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IB Mathematics HL: Applications & Interpretation 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 + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel — typically the cohort in IB-Mathematics-HL-AI + IB-Economics-HL + IB-Business-Management-HL + IB-Biology-HL + IB-Psychology-HL + IB-Environmental-Systems-and-Societies-HL + IB-Computer-Science-HL + IB-Further-Mathematics-HL, often paired with IB-Math-HL-AI-Internal-Assessment-Modelling-Exploration + IB-Extended-Essay-in-Economics + IB-TOK-exhibition + IB-CAS-creativity-activity-service. Covers IB Math HL AI teachers who want an AI workflow for grading IA-modelling-explorations + Paper-1-short-response + Paper-2-extended-response + Paper-3-optional-topic, parents paying for IB-Math-HL-AI-prep ($300-$3000 for prep-books + $1000-$5000 for prep-courses + $2000-$8000 for private-tutors), IB-World-Schools seeking IB-Math-HL-AI-internal-assessment-rubric alignment, and overseas IB-Diploma-candidates applying to MIT + Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST + KAIST + SNU + UCL + Edinburgh + Manchester + Bristol + Durham + KCL + Georgia-Tech + UT-Austin + Berkeley + UCLA + Michigan + CMU + Cornell + Columbia + Princeton + Yale + Harvard + Brown + Dartmouth + Penn + Johns-Hopkins + Duke + Northwestern + Rice.

Hook: IB Math HL AI is the most-respected pre-university statistics + modelling + applied-calculus qualification globally — the standard for IB-Diploma-Programme Year-12 + Year-13 candidates at IB-World-Schools targeting MIT + Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST + KAIST + SNU + UCL + Edinburgh + Manchester + Bristol + Durham + KCL + Georgia-Tech + UT-Austin + Berkeley + UCLA + Michigan + CMU + Cornell + Columbia + Princeton + Yale + Harvard + Brown + Dartmouth + Penn + Johns-Hopkins + Duke + Northwestern + Rice. The 2025 score distribution is selective: score-7 rate of approximately 12-15 percent (highest honours + university-credit at Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST), score-6 rate of approximately 21 percent, score-5 rate of approximately 24 percent (the score-5+ cumulative rate 57-60 percent is the IB Diploma + university-readiness benchmark), score-4 rate of approximately 19 percent, score-3 rate of approximately 14 percent, score-2 rate of approximately 8 percent, score-1 rate of approximately 3 percent. The 5-core-topics-of-IB-Math-HL-AI (Topic 1 Number and Algebra + Topic 2 Functions + Topic 3 Geometry and Trigonometry + Topic 4 Statistics and Probability + Topic 5 Calculus) + 5-HL-additional-topics (Algebra + Logarithmic + Exponential + Functions + Trigonometric + Functions + Vectors + Statistics + Probability) + Internal-Assessment-Modelling-Exploration map onto Year-12 + Year-13 applied-mathematics + first-year-undergraduate-Economics + Finance + Business + Statistics + Actuarial-Science + Psychology + Biology + Environmental-Science + Data-Science + Computer-Science at MIT + Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST + KAIST + SNU + UCL + Edinburgh + Manchester + Bristol + Durham + KCL + Georgia-Tech + UT-Austin + Berkeley + UCLA + Michigan + CMU + Cornell + Columbia + Princeton + Yale + Harvard + Brown + Dartmouth + Penn + Johns-Hopkins + Duke + Northwestern + Rice:

Section 1 — Why IB Math HL AI is the most-respected pre-university statistics + modelling + applied-calculus qualification + the Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po first-year-undergraduate-Economics + Finance + Business + Statistics + IB-Diploma-applied-track subject

IB Math HL AI is the IBO-standard pre-university statistics + modelling + applied-calculus qualification for IB-Diploma-Programme Year-12 + Year-13 candidates — modelling-driven, applied-calculus-required, statistics-heavy, GDC-required, IA-modelling-exploration-assessed. It is the standard for IB-World-Schools in 145+ countries. Unlike A-Level Mathematics (3-papers-100%-calculator-allowed + pure-mechanics-statistics-decision-modular) + AP Statistics (MCQ-FRQ-only + 90-minute-total + non-calculus-heavy), IB Math HL AI integrates modelling-and-optimization + statistics-and-probability-applied + financial-modelling + discrete-modelling across all 5-core-topics + 5-HL-additional-topics + IA-modelling-exploration + Paper-3-optional-topic-mastery. 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 Economics + Finance + Business + Statistics + Actuarial-Science + Psychology + Biology + Environmental-Science + Data-Science + Pre-Computer-Science + first-year-undergraduate-Applied-Mathematics admissions at MIT + Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST + KAIST + SNU + UCL + Edinburgh + Manchester + Bristol + Durham + KCL + Georgia-Tech + UT-Austin + Berkeley + UCLA + Michigan + CMU + Cornell + Columbia + Princeton + Yale + Harvard + Brown + Dartmouth + Penn + Johns-Hopkins + Duke + Northwestern + Rice. This playbook gives the 30-week IB Math HL AI workflow.

Section 2 — The 30-week IB Math HL AI AI tutor study plan: weeks 1-4 = Topic 1 Number-and-Algebra + Topic 2 Functions foundations + diagnostic, weeks 5-13 = Topic 3-5 core-topic mastery (Geometry-Trigonometry + Statistics-Probability + Calculus), weeks 14-20 = Topic 6-10 HL-additional mastery + IA-modelling-exploration, weeks 21-26 = Paper 1 + Paper 2 + Paper 3 extended-response + paper-strategy, weeks 27-30 = mock-exams + IBO-past-papers + polish

The IB Math HL AI workflow is built around five cycles of six weeks each, with the IA-modelling-exploration running in parallel during weeks 14-20. Weeks 1-4 are foundations: number-and-algebra (sequences, series, binomial theorem, partial fractions, financial mathematics, simple + compound interest, depreciation, amortisation, modelling linear systems), functions (domain, range, inverses, transformations, composition, even/odd, polynomial, rational, exponential, logarithmic, sinusoidal). Weeks 5-8 cover Topic 3 geometry-and-trigonometry (analytic geometry, conic sections in context, trigonometric identities, triangle trigonometry, vectors in 2D/3D, complex numbers for signal-processing). Weeks 9-13 cover Topic 4 statistics-and-probability + Topic 5 calculus (Bayes' theorem extended, binomial/Poisson/normal distributions, confidence intervals, hypothesis testing, chi-squared test, regression-correlation, continuity, limits, derivatives, applications of derivatives to modelling, integration, applications of integration to area-under-curve + volume, differential equations for growth-and-decay). Weeks 14-20 layer in the HL-additional-topics (advanced financial mathematics, modelling with differential equations, vectors in 3D modelling, statistical inference for decision-making, time-series-and-trend) AND the IA-modelling-exploration (15-20 page investigation). Weeks 21-26 are paper-strategy mastery: Paper 1 (Section A calculator-required short-response + Section B calculator-required extended-response — both GDC-permitted), Paper 2 (graph-display-calculator-required extended-response), Paper 3 (2-of-4 optional-topic questions chosen from Statistics-Probability-Modelling + Calculus-Applied-Series + Financial-Modelling + Discrete-Modelling + Optimisation-Applications). Weeks 27-30 are mock-exams + IBO-past-papers + polish: TZ1 (May 2024 + May 2025) + TZ2 (June 2024) + TZ3 (October 2024) + specimen papers + IA-exemplar analysis. The 30-week schedule front-loads the IA-modelling-exploration to allow 10+ weeks for revision, peer-review, and teacher-feedback before the IB-math-coordinator-form-4-submission-window in February 2027.

Section 3 — Topic 1 Number and Algebra: arithmetic + geometric + sequences + series + financial mathematics + simple interest + compound interest + depreciation + amortisation + modelling linear systems

Topic 1 Number and Algebra is the foundation. Arithmetic sequences: u_n = u_1 + (n-1)d. Sum of arithmetic series: S_n = n/2(2u_1 + (n-1)d). Geometric sequences: u_n = u_1 × r^(n-1). Sum of geometric series: S_n = u_1(r^n - 1)/(r-1). Sum to infinity (|r|<1): S_∞ = u_1/(1-r). Binomial theorem: (a+b)^n = Σ C(n,k)a^(n-k)b^k. Partial fractions: linear + repeated-linear + irreducible-quadratic cases. Financial mathematics: A = P(1 + r/100)^n for compound interest; A = Pe^(rt) for continuous compounding; loan repayments using present value + annuity formulas; depreciation using reducing-balance + straight-line methods. Modelling linear systems: 2x2 + 3x3 systems using elimination + matrix methods; matrix algebra for transitions (Markov chains); eigenvectors for stable states; applications to population dynamics + market equilibrium. The AI tutor prompt library scores every Number-Algebra response against the IBO rubric. Common gap: candidates confuse compound interest formula with simple interest — the AI tutor flags the specific formula-misuse pattern.

Section 4 — Topic 2 Functions: domain + range + inverses + transformations + composition + even/odd + polynomial + rational + exponential + logarithmic + sinusoidal + reciprocal-trigonometric

Topic 2 Functions builds the modelling toolkit. Domain + range: explicit intervals, including asymptotes + restricted domains for inverse functions. Inverses: f^(-1)(x) restricted to monotonic intervals. Transformations: y = af(b(x-c)) + d for any base function; sketch the transformed graph + state domain + range. Composition: (f∘g)(x) = f(g(x)) + decomposition into known functions. Even/odd: f(-x) = f(x) (even) + f(-x) = -f(x) (odd) + graph symmetry. Polynomial: zeros, end-behaviour, turning points, sketch from factorised form. Rational: vertical + horizontal + oblique asymptotes, behaviour near asymptotes. Exponential: y = a × b^x + asymptote + domain + range. Logarithmic: y = a × log_b(x) + inverse of exponential + domain + asymptote. Sinusoidal: y = A sin(B(x-C)) + D for amplitude + period + phase-shift + vertical-shift. Reciprocal-trigonometric: y = sec(x) + csc(x) + cot(x) + asymptotes. The AI tutor prompt library scores every Functions response against the IBO rubric. Common gap: candidates mis-identify transformations — the AI tutor highlights the parent-function-vs-transformed-function gap.

Section 5 — Topic 3 Geometry and Trigonometry: analytic geometry + conic sections in context + trigonometric identities + triangle trigonometry + vectors in 2D/3D + complex numbers for signal-processing

Topic 3 Geometry and Trigonometry grounds the modelling applications. Analytic geometry: lines + circles + distance + midpoint + intersection. Conic sections in context: parabola y² = 4ax (projectile motion + satellite dish); ellipse x²/a² + y²/b² = 1 (planetary orbit + acoustics); hyperbola x²/a² - y²/b² = 1 (navigation + relativity); focus-directrix + eccentricity. Trigonometric identities: sin²θ + cos²θ = 1; sin(θ±φ) + cos(θ±φ); double-angle + half-angle. Triangle trigonometry: sine rule + cosine rule + area = ½ab sin C. Vectors in 2D/3D: position + displacement + velocity + force + component form; unit vector + direction cosines; scalar product + vector product (cross); angle between vectors + projection. Complex numbers for signal-processing: argand diagram; modulus + argument; polar form r(cosθ + i sinθ) = re^(iθ); De Moivre's theorem; roots of unity; AC-circuit analysis. The AI tutor prompt library scores every Geometry-Trigonometry response against the IBO rubric. Common gap: candidates confuse direction-cosines with direction-ratios — the AI tutor highlights the cosine-extraction step.

Section 6 — Topic 4 Statistics and Probability: descriptive statistics + probability axioms + Bayes' theorem + binomial + Poisson + normal distributions + confidence intervals + hypothesis testing + chi-squared test + regression-correlation + sampling

Topic 4 Statistics and Probability is the highest-weight IB Math HL AI topic. Descriptive statistics: mean + median + mode + standard deviation + variance + interquartile-range + box-plot + outlier-detection. Probability axioms: P(A∪B) = P(A) + P(B) - P(A∩B); conditional probability P(A|B) = P(A∩B)/P(B); independence P(A∩B) = P(A)P(B); tree-diagrams + Venn-diagrams + 2x2-tables. Bayes' theorem: P(A|B) = P(B|A)P(A)/P(B) for medical-testing + spam-filtering + reverse-engineering applications. Binomial: B(n,p) for n-independent-trials + probability-of-k-successes. Poisson: P(X=k) = λ^k e^(-λ)/k! for rare-events + queueing. Normal: N(μ,σ²) + standardised-score z = (x-μ)/σ + inverse-normal for confidence-intervals. Confidence intervals: 95%-CI for mean (σ-known + σ-unknown t-distribution) + proportion. Hypothesis testing: H₀ + H₁ + test-statistic + p-value + significance-level α = 0.05 + decision rule + type-I + type-II errors + power-of-test. Chi-squared test: goodness-of-fit (fair-die + Mendelian-genetics) + independence (contingency-table 2x2 + r×c). Regression: least-squares line y = a + bx; correlation coefficient r; coefficient of determination R²; residual-analysis + outlier-detection. Sampling: simple-random-sampling + stratified-sampling + cluster-sampling + systematic-sampling + bias-types. The AI tutor prompt library scores every Statistics-Probability response against the IBO rubric. Common gap: candidates confuse p-value with probability-of-H₀-true — the AI tutor highlights the p-value-as-extremeness-measure interpretation.

Section 7 — Topic 5 Calculus: limits + continuity + derivatives + applications of derivatives to modelling + integration + applications of integration to area-under-curve + volume + differential equations for growth-and-decay + Maclaurin series + L'Hôpital's rule + optimisation

Topic 5 Calculus is the applied-calculus backbone. Limits: limit-laws + one-sided + infinite + indeterminate-forms. Continuity: ε-δ definition + types-of-discontinuity. Derivatives: product + quotient + chain-rule; implicit-differentiation; second-derivative; higher-order; parametric-differentiation. Applications of derivatives to modelling: rate-of-change + related-rates + curve-sketching + optimisation-constrained; linearisation + tangent-line approximation. Integration: definite + indefinite + substitution + by-parts + partial-fractions; standard-results. Applications of integration: area-under-curve + area-between-curves + volume-of-revolution (disc + shell) + arc-length + surface-area + numerical-integration (trapezoidal-rule + Simpson's-rule + GDC-application). Differential equations for growth-and-decay: dy/dx = ky → y = Ae^(kx); separable-equations; Euler's-method; modelling population-growth + radioactive-decay + Newton's-law-of-cooling + logistic-growth + SIR-epidemic. Maclaurin series: f(x) = f(0) + f'(0)x + f''(0)x²/2! + ... + e^x + sin x + cos x + ln(1+x) + (1+x)^n + application to limits + integration. L'Hôpital's rule: 0/0 + ∞/∞ indeterminate-forms. Optimisation: minimise/maximise with constraints using Lagrange-multipliers (HL). The AI tutor prompt library scores every Calculus response against the IBO rubric. Common gap: candidates mis-set-up the differential equation — the AI tutor highlights the dy/dt-vs-rate-pattern identification.

Section 8 — Topic 6 HL-Additional Algebra: sequences extended + series convergence tests + binomial theorem extended + complex numbers extended form + modelling with linear algebra

Topic 6 HL-Additional Algebra extends the foundation. Sequences extended: arithmetic + geometric + recursive sequences + u_{n+1} = au_n + b linear-recurrence (solved by iteration). Series convergence tests: Σ 1/n diverges + Σ 1/n² converges; comparison-test + ratio-test + integral-test (HL). Binomial theorem extended: negative + fractional index; C(n,k) for n∉ℕ via Γ-function (HL). Complex numbers extended form: r e^(iθ) + De Moivre's theorem; roots-of-unity; loci-of-points-in-argand-diagram; transformation-of-planes. Modelling with linear algebra: matrix-arithmetic (3x3-case) + determinants + inverses (3x3-case) + transition-matrices + Markov-chains + eigenvectors + eigenvalues (HL); applications to population-models + market-equilibrium + Leslie-matrix + Leslie-prediction. The AI tutor prompt library scores every HL-Additional-Algebra response against the IBO rubric. Common gap: candidates confuse inverse-matrix with reciprocal — the AI tutor highlights the matrix-arithmetic-vs-number-arithmetic distinction.

Section 9 — Topic 7 HL-Additional Functions + Trigonometry: reciprocal-trigonometric extended + inverse-trigonometric extended + compound-angle extended + harmonic form + hyperbolic functions

Topic 7 HL-Additional Functions + Trigonometry deepens the modelling toolkit. Reciprocal-trigonometric extended: sec(x) = 1/cos(x) + csc(x) = 1/sin(x) + cot(x) = cos(x)/sin(x) + identities + asymptotes + graphs. Inverse-trigonometric: arcsin(x) + arccos(x) + arctan(x) + domain + range + principal-value + derivatives d/dx[arcsin(x)] = 1/√(1-x²). Compound-angle extended: sin(A±B) + cos(A±B) + tan(A±B) + double-angle + half-angle; R-form a sin θ + b cos θ = R sin(θ+α) for amplitude-modelling + harmonic-motion. Harmonic form: simple-harmonic-motion y = A cos(ωt + φ) + period T = 2π/ω + frequency f = ω/2π + applications to springs + pendulums + waves + AC-circuits. Hyperbolic functions: sinh(x) + cosh(x) + tanh(x) + identities cosh²x - sinh²x = 1 + derivatives + inverses + Gudermannian (HL). The AI tutor prompt library scores every HL-Additional-Functions-Trigonometry response against the IBO rubric. Common gap: candidates mis-state principal-range — the AI tutor highlights the [-π/2, π/2] arcsin-range rule.

Section 10 — Topic 8 HL-Additional Vectors + Complex Numbers: vectors in 3D modelling + dot + cross product + complex number roots of unity + transformation matrices

Topic 8 HL-Additional Vectors + Complex Numbers anchors 3D-modelling + geometric-transformations. Vectors in 3D modelling: position + displacement + velocity + force + acceleration + vector-equation-of-line r = a + tb + vector-equation-of-plane r·n = d + intersection-of-line-and-plane + angle-between-line-and-plane + shortest-distance-from-point-to-plane. Dot product: a·b = |a||b|cos θ + projection + work-done = F·d. Cross product: a × b = |a||b|sin θ n̂ + right-hand-rule + torque + area-of-parallelogram. Complex number roots of unity: nth-roots = e^(2πik/n) for k = 0,1,...,n-1 + equispaced-on-unit-circle + geometric-pattern + sum-of-roots = 0. Transformation matrices: 2x2-rotation + 2x2-reflection + 2x2-scaling + 2x2-shear + composition + inverse + determinant-as-area-scale-factor. The AI tutor prompt library scores every HL-Additional-Vectors-Complex-Numbers response against the IBO rubric. Common gap: candidates forget that line-and-plane-intersection requires substituting parametric-into-Cartesian — the AI tutor highlights the substitution-step.

Section 11 — Topic 9 HL-Additional Calculus: integration by parts + partial fractions integration + improper integrals + volume of revolution extended + Maclaurin series extended + differential equations extended + Euler's method

Topic 9 HL-Additional Calculus extends the modelling applications. Integration by parts: ∫u dv = uv - ∫v du + LIATE-rule + tabular-method + reduction-formulas + repeated-application. Partial fractions integration: cases + cover-up-method + repeated-linear-factor-cases. Improper integrals: ∫_a^∞ f(x) dx + ∫a^b f(x) dx with vertical-asymptote + convergent-vs-divergent + comparison-test. Volume of revolution extended: disc-method + shell-method + washer-method + Pappus-theorem. Maclaurin series extended: e^x + sin x + cos x + ln(1+x) + (1+x)^n + arctan(x); radius-of-convergence; interval-of-convergence; application-to-limits-of-indeterminate-form + integration-of-non-elementary-functions. Differential equations extended: second-order-linear-ODE y'' + ay' + by = 0 + complementary-function + particular-integral + general-solution; system-of-ODEs; phase-plane (HL). Euler's method: y{n+1} = y_n + hf(t_n,y_n) + step-size h + error-analysis + improved-Euler (HL). The AI tutor prompt library scores every HL-Additional-Calculus response against the IBO rubric. Common gap: candidates mis-choose u and dv in integration by parts — the AI tutor highlights the LIATE-rule.

Section 12 — Topic 10 HL-Additional Statistics + Probability: continuous random variables extended + normal distribution extended + sampling distributions extended + central limit theorem + unbiased estimators + t-distribution + chi-squared test extended + non-parametric tests + Bayesian inference

Topic 10 HL-Additional Statistics + Probability is the IB Math HL AI mastery-track. Continuous random variables extended: probability-density-function f(x) + cumulative-distribution-function F(x) + ∫f(x)dx = 1 + E[X] = ∫xf(x)dx + Var[X] = ∫(x-μ)²f(x)dx; uniform + exponential + Weibull + gamma distributions. Normal distribution extended: N(μ,σ²) + linear-combination-of-normals + sum-of-independent-normals; lognormal; central-limit-theorem: sample-mean-of-n-iid-random-variables ~ N(μ, σ²/n) for large-n; sample-sum + sample-variance-distributions. Unbiased estimators: E[X̄] = μ + E[S²] = σ² + bias-correction + efficiency + consistency. t-distribution: t = (X̄ - μ)/(S/√n) with n-1-degrees-of-freedom; 95%-CI-of-mean-with-σ-unknown + hypothesis-testing-with-σ-unknown. Chi-squared test extended: goodness-of-fit + independence + χ²-test-statistic + degrees-of-freedom + critical-value + p-value. Non-parametric tests: sign-test + Wilcoxon-signed-rank + Mann-Whitney-U + Spearman-rank-correlation (HL); when-data-violates-normality-or-is-ordinal. Bayesian inference: prior + likelihood + posterior = (likelihood × prior) / evidence + Bayesian-update + posterior-distribution + credible-interval (HL). The AI tutor prompt library scores every HL-Additional-Statistics-Probability response against the IBO rubric. Common gap: candidates confuse p-value with significance-threshold — the AI tutor highlights the p-value-as-extreme-or-more-extreme probability.

Section 13 — Paper 1: short-response calculator-required + extended-response calculator-required + weighted 40%

Paper 1 is the foundational skill check + GDC-skills-check. Format: Section A (short-response-questions-with-calculator-required + 10-15-questions + 60-90-minutes + weighted 30%) + Section B (extended-response-with-calculator-required + 5-7-questions + weighted 10% + answer-3-of-5-questions-with-detailed-working). The GDC (graph-display-calculator — TI-84 + TI-Nspire + Casio-fx-CG50 + HP-Prime) is required for both sections — Paper 1 is calculator-required throughout. Topic coverage: Topic 1 Number-Algebra + Topic 2 Functions + Topic 3 Geometry-Trigonometry + Topic 4 Statistics-Probability + Topic 5 Calculus + select HL-additional-topics from Topic 6-10. Time pressure: 80-90-questions-in-120-minutes — strict-pacing at 1.5-minutes-per-question. Strategy: short-response first (highest-yield) + extended-response-after; sketch graphs + write units + show intermediate steps. Common gap: candidates over-rely on GDC without showing intermediate steps — the AI tutor flags the working-vs-answer-only gap.

Section 14 — Paper 2: graph-display-calculator-required extended-response + weighted 40%

Paper 2 is the extended-response + modelling-skills-check. Format: extended-response-with-graph-display-calculator-required + 5-7-questions + weighted 40% + answer-3-of-5-or-6-questions-with-detailed-working-out-over-120-minutes. Topic coverage: Topic 1-5 + Topic 6-10-HL-additional + extended-modelling-questions + Paper-2-typical-format-of-15-25-mark-questions-with-multi-parts-(a)-(b)-(c)-(d)-(e). The GDC is required throughout — candidates are expected to use calculus + statistics + graph-features via the GDC. Strategy: scan all questions first + pick the 3 with highest-confidence + budget 35-minutes-per-question + show all working + interpret-modelling-results-in-context. Common gap: candidates skip context-interpretation — the AI tutor flags the "interpret in context" step as a guaranteed-mark-losing-step.

Section 15 — Paper 3: Optional Topic — 2-of-4 chosen + weighted 30%

Paper 3 is the optional-topic-mastery test. Format: 4-optional-topic-questions + answer-2-of-4-questions + weighted 30% + 60-minutes. Optional topics: (i) Statistics-Probability-Modelling + (ii) Calculus-Applied-Series + (iii) Financial-Modelling + (iv) Discrete-Modelling + (v) Optimisation-Applications (5-options-but-only-2-required-on-exam-day). Strategy: pre-decide which 2-of-4-or-5 match your strengths + practice-past-papers-from-TZ1-TZ2-TZ3 + focus-on-the-2-questions-with-highest-success-rate. Common gap: candidates under-prepare the optional-topics — the AI tutor recommends pre-selecting 2-of-4-and-focusing-70%-of-paper-3-prep-on-them.

Section 16 — Internal Assessment Modelling Exploration: 15-20-page investigation + weighted 20%

The IA Modelling Exploration is 20% of the final grade. Format: 15-20-page-investigation-on-any-applied-modelling-topic-of-personal-interest. The exploration must include: (i) a clear-modelling-context-real-world-problem; (ii) mathematical-formulation + identification-of-variables + assumptions-and-simplifications; (iii) mathematical-solution-using-IB-Math-HL-AI-techniques; (iv) interpretation-and-critique-of-the-model + limitations; (v) conclusion + communication-of-findings. Assessment criteria (IBO rubric): (Criterion A — Use of mathematics: 0-6-marks, communication-of-mathematical-reasoning + correct-technical-execution); (Criterion B — Personal engagement: 0-4-marks, self-direction + personal-input + independent-thinking); (Criterion C — Reflection: 0-4-marks, evaluation-of-the-model + discussion-of-limitations + mathematical-justification); (Criterion D — Use of mathematics — extended: 0-4-marks, mathematical-depth + sophistication + HL-level-techniques-applied); (Criterion E — Communication: 0-4-marks, organisation + clarity + appropriate-graphs-diagrams-equations). Total: 0-22-marks (then converted to 0-20%-of-final-grade). Common IA topics: (i) modelling-population-growth-with-differential-equations; (ii) financial-modelling-of-loan-amortisation-vs-compound-investment; (iii) statistical-analysis-of-IB-exam-score-distribution; (iv) modelling-spread-of-disease-with-SIR-model; (v) optimisation-of-packaging-material; (vi) modelling-temperature-cooling-with-Newton's-law; (vii) statistical-analysis-of-stock-returns + portfolio-optimisation; (viii) modelling-traffic-flow-with-differential-equations. The AI tutor prompt library scores every IA-Modelling-Exploration against the IBO rubric-band-descriptors.

Section 17 — The 5 modelling-and-optimization competencies for IB Math HL AI

The five competencies for the score-7 candidate in Modelling-and-Optimization: (1) Real-world-problem-formulation: identify variables, assumptions, simplifications, parameters, units, context, boundary-conditions. (2) Model-selection-and-construction: choose-among-linear + exponential + logistic + polynomial + trigonometric + differential-equation + Markov-chain + regression + simulation. (3) Mathematical-solution: solve-with-IB-Math-HL-AI-techniques, use GDC-effectively, verify-solution-via-substitution + dimensionally. (4) Interpretation-in-context: explain what-the-result-means-in-the-original-real-world-problem, units, magnitude, sign. (5) Critique-and-limitations: identify what-the-model-doesn't-capture, suggest-improvements, discuss-validity-range. Common gap: candidates solve-mathematically-but-fail-to-interpret-in-context — the AI tutor highlights the "interpret-in-context" step.

Section 18 — The 6 statistics-and-probability-applied competencies for IB Math HL AI

The six competencies for the score-7 candidate in Statistics-and-Probability-Applied: (1) Data-collection-and-sampling-method-selection: simple-random + stratified + cluster + systematic + bias-types (selection + response + non-response + measurement). (2) Descriptive-statistics-and-visualisation: mean + median + mode + range + IQR + standard-deviation + boxplot + histogram + scatter-plot. (3) Probability-and-distribution-calculation: binomial + Poisson + normal + Bayes + expected-value + variance. (4) Inference-and-confidence-intervals: 95%-CI-for-mean + proportion + difference-of-means; one-sample + two-sample + paired. (5) Hypothesis-testing-and-p-values: H₀ + H₁ + test-statistic + p-value + significance-level α + decision + type-I + type-II + power. (6) Regression-and-correlation: least-squares + correlation r + R² + residual-analysis + outlier-detection + causation-vs-correlation. Common gap: candidates mis-interpret p-value — the AI tutor highlights the p-value-as-extreme-or-more-extreme-probability.

Section 19 — The 4 financial-modelling competencies for IB Math HL AI

The four competencies for the score-7 candidate in Financial-Modelling: (1) Compound-interest-and-present-value: A = P(1+r/100)^n + PV = FV/(1+r/100)^n + continuous-compounding A = Pe^(rt). (2) Annuity-and-loan-amortisation: monthly-payment-calculator + outstanding-balance + total-interest-paid + early-repayment-penalty. (3) Depreciation-and-asset-valuation: straight-line + reducing-balance + comparison + optimal-replacement-time. (4) Investment-and-portfolio-modelling: expected-return + variance + Sharpe-ratio + diversification + efficient-frontier (HL). Common gap: candidates confuse nominal-rate-with-effective-rate — the AI tutor highlights the EAR-formula (1+r/n)^n - 1.

Section 20 — The 5 discrete-modelling competencies for IB Math HL AI

The five competencies for the score-7 candidate in Discrete-Modelling: (1) Recurrence-relations-and-iteration: u_{n+1} = f(u_n) + convergence + fixed-points + cobweb-diagram. (2) Matrix-modelling-and-Markov-chains: transition-matrix + state-vector + long-run-distribution + steady-state + absorption + application-to-market-shares + population-flow + genetics. (3) Graph-theory-modelling: vertices + edges + adjacency-matrix + Eulerian + Hamiltonian + shortest-path + Dijkstra (HL). (4) Network-flow-modelling: max-flow-min-cut + bipartite-matching + assignment-problem + transportation-problem (HL). (5) Combinatorial-modelling: permutations + combinations + inclusion-exclusion + pigeonhole + recurrence-relation-for-counting. Common gap: candidates forget steady-state-condition πP = π — the AI tutor highlights the eigenvector-extraction step.

Section 21 — The 4 optimisation-applications competencies for IB Math HL AI

The four competencies for the score-7 candidate in Optimisation-Applications: (1) Single-variable-optimisation: differentiate + set-derivative-equal-to-zero + verify-via-second-derivative + boundary-checks. (2) Constrained-optimisation-with-Lagrange-multipliers: ∇f = λ∇g + interpretation-of-λ-as-shadow-price + corner-solutions (HL). (3) Linear-programming: feasible-region + corner-point-evaluation + objective-function + shadow-prices + sensitivity-analysis (HL). (4) Dynamic-optimisation-and-control: variational-methods + Euler-Lagrange-equation + applications-to-trajectory-optimisation + portfolio-rebalancing (HL). Common gap: candidates forget to check-corner-solutions-for-constrained-optimisation — the AI tutor highlights the interior-vs-corner-evaluation step.

Section 22 — The 5 calculus-applied-series competencies for IB Math HL AI

The five competencies for the score-7 candidate in Calculus-Applied-Series: (1) Differential-equations-for-growth-decay: dy/dt = ky → y = Ae^(kt) + separation-of-variables + initial-condition. (2) Second-order-ODE: y'' + ay' + by = 0 + auxiliary-equation + complementary-function + particular-integral (HL). (3) Maclaurin-series-application: e^x + sin x + cos x + ln(1+x) + (1+x)^n + arctan(x) + limit-evaluation + integration-of-non-elementary-functions. (4) Numerical-integration-methods: trapezoidal-rule + Simpson's-rule + error-estimation + GDC-implementation. (5) Series-convergence-tests: comparison + ratio + integral + alternating-series + radius-of-convergence (HL). Common gap: candidates mis-set-up the auxiliary-equation for second-order-ODE — the AI tutor highlights the characteristic-equation-formation step.

Section 23 — The 7-prompt AI tutor library for IB Math HL AI

The 7 prompts every IB Math HL AI teacher needs: (1) Prompt-1 — Diagnose-Math-HL-AI-Gap: "Analyse the candidate's responses across 8-Topics-of-IB-Math-HL-AI-(Topic-1-Number-Algebra + Topic-2-Functions + Topic-3-Geometry-Trigonometry + Topic-4-Statistics-Probability + Topic-5-Calculus + Topic-6-HL-Additional-Algebra + Topic-7-HL-Additional-Functions-Trigonometry + Topic-8-HL-Additional-Vectors-Complex-Numbers + Topic-9-HL-Additional-Calculus + Topic-10-HL-Additional-Statistics-Probability) + score-each-on-IBO-band-descriptors-(Band-1-Inadequate-+-Band-2-Adequate-+-Band-3-Competent-+-Band-4-Highly-Competent-+-Band-5-Sophisticated-+-Band-6-Excellent-+-Band-7-Outstanding) + identify-the-specific-gap-(number-algebra-vs-functions-vs-geometry-trigonometry-vs-statistics-probability-vs-calculus-vs-modelling-vs-HL-additional-topics-vs-financial-modelling-vs-discrete-modelling-vs-optimisation-applications-vs-statistics-probability-applied-vs-IA-modelling-exploration-vs-Paper-3-optional-topic-mastery)-that-is-costing-the-candidate-marks-toward-the-score-7." (2) Prompt-2 — Score-Paper-1-Short-Response: "Score-the-candidate's-Paper-1-responses-against-the-official-IBO-Math-HL-AI-marking-scheme-+-rubric-band-descriptors + flag-where-the-candidate-loses-marks-due-to-(missing-GDC-syntax-+-incorrect-formula-selection-+-incomplete-showing-of-working-+-units-omitted-+-context-interpretation-missing)." (3) Prompt-3 — Score-Paper-2-Extended-Response: "Score-the-candidate's-Paper-2-responses-against-the-official-IBO-Math-HL-AI-marking-scheme-+-rubric-band-descriptors + flag-where-the-candidate-loses-marks-due-to-(missing-modelling-context-+-incomplete-mathematical-justification-+-missing-graph-+-missing-interpretation-in-context-+-missing-limitation-discussion)." (4) Prompt-4 — Score-Paper-3-Optional-Topic: "Score-the-candidate's-Paper-3-responses-on-the-2-of-4-chosen-optional-topics-against-the-official-IBO-Math-HL-AI-marking-scheme-+-rubric-band-descriptors + flag-where-the-candidate-loses-marks-due-to-(wrong-optional-topic-selection-+-incomplete-modelling-steps-+-missing-GDC-output-+-incorrect-interpretation)." (5) Prompt-5 — Score-IA-Modelling-Exploration: "Score-the-candidate's-IA-Modelling-Exploration-against-the-official-IBO-IA-Modelling-Exploration-rubric-(Criterion-A-Use-of-mathematics: 0-6-marks-+-Criterion-B-Personal-engagement: 0-4-marks-+-Criterion-C-Reflection: 0-4-marks-+-Criterion-D-Use-of-mathematics-extended: 0-4-marks-+-Criterion-E-Communication: 0-4-marks-+-Total: 0-22-marks-converted-to-0-20%-of-final-grade)-and-surface-the-specific-criterion-where-the-candidate-is-losing-marks." (6) Prompt-6 — Generate-30-Week-Study-Plan: "Generate-a-30-week-study-plan-for-the-candidate-covering-Topic-1-Number-Algebra-+-Topic-2-Functions-+-Topic-3-Geometry-Trigonometry-+-Topic-4-Statistics-Probability-+-Topic-5-Calculus-+-Topic-6-HL-Additional-Algebra-+-Topic-7-HL-Additional-Functions-Trigonometry-+-Topic-8-HL-Additional-Vectors-Complex-Numbers-+-Topic-9-HL-Additional-Calculus-+-Topic-10-HL-Additional-Statistics-Probability-+-IA-Modelling-Exploration-+-Paper-1-+-Paper-2-+-Paper-3-+-with-daily-tasks-+-weekly-milestones-+-monthly-mock-exams-+-TZ1-TZ2-TZ3-past-paper-schedule-+-IA-modelling-exploration-deadline-aligned-with-February-2027-IB-math-coordinator-form-4-submission-window." (7) Prompt-7 — Simulate-Full-IB-Math-HL-AI-Exam: "Generate-a-full-IB-Math-HL-AI-Paper-1-+-Paper-2-+-Paper-3-+-IA-Modelling-Exploration-mock-exam-with-IBO-spec-format-+-IBO-spec-time-pressure-+-IBO-spec-calculator-permitted-+-IBO-spec-content-distribution-+-and-score-the-candidate's-responses-against-the-IBO-Math-HL-AI-marking-scheme-+-rubric-band-descriptors-+-IA-rubric + surface-the-band-descriptor-improvement-needed-to-move-from-current-band-to-target-band-(e.g.-Band-4-Highly-Competent-to-Band-5-Sophisticated-or-Band-6-Excellent-to-Band-7-Outstanding)."

Section 24 — Closing: the 30-week IB Math HL AI AI tutor playbook

IB Math HL AI is the IBO-standard pre-university statistics + modelling + applied-calculus qualification for IB-Diploma-Programme Year-12 + Year-13 candidates targeting MIT + Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST + KAIST + SNU + UCL + Edinburgh + Manchester + Bristol + Durham + KCL + Georgia-Tech + UT-Austin + Berkeley + UCLA + Michigan + CMU + Cornell + Columbia + Princeton + Yale + Harvard + Brown + Dartmouth + Penn + Johns-Hopkins + Duke + Northwestern + Rice. The 30-week workflow + 5-modelling-and-optimization + 6-statistics-and-probability-applied + 4-financial-modelling + 5-discrete-modelling + 4-optimisation-applications + 5-calculus-applied-series competencies + 7-prompt-AI-tutor-library is the playbook for closing the 5-to-7 gap on the IB-Diploma-Programme Mathematics HL Applications & Interpretation Higher-Level exam for the cohort in IB-Mathematics-HL-AI + IB-Economics-HL + IB-Business-Management-HL + IB-Biology-HL + IB-Psychology-HL + IB-Environmental-Systems-and-Societies-HL + IB-Computer-Science-HL + IB-Further-Mathematics-HL + IB-Math-HL-AI-Internal-Assessment-Modelling-Exploration + IB-Extended-Essay-in-Economics + IB-TOK-exhibition + IB-CAS-creativity-activity-service 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 + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel + European + Asian + African + South-American + North-American + Middle-Eastern + Oceanian international IB schools.

Pairs with IB Chemistry HL (post-160)

The IB Chemistry HL playbook (post-160) + [this playbook] form the IB Diploma + IB Higher-Level + IBO-applied-track + Year-13-chemistry + first-year-undergraduate-Medicine + Pharmacy + Biology + Chemical-Engineering + Biochemistry + Dentistry + Veterinary-Science pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Medicine + Pre-Pharmacy + Pre-Biology + Pre-Chemical-Engineering + Pre-Biochemistry + Pre-Dentistry + Pre-Veterinary 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 + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel targeting MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL admissions. The IB Chemistry HL 11-core-topics (Topic 1 Stoichiometric Relationships + Topic 2 Atomic Structure + Topic 3 Periodicity + Topic 4 Chemical Bonding + Topic 5 Energetics + Topic 6 Chemical Kinetics + Topic 7 Chemical Equilibrium + Topic 8 Acids and Bases + Topic 9 Redox Processes + Topic 10 Organic Chemistry + Topic 11 Measurement and Data Processing) + 4-additional-higher-level-topics (advanced-stoichiometry + advanced-energetics + advanced-kinetics + advanced-equilibrium + advanced-acids-bases + advanced-redox + advanced-organic-mechanism + advanced-spectroscopy-NMR-IR-MS-UV + transition-element-complexes + ligand-field-theory + chirality-and-stereochemistry + organic-synthesis-strategies + multi-step-synthesis) + Internal-Assessment-Individual-Investigation + Paper 1A MCQ + Paper 1B data-based + Paper 2 extended-response + Paper 3 Optional-Topic-Biochemistry-Energy-Medicinal-Chemistry-Materials-Science + stoichiometry-driven + energetics-required + organic-mechanism-heavy + kinetics-required + IA-individual-investigation-assessed + 5-stoichiometry-competencies + 5-atomic-structure-competencies + 4-periodicity-competencies + 5-bonding-competencies + 5-energetics-competencies + 5-kinetics-competencies + 5-equilibrium-competencies + 6-acids-bases-competencies + 5-redox-competencies + 8-organic-chemistry-competencies + 5-measurement-analysis-competencies + 7-AHL-advanced-spectroscopy-competencies + 7-AHL-advanced-mechanism-competencies + 7-prompt-AI-tutor-library + score-7-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-chemistry + IB-Diploma + IBO-applied-mastery-track + first-year-undergraduate-Chemistry + Medicine + Pharmacy + Biology + Chemical-Engineering + Biochemistry + Dentistry + Veterinary-Science-university-credit + Applied-Admissions-readiness at MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL. See post-160 for the IB-Chemistry-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Economics HL (post-162)

The IB Economics HL playbook (post-162) + [this playbook] form the IB Diploma + IB Higher-Level + IBO-applied-track + Year-13-economics + first-year-undergraduate-Economics + Finance + Business + Management + Public-Policy + PPE + International-Relations + Development-Studies pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Economics + Pre-Finance + Pre-Business + Pre-Management + Pre-Public-Policy + Pre-International-Relations + Pre-Development-Studies 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 + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel targeting MIT + Princeton + Harvard + Chicago + LSE + Oxford + Cambridge + LBS + Bocconi + HEC-Paris + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL admissions. The IB Economics HL 3-core-units (Unit 1 Microeconomics + Unit 2 Macroeconomics + Unit 3 International Economics + Unit 4 Development Economics) + 3-Paper-structure (Paper-1-extended-response + Paper-2-data-response + Paper-3-quantitative-methods) + Internal-Assessment-Portfolio-of-Three-Commentaries + 8-microeconomics-competencies + 10-macroeconomics-competencies + 10-international-economics-competencies + 8-development-economics-competencies + 8-quantitative-methods-competencies + 5-extended-response-essay-competencies + 5-data-response-competencies + 5-diagram-competencies + 5-calculation-competencies + 4-IA-portfolio-competencies + 7-prompt-AI-tutor-library + score-7-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-economics + IB-Diploma + IBO-applied-mastery-track + first-year-undergraduate-Economics + Finance + PPE + Business + Management + Public-Policy + International-Relations + Development-Studies + university-credit + Applied-Admissions-readiness at MIT + Princeton + Harvard + Chicago + LSE + Oxford + Cambridge + LBS + Bocconi + HEC-Paris + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL. See post-162 for the IB-Economics-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Psychology HL (post-163)

The IB Psychology HL playbook (post-163) + [this playbook] form the IB Diploma + IB Higher-Level + IBO-applied-track + Year-13-psychology + first-year-undergraduate-Psychology + Neuroscience + Medicine + Clinical-Psychology + Counselling + Sociology + Anthropology + Education + Child-Development + Behavioural-Science + Marketing + Human-Resources + PPE pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Psychology + Pre-Medicine + Pre-Neuroscience + Pre-Clinical-Psychology + Pre-Counselling + Pre-Sociology + Pre-Anthropology + Pre-Education + Pre-Child-Development + Pre-Behavioural-Science + Pre-Marketing + Pre-Human-Resources + Pre-PPE 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 + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel targeting MIT + Stanford + Caltech + Imperial + Cambridge + Oxford + UCL + LSE + Warwick + Edinburgh + Manchester + Bristol + Durham + KCL + Princeton + Harvard + Yale + Chicago + Columbia + NYU + Berkeley + Michigan + CMU + Cornell + Duke + Northwestern + Sciences-Po + Bocconi + HEC-Paris + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL admissions. The IB Psychology HL 3-core-levels-of-analysis (Level 1 Biological Approach + Level 2 Cognitive Approach + Level 3 Sociocultural Approach) + 4-Optional-Topics (Abnormal Psychology + Developmental Psychology + Health Psychology + Psychology of Individual Differences) + 3-Paper-structure (Paper-1-short-answer + Paper-1-extended-response + Paper-2-short-answer + Paper-2-extended-response + Paper-3-research-methods) + Internal-Assessment-Report-1500-words + 8-biological-approach-competencies + 8-cognitive-approach-competencies + 8-sociocultural-approach-competencies + 5-abnormal-psychology-competencies + 5-developmental-psychology-competencies + 5-health-psychology-competencies + 5-psychology-of-individual-differences-competencies + 5-qualitative-research-competencies + 5-quantitative-research-competencies + 5-experimental-method-competencies + 5-case-studies-competencies + 5-correlation-studies-competencies + 5-statistics-analysis-competencies + 5-ethics-application-competencies + 5-IA-report-competencies + 7-prompt-AI-tutor-library + score-7-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-psychology + IB-Diploma + IBO-applied-mastery-track + first-year-undergraduate-Psychology + Neuroscience + Medicine + Clinical-Psychology + Counselling + Sociology + Anthropology + Education + Child-Development + Behavioural-Science + Marketing + Human-Resources + PPE + university-credit + Applied-Admissions-readiness at MIT + Stanford + Caltech + Imperial + Cambridge + Oxford + UCL + LSE + Warwick + Edinburgh + Manchester + Bristol + Durham + KCL. See post-163 for the IB-Psychology-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Business Management HL (post-164)

The IB Business Management HL playbook (post-164) + [this playbook] form the IB Diploma + IB Higher-Level + IBO-applied-track + Year-13-business + first-year-undergraduate-Business + Finance + Accounting + Economics + Management + Marketing + Entrepreneurship + International-Business + HRM + Operations-Management + Strategy + Public-Policy + PPE + International-Relations + Development-Studies pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Business + Pre-Finance + Pre-Accounting + Pre-Management + Pre-Marketing + Pre-Entrepreneurship + Pre-Public-Policy + Pre-International-Relations + Pre-Development-Studies + Pre-PPE 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 + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel targeting MIT + Princeton + Harvard + Chicago + LSE + Oxford + Cambridge + Wharton + LBS + HBS + Chicago-Booth + Bocconi + HEC-Paris + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL admissions. The IB Business Management HL 5-units (Unit 1 Business-Activity + Unit 1 Influences-on-Business-Activity + Unit 2 Business-Operations + Unit 3 Finance-and-Accounts + Unit 4 Human-Resource-Management + Unit 4 Marketing + Administration + Strategic-Management) + 3-Paper-structure (Paper-1-case-study + Paper-2-extended-response-and-data-response + Paper-3-pre-seen-research-project) + Internal-Assessment-Research-Project + IB-Command-Terms (Analyse + Annotate + Calculate + Compare + Construct + Define + Describe + Discuss + Evaluate + Examine + Explain + Identify + Justify + Outline + State + Suggest + To-what-extent) + 80-competency-framework + 8-prompt-AI-tutor-library covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-business + IB-Diploma + IBO-applied-mastery-track + first-year-undergraduate-Business + Finance + Accounting + Economics + Management + Marketing + Entrepreneurship + International-Business + HRM + Operations-Management + Strategy + PPE + university-credit + Applied-Admissions-readiness at MIT + Princeton + Harvard + Chicago + LSE + Oxford + Cambridge + Wharton + LBS + HBS + Chicago-Booth + Bocconi + HEC-Paris + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL. See post-164 for the IB-Business-Management-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Mathematics AA HL (post-173)

The IB Mathematics Analysis and Approaches Higher Level (IB Math AA HL) playbook (post-173) + [this playbook] form the IB Diploma + IB Mathematics Higher Level + IBO-mastery + Group-5-mastery + Year-12 + Year-13-mathematics + first-year-undergraduate-Mathematics + Engineering + Physics + Computer-Science + Economics + Quantitative-Finance + Actuarial-Science + Data-Science + Machine-Learning + AI + Mathematical-Physics + Theoretical-Physics + Astrophysics + Biostatistics + Bioinformatics + Computational-Biology pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Engineering + Pre-Physics + Pre-Computer-Science + Pre-Mathematics + Pre-Statistics + Pre-Economics + Pre-Quantitative-Finance + Pre-Actuarial + Pre-Data-Science + Pre-Machine-Learning + Pre-AI 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 + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel targeting 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. The IB Mathematics AA HL 5-core-topics (Topic 1 Number and Algebra + Topic 2 Functions + Topic 3 Geometry and Trigonometry + Topic 4 Statistics and Probability + Topic 5 Calculus) + 5-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) + 4-assessment-components (Paper 1 no-calculator + Paper 2 calculator + Paper 3 extended-response + IA Mathematical Exploration 12-pages) + IB-command-terms (show-that + hence-show + determine + sketch + state + write-down + find + justify) + score-7-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-mathematics + IB-Diploma + IBO-mastery-track + first-year-undergraduate-Mathematics + Engineering + Physics + Computer-Science + Economics + Finance + Statistics + Actuarial + Data-Science + Machine-Learning + AI-university-credit + STEM-Admissions-readiness 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. See post-173 for the IB-Mathematics-AA-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IGCSE Mathematics 0580 (post-199)

The IGCSE Mathematics 0580 playbook (post-199) + [this playbook] form the IGCSE + IGCSE-Mathematics + IGCSE-Cambridge-0580 + IGCSE-Edexcel-4MA1 + IGCSE-OxfordAQA-8460 + Cambridge-CAIE-Mathematics-0580 + Edexcel-IGCSE-Mathematics-4MA1 + OxfordAQA-IGCSE-Mathematics-8460 + IGCSE-Number-and-Arithmetic + IGCSE-Algebra-and-Functions + IGCSE-Coordinate-Geometry + IGCSE-Geometry + IGCSE-Mensuration + IGCSE-Trigonometry + IGCSE-Vectors-and-Transformations + IGCSE-Probability + IGCSE-Statistics + IGCSE-Extended-Tier + IGCSE-Core-Tier + IGCSE-Quadratics + IGCSE-Simultaneous-Equations + IGCSE-Polynomials + IGCSE-Functions + IGCSE-Graphs + IGCSE-Circle-Geometry + IGCSE-Sine-Rule + IGCSE-Cosine-Rule + IGCSE-3D-Trigonometry + IGCSE-Vector-Geometry + IGCSE-Transformations + IGCSE-Matrices + IGCSE-Logarithms + IGCSE-Exponentials + IGCSE-Calculus-Differentiation + IGCSE-Calculus-Integration + IGCSE-Sets + IGCSE-Probability-Trees + IGCSE-Conditional-Probability + IGCSE-Normal-Distribution + IGCSE-Correlation + IGCSE-Regression + IGCSE-Time-Series + IGCSE-Paper-2-MCQ + IGCSE-Paper-4-Theory + IGCSE-Paper-6-Theory + IGCSE-Paper-2 + IGCSE-Paper-4 + IGCSE-Paper-6 + IGCSE-22-week-workflow + IGCSE-AI-tutor + IGCSE-rubric-drill + IGCSE-calculator-fluency-drill + IGCSE-algebraic-manipulation-drill + IGCSE-geometric-reasoning-drill + IGCSE-statistical-analysis-drill + IGCSE-calculus-drill + IGCSE-common-mistakes-drill + IGCSE-MCQ-trap-pattern + IGCSE-FRQ-rubric-points cohort companion for Year 10-11 international British-curriculum students (14-16 years old) preparing for the Summer 2027 IGCSE Mathematics exams + parents paying $200+ per hour for international British-curriculum tuition + IGCSE Mathematics teachers wanting a rubric-aligned AI workflow for Paper 2 + Paper 4 + Paper 6 scoring + number + algebra + geometry + trigonometry + calculus + statistics + probability + vectors + matrices extended-response review + homeschool families using IGCSE Mathematics for transcript strength targeting first-year-undergraduate-engineering + medicine + computer-science + economics + finance + mathematics + actuarial-science + data-science + statistics + accounting at Cambridge + Oxford + Imperial + UCL + Edinburgh + Manchester + Bristol + Warwick + KCL + Durham + Exeter + St-Andrews + Bath + Loughborough + Leeds + Liverpool + Sheffield + Southampton + Birmingham + Newcastle + Glasgow + Cardiff + Nottingham + Surrey + LSE + UCL + Cambridge-Judge + Warwick-Economics + Durham-Economics + Bath-Finance + Toronto + UBC + McGill + McMaster + Waterloo + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + KAIST + SNU + Tsinghua + Peking + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago + MIT + Stanford + Caltech + Harvard + Yale + Princeton + Brown + Dartmouth + Cornell + Columbia + NYU + Berkeley + Chicago + Penn + Rice + Duke + Johns-Hopkins + CMU + Georgia-Tech + UIUC + Michigan + Northwestern + Purdue + Wisconsin + Texas-Austin + UCLA + USC + UC-San-Diego + UC-Berkeley + UC-Santa-Barbara + Wharton + HBS + Booth + Kellogg + Columbia-Business + Stern admissions. See post-199 for the IGCSE-Mathematics-specific exam, score-distribution, and 22-week score-A*-master schedule.