International Baccalaureate (IB) Mathematics Syllabus - 2025/26 Parent & Student Guide

TL;DR
IB Maths now comes in two flavours - Analysis and Approaches (AA) for proof-heavy algebra + calculus, and Applications and Interpretation (AI) for statistics + modelling power-users.
Both streams keep the same 20 % Internal Assessment (IA), but their exam papers test rather different skills.
Choosing well depends on a student's post-IP trajectory: engineering & physics prefer AA, while data-centric fields welcome AI.

1 | Big-picture anatomy of each course

Sources: IB Analysis & Approaches subject brief p.3 , IB Applications & Interpretation subject brief p.3 .

2 | Topic maps - where the hours actually go

2.1 Shared core (both AA & AI)

• Number & algebra - arithmetic sequences, logarithms, binomial theorem.
• Functions - composition, inverse, transformations.
• Geometry & trigonometry - identities, three-D vectors.
• Statistics & probability - discrete and continuous random variables, normal model.
• Calculus - limits, differentiation, definite integrals.

2.2 Extra in AA

• Proof of series sums, derivative tests for optimisation.
• HL only: Maclaurin series, first-order differential equations, Euler method.

2.3 Extra in AI

• Spreadsheet-driven exploratory data analysis.
• HL only: Chi-square tests, linear regression t-statistics, Monte-Carlo simulation.

3 | Assessment in detail

3.1 External papers

Tables condensed from subject briefs above.

3.2 Internal Assessment (IA)

• Individually chosen exploration of max 12 pages.
• Marked on five criteria - Presentation, Mathematical communication, Personal engagement, Reflection, Use of mathematics.
• Weight 20 % across all four courses .

4 | Which route for which goal?

(*Some CS faculties still request AA HL if heavy on theory; always check university matrices.)

Insight from RevisionDojo comparison and Knowledgeum Academy guide .

5 | Grade-boundary reality check (May 2024)

HL AA edges AI by half a grade on average, reflecting the candidate cohort's stronger algebra background.

6 | Typical command terms & sample moves

• “Hence find” - a follow-on; quote previous result exactly.
• “Verify” - show algebraic steps from LHS to RHS; do not just substitute numbers.
• “Interpret” - verbalise what a gradient, intercept or correlation means in context.

Inline check: the derivative of \(f(x)=x^3\) is \(f'(x) = 3x^2\). Writing only the answer without “since \(\frac{\mathrm{d}}{\mathrm{d}x} \bigl(x^n\bigr) = nx^{n-1}\)” risks the method mark.

7 | Core formulae you still must know

IB supplies a booklet, yet speed matters. Burn in:

• Binomial coefficient \(\dbinom{n}{k} = \frac{n!}{k!(n-k)!}\).
• Normal PDF \(f(x)=\frac{1}{\sigma \sqrt{2\pi}}\exp \bigl(-\tfrac{(x-\mu)^2}{2\sigma^2}\bigr)\).
• Differential rules: \(\frac{\mathrm{d}}{\mathrm{dx}}\bigl(e^{kx}\bigr)=ke^{kx}\), product, quotient, chain.
• Definite-integral area: \[ \int_a^b v\space dt = s \].

Drill until recall time < 3 s each.

8 | Crafting a high-scoring IA

1. Pick a narrow, curious question e.g., “Modelling long-jumper trajectory with a quadratic fit”.
2. Collect primary data (tracker app, spreadsheet import).
3. Deploy at least HL-level techniques: piece-wise regression, \(r^2\), residual analysis.
4. Reflect - strength, limitations, future work.

Well-executed HL IAs use \(\ge 3\) different representations: algebra, graph, software output.

9 | Common mistakes & quick fixes

10 | Final 12-month timeline (Y5-Y6 IP student)

11 References

• IB Mathematics curriculum overview
• Subject brief - Mathematics: Analysis and Approaches
• Subject brief - Mathematics: Applications and Interpretation
• DP Mathematics best-fit guide (AA vs AI)
• DP sample exam papers
• Comparative analysis of DP and GCSE Mathematics
• IB command terms glossary
• IBO guide to Internal Assessment criteria
• GDC user manual - TI-Nspire CX II
• Desmos graphing calculator
• CASIO fx-CG50 tutorial videos
• IB Diploma Programme statistical bulletin 2024
• IB Mathematics examiner report extracts
• University of Cambridge maths requirements
• NUS Admission Requirements for Engineering Science Programme
• Stanford study on retrieval practice

Last updated 13 Jul 2025.