International Baccalaureate (IB) Math 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.

8.1 | Modelling frameworks (AA vs AI) for 2026 cohorts

🧰 Action step: Drop the three datasets into a shared Drive “IA modelling lab” folder. Encourage students to remix them—AA learners justify algebraic structure, AI learners lean on tech-driven inference. Every submission must still cite the dataset pack as a secondary source.

Workflow tips

• Kick-off workshop: Spend 60 minutes letting students interrogate each dataset. Have AA groups outline the algebraic backbone while AI groups storyboard the technology they will deploy.
• CAS vs manual balance: Require AA explorers to demonstrate at least one hand-worked derivation (e.g., solving for logistic parameters) before verifying with CAS. For AI, annotate every graph/table with the specific CAS/technology command used.
• Common reflection prompts: “What assumptions underpinned the model?”, “Where did the technology aid insight—and where could it mislead?”, “How would you collect higher-resolution primary data?”

📎 Instructors: Keep a moderation log noting which dataset variant each student picked and the level of mathematical sophistication exhibited. This guards against accidental topic overlap when multiple candidates lean on the shared pack.

Deliverable add-ons

• Publish a one-pager IA slog (Summary of Learning & Output Grid) outlining question, data source, representational forms, and integrity declarations. Collect via Google Forms for easy moderation.
• Package the three dataset packs + templates as a downloadable bundle (Google Drive/Notion) linked in the CTA so parents/students have instant scaffolding.

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 and assessment (official)
• 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
• IBO — Assessment at a glance (Diploma Programme)
• University of Cambridge maths requirements
• NUS Admission Requirements for Engineering Science Programme
• Stanford study on retrieval practice

Last updated 13 Jul 2025.