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IB Mathematics HL: Analysis & Approaches 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-AA + IB-Physics-HL + IB-Chemistry-HL + IB-Biology-HL + IB-Computer-Science-HL + IB-Further-Mathematics-HL + IB-Economics-HL, often paired with IB-Math-HL-AA-Internal-Assessment-Mathematical-Exploration + IB-Extended-Essay-in-Mathematics + IB-TOK-exhibition + IB-CAS-creativity-activity-service. Covers IB Math HL AA teachers who want an AI workflow for grading IA-mathematical-explorations + Paper-1-short-response + Paper-2-extended-response + Paper-3-optional-topic, parents paying for IB-Math-HL-AA-prep ($300-$3000 for prep-books + $1000-$5000 for prep-courses + $2000-$8000 for private-tutors), IB-World-Schools seeking IB-Math-HL-AA-internal-assessment-rubric alignment, and overseas IB-Diploma-candidates applying to MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + SNU + IIT + IISc + UCL + LSE + Warwick + 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 AA is the most-respected pre-university calculus + linear-algebra + proof-based mathematics qualification globally — the standard for IB-Diploma-Programme Year-12 + Year-13 candidates at IB-World-Schools targeting MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + IIT + IISc + UCL + LSE + Warwick + 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 14-18 percent (highest honours + university-credit at MIT + Imperial + Cambridge + ETH-Zurich + EPFL + NUS + NTU + IIT-Bombay + IIT-Delhi + IIT-Kanpur + IIT-Madras + IISc), score-6 rate of approximately 22 percent, score-5 rate of approximately 23 percent (the score-5+ cumulative rate 59-63 percent is the IB Diploma + university-readiness benchmark), score-4 rate of approximately 19 percent, score-3 rate of approximately 12 percent, score-2 rate of approximately 7 percent, score-1 rate of approximately 3 percent. The 5-core-topics-of-IB-Math-HL-AA (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-Mathematical-Exploration map onto Year-12 + Year-13 mathematics + first-year-undergraduate-Mathematics + Engineering + Physics + Computer-Science + Medicine + Architecture + Economics + Finance + Statistics + Actuarial-Science + Data-Science at MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + IIT + IISc + UCL + LSE + Warwick + 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 AA is the most-respected pre-university calculus + linear-algebra + proof-based mathematics qualification + the MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + IIT + IISc first-year-undergraduate-Mathematics + Engineering + Physics + Computer-Science + IB-Diploma-masters-track subject

IB Math HL AA is the IBO-standard pre-university calculus + linear-algebra + proof-based mathematics qualification for IB-Diploma-Programme Year-12 + Year-13 candidates — calculus-based, proof-driven, extended-response-required, IA-mathematical-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 Calculus BC (2-sections-MCQ-FRQ-only + 45-minute-each + 90-minute-total), IB Math HL AA integrates proof-by-mathematical-induction + linear-algebra + complex-numbers + vectors + differential-equations + calculus-advanced-series across all 5-core-topics + 5-HL-additional-topics + IA-mathematical-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-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 Engineering + Physics + Computer-Science + Mathematics + Pre-Medicine + Pre-Architecture + Year-13-Mathematics + first-year-undergraduate-Mathematics admissions at MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + IIT + IISc + UCL + LSE + Warwick + 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 AA workflow.

Section 2 — The 30-week IB Math HL AA 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-mathematical-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 AA workflow is built around five cycles of six weeks each, with the IA-mathematical-exploration running in parallel during weeks 14-20. Weeks 1-4 are foundations: number-and-algebra (sequences, series, binomial theorem, partial fractions, mathematical induction), functions (domain, range, inverses, transformations, composition, even/odd, polynomial, rational, exponential, logarithmic). Weeks 5-8 cover Topic 3 geometry-and-trigonometry (analytic geometry, conic sections, trigonometric identities, triangle trigonometry, vectors in 2D/3D, complex numbers). Weeks 9-13 cover Topic 4 statistics-and-probability + Topic 5 calculus (Bayes' theorem, binomial/Poisson/normal distributions, confidence intervals, hypothesis testing, continuity, limits, derivatives, applications of derivatives, integration, applications of integration, differential equations). Weeks 14-20 layer in the HL-additional-topics (proof by mathematical induction, complex numbers extended form, vectors dot/cross product, partial fractions advanced, summation notation) AND the IA-mathematical-exploration (15-20 page investigation). Weeks 21-26 are paper-strategy mastery: Paper 1 (Section A calculator-restricted short-response + Section B calculator-allowed extended-response), Paper 2 (graph-display-calculator-required extended-response), Paper 3 (2-of-4 optional-topic questions chosen from Geometry-Proofs + Statistics-Probability-Advanced + Sets-Relations-Groups + Calculus-Advanced-Series + Differential-Equations + Discrete-Mathematics). 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-mathematical-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 + binomial theorem + partial fractions + summation notation + mathematical induction + proof

Topic 1 Number and Algebra is the foundation of IB Math HL AA. Arithmetic sequences (u_n = u_1 + (n-1)d) + arithmetic series (S_n = n/2 · (2u_1 + (n-1)d)) + geometric sequences (u_n = u_1 · r^(n-1)) + geometric series (S_n = u_1 · (1-r^n)/(1-r) for r≠1; S_∞ = u_1/(1-r) for |r|<1) + sum-to-infinity + binomial theorem ((a+b)^n = Σ C(n,k) · a^(n-k) · b^k for n∈ℕ, extended to negative + fractional n via binomial series) + partial fractions (linear factors + repeated factors + irreducible quadratic factors; technique: cover-up method + long division + equate coefficients) + summation notation (Σ notation, change-of-index, telescoping series) + proof by mathematical induction (base case + inductive step + conclusion; critical for divisibility + inequality + summation + matrix-power + derivative-by-definition proofs) + counting principles (permutations P(n,r) = n!/(n-r)!, combinations C(n,r) = n!/((n-r)!·r!), inclusion-exclusion, complementary counting). The AI tutor must hold all 12+ sub-topics + 100+ formula-types + proof-by-induction-patterns + summation-notation-transformations + binomial-theorem-extensions + partial-fractions-techniques.

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

Topic 2 Functions covers the language + toolkit for the rest of IB Math HL AA. Domain (set of x for which f(x) is defined: solve denominator ≠ 0 + square-root-radicand ≥ 0 + logarithm-argument > 0) + range (set of y = f(x); analyse via monotonicity + asymptotes + extrema) + inverses (y = f(x) → x = f⁻¹(y); reflect across y=x; f(f⁻¹(x)) = x; f⁻¹(f(x)) = x) + transformations (vertical shift +y₀, horizontal shift +x₀, vertical stretch ×a, horizontal stretch ×b, reflection across x-axis (y→-y), reflection across y-axis (x→-x)) + composition (f∘g(x) = f(g(x)); decompose composite function into inner + outer) + even/odd (even: f(-x) = f(x); odd: f(-x) = -f(x)) + polynomial (P(x) = a_n·x^n + ... + a_0; degree n; roots + multiplicities; factor theorem + remainder theorem) + rational (R(x) = P(x)/Q(x); vertical asymptotes at roots of Q; horizontal/oblique asymptotes via long division; intercepts) + exponential (y = a^x, a>0; growth/decay; asymptote y=0) + logarithmic (y = log_a(x); inverse of exponential; laws: log(AB) = log A + log B, log(A/B) = log A - log B, log(A^k) = k·log A; change-of-base: log_a(x) = log(x)/log(a)) + reciprocal-trigonometric (y = sin⁻¹(x), cos⁻¹(x), tan⁻¹(x); domain [-1,1]/[-1,1]/ℝ; range [-π/2,π/2]/[0,π]/(-π/2,π/2); compositions: sin(sin⁻¹(x)) = x on [-1,1]; sin⁻¹(sin(x)) piecewise). The AI tutor must hold all 10+ sub-topics + 50+ function-types + transformation-rules + inverse-rules + composition-rules + even-odd-tests.

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

Topic 3 Geometry and Trigonometry bridges algebra + geometry + vectors. Analytic geometry (distance formula d = √((x₂-x₁)² + (y₂-y₁)²); midpoint ((x₁+x₂)/2, (y₁+y₂)/2); gradient (y₂-y₁)/(x₂-x₁); parallel lines (m₁ = m₂); perpendicular lines (m₁·m₂ = -1); line equation y = mx + c OR ax + by + c = 0; intersection of lines via simultaneous equations) + conic sections (circle (x-h)² + (y-k)² = r²; parabola y² = 4ax with focus (a,0) + directrix x = -a; ellipse x²/a² + y²/b² = 1 with foci (±c,0) where c² = a²-b²; hyperbola x²/a² - y²/b² = 1 with foci (±c,0) where c² = a²+b²; eccentricity e = c/a) + trigonometric identities (Pythagorean sin²+cos²=1, sec² = 1+tan², cosec² = 1+cot²; compound-angle sin(A±B), cos(A±B), tan(A±B); double-angle sin2A, cos2A, tan2A; product-to-sum + sum-to-product; harmonic-form R·sin(x+α)) + triangle trigonometry (sine-rule a/sin A = b/sin B = c/sin C = 2R; cosine-rule a² = b² + c² - 2bc·cos A; area = ½·a·b·sin C) + vectors in 2D + 3D (position vector, displacement, magnitude |v| = √(x²+y²+z²), direction cosines, unit vector û = v/|v|, scalar multiplication, vector addition/subtraction, dot product v·w = |v|·|w|·cos θ = x₁x₂+y₁y₂+z₁z₂; cross product v×w in 3D only) + complex numbers (z = a+bi where i²=-1; |z| = √(a²+b²); arg(z) = tan⁻¹(b/a) with quadrant correction; addition, subtraction, multiplication, division via conjugate; polar form z = r·(cos θ + i·sin θ) = r·e^(iθ) = r·cis(θ); De Moivre's theorem z^n = r^n·cis(nθ); nth roots; Argand diagram). The AI tutor must hold all 8+ sub-topics + 100+ identities + conic-section-eccentricity-rules + De Moivre's theorem applications + vector-dot-cross-product-formulas.

Section 6 — Topic 4 Statistics and Probability: descriptive statistics + probability axioms + Bayes' theorem + binomial + Poisson + normal distributions + confidence intervals + hypothesis testing

Topic 4 Statistics and Probability covers the data-analysis + inference toolkit. Descriptive statistics (mean x̄ = Σx/n; median; mode; range; IQR = Q₃-Q₁; variance s² = Σ(x-x̄)²/n; standard deviation s = √s²; quartiles + percentiles; box-plots + histograms + cumulative-frequency curves) + probability axioms (P(A∪B) = P(A) + P(B) - P(A∩B); P(A∩B) = P(A)·P(B|A); conditional P(A|B) = P(A∩B)/P(B); independent P(A∩B) = P(A)·P(B); complementary P(A') = 1-P(A)) + Bayes' theorem (P(A|B) = P(B|A)·P(A)/P(B); tree diagrams for sequential conditional probabilities) + binomial distribution XB(n,p) (P(X=r) = C(n,r)·p^r·(1-p)^(n-r); mean np; variance np(1-p)) + Poisson distribution XPo(λ) (P(X=r) = e^(-λ)·λ^r/r!; mean λ; variance λ; limit of binomial as n→∞, p→0, np→λ) + normal distribution XN(μ,σ²) (symmetric bell curve; 68-95-99.7 rule; standardised Z = (X-μ)/σ; ZN(0,1); probability via Z-table OR GDC normalcdf) + confidence intervals (CI for μ when σ known: x̄ ± z·σ/√n; CI for μ when σ unknown: x̄ ± t·(s/√n) where t has n-1 degrees-of-freedom; CI for p: p̂ ± z·√(p̂(1-p̂)/n)) + hypothesis testing (H₀ + H₁; test statistic; p-value OR critical-region; one-tailed + two-tailed; Type-I error α = P(reject H₀ | H₀ true); Type-II error β = P(fail to reject H₀ | H₀ false); power 1-β). The AI tutor must hold all 10+ sub-topics + Bayes-tree-diagrams + binomial-Poisson-normal-probability-calculations + Z-table + t-table + confidence-interval-formulas + hypothesis-testing-flowchart.

Section 7 — Topic 5 Calculus: limits + continuity + derivatives + applications of derivatives + integration + applications of integration + differential equations + Maclaurin series + L'Hôpital's rule

Topic 5 Calculus is the analytical engine of IB Math HL AA. Limits (limit notation lim_{x→a} f(x) = L; one-sided limits; limit-laws: sum, product, quotient, composite; indeterminate-forms 0/0 + ∞/∞ resolved via L'Hôpital's rule: lim_{x→a} f(x)/g(x) = lim_{x→a} f'(x)/g'(x)) + continuity (f continuous at a if lim_{x→a} f(x) = f(a); types of discontinuity: removable, jump, infinite) + derivatives (definition f'(x) = lim_{h→0} [f(x+h)-f(x)]/h; differentiation-rules: power, sum, product, quotient, chain; derivatives of standard functions x^n, e^x, ln x, sin x, cos x, tan x, sin⁻¹ x, cos⁻¹ x, tan⁻¹ x; implicit differentiation; logarithmic differentiation for y = f(x)^g(x)) + applications of derivatives (gradient at point; tangent + normal equations; increasing/decreasing intervals; stationary points f'(x)=0; second-derivative test for maxima/minima; inflection points f''(x)=0 with sign-change; optimisation problems; related rates; curve sketching with asymptotes) + integration (definition as anti-derivative; indefinite ∫ f(x) dx; definite ∫_a^b f(x) dx = F(b) - F(a); integration-techniques: substitution ∫ f(g(x))·g'(x) dx = ∫ f(u) du; integration-by-parts ∫ u·dv = uv - ∫ v·du; partial fractions; standard forms ∫x^n dx = x^(n+1)/(n+1) + C (n≠-1); ∫e^x dx = e^x + C; ∫(1/x) dx = ln|x| + C; ∫sin x dx = -cos x + C; ∫cos x dx = sin x + C; ∫sec² x dx = tan x + C; ∫(1/√(1-x²)) dx = sin⁻¹ x + C) + applications of integration (area-under-curve ∫_a^b |f(x)| dx; area-between-curves ∫_a^b (f(x)-g(x)) dx; volume-of-revolution π∫_a^b y² dx OR 2π∫_a^b x·y dx; trapezoidal-rule + Simpson's-rule for numerical integration) + differential equations (dy/dx = f(x) solvable by separation of variables ∫dy/y = ∫f(x) dx; dy/dx + P(x)·y = Q(x) solvable by integrating factor μ(x) = e^(∫P(x) dx); second-order linear with constant coefficients; slope-fields for visualisation) + Maclaurin series (f(x) = Σ f^(n)(0)/n! · x^n for n=0,1,2,3,4; series for e^x, sin x, cos x, ln(1+x), (1+x)^n; radius of convergence). The AI tutor must hold all 12+ sub-topics + 50+ derivative-rules + 50+ integration-rules + L'Hôpital-applications + related-rates-patterns + optimisation-patterns + differential-equation-types + Maclaurin-series-patterns.

Section 8 — Topic 6 HL-Additional Algebra: sequences extended + series convergence tests + binomial theorem extended + proof by mathematical induction extended + complex numbers extended form

Topic 6 HL-Additional Algebra extends Topic 1 for HL. Sequences extended (recursive sequences u_{n+1} = f(u_n); limit of recursive sequence via equilibrium-equation L = f(L); behaviour via stability-analysis |f'(L)|<1) + series convergence tests (nth-term test lim a_n ≠ 0 → diverges; comparison test; integral test; ratio test lim |a_{n+1}/a_n| = L: L<1 converges, L>1 diverges, L=1 inconclusive; alternating-series test; absolute + conditional convergence) + binomial theorem extended (general binomial theorem (1+x)^α = Σ C(α,n)·x^n for any real α where C(α,n) = α(α-1)...(α-n+1)/n!; converges for |x|<1) + proof by mathematical induction extended (strong induction; induction on n for product-inequalities; Fibonacci-sequence identities; matrix-power identities via Cayley-Hamilton) + complex numbers extended form (z = r·e^(iθ); multiplication: r₁·e^(iθ₁) · r₂·e^(iθ₂) = r₁r₂·e^(i(θ₁+θ₂)); division: z₁/z₂ = (r₁/r₂)·e^(i(θ₁-θ₂)); De Moivre's theorem z^n = r^n·e^(inθ); nth roots = r^(1/n)·e^(i(θ+2πk)/n) for k=0,1,...,n-1; locus problems |z - a| = k → circle centre a radius k; arg(z-a) = θ → ray from a). The AI tutor must hold all 8+ sub-topics + 30+ series-convergence-tests + general-binomial-theorem-applications + extended-induction-patterns + complex-number-locus-geometry.

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 extends Topic 2 + Topic 3. Reciprocal-trigonometric extended (cosec x = 1/sin x; sec x = 1/cos x; cot x = 1/tan x; identities: 1 + tan²x = sec²x; 1 + cot²x = cosec²x; sin·cosec = 1; cos·sec = 1; tan·cot = 1) + inverse-trigonometric extended (compositions sin(sin⁻¹(x)) = x on [-1,1]; sin⁻¹(sin(x)) piecewise; derivatives of inverse-trigonometric functions; implicit differentiation to find d/dx[sin⁻¹(x)] = 1/√(1-x²); integration involving inverse-trigonometric forms) + compound-angle extended (sum-to-product + product-to-sum identities; double-angle + triple-angle identities; sin(3x) + cos(3x) in terms of sin x + cos x) + harmonic form (a·sin(x) + b·cos(x) = R·sin(x + α) where R = √(a²+b²) and α = tan⁻¹(b/a) with quadrant-correction; useful for solving a·sin(x) + b·cos(x) = c → R·sin(x+α) = c) + hyperbolic functions (sinh x = (e^x - e^(-x))/2; cosh x = (e^x + e^(-x))/2; tanh x = sinh x / cosh x; identities cosh²x - sinh²x = 1; derivatives d/dx[sinh x] = cosh x; d/dx[cosh x] = sinh x; d/dx[tanh x] = sech²x; inverse-hyperbolic-functions). The AI tutor must hold all 8+ sub-topics + 50+ reciprocal-trig-identities + harmonic-form-transformations + hyperbolic-function-derivatives-integrals.

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

Topic 8 HL-Additional Vectors + Complex Numbers extends Topic 3. Vectors in 3D extended (position vector r = (x,y,z); magnitude |r| = √(x²+y²+z²); unit vector î, ĵ, k̂; parametric equations of line r = a + t·d; Cartesian equations from symmetric-form; distance from point to line; angle between two lines via dot product cos θ = (d₁·d₂)/(|d₁|·|d₂|)) + dot product extended (v·w = v₁w₁+v₂w₂+v₃w₃ = |v||w|cos θ; projection of v onto w: proj_w(v) = (v·w/|w|²)·w; component of v perpendicular to w: v - proj_w(v)) + cross product extended (v × w in 3D only = (v₂w₃-v₃w₂, v₃w₁-v₁w₃, v₁w₂-v₂w₁) = |v||w|sin θ · n̂ where n̂ is unit-normal; geometric interpretation area of parallelogram = |v × w|; volume of parallelepiped = |u · (v × w)|) + complex number roots of unity (solutions to z^n = 1: z = e^(2πik/n) for k=0,1,...,n-1; nth roots of any complex number z₀ = r·e^(iθ): z_k = r^(1/n)·e^(i(θ+2πk)/n); sum of all nth roots of unity = 0) + transformation matrices (2D transformations: rotation by θ: [[cos θ, -sin θ], [sin θ, cos θ]]; reflection across x-axis: [[1,0],[0,-1]]; reflection across y=x: [[0,1],[1,0]]; scaling by factor k: [[k,0],[0,k]]; shear [[1,k],[0,1]]; compositions = matrix multiplication; invariant vectors = eigenvectors; eigenvalues from det(A-λI)=0). The AI tutor must hold all 8+ sub-topics + 30+ vector-formulas + cross-product-component-rules + transformation-matrix-compositions + eigenvalue-patterns.

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

Topic 9 HL-Additional Calculus extends Topic 5. Integration by parts extended (∫u·dv = uv - ∫v·du; selection u = LIATE priority: Logarithmic, Inverse-trig, Algebraic, Trigonometric, Exponential; tabulation-method for repeated integration-by-parts; reduction-formulas) + partial fractions integration (linear factors ∫1/((x-a)(x-b)) dx = (1/(a-b))·ln|(x-a)/(x-b)|; repeated factors ∫1/(x-a)² dx = -1/(x-a); irreducible quadratics completing-the-square then ∫(Ax+B)/(x²+bx+c) dx splits to log + arctan) + improper integrals (∫a^∞ f(x) dx = lim{b→∞} ∫a^b f(x) dx; converges if limit finite; ∫a^b f(x) dx with discontinuity at a: lim{ε→0⁺} ∫{a+ε}^b f(x) dx; convergence-tests comparison + limit-comparison) + volume of revolution extended (disc-method π∫_a^b y² dx; shell-method 2π∫_a^b x·y dx for rotation around y-axis OR rotation around vertical-line x=h) + Maclaurin series extended (radius of convergence via ratio-test; operations on series: addition, multiplication, division, differentiation, integration term-by-term; applications: limits, integration of non-elementary integrals, differential-equation-solutions) + differential equations extended (second-order homogeneous y'' + by' + cy = 0 → auxiliary-equation λ² + bλ + c = 0; three cases: distinct real roots, repeated root, complex roots; particular-integral for forcing-terms of form polynomial·exponential·trig; Euler's method for numerical-solution; slope-fields visualisation). The AI tutor must hold all 10+ sub-topics + integration-by-parts-LIATE-rules + partial-fractions-integration-patterns + improper-integral-convergence-tests + Maclaurin-series-operations + second-order-ODE-patterns.

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

Topic 10 HL-Additional Statistics + Probability extends Topic 4. Continuous random variables (probability density function f(x) ≥ 0; ∫{-∞}^∞ f(x) dx = 1; cumulative distribution function F(x) = ∫{-∞}^x f(t) dt; mean E(X) = ∫x·f(x) dx; variance Var(X) = E(X²) - [E(X)]²) + normal distribution extended (Z = (X-μ)/σ; standard-normal-table for Φ(z) = P(Z ≤ z); inverse-normal for given percentile; normal-approximation-to-binomial with continuity-correction) + sampling distributions (sample-mean X̄ from population-mean μ + population-variance σ²/n; sample-proportion p̂ from population-proportion p + variance p(1-p)/n; sample-variance S² with (n-1) degrees-of-freedom) + central limit theorem (X̄ ~ N(μ, σ²/n) approximately for large n regardless of population-distribution-shape; p̂ ~ N(p, p(1-p)/n) approximately for large n with np > 5 + n(1-p) > 5) + unbiased estimators (sample-mean unbiased for μ; sample-variance with denominator (n-1) unbiased for σ²; sample-proportion unbiased for p) + t-distribution (X̄ ~ t_{n-1} when σ unknown; t-table for given degrees-of-freedom + tail-probability; t_{n-1} → Z as n→∞) + chi-squared test (χ² = Σ(O-E)²/E for goodness-of-fit; degrees-of-freedom = categories - 1 - parameters-estimated; χ²-table for given df + tail-probability; reject H₀ if χ² > critical-value). The AI tutor must hold all 8+ sub-topics + 20+ distribution-formulas + CLT-applications + t-table-lookups + chi-squared-test-flowcharts.

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

Paper 1 of IB Math HL AA is weighted 40% of the final grade and runs for 120 minutes. Section A (calculator-restricted, ~55 minutes, short-response-questions-worth-~5-7-marks-each, ~10-12-questions) tests fluency with Topic 1-5 + HL-additional-topics WITHOUT calculator. Section B (calculator-allowed, ~65 minutes, extended-response-questions-worth-~10-15-marks-each, ~5-6-questions) tests deeper reasoning. The 30-week Paper 1 strategy: (a) Section A requires exact-arithmetic + algebraic-manipulation fluency — practice GDC-free calculation of derivatives + integrals + trigonometric-values + log-rules; (b) Section B requires extended-response reasoning — practice the 4-step IB-method state-given-to-find-sketch-then-solve-verify; (c) the calculator-restriction in Section A means candidates MUST know: log rules (ln(ab) = ln a + ln b), trigonometric identities (sin²+cos²=1, tan = sin/cos), differentiation-rules (power, chain, product), integration-rules (substitution, parts), binomial theorem coefficients (Pascal's triangle + C(n,r) formula). The AI tutor must hold all 12+ Paper 1 question-types + 50+ calculator-restricted techniques + 30+ extended-response frameworks.

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

Paper 2 of IB Math HL AA is weighted 40% of the final grade and runs for 120 minutes. ALL questions require graph-display-calculator (GDC) — the candidate must use a TI-84-Plus-CE OR TI-Nspire OR Casio-fx-CG50 OR HP-Prime. Extended-response-questions-worth-~15-20-marks-each, ~5-6-questions. The 30-week Paper 2 strategy: (a) GDC-mastery — practice using GDC for: graph-plotting + intersection-points + zeros + extrema + inflection-points; numerical-solver for equations-not-solvable-analytically; statistics-mode for binomial/Poisson/normal-probabilities + confidence-intervals + hypothesis-tests; calculator-arithmetic for matrix-operations; (b) extended-response reasoning — practice the 5-step IB-method state-sketch-formulate-compute-interpret; (c) the GDC-requirement in Paper 2 means candidates MUST know: how to find intersection of two curves, how to find area-between-curves numerically, how to find derivative + integral numerically, how to compute binomial + Poisson + normal-probabilities, how to compute confidence-intervals + t-statistic + chi-squared. The AI tutor must hold all 8+ Paper 2 question-types + 30+ GDC-procedures + 30+ extended-response-frameworks.

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

Paper 3 of IB Math HL AA is weighted 30% of the final grade and runs for 60 minutes. Two of four optional-topic-questions chosen from: (1) Geometry + Proofs (synthetic-geometry, congruence, similarity, projective-geometry, coordinate-geometry-advanced); (2) Statistics + Probability Advanced (Markov-chains, linear-regression-advanced, non-parametric-tests, simulation); (3) Sets + Relations + Groups (set-theory, equivalence-relations, partial-order, group-axioms, permutations-as-groups, Cayley-tables); (4) Calculus + Series + Differential Equations Advanced (power-series-solutions, Laplace-transforms-introduction, Fourier-series-introduction, numerical-methods Euler + Runge-Kutta). The 30-week Paper 3 strategy: (a) candidates pick 2-of-4 based on university-application-target — Engineering + Physics candidates pick (4) Calculus-Advanced + (1) Geometry-Proofs; Mathematics + Computer-Science candidates pick (3) Sets-Groups + (4) Calculus-Advanced; Economics + Statistics candidates pick (2) Statistics-Advanced + (4) Calculus-Advanced; (b) extended-response-questions-worth-~15-marks-each, 2-questions = ~30 minutes per question; (c) the optional-topic-nature means candidates MUST master their two chosen topics to score-7-level. The AI tutor must hold all 4 optional-topics + 30+ question-patterns + topic-selection-counseling.

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

The IA Mathematical Exploration is weighted 20% of the final grade, internally-assessed-by-the-IB-Math-coordinator + externally-moderated-by-IBO. Format: 15-20-page-investigation-on-any-mathematical-topic-of-personal-interest. Five-criteria-assessment (each 0-4-marks): (1) Presentation — clarity + coherence + structure + diagrams; (2) Mathematical Communication — accurate-notation + terminology + symbols; (3) Personal Engagement — originality + reflection + insight; (4) Reflection — evaluation + critical-thinking + limitations + extensions; (5) Use of Mathematics — appropriate + sophisticated + correct + complete. The 30-week IA-strategy: weeks 14-15 = topic-selection + research-question-formulation; weeks 16-17 = literature-review + initial-exploration; weeks 18-19 = main-mathematical-development + GDC-modelling + draft; weeks 20 = peer-review + teacher-feedback + revision; weeks 21-30 = polish + reflection + final-draft + IB-math-coordinator-form-4-submission-window-in-February-2027. Strong-IA-topics: (a) modelling real-world-phenomena (population-growth, epidemic-spread, financial-investment, projectile-motion); (b) exploring-famous-mathematics (Fibonacci + golden-ratio, Euler's-identity, Riemann-zeta, fractals); (c) extending-classroom-content (paradoxes, non-Euclidean-geometry, infinity, paradoxes-in-probability). The AI tutor must hold all 5-criteria + 20+ strong-topics + reflection-frameworks + GDC-modelling-techniques.

Section 17 — The 5 proof-by-mathematical-induction competencies for IB Math HL AA

The 5 proof-by-induction competencies: (1) divisibility-proofs (show n²-1 divisible by 8 for odd-n; show 3^n - 1 divisible by 2 for n≥1); (2) inequality-proofs (show 2^n > n² for n≥5; show n! > 2^n for n≥4); (3) summation-proofs (Σr = n(n+1)/2; Σr² = n(n+1)(2n+1)/6; Σr³ = [n(n+1)/2]²); (4) matrix-power-proofs (show 2^n × 2^n matrix raised to power n has specific pattern; Cayley-Hamilton-theorem statement); (5) recurrence-proofs (show closed-form for Fibonacci, Lucas, Pell-sequences; show closed-form for compound-interest). The AI tutor must score each induction-proof against: base-case-validity, inductive-hypothesis-clarity, inductive-step-algebraic-correctness, conclusion-statement, alternative-proof-via-direct-method OR counter-example. The 7-prompt-pattern: state-base-case → verify-base-case → state-inductive-hypothesis → execute-inductive-step (algebra) → conclude → verify-by-counter-example OR alternative-proof → reflection-on-method.

Section 18 — The 6 differential-equations competencies for IB Math HL AA

The 6 differential-equations competencies: (1) first-order-separable dy/dx = f(x)·g(y) → ∫dy/g(y) = ∫f(x) dx (radioactive-decay dN/dt = -kN → N = N₀·e^(-kt); Newton's-cooling dT/dt = -k(T-T_env) → T = T_env + (T₀-T_env)·e^(-kt); population-growth dP/dt = kP → P = P₀·e^(kt)); (2) first-order-linear dy/dx + P(x)·y = Q(x) → integrating-factor μ(x) = e^(∫P(x) dx); (3) second-order-homogeneous y'' + by' + cy = 0 → auxiliary-equation λ² + bλ + c = 0 → three-cases distinct-real-roots y = A·e^(λ₁x) + B·e^(λ₂x); repeated-root y = (A + Bx)·e^(λx); complex-roots λ = α±βi → y = e^(αx)·(A·cos(βx) + B·sin(βx)); (4) second-order-non-homogeneous y'' + by' + cy = f(x) → particular-integral via undetermined-coefficients OR variation-of-parameters; (5) Euler's-method numerical-solution y_{n+1} = y_n + h·f(x_n, y_n); (6) slope-fields visualisation (draw tangent-segments at grid-points). The AI tutor must score each differential-equation against: equation-type-identification, solution-method-selection, algebraic-execution, particular-solution-application, initial-condition-usage, slope-field-drawing.

Section 19 — The 4 linear-algebra competencies for IB Math HL AA

The 4 linear-algebra competencies: (1) matrix-arithmetic (addition, subtraction, scalar-multiplication, multiplication [m×n]·[n×p] = [m×p]; commutative-multiplication fails AB ≠ BA in general; associative AB·C = A·BC; distributive A(B+C) = AB + AC); (2) determinants + inverses (2×2 det = ad-bc; inverse = 1/det · [[d,-b],[-c,a]]; 3×3 cofactor-expansion; singular-matrix det=0 → no-inverse; solving-Ax=b → x = A⁻¹·b if det(A)≠0); (3) eigenvalues + eigenvectors (characteristic-equation det(A-λI) = 0; for each-eigenvalue-λ solve (A-λI)v = 0; trace = sum-of-eigenvalues; determinant = product-of-eigenvalues); (4) transformation matrices (rotation + reflection + scaling + shear + translation-as-3×3-with-homogeneous-coordinates; composition = matrix-multiplication). The AI tutor must score each linear-algebra-problem against: matrix-dimension-tracking, operation-selection, algebraic-execution, determinant-calculation, inverse-calculation, eigenvalue-extraction, eigenvector-calculation, transformation-composition.

Section 20 — The 5 complex-numbers competencies for IB Math HL AA

The 5 complex-numbers competencies: (1) rectangular-form-operations (z = a+bi; addition z₁+z₂; multiplication (a+bi)(c+di) = (ac-bd) + (ad+bc)i; division z₁/z₂ = z₁·z̄₂/|z₂|² where z̄ = a-bi is conjugate); (2) modulus + argument (|z| = √(a²+b²); arg(z) = tan⁻¹(b/a) with quadrant-correction arg ∈ (-π,π]); (3) polar-form + exponential-form (z = r·(cos θ + i·sin θ) = r·e^(iθ); conversion between rectangular + polar); (4) De Moivre's theorem + nth-roots (z^n = r^n·(cos(nθ) + i·sin(nθ)) = r^n·e^(inθ); nth-roots of unity z^n = 1 → z = e^(2πik/n) for k=0,1,...,n-1; nth-roots of any-z₀ = r·e^(iθ) → z_k = r^(1/n)·e^(i(θ+2πk)/n) for k=0,1,...,n-1); (5) locus-problems (|z - a| = k → circle centre a radius k; arg(z - a) = θ → ray from a at angle θ; |z-a| = |z-b| → perpendicular-bisector of segment ab). The AI tutor must score each complex-numbers-problem against: form-conversion-accuracy, operation-selection, De-Moivre-application, nth-roots-all-solutions, locus-geometry-interpretation.

Section 21 — The 4 vectors-in-3D competencies for IB Math HL AA

The 4 vectors-in-3D competencies: (1) position-vectors + parametric-equations (r = (x,y,z); line r = a + t·d where a is position-vector of point-on-line, d is direction-vector; Cartesian-equations from symmetric-form x = x₀ + at, y = y₀ + bt, z = z₀ + ct → (x-x₀)/a = (y-y₀)/b = (z-z₀)/c); (2) distance-from-point-to-line + angle-between-lines (distance from P to line r = a + t·d is |(P-a) × d|/|d|; angle cos θ = (d₁·d₂)/(|d₁|·|d₂|)); (3) dot-product + projection (v·w = Σv_i·w_i = |v||w|cos θ; projection of v onto w proj_w(v) = (v·w/|w|²)·w; component-perpendicular-to-w: v - proj_w(v)); (4) cross-product + area + volume (v × w = (v₂w₃-v₃w₂, v₃w₁-v₁w₃, v₁w₂-v₂w₁); area-parallelogram = |v × w|; volume-parallelepiped = |u · (v × w)|; triple-product = determinant). The AI tutor must score each vectors-problem against: vector-notation-fluency, parametric-equation-derivation, dot-product-cross-product-selection, distance-formula-application, projection-formula-application.

Section 22 — The 5 calculus-advanced-series competencies for IB Math HL AA

The 5 calculus-advanced-series competencies: (1) Maclaurin + Taylor series (f(x) = Σ f^(n)(a)/n! · (x-a)^n; Maclaurin a=0; series for e^x = 1+x+x²/2!+x³/3!+...; sin x = x - x³/3! + x⁵/5! - ...; cos x = 1 - x²/2! + x⁴/4! - ...; ln(1+x) = x - x²/2 + x³/3 - ... for |x|≤1, x≠-1; (1+x)^α = 1 + αx + α(α-1)/2!·x² + ...); (2) radius-of-convergence (R = lim |a_n/a_{n+1}| from ratio-test; converges for |x-a|<R); (3) operations-on-series (addition term-by-term; multiplication via Cauchy-product; differentiation term-by-term within radius-of-convergence; integration term-by-term); (4) series-applications (limits: lim_{x→0} sin x / x = 1 via series; integration of non-elementary-integrals e^(-x²) via series; differential-equation-power-series-solutions); (5) convergence-tests (nth-term-test lim a_n ≠ 0 → diverges; ratio-test L = lim |a_{n+1}/a_n|: L<1 converges, L>1 diverges, L=1 inconclusive; comparison-tests; integral-test; alternating-series-test). The AI tutor must score each series-problem against: series-recognition, radius-calculation, term-by-term-operation-validity, convergence-test-selection, limit-evaluation-via-series.

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

The 7-prompt AI tutor library for IB Math HL AA scores every Paper 1 + Paper 2 + Paper 3 + IA-mathematical-exploration response against the official IBO Mathematics HL AA marking scheme + rubric-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 7 prompts:

• Prompt 1 — Paper 1 Section A calculator-restricted scoring: grades 5-7 mark short-response-questions against the GDC-free rubric, scoring exact-arithmetic + algebraic-manipulation + trigonometric-evaluation + log-rules + derivative-rules + integration-rules. Outputs: marks-awarded, working-shown-correctness, algebraic-errors, GDC-free-alternative.
• Prompt 2 — Paper 1 Section B calculator-allowed extended-response scoring: grades 10-15 mark extended-response-questions against the 5-step-IB-method rubric, scoring state-given-to-find + sketch + formulation + solution-method + verify. Outputs: marks-awarded, method-correctness, algebraic-errors, final-answer-validity.
• Prompt 3 — Paper 2 GDC-required extended-response scoring: grades 15-20 mark GDC-dependent extended-response-questions against the 5-step-IB-method rubric, scoring GDC-procedure + analytical-setup + numerical-result + interpretation. Outputs: marks-awarded, GDC-procedure-correctness, numerical-result-validity, interpretation-accuracy.
• Prompt 4 — Paper 3 optional-topic extended-response scoring: grades 15-mark optional-topic-questions against the topic-specific-rubric, scoring topic-mastery + algebraic-fluency + GDC-integration + extended-reasoning. Outputs: marks-awarded, topic-mastery, algebraic-correctness, extended-reasoning-quality.
• Prompt 5 — IA Mathematical Exploration 5-criteria scoring: grades 15-20-page-investigations against the 5-criteria-rubric (Presentation + Mathematical-Communication + Personal-Engagement + Reflection + Use-of-Mathematics), each 0-4-marks. Outputs: criterion-by-criterion-scores + reflection-depth + topic-originality + GDC-integration + mathematical-sophistication.
• Prompt 6 — Proof-by-mathematical-induction scoring: grades induction-proofs against the 5-element-rubric (base-case + inductive-hypothesis + inductive-step + conclusion + alternative-method), scoring algebraic-correctness + logical-flow + alternative-proof-via-direct-method. Outputs: marks-awarded, induction-elements-present, algebraic-errors, alternative-proof-quality.
• Prompt 7 — Differential-equations + linear-algebra + complex-numbers + vectors-in-3D + calculus-advanced-series scoring: grades the HL-additional-topics-questions against the topic-specific-rubric, scoring equation-type-identification + solution-method-selection + algebraic-execution + particular-solution-application. Outputs: marks-awarded, topic-mastery, algebraic-correctness, final-answer-validity.

Each prompt maps to a specific rubric-level (Band 1-7) and outputs the candidate's current band + the specific gap-topic-blocking-band-progression (e.g., "candidates stuck at Band 5 typically have induction-step-algebra-errors" + "candidates stuck at Band 6 typically have extended-reasoning-quality-issues"). The AI tutor's job is to surface the band-5-to-7-gap and route the candidate to the specific practice-pattern that closes it.

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

The 30-week IB Math HL AA playbook covers all 5-core-topics + 5-HL-additional-topics + IA-mathematical-exploration + Paper-1 + Paper-2 + Paper-3, integrates proof-by-mathematical-induction + differential-equations + linear-algebra + complex-numbers + vectors-in-3D + calculus-advanced-series across every section, simulates every IBO-past-paper-2016-to-2025 + TZ1-TZ2-TZ3-papers + specimen-papers + IA-exemplars, and surfaces the specific IB Math HL AA gap (number-algebra-vs-functions-vs-geometry-trigonometry-vs-statistics-probability-vs-calculus-vs-HL-additional-topics-vs-proof-by-induction-vs-differential-equations-vs-complex-numbers-vs-vectors-vs-linear-algebra-vs-IA-mathematical-exploration-vs-Paper-3-optional-topic-mastery) that is costing the candidate marks toward the score 7. The AI tutor holds the official IBO Mathematics HL AA marking scheme + rubric-band-descriptors (Band 1 Inadequate + Band 2 Adequate + Band 3 Competent + Band 4 Highly-Competent + Band 5 Sophisticated + Band 6 Excellent + Band 7 Outstanding) and outputs the candidate's current band + the specific gap-topic-blocking-band-progression. The end-state: candidate sits Paper 1 + Paper 2 + Paper 3 in May 2027, submits IA-mathematical-exploration in February 2027, and closes the 5-to-7 gap on the most-respected pre-university calculus + linear-algebra + proof-based mathematics qualification globally for IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Engineering + Pre-Medicine + Pre-Physics + Pre-Computer-Science + Pre-Architecture + Pre-Mathematics + Pre-Economics + Pre-Finance + Pre-Statistics 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 + European + Asian + African + South-American + North-American + Middle-Eastern + Oceanian international IB schools.

Pairs with IB Math HL Applications & Interpretation (post-159)

The IB Math HL Applications & Interpretation playbook (post-159) + [this playbook] form the IB Diploma + IB Mathematics Higher Level + IBO-applied-track + Year-13-applied-mathematics + first-year-undergraduate-Economics + Finance + Business + Statistics + Actuarial-Science + Psychology + Biology + Environmental-Science + Data-Science + Computer-Science pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Economics + Pre-Finance + Pre-Business + Pre-Psychology + Pre-Biology + Pre-Environmental-Science + Pre-Statistics + Pre-Data-Science + Pre-Computer-Science 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 + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL admissions. The IB Math HL AI 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-HL-additional-topics (Algebra + Logarithmic + Exponential + Functions + Trigonometric + Functions + Vectors + Statistics + Probability) + Internal-Assessment-Modelling-Exploration + Paper 1 + Paper 2 + Paper 3 Optional-Topic + modelling-driven + applied-calculus-required + statistics-heavy + GDC-required + IA-modelling-exploration-assessed + 5-modelling-and-optimization-competencies + 6-statistics-and-probability-applied-competencies + 4-financial-modelling-competencies + 5-discrete-modelling-competencies + 4-optimisation-applications-competencies + 5-calculus-applied-series-competencies + 7-prompt-AI-tutor-library + score-7-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-applied-mathematics + IB-Diploma + IBO-applied-mastery-track + first-year-undergraduate-Economics + Finance + Business + Statistics + Actuarial-Science + Psychology + Biology + Environmental-Science + Data-Science + Computer-Science-university-credit + Applied-Admissions-readiness at MIT + Imperial + Cambridge + Oxford + LSE + Warwick + UCL + LBS + Bocconi + HEC-Paris + ESSEC + INSEAD + Sciences-Po + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL. See post-159 for the IB-Math-HL-AI-specific exam, score-distribution, and 30-week score-7 master schedule.

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 Design Technology HL (post-166)

The IB Design Technology HL playbook (post-166) + [this playbook] form the IB Diploma + IB Higher-Level + IBO-applied-track + Year-13-design + first-year-undergraduate-Engineering + Architecture + Industrial-Design + Product-Design + UX-Design + Mechanical-Engineering + Materials-Engineering + Manufacturing-Engineering + Civil-Engineering + Structural-Engineering + Aerospace-Engineering + Automotive-Engineering pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Engineering + Pre-Architecture + Pre-Industrial-Design + Pre-Product-Design + Pre-UX-Design + Pre-Mechanical-Engineering + Pre-Materials-Engineering + Pre-Manufacturing-Engineering + Pre-Civil-Engineering + Pre-Structural-Engineering + Pre-Aerospace-Engineering + Pre-Automotive-Engineering 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 + RCA + Imperial + Cambridge + Oxford + Central-Saint-Martins + Architectural-Association + RISD + Parsons + Pratt + Cooper-Union + Bauhaus + TU-Munich + ETH-Zurich + EPFL + Delft + TU-Eindhoven + Politecnico-Milano + Aalto admissions. The IB Design Technology HL 6-core-topics (Design-Fundamentals + Resource-Analysis + Ideation + Evaluation + Sustainable-Production + Marketing-Design-Outputs) + 4-HL-extension-topics (User-Centred-Design + Innovation-Design + Materials-Engineering + CAD-CAM-Rapid-Manufacturing) + 2-Paper-structure (Paper-1-core + Paper-2-HL-extension) + Internal-Assessment-Design-Project + IB-Command-Terms (Define + Describe + Explain + Outline + State + Annotate + Calculate + Compare + Contrast + Discuss + Evaluate + Examine + Justify + Recommend + Suggest + To-what-extent) + 52-mark-IA-criterion-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-design + IB-Diploma + IBO-applied-mastery-track + first-year-undergraduate-Engineering + Architecture + Industrial-Design + Product-Design + UX-Design + Mechanical-Engineering + Materials-Engineering + Manufacturing-Engineering + first-year-undergraduate-Design + university-credit + Applied-Admissions-readiness at MIT + Stanford + Caltech + RCA + Imperial + Cambridge + Oxford + Central-Saint-Martins + Architectural-Association + RISD + Parsons + Pratt + Cooper-Union + Bauhaus + TU-Munich + ETH-Zurich + EPFL + Delft + TU-Eindhoven + Politecnico-Milano + Aalto + NUS + NTU + HKUST + KAIST + UCL + Edinburgh + Manchester + Bristol + Durham + KCL admissions. See post-166 for the IB-Design-Technology-HL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Sports Exercise and Health Science SL (post-167)

The IB Sports Exercise and Health Science SL playbook (post-167) + [this playbook] form the IB Diploma + IB Standard-Level + IB Group-4 + IBO-applied-sports-science-track + Year-13-sports-science + first-year-undergraduate-Sports-Science + Sport-Medicine + Sport-Psychology + Sport-Sociology + Sport-Physiotherapy + Sport-Nutrition + Exercise-Physiology + Health-Sciences + Medicine + Biomedical-Science + Public-Health + Physical-Therapy + Nursing + Kinesiology pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Sports-Science + Pre-Sport-Medicine + Pre-Sport-Psychology + Pre-Physiotherapy + Pre-Sport-Nutrition + Pre-Exercise-Physiology + Pre-Health-Sciences + Pre-Medicine + Pre-Biomedical-Science + Pre-Public-Health + Pre-Physical-Therapy + Pre-Nursing + Pre-Kinesiology 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 Loughborough + Bath + Stanford + Cambridge + Oxford + Imperial + UCL + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough-London + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. The IB SEHS SL 8-topics (Anatomy + Exercise-Physiology + Energy-Systems + Movement-Analysis + Physical-Activity + Health-Wellbeing + Sport-Psychology + Sociocultural-Issues) + 2-Paper-structure (Paper-1-multiple-choice-and-data-response + Paper-2-extended-response) + Internal-Assessment-Practical-Investigation + IB-Command-Terms (State + Describe + Explain + Discuss + Evaluate + Compare + Contrast + Analyse + To-what-extent + Outline + Identify + Suggest) + 20-mark-IA-criterion-rubric (Personal-Engagement + Exploration + Analysis + Evaluation + Communication) covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-sports-science + IB-Diploma + IBO-applied-sports-science-track + first-year-undergraduate-Sports-Science + Sport-Medicine + Sport-Psychology + Sport-Sociology + Sport-Physiotherapy + Sport-Nutrition + Exercise-Physiology + Health-Sciences + Medicine + Biomedical-Science + Public-Health + Physical-Therapy + Nursing + Kinesiology + university-credit + Sports-Science-Admissions-readiness at Loughborough + Bath + Stanford + Cambridge + Oxford + Imperial + UCL + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough-London + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. See post-167 for the IB-SEHS-SL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Environmental Systems and Societies SL (post-168)

The IB Environmental Systems and Societies SL playbook (post-168) + [this playbook] form the IB Diploma + IB Standard-Level + IB Group-3 + IB Group-4 + IBO-applied-environmental-science-track + Year-13-environmental-science + first-year-undergraduate-Environmental-Science + Environmental-Studies + Environmental-Policy + Environmental-Engineering + Environmental-Law + Sustainability + Climate-Science + Conservation-Biology + Marine-Biology + Ecology + Earth-Sciences + Geography + International-Development + Public-Health pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Environmental-Science + Pre-Environmental-Studies + Pre-Environmental-Policy + Pre-Environmental-Engineering + Pre-Environmental-Law + Pre-Sustainability + Pre-Climate-Science + Pre-Conservation-Biology + Pre-Marine-Biology + Pre-Ecology + Pre-Earth-Sciences + Pre-Geography + Pre-International-Development + Pre-Public-Health 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 Cambridge + Oxford + UCL + Stanford + MIT + ETH-Zurich + LSE + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. The IB ESS SL 8-topics (Foundations-Environmental-Science + Ecosystems-Ecology + Biodiversity-Conservation + Water-Food-Soil + Atmospheric-Science + Climate-Change + Energy-Resources + Pollution + Sustainability) + 2-Paper-structure (Paper-1-case-study + Paper-2-short-answer-and-structured-essay) + Internal-Assessment-Individual-Investigation + IB-Command-Terms (Define + Describe + Explain + Discuss + Evaluate + Compare + Contrast + Analyse + To-what-extent + Outline + Identify + Suggest + Justify + Examine) + 25-mark-IA-criterion-rubric (Personal-Engagement + Exploration + Analysis + Evaluation + Communication) covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-environmental-science + IB-Diploma + IBO-applied-environmental-science-track + first-year-undergraduate-Environmental-Science + Environmental-Studies + Environmental-Policy + Sustainability + Climate-Science + Conservation-Biology + Marine-Biology + Ecology + Earth-Sciences + Geography + International-Development + Public-Health + university-credit + Environmental-Science-Admissions-readiness at Cambridge + Oxford + UCL + Stanford + MIT + ETH-Zurich + LSE + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. See post-168 for the IB-ESS-SL-specific exam, score-distribution, and 30-week score-7 master schedule.

Pairs with IB Geography SL (post-169)

The IB Geography SL playbook (post-169) + [this playbook] form the IB Diploma + IB Standard-Level + IB Group-3 + IB Group-4 + IBO-applied-geography-track + Year-13-geography + first-year-undergraduate-Geography + Human-Geography + Physical-Geography + Environmental-Geography + Urban-Planning + International-Development + GIS + Earth-Sciences + Environmental-Science + Public-Policy + International-Relations + Sociology + Economics + Public-Health pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Geography + Pre-Human-Geography + Pre-Physical-Geography + Pre-Environmental-Geography + Pre-Urban-Planning + Pre-International-Development + Pre-GIS + Pre-Earth-Sciences + Pre-Environmental-Science + Pre-Public-Policy + Pre-International-Relations + Pre-Sociology + Pre-Economics + Pre-Public-Health 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 Cambridge + Oxford + UCL + LSE + Stanford + MIT + ETH-Zurich + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. The IB Geography SL 7-core-optional-units (Changing-Population + Global-Climate-Vulnerability + Global-Resource-Consumption + Geophysical-Hazards + Freshwater + Oceans-Coastal-Margins + Leisure-Tourism-Sport + Food-Health-Wellbeing + Urban-Environments + Globalization-Interactions) + 2-Paper-structure (Paper-1-structured-questions + Paper-2-extended-response) + Internal-Assessment-Fieldwork-Investigation + IB-Command-Terms (Outline + Describe + Explain + Discuss + Evaluate + Compare + Contrast + Analyse + State + Annotate + Construct + Identify + Justify + Suggest + To-what-extent) + 25-mark-IA-criterion-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-geography + IB-Diploma + IBO-applied-geography-track + first-year-undergraduate-Geography + Human-Geography + Physical-Geography + Environmental-Geography + Urban-Planning + International-Development + GIS + Earth-Sciences + Environmental-Science + Public-Policy + International-Relations + Sociology + Economics + Public-Health + university-credit + Geography-Admissions-readiness at Cambridge + Oxford + UCL + LSE + Stanford + MIT + ETH-Zurich + Edinburgh + Manchester + Bristol + KCL + Durham + Exeter + St-Andrews + Loughborough + Bath + Toronto + UBC + McGill + McMaster + Western + Queens + Alberta + Calgary + Dalhousie + NUS + NTU + HKUST + Sydney + Melbourne + Monash + UNSW + Queensland + Auckland + Otago admissions. See post-169 for the IB-Geography-SL-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.