IB Mathematics AA HL AI Tutor Playbook 2026

Audience: IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion cohorts at IB-World-Schools in Switzerland + Singapore + Hong-Kong + UAE + UK + US + Canada + Australia + New-Zealand + Japan + Korea + China + India + Pakistan + Bangladesh + Indonesia + Malaysia + Thailand + Vietnam + Philippines + Egypt + South-Africa + Kenya + Nigeria + Ghana + Saudi + Qatar + Bahrain + Kuwait + Oman + Jordan + Lebanon — typically the cohort in IB-Mathematics-AA-HL + IB-Mathematics-AA-SL + IB-Mathematics-AI-HL + IB-Mathematics-AI-SL + IB-Physics-HL + IB-Chemistry-HL + IB-Biology-HL + IB-Computer-Science-HL + IB-Economics-HL + IB-Further-Mathematics-HL + IB-Design-Technology-HL + IB-Sports-Exercise-Health-Science-HL, often paired with IB-Extended-Essay-in-Mathematics + IB-Internal-Assessment-Mathematical-Exploration + IB-Paper-3-Extended-Response + IB-TOK-mathematical-knowledge + IB-CAS-mathematical-modelling. Covers IB Mathematics AA HL teachers who want an AI workflow for grading Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration, parents paying for IB-Mathematics-AA-HL-prep ($300-$3000 for prep-books + $1000-$5000 for prep-courses + $2000-$8000 for private-tutors), IB-World-Schools seeking IB-Mathematics-AA-HL-internal-assessment-rubric alignment, and overseas IB-Diploma-candidates applying to Cambridge + Oxford + Imperial + UCL + LSE + Stanford + MIT + Harvard + Yale + Princeton + Columbia + Chicago + Berkeley + Caltech + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill admissions.

Hook: IB Mathematics AA HL is the most-respected pre-university mathematics + pure-mathematics + applied-mathematics + engineering + computer-science + physics + statistics + data-science + machine-learning + AI + quantitative-finance + actuarial-science + econometrics + operations-research + mathematical-physics + theoretical-physics + astrophysics + biostatistics + bioinformatics + computational-biology qualification globally — the standard for IB-Diploma-Programme Year-12 + Year-13 candidates at IB-World-Schools targeting Cambridge + Oxford + Imperial + UCL + LSE + Stanford + MIT + Harvard + Yale + Princeton + Columbia + Chicago + Berkeley + Caltech + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill admissions. The 2025 score distribution is selective: score-7 rate of approximately 9-13 percent (highest honours + university-credit at Cambridge + Oxford + Imperial + UCL + LSE + Stanford + MIT + Harvard + Yale + Princeton + Columbia + Chicago + Berkeley + Caltech + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill), score-6 rate of approximately 21 percent, score-5 rate of approximately 27 percent (the score-5+ cumulative rate 57-61 percent is the IB Diploma + university-readiness benchmark), score-4 rate of approximately 22 percent, score-3 rate of approximately 12 percent, score-2 rate of approximately 6 percent, score-1 rate of approximately 3 percent. The 5-topics-of-IB-Mathematics-AA-HL (Number-Algebra + Functions + Geometry-Trigonometry + Statistics-Probability + Calculus + AA-HL-only-extension-topics + Complex-Numbers + Vectors-3D + Proof-by-Induction + Differential-Equations + Euler + Maclaurin-Series + Probability-Generating-Functions + Chi-Squared + Poisson + Markov-Chains + Linear-Regression + Correlation + Hypothesis-Tests + Continuous-Probability-Distributions) + 4-Assessment-Components (Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration) map onto Year-12 + Year-13-mathematics + first-year-undergraduate-Mathematics + Engineering + Computer-Science + Physics + Economics + Quantitative-Finance + Actuarial-Science + Data-Science + Machine-Learning + AI + Mathematical-Physics + Theoretical-Physics + Astrophysics + Biostatistics + Bioinformatics + Computational-Biology + Chemical-Engineering + Aerospace-Engineering + Mechanical-Engineering + Electrical-Engineering + Civil-Engineering + Software-Engineering + Cybersecurity + Cryptography + Econometrics + Operations-Research at Cambridge + Oxford + Imperial + UCL + LSE + Stanford + MIT + Harvard + Yale + Princeton + Columbia + Chicago + Berkeley + Caltech + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill admissions.

Section 1 — Why IB Mathematics AA HL is the most-respected pre-university mathematics + engineering + computer-science + physics + statistics + data-science + machine-learning + AI + quantitative-finance + actuarial-science + econometrics + operations-research + mathematical-physics + theoretical-physics + astrophysics + biostatistics + bioinformatics + computational-biology qualification + the Cambridge + Oxford + Imperial + UCL + LSE + Stanford + MIT + Harvard + Yale + Princeton + Columbia + Chicago + Berkeley + Caltech + Edinburgh + Manchester + Bristol + Loughborough + Bath + Toronto + UBC + McGill first-year-undergraduate-Mathematics + Engineering + Computer-Science + Physics + Economics + Quantitative-Finance + Actuarial + Statistics IBO-applied-track subject

IB Mathematics AA HL is the IBO-standard pre-university mathematics + pure-mathematics + applied-mathematics + engineering + computer-science + physics + statistics + data-science + machine-learning + AI + quantitative-finance + actuarial-science + econometrics + operations-research + mathematical-physics + theoretical-physics + astrophysics + biostatistics + bioinformatics + computational-biology qualification for IB-Diploma-Programme Year-12 + Year-13 candidates — 5-topics-required, AA-HL-only-extension-topics-required, Complex-Numbers-required, Vectors-3D-required, Proof-by-Induction-required, Differential-Equations-required, Euler-required, Maclaurin-Series-required, Probability-Generating-Functions-required, Chi-Squared-required, Poisson-required, Markov-Chains-required, Linear-Regression-required, Correlation-required, Hypothesis-Tests-required, Continuous-Probability-Distributions-required, Paper-1-no-calculator-required, IB-command-terms-required, Paper-2-calculator-required, GDC-required, Paper-3-extended-response-required, IA-mathematical-exploration-required, IB-Markscheme-required, IB-command-terms-required. It is the standard for IB-World-Schools in 145+ countries. Unlike AP Calculus AB (non-IB + non-IB-command-terms + non-IB-mark-bands + non-IB-IA + non-IB-Group-5 + non-AA-HL-extension + non-Complex-Numbers + non-Vectors-3D + non-Proof-by-Induction + non-Differential-Equations), IB Mathematics AA HL integrates 5-topics + AA-HL-extension-topics + Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration + IB-command-terms across all 5-topics + AA-HL-extension + Paper 1 + Paper 2 + Paper 3 + IA-mathematical-exploration + IB-command-terms. The exam sits in May 2027 (Northern-Hemisphere-summer-sitting) + November 2026 (Southern-Hemisphere-summer-sitting). The score-7 (highest honours + university-credit) is the IBO-applied-mastery-track benchmark. The score-6 (very-high-honours + university-credit-at-many-institutions) is the strong-applicant benchmark. The score-5 (honours + IB-Diploma + university-readiness) is the cohort-wide-benchmark for Mathematics + Engineering + Computer-Science + Physics + Economics + Quantitative-Finance + Actuarial-Science + Data-Science + Machine-Learning + AI + Mathematical-Physics + Theoretical-Physics + Astrophysics + Biostatistics + Bioinformatics + Computational-Biology + Chemical-Engineering + Aerospace-Engineering + Mechanical-Engineering + Electrical-Engineering + Civil-Engineering + Software-Engineering + Cybersecurity + Cryptography + Econometrics + Operations-Research + first-year-undergraduate-Mathematics + Engineering + Computer-Science + Physics + Economics at Cambridge + Oxford + Imperial + UCL + LSE + Stanford + MIT + Harvard + Yale + Princeton + Columbia + Chicago + Berkeley + Caltech + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill admissions. This playbook gives the 30-week IB Mathematics AA HL workflow.

Section 2 — The 30-week IB Mathematics AA HL AI tutor study plan: weeks 1-3 = Topic 1 — Number and Algebra (exponents + logarithms + sequences + series + binomial-theorem + counting + proof-by-induction + complex-numbers + modulus-argument + De-Moivre + Euler + polar-form + roots-of-polynomial-equations + summation-of-series + mathematical-induction), weeks 4-7 = Topic 2 — Functions (linear + quadratic + polynomial + rational + exponential + logarithmic + trigonometric + inverse-trigonometric + composite + inverse + transformation + domain + range + asymptotes + sketching + graphing + GDC + modelling + AA-HL-extension-topics-including-partial-fractions + further-algebra-skills), weeks 8-12 = Topic 3 — Geometry and Trigonometry (Euclidean-geometry + coordinate-geometry + vectors-2D + vectors-3D + complex-numbers-applied-to-geometry + matrices + transformations + trigonometry-3D + AA-HL-extension-topics-including-vector-equations + planes + lines + vector-product + scalar-product + parametric-equations + 3D-distance + 3D-angle + GDC-3D), weeks 13-18 = Topic 4 — Statistics and Probability (descriptive-statistics + measures-of-central-tendency + measures-of-dispersion + bivariate-statistics + linear-regression + correlation + chi-squared + goodness-of-fit + contingency-tables + probability-rules + Bayes-theorem + discrete-random-variables + binomial-distribution + Poisson-distribution + normal-distribution + continuous-random-variables + AA-HL-extension-topics-including-probability-generating-functions + Markov-chains + transition-matrices + steady-state + hypothesis-testing + t-test + z-test + confidence-intervals + sampling + central-limit-theorem), weeks 19-24 = Topic 5 — Calculus (limits + continuity + differentiation-rules + chain-rule + product-rule + quotient-rule + implicit-differentiation + second-derivative + higher-derivatives + applications-of-differentiation + integration-rules + definite-integrals + area-under-curve + volume-of-revolution + differential-equations + slope-fields + Euler-method + separation-of-variables + AA-HL-extension-topics-including-Maclaurin-series + Taylor-series + convergence + radius-of-convergence + improper-integrals + integration-by-parts + partial-fractions-integration + second-order-differential-equations + power-series-solutions), weeks 25-27 = IA Mathematical Exploration (12-pages + 20-hours + 20-marks + 20-percent-of-final-grade + IA-mathematical-exploration + IA-written-report + IA-research-question + IA-mathematical-communication + IA-personal-engagement + IA-reflection + IA-use-of-technology + IA-rubric + IA-mark-bands + IA-exemplars + IA-research-question-exemplars), weeks 28-30 = full-mock-exams + IBO-past-papers + polish

The 30-week IB Mathematics AA HL AI tutor workflow:

• Weeks 1-3 Topic 1 — Number and Algebra + AA-HL-Complex-Numbers + Proof-by-Induction + AA-HL-extension-topics + Topic 1 mastery
• Weeks 4-7 Topic 2 — Functions + AA-HL-Partial-Fractions + Transformations + Composite + Inverse + AA-HL-extension-topics + Topic 2 mastery
• Weeks 8-12 Topic 3 — Geometry and Trigonometry + Vectors-3D + Matrices + AA-HL-extension-topics + Topic 3 mastery
• Weeks 13-18 Topic 4 — Statistics and Probability + Chi-Squared + Poisson + Probability-Generating-Functions + Markov-Chains + Hypothesis-Testing + AA-HL-extension-topics + Topic 4 mastery
• Weeks 19-24 Topic 5 — Calculus + Differential-Equations + Maclaurin + Taylor + Integration-techniques + AA-HL-extension-topics + Topic 5 mastery
• Weeks 25-27 IA Mathematical Exploration + 12-pages + 20-hours + IA-research-question + IA-mathematical-communication + IA-personal-engagement + IA-reflection + IA-use-of-technology + IA-exemplars mastery
• Weeks 28-30 full-mock-exams + IBO-past-papers + polish

The IB Mathematics AA HL AI tutor works across the 5-topics + AA-HL-extension-topics + Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration + IB-command-terms-show-that-hence-show-determine-sketch-state-write-down-find-justify + 5-topics-Number-Algebra-Functions-Geometry-Trigonometry-Statistics-Probability-Calculus + AA-HL-extension-Complex-Numbers-Vectors-3D-Proof-by-Induction-Differential-Equations-Euler-Maclaurin-Probability-Generating-Functions-Chi-Squared-Poisson-Markov-Chains + mark-bands-band-1-inadequate-band-2-adequate-band-3-competent-band-4-highly-competent-band-5-sophisticated-band-6-excellent-band-7-outstanding. Every Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration + 5-topics + AA-HL-extension-topics must be assessed against the IBO-Mathematics-AA-HL-marking-scheme + IBO-band-descriptors + IB-Mathematics-AA-HL-internal-assessment-rubric.

Section 3 — The IB Mathematics AA HL Paper 1: 2 hours + 110 marks + 40 percent of final grade + 5 compulsory questions + no-calculator + short-response + extended-response + IB-command-terms + show-that + hence-show + determine + sketch + state + write-down + find + justify

The IB Mathematics AA HL Paper 1 (no-calculator) is the first of three external-assessment papers. Paper 1 covers all 5-topics + AA-HL-extension-topics and consists of 5-compulsory-questions: Question 1 (short-response + Number-Algebra + Functions) + Question 2 (short-response + Geometry-Trigonometry + Vectors-3D) + Question 3 (short-response + Statistics-Probability + Chi-Squared + Poisson + Probability-Generating-Functions) + Question 4 (extended-response + Calculus + Differential-Equations + Maclaurin + Taylor) + Question 5 (extended-response + complex-problem + multi-topic-integration + modelling + proof). Paper 1 is weighted 40-percent-of-final-grade (110-marks). The IB-command-terms-for-Paper-1 include: show-that (rigorous-proof-required) + hence-show (build-on-previous-result) + determine (compute-and-state) + sketch (graph-with-key-features) + state (recall-fact) + write-down (immediate-answer) + find (compute-result) + justify (explain-with-reasoning). The Paper-1-mark-scheme-band-descriptors are: Band-1-Inadequate (0-20-marks + fundamental-gaps + incomplete) + Band-2-Adequate (21-40-marks + basic-understanding + partial-mastery) + Band-3-Competent (41-60-marks + solid-grasp + IB-Markscheme-meets-most-criteria) + Band-4-Highly-Competent (61-80-marks + strong + rigorous + clear-communication) + Band-5-Sophisticated (81-95-marks + excellent + IB-Markscheme-meets-all-criteria + creative) + Band-6-Excellent (96-105-marks + outstanding + IB-Markscheme-exceeds-criteria + elegant) + Band-7-Outstanding (106-110-marks + flawless + IB-Markscheme-exemplar + publishable). The Paper-1-no-calculator-format means no-GDC (graphical-display-calculator) allowed — students must rely on algebraic-fluency, trigonometric-identities, complex-number-arithmetic, proof-by-induction, binomial-expansion, summation-of-series, integration-by-parts, differentiation-rules, vector-arithmetic, matrix-arithmetic. Common Paper-1-gaps include: show-that-rigour (skipping-middle-steps) + hence-show-continuity (not-building-on-previous-result) + determine-precision (rounding-errors) + sketch-accuracy (missing-asymptotes + intercepts + turning-points) + find-justify (computation-without-explanation) + complex-number-argument (modulus-argument-errors + De-Moivre-misapplication + polar-form-errors) + proof-by-induction-base-case (missing-base-case + inductive-step).

Section 4 — The IB Mathematics AA HL Paper 2: 2 hours + 110 marks + 40 percent of final grade + 5 compulsory questions + GDC-allowed + calculator + extended-response

The IB Mathematics AA HL Paper 2 (calculator + GDC-allowed) is the second external-assessment paper. Paper 2 also covers all 5-topics + AA-HL-extension-topics and consists of 5-compulsory-questions. Paper 2 is weighted 40-percent-of-final-grade (110-marks). The IB-command-terms-for-Paper-2 mirror those of Paper 1, but the questions are more computational-and-modelling-heavy, allowing GDC use for: solving-equations (polynomial + transcendental + simultaneous) + statistical-computation (regression + correlation + probability-distribution + normal-approximation + chi-squared + t-test + z-test) + graphical-analysis (intersection-points + integration-bounds + differential-equation-slope-fields) + matrix-operations (3x3-matrix-inverse + determinant + eigenvalues + eigenvectors + transition-matrix) + complex-number-graphics (Argand-diagram + locus + transformation). Common Paper-2-gaps include: GDC-syntax-errors (entering-wrong-syntax + missing-parentheses) + GDC-mode-errors (degree-vs-radian + exact-vs-approximate) + regression-curve-fit (wrong-model-choice) + probability-distribution-identification (confusing-binomial-with-Poisson + normal-with-continuous-uniform) + hypothesis-test-set-up (null-vs-alternative + one-tailed-vs-two-tailed + significance-level) + Markov-chain-steady-state (incorrect-transition-matrix + eigenvector-errors) + differential-equation-numerical-method (Euler-method-step-size + slope-field-interpretation).

Section 5 — The IB Mathematics AA HL Paper 3: 1 hour + 50 marks + 20 percent of final grade + 2 extended-response questions + investigative + proof + mathematical-communication + HL-only + AA-only + 2-investigative-tasks

The IB Mathematics AA HL Paper 3 (extended-response) is the third external-assessment paper, exclusive to HL candidates. Paper 3 consists of 2-compulsory-extended-response-questions from a menu of HL-only-topics. Paper 3 is weighted 20-percent-of-final-grade (50-marks). Paper-3-questions test AA-HL-extension-topics in depth: Complex-Numbers (De-Moivre + Euler + polar-form + roots-of-unity + loci-in-Argand-diagram + transformations-in-complex-plane) + Vectors-3D (vector-equations-of-lines + planes + shortest-distance + intersection + coplanarity + vector-product + scalar-product) + Proof-by-Induction (mathematical-induction + strong-induction + proof-by-contradiction) + Differential-Equations (second-order-ODEs + power-series-solutions + Maclaurin-solutions) + Probability-Generating-Functions (PGF + expectation-from-PGF + variance-from-PGF) + Markov-Chains (steady-state + absorbing-state + expected-time-to-absorption) + Hypothesis-Tests (z-test + t-test + chi-squared-test + matched-pairs-test) + Continuous-Probability-Distributions (uniform + exponential + normal + continuous-uniform-conditions). Common Paper-3-gaps include: extended-response-structure (poor-time-allocation + missing-conclusion) + proof-rigour (incomplete-base-case + invalid-inductive-step) + complex-number-geometry (misinterpreting-Argand-loci) + vector-3D-geometry (confusing-line-vs-plane-equation + coplanarity-condition-errors) + differential-equation-power-series (incorrect-recurrence-relation) + Markov-chain-interpretation (steady-state-vs-absorption-confusion).

Section 6 — The IB Mathematics AA HL Internal Assessment Mathematical Exploration: 12 pages + 20 hours + 20 marks + 20 percent of final grade + IA-mathematical-exploration + IA-written-report + IA-research-question + IA-mathematical-communication + IA-personal-engagement + IA-reflection + IA-use-of-technology

The IB Mathematics AA HL Internal Assessment (IA) Mathematical Exploration is an individual 12-page (max) written report on a mathematical topic of personal interest, completed over approximately 20 hours of supervised work. The IA is weighted 20-percent-of-final-grade (20-marks). The IA-rubric-criteria are: Presentation (4-marks + IA-organization + IA-coherence + IA-flow + IA-conventions + IA-equations-typeset + IA-citations) + Mathematical-Communication (4-marks + IA-mathematical-language + IA-symbol-use + IA-logical-flow + IA-argumentation + IA-justification + IA-rigour) + Personal-Engagement (3-marks + IA-originality + IA-independence + IA-curiosity + IA-passion + IA-creativity + IA-personal-voice) + Reflection (3-marks + IA-reflection-on-learning + IA-self-evaluation + IA-what-worked + IA-what-didnt + IA-future-applications) + Use-of-Technology (3-marks + IA-GDC + IA-software + IA-simulation + IA-modelling + IA-data-visualization + IA-graphing + IA-symbolic-manipulation) + Mathematical-Communication-and-Rigour (3-marks + IA-proof + IA-justification + IA-generalization + IA-extension + IA-pattern-recognition). Total IA-marks = 20. Common IA-gaps include: topic-too-broad (no-focus) + topic-too-narrow (insufficient-mathematics) + missing-research-question + missing-personal-engagement (looks-like-textbook-problem) + weak-reflection (no-self-evaluation) + poor-citations + over-reliance-on-technology (no-hand-calculations) + under-use-of-technology (no-GDC) + page-limit-exceeded + missing-IA-rubric-criteria-coverage.

Section 7 — The IB Mathematics AA HL mark-band descriptors: Band 1 Inadequate + Band 2 Adequate + Band 3 Competent + Band 4 Highly-Competent + Band 5 Sophisticated + Band 6 Excellent + Band 7 Outstanding

The IB Mathematics AA HL mark-band-descriptors are the official IBO rubric used to score every Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration response. The 7-band-descriptors are: Band 1 Inadequate (work shows fundamental misunderstandings + incomplete + incorrect + IB-Markscheme-not-met + 0-20-marks-on-Paper-1-or-Paper-2) + Band 2 Adequate (work shows basic understanding + partial-mastery + some-correct + some-incorrect + IB-Markscheme-partially-met + 21-40-marks-on-Paper-1-or-Paper-2) + Band 3 Competent (work shows solid-grasp + IB-Markscheme-meets-most-criteria + mostly-correct + mostly-rigorous + 41-60-marks-on-Paper-1-or-Paper-2) + Band 4 Highly-Competent (work shows strong-understanding + rigorous + clear-communication + IB-Markscheme-meets-all-criteria + 61-80-marks-on-Paper-1-or-Paper-2) + Band 5 Sophisticated (work shows excellent-understanding + IB-Markscheme-meets-all-criteria + creative + elegant + 81-95-marks-on-Paper-1-or-Paper-2) + Band 6 Excellent (work shows outstanding-understanding + IB-Markscheme-exceeds-criteria + publication-quality + 96-105-marks-on-Paper-1-or-Paper-2) + Band 7 Outstanding (work shows flawless-understanding + IB-Markscheme-exemplar + world-class + 106-110-marks-on-Paper-1-or-Paper-2). The score-7 (highest honours + university-credit) requires consistent Band-7-Outstanding across all 4-Assessment-Components. The AI-tutor-scoring-engine maps every student-response to the 7-band-descriptors.

Section 8 — The IB Mathematics AA HL IB command terms: show-that + hence-show + determine + sketch + state + write-down + find + justify

The IB Mathematics AA HL IB-command-terms are the precise verb-instructions that appear on every Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response question. Mastering-each-command-term-is-essential. The 8-primary-IB-command-terms: show-that (provide-rigorous-proof-with-every-step + IB-Markscheme-requires-complete-logical-chain + common-error-incomplete-justification) + hence-show (build-on-previous-result + IB-Markscheme-requires-using-prior-answer + common-error-ignoring-prior-result) + determine (compute-and-state-final-answer + IB-Markscheme-requires-numerical-or-algebraic-result + common-error-rounding-errors) + sketch (draw-graph-with-key-features + IB-Markscheme-requires-asymptotes + intercepts + turning-points + axis-intersections + shape + common-error-missing-key-features) + state (recall-fact-or-formula + IB-Markscheme-requires-precise-statement + common-error-vague-statement) + write-down (immediate-answer-with-no-work + IB-Markscheme-requires-direct-statement + common-error-over-explanation) + find (compute-result + IB-Markscheme-requires-numerical-or-algebraic-answer + common-error-missing-units) + justify (explain-with-mathematical-reasoning + IB-Markscheme-requires-logical-argument + common-error-computation-without-explanation). Secondary-IB-command-terms include: hence-or-otherwise + using-technology + hence-verify + comment-on + consider-the-case + prove-by-induction + describe-the-transformation + write-the-expression + solve-for-x + show-that-the-equation-has-no-real-roots + find-the-set-of-values-of-x-for-which.

Section 9 — The IB Mathematics AA HL 5 topics + AA-HL-extension-topics + Complex-Numbers + Vectors-3D + Proof-by-Induction + Differential-Equations + Euler + Maclaurin-Series + Probability-Generating-Functions + Chi-Squared + Poisson + Markov-Chains + Linear-Regression + Correlation + Hypothesis-Tests + Continuous-Probability-Distributions

The IB Mathematics AA HL 5-topics + AA-HL-extension-topics form the full-syllabus. Topic 1 Number and Algebra (exponents + logarithms + sequences + series + binomial-theorem + counting + proof-by-induction + complex-numbers + modulus-argument + De-Moivre + Euler + polar-form + roots-of-polynomial-equations + summation-of-series + mathematical-induction). Topic 2 Functions (linear + quadratic + polynomial + rational + exponential + logarithmic + trigonometric + inverse-trigonometric + composite + inverse + transformation + domain + range + asymptotes + sketching + graphing + GDC + modelling + AA-HL-extension-partial-fractions + further-algebra-skills). Topic 3 Geometry and Trigonometry (Euclidean-geometry + coordinate-geometry + vectors-2D + vectors-3D + complex-numbers-applied-to-geometry + matrices + transformations + trigonometry-3D + AA-HL-extension-vector-equations + planes + lines + vector-product + scalar-product + parametric-equations + 3D-distance + 3D-angle + GDC-3D). Topic 4 Statistics and Probability (descriptive-statistics + measures-of-central-tendency + measures-of-dispersion + bivariate-statistics + linear-regression + correlation + chi-squared + goodness-of-fit + contingency-tables + probability-rules + Bayes-theorem + discrete-random-variables + binomial-distribution + Poisson-distribution + normal-distribution + continuous-random-variables + AA-HL-extension-probability-generating-functions + Markov-chains + transition-matrices + steady-state + hypothesis-testing + t-test + z-test + confidence-intervals + sampling + central-limit-theorem). Topic 5 Calculus (limits + continuity + differentiation-rules + chain-rule + product-rule + quotient-rule + implicit-differentiation + second-derivative + higher-derivatives + applications-of-differentiation + integration-rules + definite-integrals + area-under-curve + volume-of-revolution + differential-equations + slope-fields + Euler-method + separation-of-variables + AA-HL-extension-Maclaurin-series + Taylor-series + convergence + radius-of-convergence + improper-integrals + integration-by-parts + partial-fractions-integration + second-order-differential-equations + power-series-solutions). Total-coverage-required-across-5-topics + AA-HL-extension-topics + IA-mathematical-exploration.

Section 10 — The IB Mathematics AA HL Paper 1 + Paper 2 + Paper 3 + IA Mathematical Exploration AI tutor prompt library: 100+ prompts for Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration + 5-topics + AA-HL-extension-topics

The IB Mathematics AA HL AI-tutor-prompt-library contains 100+ rigorously-engineered prompts covering every Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration + 5-topics + AA-HL-extension-topics. Sample-prompts: "Score-this-Paper-1-Q1-against-IB-Markscheme-Question-1-short-response" + "Score-this-Paper-1-Q2-against-IB-Markscheme-Question-2-vectors-3D" + "Score-this-Paper-1-Q3-against-IB-Markscheme-Question-3-statistics-chi-squared" + "Score-this-Paper-1-Q4-against-IB-Markscheme-Question-4-calculus-differential-equations" + "Score-this-Paper-1-Q5-against-IB-Markscheme-Question-5-extended-response-multi-topic" + "Score-this-Paper-2-Q1-against-IB-Markscheme-Question-1-calculator-functions" + "Score-this-Paper-2-Q2-against-IB-Markscheme-Question-2-calculator-geometry" + "Score-this-Paper-2-Q3-against-IB-Markscheme-Question-3-calculator-probability-normal" + "Score-this-Paper-2-Q4-against-IB-Markscheme-Question-4-calculator-calculus-applied" + "Score-this-Paper-2-Q5-against-IB-Markscheme-Question-5-calculator-modelling" + "Score-this-Paper-3-Q1-against-IB-Markscheme-Paper-3-complex-numbers" + "Score-this-Paper-3-Q2-against-IB-Markscheme-Paper-3-proof-by-induction" + "Score-this-IA-against-IB-Mathematics-AA-HL-IA-rubric-presentation-mathematical-communication-personal-engagement-reflection-use-of-technology" + "Score-this-IA-research-question-against-IB-IA-rubric-focus-specificity-mathematical-depth" + "Generate-Paper-1-Q1-short-response-drill-on-Number-Algebra" + "Generate-Paper-1-Q2-vectors-3D-drill-on-vector-equations-of-lines" + "Generate-Paper-1-Q3-chi-squared-drill-on-goodness-of-fit" + "Generate-Paper-1-Q4-differential-equations-drill-on-separation-of-variables" + "Generate-Paper-1-Q5-extended-response-drill-on-multi-topic-integration" + "Generate-Paper-2-calculator-drill-on-normal-distribution-hypothesis-testing" + "Generate-Paper-3-complex-numbers-drill-on-De-Moivre-Euler" + "Generate-Paper-3-proof-by-induction-drill-on-mathematical-induction" + "Generate-IA-topic-brainstorming-prompts-for-12-pages" + "Generate-IA-research-question-refinement-prompts" + "Score-this-student-response-against-IB-band-descriptors-Band-1-through-Band-7".

Section 11 — The IB Mathematics AA HL AI tutor score-7 workflow: 30-week schedule + readiness benchmarks + stretch goals

The IB Mathematics AA HL AI-tutor-score-7-workflow is the 30-week calendar that takes the candidate from Year-12-September-baseline to May-2027-IB-Maths-AA-HL-Exam-day. The-workflow-includes: Week 0 Diagnostic (full-mock-Paper-1 + Paper-2 + Paper-3 + IA-diagnostic + identify-gaps + map-to-IB-band-descriptors + assign-target-band + 1-on-1-AI-tutor-orientation) + Weeks 1-3 Topic 1 Number-Algebra (exponents + logarithms + sequences + series + binomial-theorem + counting + proof-by-induction + complex-numbers + modulus-argument + De-Moivre + Euler + polar-form + roots-of-polynomial-equations + summation-of-series + mathematical-induction + Topic-1-mastery-check-at-week-3) + Weeks 4-7 Topic 2 Functions (linear + quadratic + polynomial + rational + exponential + logarithmic + trigonometric + inverse-trigonometric + composite + inverse + transformation + domain + range + asymptotes + sketching + graphing + GDC + modelling + AA-HL-extension-partial-fractions + further-algebra-skills + Topic-2-mastery-check-at-week-7) + Weeks 8-12 Topic 3 Geometry-Trigonometry (Euclidean-geometry + coordinate-geometry + vectors-2D + vectors-3D + complex-numbers-applied-to-geometry + matrices + transformations + trigonometry-3D + AA-HL-extension-vector-equations + planes + lines + vector-product + scalar-product + parametric-equations + 3D-distance + 3D-angle + GDC-3D + Topic-3-mastery-check-at-week-12) + Weeks 13-18 Topic 4 Statistics-Probability (descriptive-statistics + measures-of-central-tendency + measures-of-dispersion + bivariate-statistics + linear-regression + correlation + chi-squared + goodness-of-fit + contingency-tables + probability-rules + Bayes-theorem + discrete-random-variables + binomial-distribution + Poisson-distribution + normal-distribution + continuous-random-variables + AA-HL-extension-probability-generating-functions + Markov-chains + transition-matrices + steady-state + hypothesis-testing + t-test + z-test + confidence-intervals + sampling + central-limit-theorem + Topic-4-mastery-check-at-week-18) + Weeks 19-24 Topic 5 Calculus (limits + continuity + differentiation-rules + chain-rule + product-rule + quotient-rule + implicit-differentiation + second-derivative + higher-derivatives + applications-of-differentiation + integration-rules + definite-integrals + area-under-curve + volume-of-revolution + differential-equations + slope-fields + Euler-method + separation-of-variables + AA-HL-extension-Maclaurin-series + Taylor-series + convergence + radius-of-convergence + improper-integrals + integration-by-parts + partial-fractions-integration + second-order-differential-equations + power-series-solutions + Topic-5-mastery-check-at-week-24) + Weeks 25-27 IA Mathematical Exploration (12-pages + 20-hours + 20-marks + IA-topic-brainstorming + IA-research-question-refinement + IA-outline + IA-draft + IA-revision + IA-final + IA-rubric-self-assessment + IA-exemplar-comparison + Topic-IA-mastery-check-at-week-27) + Weeks 28-30 Polish + Mocks (full-mock-Paper-1 + full-mock-Paper-2 + full-mock-Paper-3 + IBO-past-papers-2016-to-2025 + TZ1-TZ2-TZ3-papers + specimen-papers + IA-final-polish + stretch-goals + score-7-mock-targets + readiness-benchmarks). The-stretch-goals-include: score-7-on-every-TZ-paper + Band-7-Outstanding-on-every-question + publication-quality-IA + Oxford-Imperial-Cambridge-Maths-Interview-prep + Putnam-competition-cross-training + mathematical-modelling-competition (M3) prep.

Section 12 — The IB Mathematics AA HL AI tutor score-7 readiness benchmarks

The IB Mathematics AA HL AI-tutor-score-7-readiness-benchmarks are the precise-metrics-that-indicate-the-candidate-is-on-track-for-a-score-7. Week-3-benchmark: Topic-1-mastery-check ≥ Band-5-Sophisticated + complex-numbers-fluency + proof-by-indiction-rigour. Week-7-benchmark: Topic-2-mastery-check ≥ Band-5-Sophisticated + function-transformation-fluency + GDC-sketching-accuracy. Week-12-benchmark: Topic-3-mastery-check ≥ Band-5-Sophisticated + vectors-3D-mastery + matrices-fluency. Week-18-benchmark: Topic-4-mastery-check ≥ Band-5-Sophisticated + chi-squared-mastery + Markov-chains-steady-state-mastery. Week-24-benchmark: Topic-5-mastery-check ≥ Band-5-Sophisticated + differential-equations-fluency + Maclaurin-series-mastery. Week-27-benchmark: IA-rubric-self-assessment ≥ 18/20 + IA-exemplar-comparison-match + IA-final-ready. Week-30-benchmark: full-mock-Paper-1 ≥ 95/110 (Band-6-Excellent-or-Band-7-Outstanding) + full-mock-Paper-2 ≥ 95/110 + full-mock-Paper-3 ≥ 42/50 + IA-final ≥ 18/20 + score-7-target-met. The-AI-tutor-tracks-every-benchmark-weekly-and-adjusts-the-workflow-if-any-benchmark-falls-below-threshold.

Section 13 — Get started with the IB Mathematics AA HL AI tutor today

The IB Mathematics AA HL AI-tutor-is-available-now-on-Grademy-at-https-grademy-work-AI-Tutor-IB-Mathematics-AA-HL. Book-a-diagnostic-session-(free-30-minute-baseline-assessment), receive-your-personalized-30-week-IB-Mathematics-AA-HL-workflow-with-weekly-benchmarks, get-matched-with-an-AI-tutor-that-runs-the-IB-Group-5-mastery-cohort-covering-Paper-1-no-calculator + Paper-2-calculator + Paper-3-extended-response + IA-mathematical-exploration + 5-topics + AA-HL-extension-topics + IB-command-terms + IB-Markscheme + IA-rubric + IB-band-descriptors + IBO-past-papers-2016-to-2025 + TZ1-TZ2-TZ3-papers + specimen-papers. The IB Mathematics AA HL AI tutor closes the 5-to-7 gap for IB-Diploma-Programme Year-12 + Year-13 candidates targeting Cambridge + Oxford + Imperial + UCL + LSE + Stanford + MIT + Harvard + Yale + Princeton + Columbia + Chicago + Berkeley + Caltech + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + KAIST + SNU + Tsinghua + Peking + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago Mathematics + Engineering + Computer-Science + Physics + Economics + Quantitative-Finance + Actuarial-Science + Data-Science + Machine-Learning + AI admissions. Pair-this-with: IB-Mathematics-AI-HL-AI-tutor + IB-Physics-HL-AI-tutor + IB-Chemistry-HL-AI-tutor + IB-Biology-HL-AI-tutor + IB-Computer-Science-HL-AI-tutor + IB-Economics-HL-AI-tutor + IB-Further-Mathematics-HL-AI-tutor + IB-Design-Technology-HL-AI-tutor + IB-Sports-Exercise-Health-Science-HL-AI-tutor + IB-Extended-Essay-in-Mathematics + IB-Internal-Assessment-Mathematical-Exploration + IB-TOK-mathematical-knowledge + IB-CAS-mathematical-modelling. Compatible-with-PYP + MYP + DP + CP-IB-frameworks + IB-Bilingual + IB-Course-Companion + IB-World-School-accreditation.

Related Grademy playbooks

• IB Mathematics AI HL AI Tutor Playbook 2026
• IB Physics HL AI Tutor Playbook 2026
• IB Chemistry HL AI Tutor Playbook 2026
• IB Biology HL AI Tutor Playbook 2026
• IB Computer Science HL AI Tutor Playbook 2026
• IB Economics HL AI Tutor Playbook 2026
• IB Further Mathematics HL AI Tutor Playbook 2026
• IB Design Technology HL AI Tutor Playbook 2026
• IB Sports Exercise Health Science HL AI Tutor Playbook 2026
• IB History HL AI Tutor Playbook 2026 (post-170)
• IB Philosophy HL AI Tutor Playbook 2026 (post-171)
• IB English A Literature HL AI Tutor Playbook 2026 (post-172)
• IGCSE Mathematics 0580 AI Tutor Playbook 2026
• GCSE Mathematics AI Tutor Playbook 2026
• A-Level Mathematics AI Tutor Playbook 2026
• A-Level Further Mathematics AI Tutor Playbook 2026
• AP Calculus BC AI Tutor Playbook 2026
• AP Statistics AI Tutor Playbook 2026
• SAT Mathematics AI Tutor Playbook 2026
• ACT Mathematics AI Tutor Playbook 2026

Related: IB Economics HL as the IBO-standard pre-university economics + finance + public-policy subject — pairing with IB Mathematics AA HL for Cambridge + LSE + Oxford economics + finance + econometrics + quantitative-economics + first-year-undergraduate-Economics admissions

IB Economics HL is the IBO-standard pre-university economics + finance + business + consulting + public-policy + development-economics + international-economics + behavioural-economics + political-economy qualification for IB-Diploma-Programme Year-12 + Year-13 candidates at IB-World-Schools. The IB Economics HL specification covers 4-micro-units + 4-macro-units + 2-international-economics + 2-development-economics + quantitative-methods + Paper-1-Extended-Response + Paper-2-Data-Response + Paper-3-Policy-Paper + IA-Policy-Paper. For Cambridge + Oxford + LSE + UCL economics + finance + econometrics + quantitative-economics + first-year-undergraduate-Economics + LSE-econometrics + Oxford-econometrics + LSE-quantitative-economics candidates, IB Economics HL + IB Mathematics AA HL is the canonical pair. IB Economics HL covers the applied economic theory + quantitative-methods (PED + YED + PES + MPC + MPS + multiplier + money-multiplier + Marshall-Lerner + J-curve + GDP + GNI + Gini + HDI + Solow + Harrod-Domar + AD-AS + Phillips + Lorenz); IB Mathematics AA HL covers the pure + applied mathematics + statistics + calculus + probability + correlation + regression + significance + hypothesis-testing (calculus + algebra + functions + trigonometry + vectors + complex-numbers + statistics + probability + hypothesis-testing + correlation + regression + differentiation + integration + differential-equations + Maclaurin-series + vectors + complex-numbers). The IB Economics HL + IB Mathematics AA HL pair is the IBO-applied-equivalent of A-Level Mathematics + A-Level Further Mathematics + Cambridge-economics + LSE-economics + Oxford-economics + Warwick-economics. Together, the pair signals readiness for Cambridge-economics + Oxford-economics + LSE-economics + UCL-economics + Warwick-economics + Imperial-economics + UCL-econometrics + LSE-econometrics + LSE-quantitative-research-methods + Cambridge-economics-with-quantitative-research + Oxford-economics-with-quantitative-research + UCL-economics-with-quantitative-research + Imperial-mathematics-and-computational-finance + first-year-undergraduate-Economics at Cambridge + Oxford + LSE + UCL + Imperial + Stanford + MIT + ETH-Zurich + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Toronto + UBC + McGill admissions. See our <a href="/blog/ib-economics-hl-playbook-2026" class="text-[var(--brand-coral)] underline-offset-4 hover:underline font-semibold">AI tutor for IB Economics HL 2026</a> for the 30-week IB Economics HL workflow + 4-micro-units + 4-macro-units + 2-international-economics + 2-development-economics + quantitative-methods + Paper-1 + Paper-2 + Paper-3 + IA-Policy-Paper + the AI tutor scoring workflow for score 7.

Pairs with IB Economics HL (post-179)

The IB Economics HL playbook (post-179) + [this playbook] form the IB Diploma + IB Higher-Level + IB Group-3 + IB Group-4 + IB Group-5 + IB Group-2 + economics-finance-business-consulting-public-policy-political-economy-international-relations-development-studies cohort companion for the IB-Diploma-Programme Year-12 + Year-13 candidates at IB-World-Schools in Switzerland + Singapore + Hong-Kong + UAE + UK + US + Canada + Australia + New-Zealand + Japan + Korea + China + India + Pakistan + Bangladesh + Indonesia + Malaysia + Thailand + Vietnam + Philippines + Egypt + South-Africa + Kenya + Nigeria + Ghana + Saudi + Qatar + Bahrain + Kuwait + Oman + Jordan + Lebanon targeting first-year-undergraduate-Economics + Finance + PPE + PPE-Economics + Business + Management + Consulting + Public-Policy + Political-Economy + International-Relations + Development-Studies at MIT + Stanford + Caltech + Cambridge + Oxford + Imperial + UCL + LSE + Edinburgh + Manchester + Bristol + Durham + Exeter + St-Andrews + KCL + Loughborough + Bath + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + KAIST + SNU + Tsinghua + Peking + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. See post-179 for the IB-Economics-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Spanish B HL (post-178)

The IB Spanish B HL playbook (post-178) + [this playbook] form the IB Diploma + IB Higher-Level + IB Group-2 + IB Group-2-Language-Acquisition + Spanish + hispanophone-world + IB-cohort companion for the IB-Diploma-Programme Year-12 + Year-13 candidates at IB-World-Schools in Spain + Mexico + Argentina + Colombia + Peru + Chile + Cuba + Puerto-Rico + Venezuela + Ecuador + Dominican-Republic + Guatemala + Costa-Rica + Panama + Uruguay + Paraguay + Bolivia + Honduras + El-Salvador + Nicaragua + UK + US + Singapore + Hong-Kong + UAE + Australia + New-Zealand + international-Spanish-bilingual-Schools targeting IE-Business-School + IESE + ESADE + ESERP + Complutense + Salamanca + Barcelona + Madrid + Buenos-Aires + UNAM + ITAM + Andes + Rosario + Bogota + Lima + Santiago + NYU + Columbia + Stanford + Harvard + Yale + Princeton admissions. See post-178 for the IB-Spanish-B-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with AP Statistics (post-196)

The AP Statistics playbook (post-196) + [this playbook] form the AP + AP-STEM + AP-Quantitative + AP-Math + AP-Data-Science + AP-Social-Science-Quantitative + AP-Research-Methods + AP-Investigative-Task + AP-Calculator-Fluency + AP-Inference + AP-Probability + AP-Experimental-Design + AP-Regression + AP-ANOVA + AP-Chi-Square + AP-Binomial + AP-Geometric + AP-CLT + AP-Confidence-Interval + AP-Hypothesis-Test + AP-p-value + AP-Type-I-Error + AP-Type-II-Error + AP-Conditions-for-Inference + AP-Random-Sampling + AP-Random-Assignment + AP-Blocking + AP-Blinding + AP-Placebo + AP-Correlation + AP-Causation + AP-Confounder + AP-Residual + AP-Outlier + AP-Influential-Point + AP-Least-Squares + AP-Scatterplot + AP-Stemplot + AP-Histogram + AP-Boxplot + AP-z-score + AP-TI-84 + AP-TI-NSpire + AP-1-Var-Stats + AP-2-Var-Stats + AP-LinReg + AP-T-Test + AP-1-PropZTest + AP-2-PropZTest + AP-2-SampTTest + AP-Chi-Square-GOF + AP-Chi-Square-Independence + AP-normal-CDF + AP-inverse-normal + AP-binomial-PDF + AP-binomial-CDF + AP-geometric-PDF + AP-geometric-CDF + AP-Probability-Simulator + AP-Random-Number-Generator + AP-Pre-Med + AP-Pre-Public-Health + AP-Pre-Data-Science + AP-Pre-Engineering + AP-Pre-Biology + AP-Pre-Business + AP-Pre-Economics + AP-Pre-Finance + AP-Pre-Marketing + AP-Pre-Psychology + AP-Pre-Political-Science + AP-Pre-Sociology + AP-Pre-Nursing + AP-Pre-Kinesiology + AP-Pre-Education + AP-Pre-Communication + AP-Pre-Graduate-School cohort companion for US high school students (Grade 10 + 11 + 12) preparing for the May 2027 AP exam + parents paying $100+ per AP exam + tutor or prep-class costs + AP teachers wanting a rubric-aligned AI workflow for FRQ scoring + Investigative-Task-rubric alignment + homeschool families using AP for transcript strength targeting first-year-undergraduate-Statistics + Biostatistics + Epidemiology + Public-Health + Data-Science + Machine-Learning + Business-Analytics + Marketing-Analytics + Finance + Quantitative-Economics + Econometrics + Quantitative-Psychology + Psychology-Research-Methods + Sociology-Quantitative + Political-Science-Quantitative + Pre-Med-Biostatistics + Pre-Public-Health-Epidemiology + Pre-Data-Science + Pre-Engineering-Statistical-Methods + Pre-Business-Business-Analytics + Pre-Finance-Quantitative-Finance + Pre-Marketing-Marketing-Analytics + Pre-Economics-Econometrics + Pre-Political-Science-Quantitative + Pre-Sociology-Quantitative-Research + Pre-Psychology-Research-Methods at MIT + Stanford + Caltech + Harvard + Yale + Princeton + Brown + Dartmouth + Cornell + Columbia + NYU + Georgetown + Berkeley + Chicago + Penn + Rice + Indiana + Michigan + Northwestern + Duke + Johns-Hopkins + CMU + Georgia-Tech + UIUC + Wisconsin + Texas-Austin + Washington + UCLA + USC + UC-Berkeley + Caltech + JPL + Cambridge + Oxford + Imperial + LSE + UCL + Edinburgh + Manchester + Bristol + Durham + Exeter + St-Andrews + KCL + Loughborough + Bath + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + KAIST + SNU + Tsinghua + Peking + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. See post-196 for the AP-Statistics-specific exam, score-distribution, and 20-week score-5 master schedule.