Year 12 IB

Excellence Programme

-Maths

Specialist summer preparation for students progressing from Year 11 into their final examination year for the IB Diploma

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4 lessons across 4 weeks

Lesson 1: Core Algebraic Foundations

This lesson strengthens students’ algebraic fluency, providing the essential foundation for advanced study across both A-Level and IB Maths.

·      Expanding Brackets Including Binomial Expansion: Multiplying single, double, and triple brackets efficiently without making sign errors.

·      Factorising: Spotting common factors and grouping terms, focusing heavily on monic and non-monic quadratics.

·      Algebraic Fractions: Applying numerical fraction rules to algebraic terms to simplify, multiply, and divide complex expressions

Lesson 2: Equations and Inequalities

This session develops the transition from GCSE or MYP methods to the more analytical techniques required for solving equations and inequalities with confidence and precision.

·       Solving Equations: Mastering linear equations, and solving quadratics using factoring, completing the square, the quadratic formula and basic cubic equations. Using the discriminant to find the number of roots.

·       Simultaneous Equations: Eliminating variables or using substitution to find intersections, particularly between one linear and one quadratic equation.

·       Linear Inequalities: Solving inequalities, flipping inequality signs when multiplying by negatives, and expressing solution sets using set notation.

Lesson 3: Number Laws and Formulae

This lesson focuses on number laws, exact values, and the manipulation of formulae, helping students build accuracy and flexibility in mathematical working.

·       Laws of Indices: Working fluidly with negative, fractional, and zero indices to rewrite expressions for future calculus work. A brief introduction to logs.

·       Surds & Rationalising: Simplifying root expressions and rationalising denominators using conjugate expressions to keep values exact.

·       Rearranging Formulas: Changing the subject of an equation where the target variable appears multiple times or inside roots and fractions.

Lesson 4: Geometry, Graphs and Trigonometry

The final lesson brings together geometry, graphs, and trigonometry, enabling students to connect algebraic methods with visual and spatial reasoning.

  • Coordinate Geometry: Calculating midpoints, distances, and gradients using parallel and perpendicular lines.

  • Graph Sketching: Drawing the distinct shapes of quadratic, cubic, and reciprocal functions, identifying roots and asymptotes.

  • Trigonometry: Mastering right-angled triangle properties, non-right-angled rules (Sine/Cosine rules), and the area of a triangle formula.

 

Personalised Action Plan

Following the diagnostic assessment, students receive:

  • Individual strengths analysis

  • Areas for improvement

  • Target grade roadmap

  • Recommended revision tasks

  • Ongoing progress monitoring