GCSE Higher Masterclass Program (24 Lessons)

• When: Thursdays, 5:30 PM – 6:30 PM, commencing Thursday, 12th November

• Capped Numbers: To ensure personalised support

• Price: £15 per student / lesson (or £75 for a 6-Week Term Pass)

Block 1: High-Tariff Algebra & Geometry (Lessons 1–6)

• Week 1: Quadratic Mastery & Factoring

  • Focus: Factoring complex quadratics, applying the quadratic formula efficiently, and identifying key features on quadratic graphs.

• Week 2: Advanced Algebra — Rearranging Formulas

  • Focus: Isolating target variables when they appear inside fractions, under square roots, or twice in the expression (factoring out the subject).

• Week 3: 2D & 3D Trigonometry & Pythagoras

  • Focus: Moving beyond basic SOH CAH TOA into 3D prisms, pyramids, and applying the Sine/Cosine rules to non-right-angled triangles.

• Week 4: Simultaneous Equations (Linear vs. Non-Linear)

  • Focus: Solving simultaneous equations where one is quadratic (e.g., circle and line intersections) using substitution.

• Week 5: Conditional Probability & Set Notation

  • Focus: Master class on "without replacement" probability trees, two-way tables, and Venn diagrams and complement notation).

• Week 6: Exam Paper Walkthrough & Examiner Mark-Scheme Secrets

  • Focus: Breakdown of high-tariff 5-mark questions, how to pick up method marks when stuck, and avoiding common careless mistakes.

Block 2: Functions, Sequences & Non-Linear Graphs (Lessons 7–12)

• Week 7: Advanced Function Notation f(x), gf(x), f^-1(x)

  • Focus: Master composite functions fg(x) vs gf(x), algebraic inverse functions, and working with restricted domains and ranges.

• Week 8: Quadratic Sequences & Structural Derivations

  • Focus: Finding nth terms of quadratic sequences using second differences, and proving algebraically why the second difference equals 2a.

• Week 9: Graph Transformations

  • Focus: Visualizing and sketching translations, reflections, and stretches of non-specific function curves, identifying how turning points shift.

• Week 10: Circle Equations & Tangents

  • Focus: Finding equations of circles centered at the origin, determining points of intersection, and deriving equations of perpendicular tangent lines.

• Week 11: Iteration & Numerical Methods

  • Focus: Using iterative formulasto find approximate roots of complex equations, constructing cobweb diagrams, and testing root existence.

• Week 12: Inequalities & 2D Region Shading

  • Focus: Solving non-linear quadratic inequalities using sign charts or sketches, and shading complex linear/quadratic multi-region inequalities on 2D grids.

Block 3: Advanced Geometry, Vectors & Proof (Lessons 13–18)

• Week 13: Geometric Proof & Circle Theorems (Part 1)

  • Focus: Formal proofs for fundamental circle theorems (e.g., angle at center is twice angle at circumference) using isosceles triangle properties.

• Week 14: Harder Circle Theorems & Alternate Segment Theorem

  • Focus: Advanced multi-theorem proofs, applying the Alternate Segment Theorem, and solving non-routine Grade 9 geometric angle-chasing problems.

• Week 15: Vector Geometry — Arithmetic & Ratio Paths

  • Focus: Expressing paths along 2D shapes in terms of vectors, handling midpoints, ratio divisions, and vector arithmetic.

• Week 16: Vector Proofs & Collinearity

  • Focus: Proving 3 points lie on a straight line (collinear) using scalar multiples with shared points, and proving geometric shapes.

• Week 17: Sine & Cosine Graph Oscillations

  • Focus: Graphing y = sin x, y = cos x, and y = tan x, finding exact values without a calculator, and solving trig equations.

• Week 18: Area & Volume Scale Factors in 3D Shapes

  • Focus: Exploring length k, area k^2, and volume k^3 scale factors in frustums, truncated cones, and composite 3D solids.

Block 4: Calculus, Kinematics & Applied Olympiad Rigour (Lessons 19–24)

• Week 19: Gradients of Curves & Estimating Area (Trapezium Rule)

  • Focus: Estimating instantaneous rates of change using tangents to non-linear graphs, and calculating distance under velocity-time curves using the Trapezium Rule.

• Week 20: Introduction to Differentiation & Turning Points

  • Focus: Applying the power rule to derive gradients, and finding exact maximum/minimum turning points

• Week 21: Upper & Lower Bounds in Multi-Step Calculations

  • Focus: Calculating error intervals and evaluating maximum/minimum bounds in complex formulas

• Week 22: Advanced Combinatorics & The Product Rule for Counting

  • Focus: Systematic counting strategies (n x m), permutations (n!), and introductions to combinations for multi-stage selection puzzles.

• Week 23: UKMT Intermediate Olympiad Problem Solving

  • Focus: Tackling non-routine multi-topic questions from Hamilton/Maclaurin papers, training students to decompose unfamiliar problems without guidance.

• Week 24: Grand Synoptic Mock & Grade 9 Strategy Masterclass

  • Focus: 60-minute full synoptic challenge paper covering all 24 topics, followed by a mark scheme breakdown focusing on timing and high-tariff execution.