered
- Trigonometric identities and equations
- Vectors (operations, dot product, cross product)
- Vector equations of lines and planes
- Complex numbers (Cartesian, polar, exponential form)
- De Moivre theorem
Calculus (DP2 dominant)
The high-mark Paper 1 and Paper 3 area.
Topics covered
- Limits and continuity
- Differentiation (techniques, applications, related rates)
- Integration (substitution, by parts, partial fractions)
- Definite integrals and applications (areas, volumes)
- Differential equations (first-order, separable, linear)
- Maclaurin series
Statistics, IA, Paper 3
The DP2 capstone components.
Topics covered
- Probability and discrete distributions
- Continuous distributions (normal, sampling)
- Bayes' theorem and conditional probability
- Internal Assessment exploration design
- IA mathematical content and structure
- Paper 3 problem-solving practice
Why parents pick us
IB DP-Specialist Tutors
Our Math AA HL tutors teach to the IB curriculum, marking criteria and IA expectations.
Dedicated IA Coaching
The Internal Assessment is 20 percent of the final grade and is built over months. We coach exploration topic selection, mathematical content depth, and the rubric criteria (presentation, mathematical communication, personal engagement, reflection, use of mathematics).
Paper 3 Coverage
Paper 3 is an HL-only problem-solving paper worth 20 percent of the final grade. We match tutors who have taught it.
Meet one of our IB Math AA HL tutors
Christin, Mathematics AA HL tutor
Credentials: Information Systems, SMU
Specialises in: Last-minute exam revision, Intensive crash courses for O/N-Level Maths & Science
Track record: 5 years tutoring experience
A note from Christin: "I am a Mathematics & Science tutor specialising in Upper Secondary A-Mathematics, E-Mathematics, Pure/Combined Physics and Pure/Combined Chemistry, with first-hand experience of the O Level and JC system before progressing to university studies at SMU."
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IB Math AA HL: frequently asked questions
What is IB Math AA HL?
Analysis and Approaches Higher Level, the most abstract, proof-oriented IB Mathematics route, expected for most quantitative university courses.
How is IB Math AA HL assessed?
Written examination papers plus the internally-assessed Exploration (IA), a student-chosen mathematical investigation that is a substantial part of the grade.
How does AA differ from AI?
Analysis and Approaches (AA) is abstract and calculus-heavy. Applications and Interpretation (AI) is applied and statistics-heavy. AA HL is the more common university expectation.
IB Math AA HL Support Across DP1 and DP2
Math AA HL is commonly expected for Engineering, Computer Science, Economics, Mathematics and Quantitative Finance courses.