Overzicht
AQA A-Level Maths : Year 13 Pure
This GeoGebra companion maps directly to Chapters 1–16 of the Cambridge Student Book 2 (Year 2). Each chapter contains short, interactive GeoGebra investigations that mirror the textbook topics so students can explore definitions, transform graphs, test proofs, visualise calculus, and model applications dynamically.
- Proof and mathematical communication — GeoGebra constructions and dynamic diagrams to illustrate proofs, generate counterexamples, and practise communicating reasoning.
- Functions — interactive mappings, domain/range sliders, inverse/composite function visualisers.
- Further transformations of graphs — combined translations, stretches/reflections with parameter sliders and step-through animations.
- Sequences and series — animated sequence generation, partial-sum plots, and convergence visualisations.
- Rational functions and partial fractions — asymptotes, removable holes, and dynamic decomposition into partial-fraction pieces.
- General binomial expansion — coefficient visualisers, series expansion explorer, and approximation demonstrations.
- Radian measure — unit-circle interactives linking radians, arc length and trig values; angle-to-coordinate mapping.
- Further trigonometry — dynamic trig-identity verifiers, sum/difference formula visualisations and waveform manipulations.
- Calculus of exponential and trigonometric functions — differentiation/integration demonstrations for exp & trig functions with live tangent/area displays.
- Further differentiation — higher derivatives, stationary points and inflection-point explorers with curvature/concavity sliders.
- Further applications of calculus — optimisation, kinematics and area/volume modelling built from interactive parameters.
- Further integration techniques — substitution, parts and partial-fractions integration illustrated and compared with numerical approximations.
- Differential equations — slope fields, families of solution curves, and parameter-driven modelling (separable equations).
- Numerical solutions of equations — root-locating tools: bisection, Newton–Raphson, fixed-point iterations with visual convergence diagnostics.
- Numerical integration — trapezium rule and error visualisations with adjustable partitioning.
- Applications of vectors — 2-D motion, position/velocity vectors, and geometric/vector proofs with dynamic components.
Inhoudstafel
Chapter 1 : Proof and Mathematical Communication
Chapter 2 : Functions
Chapter 3 : Further Transformations and Graphs
Chapter 4 : Sequences and Series
Chapter 5 : Rational Functions and Partial Fractions
Chapter 6 : General Binomial Expansion
Chapter 7 : Radian Measure
Chapter 8 : Further Trigonometry
Chapter 9 : Calculus of Exponential and Trigonometric Functions
Chapter 10 : Further Differentiation
Chapter 11 : Further Integration Techniques
Chapter 12 : Further Applications of Calculus
Chapter 13 : Differential Equations
Chapter 14 : Numerical Solutions of Equations
Chapter 15 : Numerical Integration
Chapter 16 : Applications of Vectors