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Nine modules · 30 tutorials · the complete OCR specification
The complete OCR GCSE Mathematics J560 specification, taught by simulacra of the mathematicians who built the subject. The course covers the six strands of the DfE subject content — Number, Algebra, Ratio and Proportion, Geometry and Measures, Probability, and Statistics — organised into nine modules that follow the specification's own topic structure. Each scholar leads the module where their work is most directly foundational: Pythagoras Simulacrum on number, Eratosthenes Simulacrum on ratio and proportion, Diophantus Simulacrum on algebraic expressions, Euler Simulacrum on equations, Gauss Simulacrum on graphs, Euclid Simulacrum on geometry, Archimedes Simulacrum on mensuration and trigonometry, Fermat Simulacrum on probability, and Fisher Simulacrum on statistics.
Three papers per tier (Foundation 1–3, Higher 4–6), each 1 hour 30 minutes, equal weight. One paper per tier is non-calculator. Content is presented in three progressive columns (Initial → Foundation → Higher). The modules can be taken in specification order or topic-by-topic for targeted revision.
Led by Pythagoras Simulacrum
Integers, primes, HCF and LCM · fractions, decimals and percentages · indices, surds and standard form · approximation, estimation and bounds. The foundations of numerical fluency.
Open module →Led by Eratosthenes of Cyrene Simulacrum
Ratio and division in a given ratio · direct and inverse proportion (algebraic forms at Higher) · growth and decay (compound interest, depreciation, exponential formulae).
Open module →Led by Diophantus of Alexandria Simulacrum
Collecting terms, expanding and factorising · completing the square and algebraic fractions (Higher) · substitution, rearrangement and the standard formulae required from memory.
Open module →Led by Leonhard Euler Simulacrum
Linear and quadratic equations · simultaneous equations and iteration · inequalities in one and two variables · functions, arithmetic and quadratic sequences, the nth term.
Open module →Led by Carl Friedrich Gauss Simulacrum
Plotting and sketching functions (linear through trigonometric) · straight line algebra (y = mx + c, parallel, perpendicular) · transformations of curves · interpreting real-world graphs (gradients as rates of change, areas under curves).
Open module →Led by Euclid Simulacrum
Conventions and constructions (ruler, compasses, loci) · angle facts and properties of polygons · circle theorems (angle at centre, angle in semicircle, cyclic quadrilateral, tangent-radius, alternate segment).
Open module →Led by Archimedes Simulacrum
Congruence and similarity · perimeter, area and volume of all standard shapes · Pythagoras and trigonometry (SOH CAH TOA, sine/cosine rules at Higher) · vectors (column notation, geometric proof).
Open module →Led by Pierre de Fermat Simulacrum
Probability scales and sample spaces · combined events, tree diagrams and Venn diagrams · conditional probability and set notation at Higher.
Open module →Led by Ronald Fisher Simulacrum
Data collection and representation (all diagram types including histograms with unequal class widths) · averages, scatter diagrams, box plots, correlation, and critical interpretation of statistical claims.
Open module →