IGCSE Mathematics 0580 AI Tutor Playbook 2026

Audience: International British-curriculum Year 10-11 students (14-16 years old) preparing for the Summer 2027 IGCSE Mathematics exams (Cambridge CAIE 0580, Edexcel 4MA1, OR OxfordAQA 8300 specification) — typically the cohort interested in A-Level Mathematics, A-Level Further Mathematics, IB Mathematics AA HL/SL, AP Calculus AB/BC, AP Statistics, engineering (mechanical + electrical + civil + chemical + aerospace + materials + robotics + computing), physics, astrophysics, computer science, mathematics, economics, finance, PPE (politics + philosophy + economics), data science, machine learning, AI, actuarial science, and any quantitative + analytical university course. Covers international candidates in Singapore, Hong Kong, UAE, Saudi Arabia, Malaysia, Indonesia, India, Pakistan, Bangladesh, Sri Lanka, Nepal, Egypt, Nigeria, South Africa, Ghana, Kenya, Tanzania, Uganda, China, Japan, Korea, Australia, NZ, Canada, the Caribbean, Mexico, Brazil, Argentina, Chile, Colombia, the Philippines, Thailand, Vietnam, and any other country where the IGCSE is taken. Covers IGCSE Mathematics teachers who want an AI workflow for grading numerical calculations, algebraic manipulation, geometric reasoning, coordinate-geometry problems, trigonometry scenarios, probability + statistics reasoning, function analysis, calculus calculations, and extended-response reasoning, parents paying for international British-curriculum tuition, homeschool families using IGCSE Mathematics for transcript strength in engineering + physics + computer-science + economics + finance + PPE + data-science + Russell Group + Oxbridge + Imperial + MIT + Stanford + Caltech + LSE + UCL + Warwick + Edinburgh admissions, and overseas students applying to UK Russell Group + US + Canadian + Australian universities where IGCSE Mathematics at A* is the gold-standard British-curriculum signal (treated as equivalent to GCSE Mathematics grade 9 at UK universities, and stronger than AP Calculus AB 5 at most US universities for the breadth of pure + mechanics + statistics content coverage).

Hook: IGCSE Mathematics had approximately 250,000+ Cambridge CAIE 0580 candidates globally in 2025 — making it the single highest-volume IGCSE subject globally (more candidates than IGCSE English Language + IGCSE English Literature + IGCSE Physics + IGCSE Chemistry + IGCSE Biology combined for many international cohorts, and roughly 4x the volume of A-Level Mathematics). The grade distribution is competitive but achievable: A*-rate of approximately 17.2 percent (highest A*-rate of any IGCSE science + mathematics subject — reflecting both the volume of candidates and the depth of numerical + algebraic + geometric + trigonometric + statistical + calculus mastery required at A*-tier), A-rate of approximately 28.4 percent, B-rate of approximately 26.3 percent, C-rate of approximately 16.8 percent, D-rate approximately 6.2 percent, E-rate approximately 2.7 percent, F-rate approximately 1.1 percent, G/U-rate approximately 0.3 percent. The A*-A combined rate (45.6 percent) is the IGCSE benchmark for A-Level Mathematics + A-Level Further Mathematics + IB Mathematics AA/SL + AP Calculus AB/BC + AP Statistics + engineering + physics + computer-science + economics + finance + PPE + data-science + machine-learning + AI admissions readiness — students who score an A* at IGCSE Mathematics are well-positioned to take A-Level Mathematics, A-Level Further Mathematics, IB Mathematics AA HL/SL, AP Calculus AB/BC, AP Statistics, and progress to top-tier engineering + physics + computer-science + economics + finance + PPE + data-science + Russell Group + Oxbridge + Imperial + MIT + Stanford + Caltech admissions globally.

The Cambridge CAIE 0580 specification: Paper 2 (Multiple-Choice, 45 minutes, 40 marks, 40 weighted questions testing all 25 topics at extended-tier depth, weighted 30 percent of the IGCSE grade), Paper 4 (Extended Theory, 2 hours 30 minutes, 80 marks, structured + free-response questions testing all 25 topics + the numerical + algebraic + geometric + trigonometric + statistical + calculus toolkit, weighted 50 percent of the IGCSE grade), Paper 6 (Investigation OR Alternative-to-Practical, 1 hour 30 minutes, 40 marks, testing investigation + modelling + reasoning + proof depth, weighted 20 percent of the IGCSE grade). The Core vs Extended tier choice: candidates aiming for A-Level + IB + AP progression MUST take the Extended tier (grades available A*-E; Core tier caps at grade C and is for non-progression candidates). Edexcel IGCSE Mathematics 4MA1 covers 26 topics across 2 papers (Paper 1: Core Tier 2 hours 110 marks, grades C-G available; Paper 2: Extended Tier 2 hours 110 marks, grades A*-G available). OxfordAQA IGCSE Mathematics 8300 covers 27 topics across 3 papers (Paper 1: Non-Calculator 1 hour 30 minutes 80 marks, Paper 2: Calculator 1 hour 30 minutes 80 marks, Paper 3: Calculator Higher 1 hour 30 minutes 80 marks).

For international applicants (Singapore, Hong Kong, UAE, KSA, India, Pakistan, Bangladesh, Malaysia, Indonesia, Egypt, Nigeria, South Africa, Ghana, Kenya, China, Japan, Korea, Australia, NZ, Canada, Caribbean), the IGCSE Mathematics A* is the gold-standard British-curriculum signal for A-Level Mathematics + A-Level Further Mathematics + IB Mathematics AA + AP Calculus AB/BC progressions globally — and is treated as equivalent to GCSE Mathematics grade 9 at UK Russell Group universities, and stronger than AP Calculus AB 5 at most US universities for the breadth of pure + mechanics + statistics content coverage (Cambridge 0580 covers more statistics + probability + mechanics + financial mathematics depth than AP Calculus AB). For engineering + physics + computer-science + economics + finance + PPE + data-science + machine-learning + AI admissions globally, IGCSE Mathematics at A* is the foundation mathematics for the A-Level Mathematics + A-Level Further Mathematics + IB Mathematics AA + AP Calculus + AP Statistics pre-quantitative pair at A-Level-equivalent.

The 22-Week IGCSE Mathematics Workflow

Weeks 1-4 (September-October): Number Toolkit + Algebra Toolkit Foundation

Topics covered: 1 Number (surds, indices, standard form, ratio, proportion, percentage, bounds, estimation, error intervals, set notation, Venn diagrams), 2 Algebra + Functions (linear equations, simultaneous equations, quadratic equations, completing-the-square, quadratic formula, inequalities, polynomials, algebraic fractions, functions, composite, inverse, iteration, transformation of functions).

AI tutor prompt for this phase:

You are an IGCSE Mathematics 0580 tutor working with a Year 10-11 candidate
preparing for the Summer 2027 Cambridge / Edexcel / OxfordAQA exams.

Score every calculation + extended-response against the 9-1 mark scheme.
For every question:
1. Identify the topic (1 Number / 2 Algebra / 3 Coordinate Geometry /
   4 Geometry / 5 Mensuration / 6 Trigonometry / 7 Probability /
   8 Statistics / 9 Calculus).
2. State the working answer.
3. Show the full method step-by-step.
4. Identify any mark-scheme-aligned partial credit (M1, M2, A1 marks).
5. If the answer is incorrect, diagnose the specific error (sign error,
   index error, surd simplification, completing-the-square setup,
   quadratic-formula substitution, inequality flip, function evaluation
   order, composite-function composition order, inverse-function swap).
6. Surface the candidate's pattern (e.g. "loses 1-2 marks per question
   on surd simplification + completing-the-square setup").
7. Drill 3-5 follow-up questions of the same topic at A*-tier
   difficulty.
8. Set the next review checkpoint (1 day, 3 days, 7 days, 14 days
   depending on confidence).

Expected output:

• Surds simplification (√a × √b = √ab, √(a/b) = √a/√b, rationalising the denominator)
• Indices laws (a^m × a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(mn), a^0 = 1, a^(-n) = 1/a^n)
• Standard form conversion (move decimal to between 1 and 10, count shifts)
• Ratio + proportion (sharing in a ratio, scale-factor problems, direct + inverse proportion)
• Percentage (compound interest, percentage change, reverse percentage, profit + loss)
• Bounds + estimation (upper + lower bounds for calculations, significant figures)
• Linear equations (one-step + two-step + variables on both sides)
• Simultaneous equations (elimination + substitution + graphical)
• Quadratic equations (factorise, completing-the-square, quadratic formula, discriminant, sum + product of roots)
• Inequalities (one-variable + two-variable + graphical, including flip on negative multiply/divide)
• Polynomials (add, subtract, multiply, divide long + synthetic)
• Algebraic fractions (add, subtract, multiply, divide, simplify, partial fractions extended)
• Functions (f(x) notation, composite f(g(x)), inverse f^(-1)(x), iteration)

Mastery benchmark: 25/30 in Paper 2 multiple-choice + 60+/80 in Paper 4 extended theory.

Weeks 5-8 (November-December): Coordinate Geometry + Geometry + Mensuration

Topics covered: 3 Coordinate Geometry (line equations, gradient, parallel, perpendicular, mid-point, distance, circle equations, tangent, intersection, locus, transformation of curves), 4 Geometry (angle properties, similar shapes, congruent triangles, circle theorems, Pythagoras), 5 Mensuration (perimeter, area, volume, surface area, arc length, sector area, segment area, similar-area, similar-volume, frustum, cone, sphere, hemisphere, pyramid, prism, cylinder — extended: 3D trigonometry, 3D Pythagoras).

AI tutor prompt for this phase:

You are an IGCSE Mathematics 0580 tutor working with a Year 10-11 candidate.

For every coordinate-geometry + geometry + mensuration question:
1. Identify the topic + sub-topic.
2. State the working answer.
3. Show the full method (line equation y = mx + c OR mx + c = y, gradient
   m = (y2-y1)/(x2-x1), perpendicular gradient m1 × m2 = -1, circle
   equation (x-a)² + (y-b)² = r², tangent perpendicular to radius at
   point of tangency).
4. For geometry: identify which circle theorem (alternate segment,
   angle at centre = 2 × angle at circumference, angles in same
   segment equal, cyclic quadrilateral opposite angles sum to 180,
   tangent perpendicular to radius).
5. For mensuration: identify the shape + the formula + the correct
   unit (cm² for area, cm³ for volume).
6. Diagnose the error (forgot to convert units, wrong formula, sign
   error in completing-the-square for circle equation, wrong
   interpretation of "perpendicular" gradient).
7. Drill 3-5 follow-up questions at A*-tier.
8. Set review checkpoint.

Expected output:

• Line equations (y = mx + c form, finding m from two points, finding c from a point, parallel + perpendicular)
• Circle equations (centre-radius form, general form completion-of-square, tangent equation, intersection line-circle)
• Locus problems (loci of points equidistant from a line/point, compound locus, shaded regions)
• Similar shapes (scale factor, length/area/volume ratios, similarity proof, SSS/SAS/ASA similarity)
• Congruent triangles (SSS, SAS, ASA, RHS, congruence proof)
• Circle theorems (8 standard theorems + the extended alternate-segment + cyclic-quadrilateral theorems)
• Pythagoras (2D + 3D, including distance from point to line)
• Area (parallelogram, trapezium, triangle, kite, rhombus, compound shapes)
• Volume (prism, cylinder, cone, pyramid, sphere, hemisphere, frustum, compound solids)
• Surface area (same set + composite solids)

Mastery benchmark: 28/30 in Paper 2 + 65+/80 in Paper 4.

Weeks 9-12 (January-February): Trigonometry + Probability + Statistics

Topics covered: 6 Trigonometry (SOH-CAH-TOA, sine rule, cosine rule, area of triangle = ½ab sin C, 3D trigonometry, exact values, radians, trig identities, trig equations, transformation of trig graphs), 7 Probability (single-event, independent-events, mutually-exclusive, tree-diagrams, conditional probability, Venn-diagrams, Bayes-theorem, expected-value), 8 Statistics (mean, median, mode, range, interquartile-range, box-plots, histograms, cumulative-frequency, scatter-graphs, correlation, regression, standard-deviation, normal-distribution).

AI tutor prompt for this phase:

You are an IGCSE Mathematics 0580 tutor working with a Year 10-11 candidate.

For every trigonometry + probability + statistics question:
1. Identify the topic + sub-topic.
2. State the working answer.
3. For trig: state whether it's a right-angled (SOH-CAH-TOA), non-
   right-angled (sine rule, cosine rule, area = ½ab sin C), or 3D
   (find a face-diagonal first, then Pythagoras OR cosine rule in
   that face).
4. For probability: identify the rule (independent P(A∩B) = P(A)×P(B),
   mutually-exclusive P(A∪B) = P(A)+P(B), conditional P(A|B) = P(A∩B)/P(B),
   Bayes' theorem P(A|B) = P(B|A)×P(A) / P(B)).
5. For statistics: state the measure (mean = Σx/n, IQR = Q3-Q1,
   standard deviation = √(Σ(x-μ)²/n), z-score = (x-μ)/σ).
6. Show the full method.
7. Diagnose the error (wrong trig function, wrong angle in non-right-
   angled triangle, missing "and"/"or" probability interpretation,
   forgetting to square the standard deviation in variance).
8. Drill 3-5 follow-up questions at A*-tier.
9. Set review checkpoint.

Expected output:

• SOH-CAH-TOA (sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent, including inverse sin/cos/tan)
• Sine rule (a/sin A = b/sin B = c/sin C = 2R where R = circumradius)
• Cosine rule (a² = b² + c² - 2bc cos A, cos A = (b² + c² - a²)/(2bc))
• Area of triangle (½ab sin C)
• 3D trigonometry (find a face-diagonal first, then Pythagoras OR cosine rule)
• Exact values (sin 30° = ½, sin 45° = √2/2, sin 60° = √3/2, cos + tan equivalents)
• Radian measure (π rad = 180°, arc length = rθ, sector area = ½r²θ)
• Trig identities (sin²θ + cos²θ = 1, tan θ = sin θ/cos θ, sin(180-θ) = sin θ, cos(180-θ) = -cos θ)
• Trig equations (find all solutions in 0°-360° OR 0-2π)
• Probability rules (single + combined events, independent vs mutually-exclusive)
• Tree diagrams (with + without replacement, conditional branches, multi-stage)
• Conditional probability (P(A|B) interpretation, two-way tables, Venn-diagram regions)
• Bayes' theorem (extended-tier: prior + likelihood + posterior)
• Mean + median + mode + range (including grouped data: Σfx/Σf for mean, midpoint × frequency)
• Interquartile range + box-plots (Q1, Q2, Q3, IQR, outliers beyond 1.5×IQR)
• Histograms (frequency density = frequency/class width, equal-area bars)
• Cumulative frequency (find median, quartiles, percentiles from ogive)
• Scatter graphs + correlation (positive, negative, zero, strong, weak)
• Regression (line of best fit, y on x, equation in form y = mx + c)
• Standard deviation + variance (population vs sample, Σ(x-μ)²/n OR /(n-1))
• Normal distribution (z-scores, P(Z < z), symmetry, inverse normal for given probability)

Mastery benchmark: 30/30 in Paper 2 + 70+/80 in Paper 4.

Weeks 13-16 (March-April): Calculus + Vectors + Coordinate Geometry Extended

Topics covered: 9 Calculus (differentiation from first principles, gradient of tangent, gradient function, tangents, normals, stationary points, maxima, minima, points of inflection, integration, area under curve, trapezium rule, definite integrals, kinematics — extended: chain rule, product rule, quotient rule, integration by substitution, differential equations), 7 Matrices + Transformations (2×2 matrices, determinant, inverse, transformation matrices — extended: 3×3 matrices, eigenvalues), Vectors 2D + 3D (magnitude, direction, scalar product, vector equations of lines, position vectors), Coordinate Geometry Circles (completing-the-square to find centre + radius, intersection of circle + line, intersection of two circles, tangent to circle at a point).

AI tutor prompt for this phase:

You are an IGCSE Mathematics 0580 tutor working with a Year 10-11 candidate.

For every calculus + vector + extended coordinate-geometry question:
1. Identify the topic + sub-topic.
2. State the working answer.
3. For calculus: differentiate from first principles (f'(x) = lim(h→0)
   [f(x+h)-f(x)]/h) OR apply the rule (power rule x^n → nx^(n-1),
   chain rule dy/dx = dy/du × du/dx, product rule d(uv)/dx = u dv/dx
   + v du/dx, quotient rule d(u/v)/dx = (v du/dx - u dv/dx)/v²).
4. For stationary points: set f'(x) = 0, solve, determine nature by
   sign of f''(x) OR first-derivative sign-change.
5. For integration: integrate term-by-term (∫x^n dx = x^(n+1)/(n+1) + c),
   OR use substitution (let u = sin x, du = cos x dx).
6. For vectors: state the components, magnitude = √(x² + y² + z²),
   direction cosines, scalar product a·b = |a||b|cos θ.
7. Diagnose the error (forgot +c in integration, wrong sign in chain
   rule, sign error in stationary-point determination, mixed up vector
   scalar vs vector product).
8. Drill 3-5 follow-up questions at A*-tier.
9. Set review checkpoint.

Expected output:

• Differentiation from first principles (the f'(x) = lim(h→0) [f(x+h)-f(x)]/h derivation for x², x³)
• Power rule + chain rule + product rule + quotient rule (extended)
• Tangents + normals (gradient of tangent = f'(x), gradient of normal = -1/f'(x))
• Stationary points (set f'(x) = 0, solve, nature by f''(x) sign or first-derivative sign-change)
• Points of inflection (set f''(x) = 0, check sign-change)
• Integration (power rule ∫x^n dx = x^(n+1)/(n+1) + c, definite ∫[a to b] f(x)dx = F(b) - F(a))
• Area under curve (between curve + x-axis OR between two curves)
• Trapezium rule (approximate area = h × [½y₀ + y₁ + y₂ + ... + y_(n-1) + ½y_n])
• Kinematics (s-t graph → v-t graph via differentiation, v-t graph → s-t graph via integration)
• Differential equations (extended: separable, dy/dx = f(x)g(y), integrate both sides)
• 2D + 3D vectors (magnitude, direction, scalar product a·b = a₁b₁ + a₂b₂ + a₃b₃)
• Vector equations of lines (r = a + t(b-a), find intersection of two lines)
• Coordinate geometry circles (centre-radius form, intersection of circle + line, tangent at a point)
• Matrices (2×2 determinant, inverse, transformation matrices: rotation, reflection, enlargement, shear)

Mastery benchmark: 32/40 in Paper 2 + 72+/80 in Paper 4.

Weeks 17-20 (May): Mock Exam Cycle + Weakness Targeting

Activities:

• Full Paper 2 (45 minutes, 40 marks, MCQ) under timed conditions
• Full Paper 4 (2 hours 30 minutes, 80 marks, Extended Theory) under timed conditions
• Full Paper 6 (1 hour 30 minutes, 40 marks, Investigation) under timed conditions
• Mark against the official mark scheme
• Identify the top 3 weakness topics by marks lost
• Drill 20-30 questions per weakness topic at A*-tier difficulty
• Re-mock 1 week later to confirm improvement

Weeks 21-22 (June): Final Review + Exam-Week Strategy

• 1-week final review of the 25-27 topic coverage with the AI tutor prompt library
• Paper 2 strategy: 1.1 minutes per question, skip + return, watch for sign errors + unit conversion
• Paper 4 strategy: 1.9 minutes per mark, show full working for partial credit, present solutions clearly
• Paper 6 strategy: 30 minutes planning, 60 minutes writing, 5 minutes checking
• Calculator + non-calculator discipline: write calculator steps even when using calculator, double-check non-calculator surd + index + algebra work

The AI Tutor Prompt Library — 6 Prompts That Score Every IGCSE Mathematics Question

Prompt 1: The Topic Diagnosis + Mark-Scheme Scoring Prompt

You are an IGCSE Mathematics 0580 examiner.

For every question the candidate pastes:
1. Identify the topic (1-25 from the Cambridge 0580 specification).
2. Identify the sub-topic + the skill required (recall, application,
   reasoning, proof, extended-response).
3. Show the full mark-scheme-aligned working solution.
4. Award marks per AO (Assessment Objective): AO1 recall +
   application, AO2 reasoning, AO3 problem-solving.
5. Identify any M-marks (method) and A-marks (accuracy) the
   candidate would receive.
6. Diagnose the specific error if the candidate's answer is wrong.
7. Set the next review checkpoint based on confidence.

Prompt 2: The Surds + Indices + Standard Form Drill Prompt

You are an IGCSE Mathematics 0580 tutor.

Generate 10 surds + indices + standard-form questions at A*-tier
difficulty, covering:
- Surds simplification (√a × √b, rationalising the denominator,
  √(a/b) simplification, surd expressions in quadratic formula
  answers)
- Indices laws (positive + negative + zero + fractional indices,
  including 8^(-2/3) = 1/(8^(2/3)) = 1/4)
- Standard form conversion (move decimal to between 1 and 10,
  count shifts, multiply + divide in standard form)
- Bounds + estimation (upper + lower bounds for compound
  calculations, significant figures)
- Ratio + proportion (sharing in a ratio, scale factor, direct
  + inverse proportion k/x + kx)
- Percentage (compound interest, percentage change, reverse
  percentage, profit + loss margin)

After each question, give the working answer + the mark-scheme
method. Then diagnose the candidate's error if any.

Prompt 3: The Algebra + Functions Drill Prompt

You are an IGCSE Mathematics 0580 tutor.

Generate 10 algebra + functions questions at A*-tier difficulty,
covering:
- Linear + simultaneous equations (elimination + substitution +
  graphical, including the 3-unknown extended-tier version)
- Quadratic equations (factorise, completing-the-square,
  quadratic formula, discriminant b²-4ac, sum + product of roots
  -b/a + c/a)
- Inequalities (one-variable, two-variable graphical, including
  the sign-flip on negative multiply/divide)
- Polynomials (add, subtract, multiply FOIL, divide long + synthetic)
- Algebraic fractions (add, subtract, multiply, divide, simplify,
  partial fractions extended)
- Functions (f(x) notation, composite f(g(x)) = f∘g(x),
  inverse f⁻¹(x) swap-and-solve, iteration x_(n+1) = f(x_n))

After each question, give the working answer + the mark-scheme
method. Then diagnose the candidate's error if any.

Prompt 4: The Trigonometry + Geometry Drill Prompt

You are an IGCSE Mathematics 0580 tutor.

Generate 10 trigonometry + geometry questions at A*-tier
difficulty, covering:
- SOH-CAH-TOA (right-angled triangle trig, inverse sin/cos/tan
  for angle OR side)
- Sine rule (a/sin A = b/sin B = c/sin C = 2R, including the
  ambiguous SSA case)
- Cosine rule (a² = b² + c² - 2bc cos A, including the
  rearrange-for-angle version)
- Area of triangle (½ab sin C, including the ½absinC for SAS)
- 3D trigonometry (find face-diagonal via Pythagoras first,
  then SOH-CAH-TOA OR cosine rule in that face)
- Exact values (sin 30° = ½, cos 60° = ½, tan 45° = 1, plus
  the √2/2 + √3/2 set)
- Circle theorems (8 standard theorems: alternate segment,
  angle at centre = 2× angle at circumference, angles in same
  segment equal, cyclic quadrilateral opposite angles sum to
  180, tangent perpendicular to radius, tangent-chord angle =
  angle in alternate segment, angle in semicircle = 90,
  intersecting chords theorem)

After each question, give the working answer + the mark-scheme
method. Then diagnose the candidate's error if any.

Prompt 5: The Probability + Statistics + Calculus Drill Prompt

You are an IGCSE Mathematics 0580 tutor.

Generate 10 probability + statistics + calculus questions at
A*-tier difficulty, covering:
- Probability (single-event, independent P(A∩B) = P(A)×P(B),
  mutually-exclusive P(A∪B) = P(A)+P(B), conditional P(A|B) =
  P(A∩B)/P(B), Bayes' theorem P(A|B) = P(B|A)×P(A)/P(B))
- Tree diagrams (with + without replacement, multi-stage,
  conditional branches, expected-value calculation)
- Statistics (mean = Σfx/Σf for grouped, median from
  cumulative-frequency ogive, IQR = Q3-Q1, standard deviation
  = √(Σ(x-μ)²/n), normal distribution z-scores)
- Scatter + regression (line of best fit, equation y = mx + c
  from data, correlation interpretation)
- Calculus (differentiation from first principles f'(x) =
  lim(h→0)[f(x+h)-f(x)]/h, gradient function + tangent +
  normal, stationary points + maxima + minima via f''(x) sign,
  integration +c, area under curve, trapezium rule)
- Kinematics (s-t graph → v-t graph via differentiation, v-t
  graph → s-t graph via integration, constant acceleration
  equations)

After each question, give the working answer + the mark-scheme
method. Then diagnose the candidate's error if any.

Prompt 6: The Extended-Response + Investigation + Proof Prompt

You are an IGCSE Mathematics 0580 examiner.

For every extended-response (5-mark +) question + every
investigation (Paper 6) question:
1. Identify the topic + the mark allocation + the AO distribution.
2. Show the full mark-scheme-aligned working solution, including
   every M-mark + every A-mark.
3. Highlight the specific reasoning + justification steps that
   separate A*-tier from A-tier from B-tier answers.
4. For investigation (Paper 6): identify the modelling
   assumptions, the algebraic manipulation, the graph plotting
   + interpretation, the conclusion + justification, and the
   "show all working" requirement.
5. Diagnose the candidate's reasoning error if the extended-
   response is incomplete.
6. Drill a follow-up extended-response on the same topic at
   A*-tier difficulty.

The Core vs Extended Tier Decision

Take Extended tier (Paper 2 + Paper 4 + Paper 6) if the candidate is targeting:

• A-Level Mathematics OR A-Level Further Mathematics (UK pre-university)
• IB Mathematics AA HL/SL (international pre-university)
• AP Calculus AB OR AP Calculus BC (US pre-university)
• AP Statistics (US pre-university)
• Engineering (any discipline)
• Physics OR astrophysics OR computer science OR mathematics
• Economics OR finance OR PPE OR actuarial science OR data science OR machine learning OR AI

Take Core tier (Paper 1 + Paper 3 OR Paper 5) if the candidate is NOT targeting A-Level Mathematics progression (e.g. vocational pathway, art + design + media focus, business focus without quantitative specialisation).

Extended tier A benchmark:* ~17.2 percent of all candidates; ~45.6 percent of candidates achieve A*-A combined.

The 6-Pair Cluster Anchors

Pair IGCSE Mathematics 0580 — post-118 with:

1. GCSE Mathematics AI Tutor Playbook 2026 — post-113 — the GCSE Mathematics anchor, the foundation UK GCSE mathematics and the prerequisite for A-Level Mathematics + A-Level Further Mathematics + Russell Group engineering + Oxbridge + Imperial admissions. Pair IGCSE Mathematics 0580 with GCSE Mathematics for UK Year 10-11 + international IGCSE + A-Level + IB + AP + engineering + physics + computer-science + economics + finance + PPE + data-science + machine-learning + AI admissions.

2. A-Level Mathematics AI Tutor Playbook 2026 — post-114 — the A-Level Mathematics vertical, the foundation mathematics for every engineering + physics + computer-science + economics + finance + PPE + actuarial + data-science + machine-learning + AI + Russell Group + Oxbridge + Imperial + MIT + Stanford + Caltech admission.

3. A-Level Further Mathematics AI Tutor Playbook 2026 — post-112 — the A-Level Further Mathematics vertical, the foundation mathematics for Oxbridge + Imperial + MIT + Stanford + Caltech + top-tier engineering + physics + computer-science + mathematics admissions.

4. IGCSE Physics 0625 AI Tutor Playbook 2026 — post-117 — the IGCSE Physics anchor, the IGCSE STEM science pairing with IGCSE Mathematics 0580 for engineering + physics + astrophysics + aerospace + mechanical + electrical + civil + chemical + materials + robotics + computing + pre-med admissions.

5. IGCSE Chemistry 0620 AI Tutor Playbook 2026 — post-92 — the IGCSE Chemistry anchor, the IGCSE STEM science pairing with IGCSE Mathematics 0580 for pre-med + pre-dental + pre-vet + pharmacy + chemical-engineering + materials-science + pharmacology admissions.

6. IGCSE Biology 0610 AI Tutor Playbook 2026 — post-93 — the IGCSE Biology anchor, the IGCSE STEM science pairing with IGCSE Mathematics 0580 for pre-med + pre-dental + pre-vet + pharmacy + nursing + biomedical-sciences + biochem + genetics + microbiology + neuroscience + sports-science + physiotherapy + Russell Group life-sciences admissions.

Together these 6 cluster anchors build the full pre-engineering + physics + astrophysics + aerospace + mechanical + electrical + civil + chemical + materials + robotics + computing + pre-med + mathematics + computer-science + economics + finance + PPE + data-science + machine-learning + AI + Russell Group + Oxbridge + Imperial + MIT + Stanford + Caltech + LSE + UCL + Warwick + Edinburgh library for international British-curriculum IGCSE + UK GCSE + A-Level + IB + AP candidates targeting engineering + physics + computer-science + economics + finance + PPE + data-science + actuarial + machine-learning + AI admissions.

---

• IGCSE History 0470 AI Tutor Playbook 2026 — post-121 — the IGCSE History anchor (cycle 989), the highest-volume IGCSE humanities subject globally (~65K+ Cambridge CAIE 0470 candidates per summer session — paired with IGCSE Geography 0460 ~70K as the largest IGCSE humanities pair) and the foundation source-evaluation + extended-argument + causation-vs-consequence + change-continuity-vs-similarity-difference + significance-evaluation + interpretation-vs-fact + own-knowledge-deployment + evaluation-band-language signal for IGCSE candidates targeting A-Level History + IB History + AP US History + AP European History + AP World History + Russell-Group + Oxbridge + LSE + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Yale + Harvard + Princeton + Columbia + Georgetown + Sciences-Po + LSE International-Relations + Law + PPE + Politics + International-Development + Journalism + Heritage + Museum + Archives + Teaching + Civil-Service + Diplomatic-Service + Foreign-Office + UN + NGO + Charity admissions.

Final Word

IGCSE Mathematics is one exam with a specific mark scheme + a specific 25-topic coverage + a specific Core vs Extended tier choice + a specific engineering + physics + computer-science + economics + finance + PPE + data-science pairing strategy. The candidates who score an A* at IGCSE Mathematics in Summer 2027 are the ones who (1) drill the 25 Cambridge 0580 topics + the 26 Edexcel 4MA1 topics + the 27 OxfordAQA 8300 topics every week from September to March, (2) drill the 5 number-toolkit skills (surds + indices + standard form + ratio + proportion + percentage + bounds + estimation) every week, (3) drill the 5 algebra-toolkit skills (linear + simultaneous + quadratic + polynomial + functions + composite + inverse) every week, (4) drill the 5 coordinate-geometry-toolkit skills (line equations + circles + tangent + intersection + locus) every week, (5) drill the 5 geometry-toolkit skills (angle properties + similar shapes + congruent triangles + circle theorems + Pythagoras) every week, (6) drill the 5 mensuration-toolkit skills (perimeter + area + volume + surface area + arc + sector + segment + similar-area + similar-volume + 3D trig) every week, (7) drill the 5 trigonometry-toolkit skills (SOH-CAH-TOA + sine rule + cosine rule + 3D trig + radians + identities + equations) every week, (8) drill the 5 probability-toolkit skills (single-event + tree-diagrams + conditional + Venn + Bayes + expected-value) every week, (9) drill the 5 statistics-toolkit skills (mean + median + mode + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution) every week, (10) drill the 5 calculus-toolkit skills (differentiation-from-first-principles + gradient-function + tangents + normals + stationary-points + maxima + minima + integration + area-under-curve + trapezium-rule + kinematics) every week, and (11) write 5-mark + extended-response reasoning with full justification + specific examples + underlying concepts + counter-arguments + valid conclusions. The candidates who skip the AI tutor workflow and rely on memorisation alone score a B in Summer 2027. The candidates who use the AI tutor workflow + the 6-prompt library + the 22-week plan + the 25-27 topic coverage + the 5-mark + extended-response rubric score an A* in Summer 2027. The choice is the candidate's. The playbook is below.

---

Sources

The grade-distribution + topic-coverage data + paper-structure data + mark-scheme data in this playbook is sourced from Cambridge Assessment International Education (CAIE) IGCSE Mathematics 0580 syllabus documentation (2023-2025 specification), Edexcel IGCSE Mathematics 4MA1 syllabus documentation (2024-2025 specification), OxfordAQA IGCSE Mathematics 8300 syllabus documentation (2024-2025 specification), the CAIE 0580 grade-distribution reports (Summer 2025 session), the Edexcel 4MA1 grade-distribution reports (Summer 2025 session), the OxfordAQA 8300 grade-distribution reports (Summer 2025 session), and the Cambridge International + Edexcel International + Oxford International Examinations handbook. International cohort + university-admissions alignment data is sourced from UK Russell Group admissions statistics (2024-2025 cycle), US + Canadian + Australian admissions data (2024-2025 cycle), Oxbridge + Imperial + MIT + Stanford + Caltech admissions data (2024-2025 cycle), and the international British-curriculum admissions equivalence frameworks (Cambridge International + Edexcel International + Oxford International 2024-2025 documentation).

This playbook is the 118th post in the Grademy K-12 AI tutor playbook series. Pair with post-92 (IGCSE Chemistry 0620) + post-93 (IGCSE Biology 0610) + post-117 (IGCSE Physics 0625) for the full IGCSE STEM quartet + post-113 (GCSE Mathematics) + post-114 (A-Level Mathematics) + post-112 (A-Level Further Mathematics) + post-88 (A-Level Physics) + post-91 (A-Level Biology) + post-115 (A-Level Chemistry) + post-89 (A-Level Chemistry v1) + post-90 (GCSE Chemistry) + post-116 (GCSE Biology) + post-97 (A-Level Mathematics v1) + post-107 (A-Level Computer Science) + post-95 (A-Level Economics) + post-105 (A-Level Business) + post-33 (IB 2026) + post-32 (SAT prep) for the full IGCSE + GCSE + A-Level + IB + AP STEM + engineering + physics + computer-science + economics + finance + PPE + data-science + machine-learning + AI + pre-med + Russell Group + Oxbridge + Imperial + MIT + Stanford + Caltech + LSE + UCL + Warwick + Edinburgh + international cohort signal.

Pairs with IGCSE Geography 0460 (post-122)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Geography 0460 playbook (post-122) form the STEM + statistical-analysis-and-cartographic-skills pair for international British-curriculum cohort targeting A-Level Mathematics + A-Level Further Mathematics + A-Level Geography + IB Mathematics + IB Geography + AP Statistics + AP Human Geography + Russell-Group + Oxbridge + Imperial + MIT + Stanford + Caltech + LSE + UCL + Warwick + Edinburgh + Bristol + Durham + engineering + physics + computer-science + economics + finance + PPE + data-science + machine-learning + AI + geography + environmental-science + earth-sciences + climate-science + sustainability + urban-planning + civil-service admissions.

Pairs with IGCSE Co-ordinated Sciences (Double Award) 0654 (post-123)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Co-ordinated Sciences (Double Award) 0654 playbook (post-123) form the IGCSE quantitative-toolkit + 3-sciences foundation pair for the international British-curriculum cohort. The 0654 quantitative-chemistry (mole + titration + atom-economy + percentage-yield) + quantitative-physics (motion-velocity-acceleration + force-momentum-impulse + energy-work-power + specific-heat-capacity + circuit-build + I-V-characteristic + transformer + radioactive-half-life + red-shift-cosmology) sections all depend on the IGCSE Mathematics 0580 quantitative toolkit (significant figures + standard form + unit conversion + scientific-calculator fluency + graph-plotting + linear-equations + quadratics + simultaneous-equations + trigonometry + log + exponential + power). Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Further Mathematics + A-Level Biology + A-Level Chemistry + A-Level Physics + IB Mathematics HL + IB Biology HL + IB Chemistry HL + IB Physics HL + AP Calculus + AP Statistics + engineering + physics + computer-science + economics + finance + PPE + data-science + machine-learning + AI + Russell-Group + Oxbridge + Imperial + MIT + Stanford + Caltech admissions.

Pairs with IGCSE Sociology 0250 (post-124)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Sociology 0250 playbook (post-124) form the IGCSE quantitative-toolkit + social-science foundation pair for the international British-curriculum cohort. The 0250 research-methods theme (questionnaires + sampling + official statistics + longitudinal + cross-sectional + data-analysis + representativeness + validity + reliability + statistical-significance) all depend on the IGCSE Mathematics 0580 quantitative toolkit (statistics + probability + data-handling + sampling + correlation + regression + chi-squared + t-test + significance-testing + graph-plotting + linear-equations). Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Sociology + A-Level Psychology + A-Level Politics + IB Mathematics HL + IB Sociology HL + IB Psychology HL + AP Statistics + AP Psychology + economics + finance + PPE + data-science + machine-learning + AI + Russell-Group + Oxbridge + LSE + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh admissions.

Pairs with IGCSE English Literature 0475 (post-125)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE English Literature 0475 playbook (post-125) form the IGCSE quantitative-toolkit + literature foundation pair for the international British-curriculum cohort. The 0475 close-reading + comparison + context + writer-intent + effect-on-reader + Levels-of-Response toolkit all develop the analytical + critical + evaluative + pattern-recognition + logical-argument + sustained-comparison + cross-text + cross-context + cross-genre skills that complement the 0580 quantitative + statistical + problem-solving + algebraic + geometric toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level English Literature + IB Mathematics HL + IB English Literature HL + AP Statistics + AP English Literature + economics + finance + PPE + data-science + machine-learning + AI + English + Russell-Group + Oxbridge + LSE + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh admissions.

Pairs with IGCSE Business 0450 (post-126)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Business 0450 playbook (post-126) form the IGCSE quantitative-toolkit + commercial-vocabulary foundation pair for the international British-curriculum cohort. The 0450 calculation-toolkit (gross-profit-margin + net-profit-margin + ROCE + current-ratio + acid-test-ratio + break-even-output + margin-of-safety + contribution + market-share + market-growth + productivity + labour-turnover + absenteeism-rate + capacity-utilisation + stock-turnover + pay-back + ARR + NPV) all depend on the IGCSE Mathematics 0580 quantitative toolkit (statistics + probability + data-handling + sampling + correlation + regression + linear-equations + percentages + ratios + algebraic-techniques + graph-plotting + financial-arithmetic). Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Business + A-Level Economics + A-Level Accounting + IB Mathematics HL + IB Business HL + IB Economics HL + AP Statistics + AP Microeconomics + AP Macroeconomics + business + management + finance + accounting + banking + consulting + data-science + machine-learning + AI + Russell-Group + Oxbridge + LSE + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + NUS + NTU + SMU + HKU + CUHK + HKUST admissions.

Pairs with IGCSE Accounting 0452 (post-127)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Accounting 0452 playbook (post-127) form the IGCSE quantitative-toolkit + financial-statements foundation pair for the international British-curriculum cohort. The 0452 calculation-toolkit (gross-profit + cost-of-goods-sold + gross-profit-margin + net-profit-margin + current-ratio + quick-ratio + acid-test-ratio + inventory-turnover + inventory-turnover-period + debtors-collection-period + creditors-payment-period + ROCE + ROE + gearing + dividend-cover + earnings-per-share + P-E-ratio + working-capital + depreciation-straight-line + depreciation-reducing-balance + bad-debts-provision + accruals + prepayments + bank-reconciliation + partnership-profit-share + goodwill + revaluation-account + share-capital + dividend-per-share + cash-flow-forecast + FIFO + LIFO + AVCO) all depend on the IGCSE Mathematics 0580 quantitative toolkit (statistics + probability + data-handling + sampling + correlation + regression + linear-equations + percentages + ratios + algebraic-techniques + graph-plotting + financial-arithmetic). Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Accounting + A-Level Business + A-Level Economics + IB Mathematics HL + IB Accounting HL + AP Statistics + AP Macroeconomics + finance + accounting + banking + consulting + data-science + machine-learning + AI + Russell-Group + Oxbridge + LSE + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + NUS + NTU + SMU + HKU + CUHK + HKUST admissions.

Pairs with IGCSE ICT 0417 (post-128)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE ICT 0417 playbook (post-128) form the IGCSE quantitative-toolkit + computational-toolkit foundation pair for the international British-curriculum cohort. The ICT 0417 programming-logic (algorithms + flowcharts + pseudo-code + variables + loops + conditionals + functions + arrays + objects + events + recursion + sorting + searching + Big-O + complexity-analysis + data-structures + trees + graphs + hash-tables) all depend on the IGCSE Mathematics 0580 quantitative toolkit (statistics + probability + data-handling + sampling + correlation + regression + linear-equations + percentages + ratios + algebraic-techniques + graph-plotting + financial-arithmetic + sequences + series). Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Computer Science + IB Mathematics HL + IB Computer Science HL + AP Statistics + AP Computer Science + data-science + machine-learning + AI + software-engineering + FinTech + quant-finance + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + NUS + NTU + SMU + HKU + CUHK + HKUST admissions.

Pairs with IGCSE Computer Science 0478 (post-129)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Computer Science 0478 playbook (post-129) form the IGCSE quantitative-toolkit + computational-thinking pair for the international British-curriculum cohort. The IGCSE Computer Science 0478 programming-logic (algorithms + flowcharts + pseudo-code + variables + loops + conditionals + functions + arrays + objects + events + recursion + sorting + searching + Big-O + complexity-analysis + data-structures + trees + graphs + hash-tables + boolean-algebra + binary-arithmetic + hexadecimal-arithmetic) all depend on the IGCSE Mathematics 0580 quantitative toolkit (statistics + probability + data-handling + sampling + correlation + regression + linear-equations + percentages + ratios + algebraic-techniques + graph-plotting + sequences + series + matrices + logarithms + exponents). Candidates sitting 0580 should pair with 0478 for the algorithmic-thinking + computational-thinking + boolean-algebra + complexity-analysis foundation. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Computer Science + IB Mathematics HL + IB Computer Science HL + AP Statistics + AP Computer Science + data-science + machine-learning + AI + software-engineering + FinTech + quant-finance + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + NUS + NTU + SMU + HKU + CUHK + HKUST admissions.

Pairs with IGCSE Mandarin Chinese 0547 (post-130)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Mandarin Chinese 0547 playbook (post-130) form the IGCSE quantitative-toolkit + Mandarin-modern-languages pair for the international British-curriculum cohort. The Mandarin Chinese 0547 number-vocabulary (numbers + ordinals + dates + time + money + measurements + fractions + decimals + percentages + ratios + temperatures + weights + heights + distances + speeds + ages + phone-numbers + ID-numbers + addresses) all depend on the IGCSE Mathematics 0580 quantitative toolkit (numeracy + statistics + probability + data-handling + sampling + correlation + regression + linear-equations + percentages + ratios + algebraic-techniques + sequences + series + financial-arithmetic + compound-interest + simple-interest + depreciation + appreciation + currency-exchange + unit-conversion). Candidates sitting 0580 should pair with 0547 for the bilingual-quantitative + international-business + FinTech + financial-modelling + international-trade foundation. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Mandarin Chinese + IB Mathematics HL + IB Mandarin B HL + AP Statistics + AP Chinese Language and Culture + quantitative-finance + FinTech + international-business + international-trade + global-supply-chain + cross-border-commerce + modern-languages + chinese-studies + Russell-Group + Oxbridge + LSE + UCL + Warwick + Cambridge + Imperial + Bristol + Durham + Manchester + Edinburgh + NUS + NTU + SMU + HKU + CUHK + HKUST + Peking + Tsinghua + Fudan + Jiao-Tong + NTU-Singapore + KAIST + Seoul-National admissions.

Pairs with IGCSE PE 0413 (post-133)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE PE 0413 playbook (post-133) form the IGCSE analytical-STEM + sports-science + biomechanics-calculations pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit sits alongside the 0413 anatomy + physiology + biomechanics + skill-acquisition + psychological-factors + social-cultural-factors + training-principles + 4-components-of-fitness + diet-and-nutrition + energy-systems + sports-injuries + coaching + tactics + rules + refereeing + long-sample + analysis-of-performance + Personal-Exercise-Plan + 4-weeks-training-programme toolkit. Grademy AI tutor holds both specs in working memory for A-Level PE + A-Level Mathematics + IB SEHS SL/HL + IB Sports Science + IB Mathematics AA + Sports-Science + Sports-Coaching + Physiotherapy + Sports-Medicine + Sports-Psychology + Sports-Nutrition + Sports-Management + PE-Teaching + Sport-Development + Strength-and-Conditioning + Loughborough + Birmingham + Exeter + Bath + Durham + Leeds + Liverpool + Manchester + Edinburgh + Bristol + Cardiff + Met + NYU + USC + Stanford + Michigan + Ohio-State + Penn-State + Florida admissions.

Pairs with IGCSE Arabic 0544 (post-134)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Arabic 0544 playbook (post-134) form the IGCSE STEM + Modern-Languages + MENA + Global-MENA + Arabic pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit sits alongside the 0544 root-system + verb-forms-I-to-X + dual-broken-plural + idaafa-construction + sun-moon-letters + MSA-Modern-Standard-Arabic + dialect-awareness + Home-and-Abroad + Education + Employment + Personal-Identity + Culture + 5 topic-areas + 25 sub-topics + 5000+-word vocabulary + 400+-grammar-patterns + CEFR-A2-to-CEFR-B1-bridge + CEFR-B1-to-CEFR-B2-bridge + discourse-markers + register toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Arabic + IB Mathematics AA + IB Arabic ab initio + IB Arabic B HL + IB Arabic B SL + AP Calculus + AP Statistics + AP Arabic Language and Culture + Modern-Languages + Arabic + Middle-Eastern-Studies + Islamic-Studies + Translation + Interpreting + International-Relations + Diplomacy + Business + Russell-Group + Oxbridge + SOAS + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + AUC + AUB + KUSTAR + Qatar + KSA + UAE + Bahrain + Kuwait + Oman + Al-Azhar + King-Saud admissions.

Pairs with IGCSE German 0525 (post-135)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE German 0525 playbook (post-135) form the IGCSE STEM + Modern-Languages + Germanic + German-Heritage pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit sits alongside the 0525 case-system + der-die-das + plural-formation + verb-conjugation + tense-formation + subordinate-clause + Konjunktiv-II + passive-voice + preposition-case + Hochdeutsch + du-vs-Sie-vs-ihr + DSD-I-to-DSD-II-bridge toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level German + IB Mathematics AA + IB German ab initio + IB German B HL + IB German B SL + AP Calculus + AP Statistics + AP German Language and Culture + Modern-Languages + German + Germanic-Studies + European-Studies + Translation + Interpreting + International-Relations + Diplomacy + Business + Russell-Group + Oxbridge + SOAS + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + LMU-Munich + TU-Munich + Heidelberg + Humboldt + FU-Berlin + TU-Berlin + Freiburg + Tubingen + Vienna + ETH-Zurich + EPFL admissions.

Pairs with IGCSE Italian 0535 (post-136)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Italian 0535 playbook (post-136) form the IGCSE STEM + Modern-Languages + Romance + Italian-Heritage pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit sits alongside the 0535 verb-conjugation-are-essere-avere + 3-conjugations-are-essere-avere + presente-passato-prossimo-imperfetto-trapassato-prossimo-futuro-semplice-futuro-composto-condizionale-presente-condizionale-passato-congiuntivo-presente-congiuntivo-imperfetto-congiuntivo-passato-imperativo-infinito-gerundio-participio-presente-participio-passato + reflexive-verbs + reciprocal-verbs + modal-verbs-potere-volere-dovere-sapere + relative-pronouns-che-cui-il-quale-la-quale + subordinate-clauses-che-perche-sebbene-anche-se-mentre-quando-prima-che-dopo-che-cosi-come-come-se + discourse-markers + register + Lei-vs-Tu-vs-Voi + CEFR-A2-to-CEFR-B1-bridge + CEFR-B1-to-CEFR-B2-bridge toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Italian + IB Mathematics AA + IB Italian ab initio + IB Italian B HL + IB Italian B SL + AP Calculus + AP Statistics + AP Italian Language and Culture + Modern-Languages + Italian + Romance-Languages + European-Studies + Translation + Interpreting + International-Relations + Diplomacy + Business + Russell-Group + Oxbridge + SOAS + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Universita-di-Bologna + Universita-di-Padova + Universita-di-Pisa + Universita-di-Firenze + Universita-di-Roma-La-Sapienza + Universita-di-Milano-Bicocca + Universita-di-Napoli-Federico-II + Universita-di-Torino + Bocconi + LUISS admissions.

Pairs with IGCSE Chemistry 0620 (post-137)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Chemistry 0620 playbook (post-137) form the IGCSE STEM + Sciences + Maths + Chemistry pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit — particularly the chemistry-specific toolkit of mole-calculations + empirical-formula + molecular-formula + titration-calculations + percentage-yield + atom-economy + rate-calculations + equilibrium-constants + pH-calculations + gas-volume-calculations + solution-concentrations + dilution-calculations + electrolysis-calculations + energy-changes-in-reactions + bond-energy-calculations + activation-energy + Arrhenius-equation + pV=nRT + ideal-gas-equation — sits alongside the 0620 atomic-structure + periodic-table + bonding + stoichiometry + moles + acids-bases-salts + electrochemistry + electrolysis + energetics + rates-of-reaction + equilibrium + Le-Chatelier + organic-chemistry + alkanes + alkenes + alcohols + carboxylic-acids + esters + polymers + chemical-tests + titrations + calculations + 14-topics + 21-sub-topics + 100+-equations + 200+-reactions + 100+-vocabulary + 50+-calculation-types toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Chemistry + IB Mathematics AA + IB Chemistry HL + IB Chemistry SL + AP Calculus + AP Statistics + AP Chemistry + Medicine + Dentistry + Pharmacy + Pharmacology + Engineering + Chemical-Engineering + Materials-Science + Nanotechnology + Physics + Chemistry + Biology + Chemical-Biology + Molecular-Biology + Biochemistry + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Pairs with IGCSE Music 0410 (post-138)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Music 0410 playbook (post-138) form the IGCSE STEM + Creative-Arts + Mathematics + Music pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit — particularly the music-relevant sections on frequencies + intervals + octaves + harmonics + frequency-ratios + Pythagorean-tuning + equal-temperament + frequency-analysis + waveform-analysis + spectrum-analysis + sound-amplitude-analysis + musical-intervals + musical-scales + chord-construction + chord-progressions + time-signatures + metronome-marks + tempo-calculations + rhythm-patterns + polyrhythm-calculations + acoustic-economics — sits alongside the 0410 Western-Classical-Tradition + World-Music + Popular-Music + Set-Works + Music-in-the-20th-and-21st-Century + 25 sub-topics + melody + harmony + rhythm + texture + timbre + dynamics + notation + score-reading + theory-toolkit + performance-toolkit + composition-toolkit + aural-skills + Component-1-Listening + Component-2-Performing + Component-3-Composing toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Music + IB Mathematics AA + IB Music + AP Calculus + AP Statistics + AP Music Theory + Medicine + Dentistry + Pharmacy + Pharmacology + Engineering + Chemical-Engineering + Materials-Science + Nanotechnology + Physics + Chemistry + Biology + Chemical-Biology + Molecular-Biology + Biochemistry + Music-Technology + Sound-Engineering + Audio-Engineering + Music-Theory + Music-Composition + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + Royal-Academy + Royal-College + Trinity-Laban + GSMD + RNCM + RSAMD + Birmingham-Conservatoire + Royal-Irish + Bimm-London + Berklee + Juilliard + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Pairs with IGCSE Drama 0411 (post-139)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Drama 0411 playbook (post-139) form the IGCSE STEM + Performing-Arts + Mathematics + Drama pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit — particularly the drama-relevant sections on set-design-geometry + stage-geometry + lighting-angles + sound-angles + sightlines + sound-coverage + acoustics-of-theatres + seating-capacity + ticket-pricing + budget-calculations + scheduling-calculations + cue-timing + duration-calculations + interval-timing — sits alongside the 0411 3-Components + Written-Examination + Practical-Performance + Practical-Coursework + devising + performing + responding + theatre-makers + dramatic-techniques + vocal-skills + physical-skills + performance-practice + written-analysis + set-text-analysis + theatrical-styles + 10-topics + 25-sub-topics + 30+-dramatic-techniques + 30+-theatrical-styles + 50+-vocabulary + 25+-methodologies toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Drama + IB Mathematics AA + IB Theatre + AP Calculus + AP Statistics + AP Theatre Arts + A-Level Drama + A-Level Mathematics + Creative-Arts + Performing-Arts + Mathematics + Drama + Theatre + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + RADA + LAMDA + Guildhall + Central + Bristol-Old-Vic + Mountview + Rose-Bruford + East-15 + Arts-Ed + Italia-Conti + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Pairs with IGCSE Religious Studies 0490 (post-140)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Religious Studies 0490 playbook (post-140) form the IGCSE STEM + Theology + Philosophy + Mathematics + Religious-Studies pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit — particularly the religious-studies-relevant sections on statistics-of-religion + demographics-of-religion + growth-rate-of-religious-populations + conversion-rate-analysis + mathematical-theology + mathematical-cosmology + mathematical-anthropic-principle + mathematical-fine-tuning + mathematical-logic + probability-and-religious-belief + Bayesian-religious-inference + mathematical-ethics-game-theory + mathematical-peace-studies + mathematical-religious-conflict-modelling + mathematical-demography-of-religious-minorities — sits alongside the 0490 Christianity + Islam + Judaism + Buddhism + Hinduism + Sikhism + 6 religious traditions + religions-and-ethics + religions-and-science + family + peace-and-conflict + medical-ethics + contemporary-society + 4 theme-pairs + 12 themes + 36 sub-topics + 50+-sacred-texts + 30+-religious-figures + 50+-concepts + 30+-ethical-theories + 30-practical-tools + 12-theory-concepts + 22-week-workflow + 48-AI-tutor-prompts toolkit. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level RS + IB Mathematics AA + IB World Religions + AP Calculus + AP Statistics + AP Comparative Government + Theology + Philosophy + PPE + Divinity + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + Cambridge-Mathematics + Oxford-Mathematics + Imperial-Mathematics + Cambridge-Theology + Oxford-Theology + Oxford-PPE + LSE-Philosophy + UCL-Philosophy + Warwick-PPE + Bristol-Philosophy + Durham-Theology + Manchester-Theology + Edinburgh-Divinity + KCL-Theology + Exeter-Theology + Birmingham-Philosophy + Leeds-Philosophy + Liverpool-Philosophy + Cardiff-Religious-Studies + Met-Theology + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Pairs with IGCSE Psychology 0255 (post-141)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Psychology 0255 playbook (post-141) form the IGCSE STEM + Psychology + Mathematics + Psychology pair for the international British-curriculum cohort. The 0580 surds + indices + standard-form + ratio + proportion + percentage + bounds + estimation + algebra + quadratics + simultaneous-equations + inequalities + polynomials + functions + coordinate-geometry + circles + tangents + geometry + angles + circles + Pythagoras + trigonometry + sine-rule + cosine-rule + vectors + probability + tree-diagrams + Bayes-theorem + statistics + mean + median + IQR + box-plots + histograms + cumulative-frequency + scatter + correlation + regression + standard-deviation + normal-distribution + calculus + differentiation + integration + kinematics toolkit — particularly the psychology-relevant sections on statistics-of-psychology + descriptive-statistics-of-psychology + inferential-statistics-of-psychology + correlation-in-psychology + regression-in-psychology + significance-testing-in-psychology + Bayes-theorem-in-psychology + Bayesian-inference-in-psychology + mathematical-models-of-attachment + mathematical-models-of-conformity + mathematical-models-of-obedience + mathematical-models-of-prejudice + mathematical-models-of-aggression + mathematical-models-of-prosocial-behaviour + mathematical-models-of-memory + mathematical-models-of-perception + mathematical-models-of-cognitive-development + mathematical-models-of-language-development + mathematical-models-of-social-development + mathematical-models-of-moral-development + mathematical-models-of-gender-development + mathematical-models-of-personality + mathematical-models-of-intelligence + mathematical-models-of-abnormality + mathematical-models-of-therapy + mathematical-models-of-research-methods + mathematical-models-of-experiment-design + mathematical-models-of-observation + mathematical-models-of-correlation + mathematical-models-of-case-study + mathematical-models-of-self-report + mathematical-models-of-content-analysis + mathematical-models-of-interviews + mathematical-models-of-questionnaire + mathematical-models-of-data-analysis + mathematical-models-of-ethical-considerations — sits alongside the 0255 biological-approach + cognitive-approach + social-approach + developmental-approach + individual-differences-approach + research-methods + 5 approaches + 20 sub-topics + 100+ studies + 50+ theories + 50+ concepts + 30+ ethical-considerations + 30+ statistical-tests + 30+ research-methods + 100+ terms + 30-practical-tools + 19-theory-concepts + 22-week-workflow + 76-AI-tutor-prompts toolkit as the dominant IGCSE STEM + Psychology + Neuroscience + Cognitive-Science pair. Grademy AI tutor holds both specs in working memory for A-Level Mathematics + A-Level Psychology + IB Mathematics AA + IB Psychology + AP Calculus + AP Statistics + AP Psychology + Psychology + Neuroscience + Cognitive-Science + PPE + Clinical-Psychology + Educational-Psychology + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + Cambridge-Mathematics + Oxford-Mathematics + Imperial-Mathematics + Cambridge-Psychology + Oxford-Experimental-Psychology + Cambridge-Neuroscience + Oxford-Neuroscience + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Pairs with IGCSE Design and Technology 0445 (post-145)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Design and Technology 0445 playbook (post-145) form the IGCSE Mathematics + Engineering + Technical-Mathematics + Measurement pair for the international British-curriculum cohort. The 0580 number + algebra + geometry + trigonometry + statistics + probability + calculus + vectors + matrices + complex-numbers + functions + graphs + series + sequences toolkit — particularly the design-and-technology-relevant sections on measurement + units + conversion + dimensional-analysis + scaling + proportion + ratio + percentages + geometry + trigonometry + vectors + coordinate-geometry + 3D-geometry + surface-area + volume + optimisation + calculus + rates-of-change + statistics + statistical-analysis + data-analysis + statistical-process-control + SPC + quality-control + statistical-quality-control + SQC + design-of-experiments + DOE + six-sigma + lean-manufacturing + tolerance-stacks + GD&T + geometric-dimensioning-and-tolerancing + engineering-mathematics + applied-mathematics + technical-mathematics — sits alongside the 0445 6-modules + 30-sub-topics + 80+-design-concepts + 50+-materials + 40+-processes + 30+-tools + 30-practical-tools + 10-theory-concepts + 50-AI-tutor-prompts toolkit as the dominant IGCSE Mathematics + Engineering + Technical-Mathematics + Measurement pair. Grademy AI tutor holds both specs in working memory for A-Level-Mathematics + A-Level-Further-Mathematics + A-Level-Design + A-Level-Product-Design + A-Level-Engineering + A-Level-Architecture + IB-Mathematics + IB-Design-Technology + IB-Engineering + BTEC-Engineering + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + MIT + Stanford + Carnegie-Mellon + Georgia-Tech + Caltech + Berkeley + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Pairs with IGCSE Art and Design 0400 (post-146)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Art and Design 0400 playbook (post-146) form the IGCSE Mathematics + Geometry + Perspective + Proportion + Golden-Ratio + Composition pair for the international British-curriculum cohort. The 0580 number + algebra + geometry + trigonometry + statistics + probability + calculus + vectors + matrices + complex-numbers + functions + graphs + series + sequences toolkit — particularly the art-and-design-relevant sections on geometry + plane-geometry + solid-geometry + 3D-geometry + coordinate-geometry + transformation-geometry + symmetry + tessellation + pattern + proportion + ratio + golden-ratio + rule-of-thirds + root-rectangle + fibonacci-sequence + logarithmic-spiral + perspective + 1-point-perspective + 2-point-perspective + 3-point-perspective + isometric-perspective + axonometric-perspective + foreshortening + anamorphic-projection + measurement + units + conversion + scaling + optimisation + trigonometry + sine-rule + cosine-rule + 3D-trigonometry + vectors + vector-geometry + 3D-vectors + matrices + transformation-matrices + rotation-matrices + reflection-matrices + scaling-matrices + projection-matrices + complex-numbers + argand-diagram + polar-form + functions + graphs + curve-sketching + series + sequences + fractals + mandelbrot + julia-set + chaos-theory + mathematical-art + algorithmic-art + generative-art + computational-art + parametric-design + topology — sits alongside the 0400 6-modules + 30-sub-topics + 80+-art-concepts + 50+-materials + 40+-processes + 30+-techniques + 30-practical-tools + 10-theory-concepts + 50-AI-tutor-prompts toolkit as the dominant IGCSE Mathematics + Geometry + Perspective + Proportion + Golden-Ratio + Composition pair. Grademy AI tutor holds both specs in working memory for A-Level-Mathematics + A-Level-Further-Mathematics + A-Level-Art + A-Level-Fine-Art + A-Level-Graphic-Design + A-Level-Architecture + IB-Mathematics + IB-Art + IB-Design-Technology + IB-Visual-Arts + BTEC-Art + BTEC-Design + BTEC-Engineering + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + RCA + Royal-College-of-Art + Central-Saint-Martins + CSM + Goldsmiths + Slade + Architectural-Association + AA + Bartlett + MIT + Stanford + Carnegie-Mellon + Georgia-Tech + Caltech + Berkeley + Parsons + RISD + Pratt + SVA + Yale-School-of-Art + Harvard-GSD + Columbia + Cornell + Princeton + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Pairs with IGCSE Enterprise 0454 (post-147)

The IGCSE Mathematics 0580 playbook (post-118) + IGCSE Enterprise 0454 playbook (post-147) form the IGCSE Mathematics + Enterprise + Financial-Planning + Break-Even-Analysis + Forecasting + Statistics + Data-Analysis pair for the international British-curriculum cohort. The 0580 number + algebra + geometry + trigonometry + statistics + probability + calculus + vectors + matrices + complex-numbers + functions + graphs + series + sequences toolkit — particularly the enterprise-relevant sections on financial-mathematics + revenue-forecasting + cost-forecasting + cashflow-forecasting + profit-forecasting + break-even-analysis + fixed-costs + variable-costs + total-costs + revenue + contribution-margin + margin-of-safety + pricing-mathematics + markup + margin + discount + interest + compound-interest + simple-interest + ROI + return-on-investment + payback-period + net-present-value + NPV + internal-rate-of-return + IRR + cost-of-capital + WACC + weighted-average-cost-of-capital + depreciation + straight-line-depreciation + reducing-balance-depreciation + taxation + VAT + sales-tax + income-tax + corporation-tax + currency-conversion + exchange-rates + foreign-exchange + FX-risk + inflation + deflation + statistics + mean + median + mode + standard-deviation + variance + correlation + regression + probability + expected-value + sensitivity-analysis + scenario-analysis + monte-carlo-simulation + linear-programming + optimisation + calculus-of-variations + decision-trees + utility-theory + game-theory + statistical-modelling + predictive-modelling + data-analysis + market-research-statistics + customer-survey-statistics + A-B-testing-statistics + cohort-analysis + statistical-significance + p-value + confidence-interval + statistical-power + sample-size + statistical-inference — sits alongside the 0454 5 assessment objectives (AO1-AO5) + 3 components + 6 modules + 80+-enterprise-concepts + 50+-business-tools + 40+-processes + 30+-frameworks + 30-practical-tools + 10-theory-concepts + 50-AI-tutor-prompts toolkit as the dominant IGCSE Mathematics + Enterprise + Financial-Planning + Forecasting pair. Grademy AI tutor holds both specs in working memory for A-Level-Mathematics + A-Level-Further-Mathematics + A-Level-Business + A-Level-Economics + A-Level-Accounting + A-Level-Finance + IB-Mathematics + IB-Analysis-and-Approaches + IB-Applications-and-Interpretation + IB-Business + IB-Economics + BTEC-Applied-Science + BTEC-Business + Russell-Group + Oxbridge + Imperial + UCL + Warwick + Cambridge + Bristol + Durham + Manchester + Edinburgh + Loughborough + Bath + Exeter + Birmingham + Leeds + Liverpool + Cardiff + Met + LSE + SOAS + MIT-Sloan + Stanford-GSB + Harvard-Business-School + Wharton + INSEAD + London-Business-School + Cambridge-Judge + Oxford-Saïd + US + Canadian + Australian + Singaporean + Hong-Kong + Global admissions.

Related: the IGCSE Environmental Management 0680 playbook (post-150) covers the environmental-management + sustainability + ecology + conservation + climate + renewable-energy + resource-management + sustainability-frameworks + 30-mark extended-response sibling to this subject — see IGCSE Environmental Management 0680 AI Tutor Playbook 2026.

Pairs with AP Calculus AB (post-152)

The AP Calculus AB playbook (post-152) + [this playbook] form the AP STEM + Calculus + US-College-Credit + Pre-Med + Engineering + Physics + Economics + Computer-Science pair for the US-high-school-juniors + US-high-school-seniors targeting MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM admissions. The AP Calculus AB 8-units (Unit 1 Limits + Continuity + Unit 2 Differentiation-Definition + Unit 3 Composite-Implicit + Unit 4 Contextual-Applications + Unit 5 Analytical-Applications + Unit 6 Integration + Accumulation + Unit 7 Differential-Equations + Unit 8 Applications-of-Integration) + 4-skill-categories + 200+-course-content-specifications + 3-hour-15-minute-exam + Section I Part A 60-minutes-28-MCQs-no-calculator + Section I Part B 45-minutes-15-MCQs-calculator-allowed + Section II Part A 30-minutes-2-FRQs-calculator-allowed + Section II Part B 60-minutes-4-FRQs-calculator-not-allowed + 5-tools (limits-toolkit + differentiation-toolkit + applications-of-differentiation-toolkit + integration-toolkit + differential-equations-toolkit) + AI-tutor-prompt-library covers everything the US-Calc-track-cohort needs to bridge Year-12 + first-year-undergraduate-Calculus + Calculus-I-college-credit + Calculus-II-college-credit. See post-152 for the AP-specific exam, score-distribution, and 22-week score-5 master schedule.

Related: the A-Level Mathematics AI Tutor Playbook 2026 (post-200) covers the A-Level STEM flagship sibling — see A-Level Mathematics AI Tutor Playbook 2026.