Curriculum Overview:

A-Level Masterclass Program (24 Lessons)

Block 1: Pure Foundations, Mechanics & Statistics (Lessons 1–6)

• Week 1: Calculus Foundations — Differentiation Techniques

  • Focus: Differentiating polynomials, finding equations of tangents and normals, and classifying stationary points (maximum/minimum/inflection).

• Week 2: Trigonometric Identities & Solving Equations

  • Focus: Solving trigonometric equations in specific domains using key identities.

• Week 3: Integration & Area Under Curves

  • Focus: Indefinite and definite integrals, evaluating areas bounded by curves and axes, and fundamental integration rules.

• Week 4: Mechanics — Kinematics & SUVAT Equations

  • Focus: Applying constant acceleration formulas (SUVAT) in 1D and 2D, displacement-time/velocity-time graph interpretation, and calculus in kinematics.

• Week 5: Statistics — Binomial Distribution & Hypothesis Testing

  • Focus: Modelling with Binomial distributions, setting up null and alternative hypotheses, finding critical regions, and calculating p-values.

• Week 6: A-Level Exam Technique & Calculator Mastery

  • Focus: Step-by-step rigorous proof presentation, examiner traps, and leveraging the Casio fx-CG50 / fx-991EX for rapid probability and equation solving.

Block 2: Advanced Pure Calculus & Coordinate Geometry (Lessons 7–12)

• Week 7: Advanced Differentiation — Product, Quotient & Chain Rules

  • Focus: Mastering product, quotient, and chain rules, including implicit differentiation and parametric curves (x = f(t), y = g(t)).

• Week 8: Advanced Integration Techniques — Substitution & By Parts

  • Focus: Evaluating hard integrals using integration by substitution, integration by parts, and partial fraction decomposition.

• Week 9: Differential Equations & Mathematical Modelling

  • Focus: Setting up and solving first-order separable differential equations, applying initial conditions, and modelling growth/decay.

• Week 10: Logarithmic & Exponential Functions

  • Focus: Calculus of exponential base e and natural logarithms ln x, solving logarithmic equations, and transforming non-linear data into straight lines.

• Week 11: Advanced Trigonometry — Double Angle & $R\cos(x \pm \alpha)$

  • Focus: Applying double angle formula

• Week 12: Curve Sketching & Rational Functions (MAT/TMUA Style)

  • Focus: Rapidly sketching rational functions without a calculator—identifying vertical, horizontal, and oblique asymptotes, and behaviour

Block 3: Further Pure, Vectors & Rigorous Proof (Lessons 13–18)

• Week 13: 3D Vector Geometry & Scalar Product

  • Focus: Vector geometry in 3D, calculating angles between vectors using the dot/scalar product, line equations, and point intersections.

• Week 14: Formal Methods of Proof & Proof by Induction

  • Focus: Proof by Deduction, Exhaustion, Contradiction (e.g., infinitude of primes), and Mathematical Induction for summations and divisibility.

• Week 15: Sequences, Series & Binomial Expansion

  • Focus: Arithmetic and Geometric progressions (sum to infinity), sigma notation, and expanding (1+x)^n for fractional/negative indices.

• Week 16: Numerical Methods — Newton-Raphson & Trapezium Rule

  • Focus: Finding approximate roots using the Newton-Raphson method, analyzing failure cases, and estimating areas via the Trapezium Rule with error bounds.

• Week 17: Complex Numbers Intro (Argand Diagrams & Euler)

  • Focus: Imaginary unit i, solving z^2 + bz + c = 0, Argand plane representations, modulus-argument form, and Euler's relation

• Week 18: Small Angle Approximations & Radians

  • Focus: Arc length, sector area, and applying Taylor series small-angle approximationsto limiting trig problems.

Block 4: Applied Mechanics, Advanced Stats & University Entrance (Lessons 19–24)

• Week 19: Mechanics — Statics, Friction & Moments

  • Focus: Rigid bodies in static equilibrium, resolving forces in 2D, calculating moments, ladder friction problems, and limiting equilibrium.

• Week 20: Mechanics — Projectile Motion & 2D Vectors

  • Focus: Modeling 2D motion under gravity, deriving range, maximum height, and flight time equations, and using calculus for velocity/displacement vectors.

• Week 21: Statistics — Normal Distribution & Hypothesis Testing

  • Focus: Continuous random variables, standardising the normal distribution , finding unknown parameters, and 1-tail/2-tail hypothesis testing.

• Week 22: TMUA & MAT Paper 1 Logic & Multiple Choice Tactics

  • Focus: Assessing necessary vs. sufficient conditions, counter-examples, rapid logical elimination, and tackling non-calculator multiple-choice questions.

• Week 23: STEP Pure Mathematics & Long-Form Problem Solving

  • Focus: Deconstructing multi-step 20-minute Cambridge STEP-style problems, developing resilience when stuck, and constructing elegant line-by-line proof.

• Week 24: Grand Synoptic A Challenge & Oxbridge Interview Practice*

  • Focus: A 60-minute synoptic paper drawing on pure, mechanics, and statistics, followed by a live "thinking out loud" interview-style problem-solving demonstration.