1) What IB Math AI HL is really about?

AI HL is the applied/technology-heavy pathway of IB Maths. You’ll model real situations with functions, statistics, probability and calculus, using your graphing display calculator (GDC) or suitable tech throughout. Conceptual understanding + interpretation + communication are as important as calculation.

Core strands (all at HL depth):

• Number & Algebra (incl. sequences/series, finance)

• Functions & Modelling (linear → exponential → sinusoidal; piecewise; transformations)

• Geometry & Trigonometry (2D/3D, non-right triangles, arcs/sectors; some discrete topics like Voronoi)

• Statistics & Probability (a major part at HL: regression, inference, binomial/normal, hypothesis tests)

• Calculus (differentiation, integration, numerical methods and real-world modelling)

Typical HL course time ≈ 240 hours.

2) Assessment—how you’ll be graded (exam + coursework)

Paper 1 – 2 hours – 30%

• Technology allowed/expected.

• Section A short-response + Section B extended-response across all topics.

• Emphasis on modelling, interpretation, clear reasoning, and sensible use of your GDC.

Paper 2 – 2 hours – 30%

• Technology allowed/expected.

• Multi-step problems with realistic data, parameters and graphs. Show both calculator output and mathematical justification.

Paper 3 (HL only) – 1 hour – 20%

• Two extended problem-solving/modelling questions that escalate in difficulty; tech required.

• Credit for definitions, set-up, assumptions, structure, and reflection—not just the final number.

Internal Assessment (IA) – Mathematical Exploration – 20%

• A personal written investigation (about 12–20 pages) where you apply HL-level maths to a question that interests you.

• Marked on: Communication, Mathematical presentation, Personal engagement, Reflection, Use of mathematics.

Formula Booklet is provided in exams—learn to find results fast.

3) What to learn—content map (HL emphasis)

A. Number & Algebra

• Exponents & logarithms (laws, solving exponential/log equations)

• Sequences & series (arithmetic & geometric; sigma notation; modelling growth/decay)

• Financial maths: compound interest, depreciation, amortisation & annuities (AI strength)

• Approximation & estimation; error bounds; sensible rounding; units

• Using tech to solve equations (roots, intersections, tables/trace)

B. Functions & Modelling

• Function basics: domain/range, inverses, composites, transformations (shifts, stretches, reflections)

• Linear & piecewise, quadratic & cubic, exponential, sinusoidal models; direct/inverse variation

• Model selection and parameter fitting (by regression or logical constraints)

• Interpreting parameters (slope, amplitude, growth factor…), residuals, validity and limitations

C. Geometry, Trig & Discrete

• Coordinate geometry; distance, midpoint, gradients; equations of lines & circles

• Arcs & sectors; area and length formulae (radians)

• Right- and non-right-angled trigonometry (sine/cosine rules, area)

• 3D geometry: surface area & volume; density and rate contexts

• Voronoi diagrams & location problems (AI distinctive)

D. Statistics & Probability (big in AI HL)

• Data collection, types of variables, sampling methods & bias

• Descriptive stats: measures of centre/spread; box plots; z-scores; outliers

• Bivariate analysis: correlation coefficients, linear regression; interpret slope/intercept and limitations

• Probability: events, Venn/Tree/Sample-space diagrams; conditional probability

• Binomial distribution (exact/at-least/at-most; modelling conditions)

• Normal distribution (areas, inverse normal, standardisation)

• Inference & hypothesis testing (HL):

  • One-/two-tailed tests; p-values; Type I/II errors

  • Chi-squared tests (independence, goodness-of-fit)

  • t-tests (one-sample; interpretation)

E. Calculus (for modelling)

• Differentiation: rates of change; tangents/normals; turning points; optimisation

• Integration: area under curves; accumulation; average value

• Numerical methods: trapezoidal rule; using tech for definite integrals or roots

• Kinematics (if taught): velocity & acceleration from s(t); interpreting units/graphs

• Always interpret in context (increasing/decreasing; maxima/minima; concavity; meanings of parameters)

4) How to study—weekly system that works

Weekly structure (repeatable):

1. Concept lesson (90–120 min): new ideas + worked examples. Create a 1-page “how-to” per skill.

2. Core drill (60 min): 10–20 short items mixing old + new; check with GDC where appropriate.

3. Modelling & interpretation (60–90 min): one real problem using graphs/tables/regression. Conclude with a one-paragraph interpretation (in words!).

4. Exam practice (60–90 min): alternate Paper 1 and Paper 2 sets; every second week do a Paper 3-style task.

5. Review (30 min): update an Error Log: topic, mistake type, fix rule, “next time I will…”.

Time per mark rule: ~1.1 min/mark in timed practice. Move on if stuck; come back later.

5) GDC / Technology skills you must master

• Graphing multiple functions; trace, table, intersection; windowing & zoom

• Regression (linear, exponential, sinusoidal if supported); residual plots

• Solver & numerical root/optimization tools; numerical integration

• Stats: one-var & two-var summaries, z/t calculations, chi-squared tables

• Distribution calculations: binomial (pdf/cdf), normal (cdf/invNorm)

• Screenshots/outputs: learn to annotate and explain what the output shows (don’t just paste numbers)

6) Paper-by-paper tactics

Paper 1 (tech allowed)

• Set up variables and name parameters; draw a quick plan sketch before using the GDC.

• Use algebra to simplify before plugging in. Verify domain and units.

• When you use the calculator, state the command (e.g., “linReg(ax+b) gave …”) and interpret the result.

Paper 2 (tech allowed)

• Expect longer contexts. Write assumptions; justify model choice (e.g., “exponential suits constant percentage growth”).

• Always add a sentence in words for final answers: meaning, reasonableness, and limitations.

Paper 3 (HL)

• Think “mini IA”: structure your solution with headings (Understanding → Model → Solve → Validate → Reflect).

• Show parameter sensitivity or a quick alternative approach where relevant.

7) IA (Exploration) in 5 fast steps

1. Question you care about (sport performance, finance plan, spread of a trend, music tempo modelling…).

2. Background & plan: define variables, parameters, data sources, and methods (what maths you’ll use and why).

3. Do the maths: correct and HL-level (e.g., regression with diagnostics, hypothesis test, numerical integration, optimisation).

4. Validate & reflect: check assumptions, error sources, sensitivity, alternative methods, and how good the model is.

5. Presentation: clear structure, labelled figures/tables, consistent notation, citations.

Checklist for 7/7/7/7/7: Each draft section should visibly hit the five criteria (Communication, Presentation, Engagement, Reflection, Use of maths).

8) Common pitfalls (and how to fix them)

• Only doing button-pressing. → Always accompany tech with maths & interpretation.

• Forgetting context. → Every numeric answer gets a sentence (units, what it means, whether it’s reasonable).

• Misusing models. → Check residuals/fit; state limitations (e.g., extrapolation warning).

• Weak notation/diagrams. → Define variables; label axes; state domains/conditions.

• Rushing IA. → Schedule: Week 1 idea, Week 2 plan, Weeks 3–4 maths, Week 5 write-up, Week 6 polish against criteria.

9) 10-week revision sprint (final term)

Weeks 1–2: Statistics & Probability block (regression → binomial → normal → hypothesis tests).
Week 3: Modelling with functions (linear/exponential/sinusoidal; residuals & parameter meaning).
Week 4: Number/Algebra & Finance (series, annuities, amortisation).
Week 5: Calculus & kinematics (optimisation, areas, numerical integration).
Week 6: Mixed problem sets; start Paper 3 style once per week.
Week 7: Full Paper 1 under time; post-mortem with markscheme language.
Week 8: Full Paper 2 under time; post-mortem; tech workflow check.
Week 9: Weak-spot microsessions + 2 targeted mixed sets.
Week 10: Two full mocks (P1 + P2) + one P3; sleep, nutrition, light review only.

10) Quick exam-day checklist

• Approved GDC, fresh batteries/charge; formula booklet familiarity.

• Ruler & calculator-friendly mindset: sketch first, technology second.

• Show working and reasons; units everywhere; round sensibly.

• Pace with ~1.1 min/mark. Flag tough parts and return.

Need help with IB Math AI HL?

I offer 1-to-1 and small-group tutoring for IB Mathematics: Applications & Interpretation (HL). If you want structured lessons, exam-style practice, or guidance on your IA:

• Personalized study plan and weekly goals

• Paper 1/2/3 exam coaching with calculator workflows

• IA exploration support (topic selection → structure → reflection)

• Past-paper drills with markscheme language and feedback