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A Level
Maths: Pure
Edexcel
Revision Notes
Edexcel A Level Maths: Pure Revision Notes
Concise resources for the Edexcel A Level Maths: Pure course.
1. Proof
1.1 Proof
1.1.1 Language of Proof
1.1.2 Proof by Deduction
1.1.3 Proof by Exhaustion
1.1.4 Disproof by Counter Example
1.2 Proof by Contradiction
1.2.1 Proof by Contradiction
2. Algebra & Functions
2.1 Laws of Indices & Surds
2.1.1 Laws of Indices
2.1.2 Manipulating Surds
2.1.3 Surds - Rationalising the Denominator
2.2 Quadratics
2.2.1 Quadratic Graphs
2.2.2 Discriminants
2.2.3 Completing the Square
2.2.4 Solving Quadratic Equations
2.2.5 Further Solving Quadratic Equations (Hidden Quadratics)
2.3 Simultaneous Equations
2.3.1 Linear Simultaneous Equations - Elimination
2.3.2 Linear Simultaneous Equations - Substitution
2.3.3 Quadratic Simultaneous Equations
2.4 Inequalities
2.4.1 Linear Inequalities
2.4.2 Quadratic Inequalities
2.4.3 Inequalities on Graphs
2.5 Polynomials
2.5.1 Expanding Brackets
2.5.2 Polynomial Division
2.5.3 Factor Theorem
2.5.4 Factorisation
2.6 Rational Expressions
2.6.1 Rational Expressions
2.6.2 Improper Algebraic Fractions
2.7 Graphs of Functions
2.7.1 Sketching Polynomials
2.7.2 Reciprocal Graphs - Sketching
2.7.3 Solving Equations Graphically
2.7.4 Proportional Relationships
2.8 Functions
2.8.1 Language of Functions
2.8.2 Composite Functions
2.8.3 Inverse Functions
2.8.4 Modulus Functions - Sketching Graphs
2.8.5 Modulus Functions - Solving Equations
2.9 Transformations of Functions
2.9.1 Translations
2.9.2 Stretches
2.9.3 Reflections
2.10 Combinations of Transformations
2.10.1 Combinations of Transformations
2.11 Partial Fractions
2.11.1 Linear Denominators
2.11.2 Squared Linear Denominators
2.12 Modelling with Functions
2.12.1 Modelling with Functions
2.13 Further Modelling with Functions
2.13.1 Further Modelling with Functions
3. Coordinate Geometry
3.1 Equation of a Straight Line
3.1.1 Basic Coordinate Geometry
3.1.2 Parallel & Perpendicular Gradients
3.1.3 Equation of a Straight Line
3.1.4 Modelling with Straight Lines
3.2 Circles
3.2.1 Equation of a Circle
3.2.2 Finding the Centre & Radius
3.2.3 Bisection of Chords
3.2.4 Angle in a Semicircle
3.2.5 Radius & Tangent
4. Sequences and Series
4.1 Binomial Expansion
4.1.1 Binomial Expansion
4.2 General Binomial Expansion
4.2.1 General Binomial Expansion
4.2.2 General Binomial Expansion - Subtleties
4.2.3 General Binomial Expansion - Multiple
4.2.4 Approximating Values
4.3 Arithmetic Sequences & Series
4.3.1 Arithmetic Sequences
4.3.2 Arithmetic Series
4.4 Geometric Sequences & Series
4.4.1 Geometric Sequences
4.4.2 Geometric Series
4.5 Sequences & Series
4.5.1 Language of Sequences & Series
4.5.2 Sigma Notation
4.5.3 Recurrence Relations
4.6 Modelling with Sequences & Series
4.6.1 Modelling with Sequences & Series
5. Trigonometry
5.1 Basic Trigonometry
5.1.1 Trigonometry - Definitions
5.1.2 Right-Angled Triangles
5.1.3 Non-Right-Angled Triangles
5.2 Trigonometric Functions
5.2.1 Graphs of Trigonometric Functions
5.2.2 Transformations of Trigonometric Functions
5.3 Trigonometric Equations
5.3.1 Trigonometry - Simple Identities
5.3.2 Linear Trigonometric Equations
5.3.3 Quadratic Trigonometric Equations
5.3.4 Strategy for Trigonometric Equations
5.4 Radian Measure
5.4.1 Radian Measure
5.4.2 Trigonometry Exact Values
5.4.3 Small Angle Approximations
5.5 Reciprocal & Inverse Trigonometric Functions
5.5.1 Reciprocal Trig Functions - Definitions
5.5.2 Reciprocal Trig Functions - Graphs
5.5.3 Trigonometry - Further Identities
5.5.4 Inverse Trig Functions
5.6 Compound & Double Angle Formulae
5.6.1 Compound Angle Formulae
5.6.2 Double Angle Formulae
5.6.3 R addition formulae Rcos Rsin etc
5.7 Further Trigonometric Equations
5.7.1 Strategy for Further Trigonometric Equations
5.8 Trigonometric Proof
5.8.1 Trigonometric Proof
5.9 Modelling with Trigonometric Functions
5.9.1 Modelling with Trigonometric Functions
6. Exponentials & Logarithms
6.1 Exponential & Logarithms
6.1.1 Exponential Functions
6.1.2 Logarithmic Functions
6.1.3 "e"
6.1.4 Derivatives of Exponential Functions
6.2 Laws of Logarithms
6.2.1 Laws of Logarithms
6.2.2 Exponential Equations
6.3 Modelling with Exponentials & Logarithms
6.3.1 Exponential Growth & Decay
6.3.2 Using Exps & Logs in Modelling
6.3.3 Using Log Graphs in Modelling
7. Differentiation
7.1 Differentiation
7.1.1 Definition of Gradient
7.1.2 First Principles Differentiation
7.1.3 Differentiating Powers of x
7.2 Applications of Differentiation
7.2.1 Gradients, Tangents & Normals
7.2.2 Increasing & Decreasing Functions
7.2.3 Second Order Derivatives
7.2.4 Stationary Points & Turning Points
7.2.5 Sketching Gradient Functions
7.2.6 Modelling with Differentiation inc. Optimisation
7.3 Further Differentiation
7.3.1 First Principles Differentiation - Trigonometry
7.3.2 Differentiating Other Functions (Trig, ln & e etc)
7.3.3 Chain Rule
7.3.4 Product Rule
7.3.5 Quotient Rule
7.3.6 Differentiating Reciprocal and Inverse Trig Functions
7.4 Further Applications of Differentiation
7.4.1 Applications of the Second Derivative
7.4.2 Points of Inflection
7.4.3 Connected Rates of Change
7.5 Implicit Differentiation
7.5.1 Implicit Differentiation
8. Integration
8.1 Integration
8.1.1 Fundamental Theorem of Calculus
8.1.2 Integrating Powers of x
8.1.3 Definite Integration
8.1.4 Area Under a Curve
8.1.5 Area between a curve and a line
8.2 Further Integration
8.2.1 Integration as the limit of a sum
8.2.2 Integrating Other Functions (Trig, ln & e etc)
8.2.3 Reverse Chain Rule
8.2.4 f'(x)/f(x)
8.2.5 Substitution (Reverse Chain Rule)
8.2.6 Harder Substitution
8.2.7 Integrating with Trigonometric Identities
8.2.8 Integration by Parts
8.2.9 Integration using Partial Fractions
8.2.10 Area between 2 curves
8.2.11 Decision Making
8.3 Differential Equations
8.3.1 General Solutions
8.3.2 Particular Solutions
8.3.3 Separation of Variables
8.3.4 Modelling with Differential Equations
8.3.5 Solving & Interpreting Differential Equations
9. Parametric Equations
9.1 Parametric Equations
9.1.1 Parametric Equations - Basics
9.1.2 Parametric Equations - Eliminating the Parameter
9.1.3 Parametric Equations - Sketching Graphs
9.2 Further Parametric Equations
9.2.1 Parametric Differentiation
9.2.2 Parametric Integration
9.2.3 Modelling with Parametric Equations
10. Numerical Methods
10.1 Solving Equations
10.1.1 Change of Sign
10.1.2 Change of Sign Failure
10.1.3 x = g(x) Iteration
10.1.4 Newton-Raphson
10.1.5 Trapezium Rule (Numerical Integration)
10.2 Modelling involving Numerical Methods
10.2.1 Numerical Methods in Context
11. Vectors
11.1 Vectors in 2 Dimensions
11.1.1 Basic Vectors
11.1.2 Magnitude & Direction
11.1.3 Vector Addition
11.1.4 Position Vectors
11.1.5 Problem Solving using Vectors
11.2 Vectors in 3 Dimensions
11.2.1 Vectors in 3 Dimensions
11.2.2 Problem Solving using 3D Vectors
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Edexcel A Level Maths: Pure · Exam Questions
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