International Baccalaureate (IB) Mathematics Tuition - 2025/26 Master Guide for Integrated Programme (IP) Students
Download printable cheat-sheet (CC-BY 4.0)13 Jul 2025, 00:00 Z
TL;DR
The 2019 IB Maths revamp split the subject into Analysis and Approaches (AA) (proof-heavy) and Applications and Interpretation (AI) (data-centric), each with HL & SL tiers.
The 20 % Internal Assessment (IA) now replaces the old option paper, while May 2024 session grade boundaries show ≈ 65 % raw marks for a 7 in HL AA.
Specialist tuition that blends IP-style algebra sprints, IA coaching and timed-paper drills lifts grades by 1-2 bands within a semester.
1 | Why IB Mathematics Matters for IP Learners
IP students already race through A-Math and early calculus by Sec 3.
Yet IB Maths demands:
- Proof literacy - AA HL Paper 3 problems resemble Olympiad mini-proofs.
- Statistics & technology - AI HL expects spreadsheet or CAS fluency for chi-square tests.
- Exploration research - a 12-page IA that "must demonstrate mathematics commensurate with the level of the course" (IBO subject guide, p. 19).
Skipping O-Levels does not immunise against these jumps; algebra rust and weak data-analysis skills surface fast in Year 5.
2 | Syllabus & Assessment at a Glance
| Course | Papers & timing | Weight | Key hurdles |
| AA SL | Paper 1 (no-tech, 90 min), Paper 2 (tech-allowed, 90 min) | 40 % each | Non-calculator fluency, rigorous justification |
| AA HL | Paper 1 & 2 (each 120 min), Paper 3 (60 min exploratory) | 30 %, 30 %, 20 % | Advanced calculus, proof, novel problem contexts |
| AI SL | Paper 1 (tech, 90 min), Paper 2 (tech, 90 min) | 40 % each | Real-data modelling, statistical inference |
| AI HL | Paper 1 & 2 (each 120 min), Paper 3 (60 min) | 30 %, 30 %, 20 % | Regression, Monte-Carlo simulation, optimisation |
| IA (all) | Exploration report (≈ 12 pages) | 20 % | Topic selection, depth vs breadth, citation rigour |
Sources: IBO AA guide · IBO AI guide
3 | Common Pain-Points for IP High-Achievers
| Pain-point | Typical symptom | Tuition fix |
| Algebra -> proof leap | Can factorise but stalls on "show that" | 4-step G.R.E.P. template (Given-Rewrite-Explain-Prove) |
| Calculator over-reliance | Paper 1 AA HL errors in \(\int e^{3x}\) | Weekly no-tech sprint (60 min, 15 Q) |
| Statistics gap | Misuses \(\mu \pm \sigma\) for skewed data | Hands-on Sheets simulation of normal vs Poisson |
| IA scope creep | Chooses fractals then exceeds 20 h limit | Feasibility matrix: novelty x data access x HL-depth |
| Timed stamina | Completes 70 % of Paper 2 | 90-min mixed-topic drill + error journal loop |
4 | How Specialist Tuition Bridges the Gap
4.1 Concept-Transfer Tutorials
- IP algebra <-> IB calculus: factor-expand drills segue into \(\frac{\mathrm{d}}{\mathrm{dx}} (\sin 3x)\).
- Physics crossover: logs in RC decay appear in AI HL statistics sections.
4.2 IA Mentorship (20 %)
- Week 1 - topic triage checklist.
- Week 3 - pilot data + CAS image embed.
- Week 5 - draft -> rubric self-mark; tutor annotates.
- Week 7 - final polishing: citations, appendix, word count.
4.3 Timed-Paper Boot Camps
- MCQ blast: 30 Q / 45 min (AA) or technology-based modelling (AI).
- Post-mortem: classify slips into content, process or careless.
5 | 12-Week Grade-Jump Plan
| Weeks | Focus | Concrete action |
| 1-2 | Algebra refresh | 40 Q nightly; log <60 s fails |
| 3-4 | Calculus depth | Derive \(\int \sec^2x\) and solve \(\frac{\mathrm {d}}{\mathrm{dx}}(x^x)\) |
| 5-6 | Stats & tech | Simulate \(10^5\) dice in Sheets; fit normal curve |
| 7-8 | IA draft | Write intro, method, preliminary results |
| 9-10 | Paper 1 & 2 sprints | 90-min, 120-mark sets x3/week |
| 11-12 | Paper 3 exploration | Tackle two unfamiliar modelling tasks; time box 60 min |
6 | Sample Worked Example (AA HL)
Q. Show that the Maclaurin series of \(\ln(1+x)\) is
\[ \ln(1+x) = \sum_{n=1}^{\infty} (-1)^{n+1} \frac{x^n}{n}, \space |x|<1 \]
Sketch
- Start with \(f(x)=\ln(1+x)\).
- Compute derivatives \(f^{(n)}(0)=(-1)^{n-1}(n-1)!\).
- Apply general Maclaurin: \(f(x)=\sum_{n=1}^{\infty} \frac{f^{(n)}(0)}{n!}x^n\).
- Simplify coefficients.
Inline convergence check:
\[ \lim_{n \to \infty} |(-1)^{n+1} \frac{x^n}{n}| = 0 \]
when \(|x|<1\).
7 | FAQ
“AA or AI for engineering?”
Universities like Imperial and NTU list AA HL as strongly preferred for Engineering and Physics.
“Is a 7 achievable?”
May 2024 stats: 19 % of AA HL candidates scored 7, global mean ≈ 4.9/7.
“Does the IA need original research?”
No; depth and mathematical correctness trump novelty. A well-executed regression can outscore a shaky Gödel essay.
8 | Further Reading
Last updated 13 Jul 2025. Next auto-refresh when the IBO releases the May 2025 statistical bulletin.
