AQA A-Level Maths : Year 13 Pure

Christopher Mann, 11 sept. 2025

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. [list] [*][b]Proof and mathematical communication [/b]— GeoGebra constructions and dynamic diagrams to illustrate proofs, generate counterexamples, and practise communicating reasoning. [*][b]Functions [/b]— interactive mappings, domain/range sliders, inverse/composite function visualisers. [*][b]Further transformations of graphs [/b]— combined translations, stretches/reflections with parameter sliders and step-through animations. [*][b]Sequences and series [/b] — animated sequence generation, partial-sum plots, and convergence visualisations. [*][b]Rational functions and partial fractions[/b] — asymptotes, removable holes, and dynamic decomposition into partial-fraction pieces. [*][b]General binomial expansion[/b] — coefficient visualisers, series expansion explorer, and approximation demonstrations. [*][b]Radian measure [/b]— unit-circle interactives linking radians, arc length and trig values; angle-to-coordinate mapping. [*][b]Further trigonometry [/b]— dynamic trig-identity verifiers, sum/difference formula visualisations and waveform manipulations. [*][b]Calculus of exponential and trigonometric functions [/b]— differentiation/integration demonstrations for exp & trig functions with live tangent/area displays. [*][b]Further differentiation[/b] — higher derivatives, stationary points and inflection-point explorers with curvature/concavity sliders. [*][b]Further applications of calculus [/b]— optimisation, kinematics and area/volume modelling built from interactive parameters. [*][b]Further integration techniques [/b]— substitution, parts and partial-fractions integration illustrated and compared with numerical approximations. [*][b]Differential equations [/b] — slope fields, families of solution curves, and parameter-driven modelling (separable equations). [*][b]Numerical solutions of equations [/b]— root-locating tools: bisection, Newton–Raphson, fixed-point iterations with visual convergence diagnostics. [*][b]Numerical integration [/b]— trapezium rule and error visualisations with adjustable partitioning. [*][b]Applications of vectors [/b] — 2-D motion, position/velocity vectors, and geometric/vector proofs with dynamic components. [/list]

Table des matières

  1. Chapter 1 : Proof and Mathematical Communication
    1. Example of a Proof by Contradiction
    2. Elements I: Proposition 6
  2. Chapter 2 : Functions
    1. Mapping Diagrams and Graphs of Linear Functions
    2. Identifying Domain and Range - Continuous
    3. Composite functions
    4. Discovering Inverse Functions
    5. Inverse functions
  3. Chapter 3 : Further Transformations and Graphs
    1. Transformation of functions
    2. Combined transformations of functions.
    3. Interval Notation Illustrator: Single Sets & Conjunctions
    4. equations modulus
  4. Chapter 4 : Sequences and Series
    1. G10 Arithmetic Sequences Practice
    2. arithmetic sequences/sum, by Tom O., Atlanta, GA
    3. Arithmetic Series Visual
    4. Seeing Geometric Sequences
    5. Infinite Geometric Series
  5. Chapter 5 : Rational Functions and Partial Fractions
    1. Partial Fractions Practice
    2. Partial Fraction Decomposition
    3. Divisible Polynomials - Remainder and Factor Theorems
  6. Chapter 6 : General Binomial Expansion
    1. Binomial Coefficient and Symmetry
    2. Binomial Expansion
    3. General Binomial Expansion
    4. Binomial Expansion (C4)
  7. Chapter 7 : Radian Measure
    1. What is a Radian?
    2. Arc length in Radian Measure
    3. Arc Length and Area of Sector
    4. π and Radians
    5. small angle approximations - Sine
    6. Small angle approximations - Cosine
    7. Small Angle Approximations - Tan
  8. Chapter 8 : Further Trigonometry
    1. Double Angle Identity Activity
    2. Compound Angle Identity (Trigonometry)Activity Part 1 (Sine)
    3. f(x)=psinx+qcosx
    4. Graphs of Reciprocal and Inverse Trigonometric Functions
  9. Chapter 9 : Calculus of Exponential and Trigonometric Functions
    1. Differentiating Log and Exponential Functions
    2. Differentiating the exponential function
  10. Chapter 10 : Further Differentiation
    1. Derivative Chain Rule
    2. Chain rule (AASL/HL)
    3. Derivative Product Rule 1
    4. Product rule (AASL/HL)
    5. Quotient rule (AASL/HL)
    6. Visualizing Implicit Differentiation
    7. Implicit Differentiation
  11. Chapter 11 : Further Integration Techniques
    1. Integration by Substitution
    2. Integration by Parts
    3. Integration by parts AAHL5.20
    4. Integration Using Partial Fractions
  12. Chapter 12 : Further Applications of Calculus
    1. Differential calculus: Max/min, points of inflection
    2. One Point of Inflection
    3. Parametric Equations: dy/dx (Ex 1)
  13. Chapter 13 : Differential Equations
    1. Separable Variables DE Solver
    2. DE with Variables Separable
  14. Chapter 14 : Numerical Solutions of Equations
    1. 10.1 Locating roots: page 276, example 3
    2. Newton-Raphson Method
    3. Fixed-Point Method
    4. Fixed point iteration
  15. Chapter 15 : Numerical Integration
    1. Trapezium Rule Demonstration (Scalable)
    2. Volume of a Cone as the limit of sum of volumes of Cylinders
  16. Chapter 16 : Applications of Vectors
    1. Copy of Constant Acceleration Plots
    2. 3D Vectors (addition, subtraction, multiplication by scalar, unit vectors and magnitude)

1.

Chapter 1 : Proof and Mathematical Communication

  • 1. Example of a Proof by Contradiction
  • 2. Elements I: Proposition 6

1.1.

–

1.2.

–

2.

Chapter 2 : Functions

  • 1. Mapping Diagrams and Graphs of Linear Functions
  • 2. Identifying Domain and Range - Continuous
  • 3. Composite functions
  • 4. Discovering Inverse Functions
  • 5. Inverse functions

2.1.

–

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Chapter 3 : Further Transformations and Graphs

  • 1. Transformation of functions
  • 2. Combined transformations of functions.
  • 3. Interval Notation Illustrator: Single Sets & Conjunctions
  • 4. equations modulus

3.1.

–

3.2.

–

3.3.

–

3.4.

–

4.

Chapter 4 : Sequences and Series

  • 1. G10 Arithmetic Sequences Practice
  • 2. arithmetic sequences/sum, by Tom O., Atlanta, GA
  • 3. Arithmetic Series Visual
  • 4. Seeing Geometric Sequences
  • 5. Infinite Geometric Series

4.1.

–

4.2.

–

4.3.

–

4.4.

–

4.5.

–

5.

Chapter 5 : Rational Functions and Partial Fractions

  • 1. Partial Fractions Practice
  • 2. Partial Fraction Decomposition
  • 3. Divisible Polynomials - Remainder and Factor Theorems

5.1.

–

5.2.

–

5.3.

–

6.

Chapter 6 : General Binomial Expansion

  • 1. Binomial Coefficient and Symmetry
  • 2. Binomial Expansion
  • 3. General Binomial Expansion
  • 4. Binomial Expansion (C4)

6.1.

–

6.2.

–

6.3.

–

6.4.

–

7.

Chapter 7 : Radian Measure

  • 1. What is a Radian?
  • 2. Arc length in Radian Measure
  • 3. Arc Length and Area of Sector
  • 4. π and Radians
  • 5. small angle approximations - Sine
  • 6. Small angle approximations - Cosine
  • 7. Small Angle Approximations - Tan

7.1.

–

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

–

8.

Chapter 8 : Further Trigonometry

  • 1. Double Angle Identity Activity
  • 2. Compound Angle Identity (Trigonometry)Activity Part 1 (Sine)
  • 3. f(x)=psinx+qcosx
  • 4. Graphs of Reciprocal and Inverse Trigonometric Functions

8.1.

–

8.2.

–

8.3.

–

8.4.

–

9.

Chapter 9 : Calculus of Exponential and Trigonometric Functions

  • 1. Differentiating Log and Exponential Functions
  • 2. Differentiating the exponential function

9.1.

–

9.2.

–

10.

Chapter 10 : Further Differentiation

  • 1. Derivative Chain Rule
  • 2. Chain rule (AASL/HL)
  • 3. Derivative Product Rule 1
  • 4. Product rule (AASL/HL)
  • 5. Quotient rule (AASL/HL)
  • 6. Visualizing Implicit Differentiation
  • 7. Implicit Differentiation

10.1.

–

10.2.

–

10.3.

–

10.4.

–

10.5.

–

10.6.

–

10.7.

–

11.

Chapter 11 : Further Integration Techniques

  • 1. Integration by Substitution
  • 2. Integration by Parts
  • 3. Integration by parts AAHL5.20
  • 4. Integration Using Partial Fractions

11.1.

–

11.2.

–

11.3.

–

11.4.

–

12.

Chapter 12 : Further Applications of Calculus

  • 1. Differential calculus: Max/min, points of inflection
  • 2. One Point of Inflection
  • 3. Parametric Equations: dy/dx (Ex 1)

12.1.

–

12.2.

–

12.3.

–

13.

Chapter 13 : Differential Equations

  • 1. Separable Variables DE Solver
  • 2. DE with Variables Separable

13.1.

–

13.2.

–

14.

Chapter 14 : Numerical Solutions of Equations

  • 1. 10.1 Locating roots: page 276, example 3
  • 2. Newton-Raphson Method
  • 3. Fixed-Point Method
  • 4. Fixed point iteration

14.1.

–

14.2.

–

14.3.

–

14.4.

–

15.

Chapter 15 : Numerical Integration

  • 1. Trapezium Rule Demonstration (Scalable)
  • 2. Volume of a Cone as the limit of sum of volumes of Cylinders

15.1.

–

15.2.

–

16.

Chapter 16 : Applications of Vectors

  • 1. Copy of Constant Acceleration Plots
  • 2. 3D Vectors (addition, subtraction, multiplication by scalar, unit vectors and magnitude)

16.1.

–

16.2.

–

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