C3 Edexcel Maths Tutorials


It is advisable to check the official C3 Edexcel Specification in case of changes: Specification

Contents for C3 Edexcel

Rational Expressions
Simplifying
Functions
Working with Functions
Graph Transformations and Asymptotes
Modulus Functions, Equations and Inequalities
Logarithmic and Exponential Functions
The Exponential Function and Natural Log Functions
Trigonometry
Sec, Cosec and Cot
Inverse Trigonometric Functions
Identities and Equations – Pythagorean Type
Identities – Addition Type
Identities and Equations – Double Angle Type
Identities – Half Angle Type
-Triple Angle Type
-Factor Formulae
Identities and Equations – Harmonic Formulae
Exam Questions – Mixed Trigonometry
Differentiation
Standard Differentials
The Chain Rule
The Product and Quotient Rules
More Standard Differentials
The Reciprocal Form of dy/dx
Exam Questions – Differentiation
Numerical Solution of Equations
Solution of Equations by Numerical Methods

Rational Expressions

Rational Expressions – Simplifying

  1. Simplifying algebraic fractions
  2. Exam Questions - Simplifying a rational expression
  3. Addition and subtraction of algebraic fractions
  4. Exam Questions - Addition & subtraction
  5. Multiplication of algebraic fractions
  6. Further simplifying of 'stacked fractions'
  7. Exam Questions - Algebraic long division

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Functions

Working with Functions

  1. Mappings
  2. Mappings - More examples
  3. Mappings, functions or both?
  4. f(x) notation
  5. Domain and range
  6. Exam Questions - Domain and range
  7. Combination of functions
  8. The inverse of a function
  9. Graphical relationship between f(x) and its inverse
  10. Exam Questions - Inverse functions
  11. Exam Questions - Functions

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Graph Transformations and Asymptotes

  1. Basic graphs used in transformations
  2. Translations of graphs
  3. Reflections of graphs
  4. Stretches of graphs
  5. Exam Questions - Graph transformations

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Modulus Functions, Equations and Inequalities

  1. The modulus function
  2. Graphing y=|f(x)|
  3. Graphing y=f(|x|)
  4. Exam Questions - Modulus functions graphing
  5. Modulus equations
  6. Exam Questions - Modulus equations
  7. Modulus inequalities
  8. Exam Questions - Modulus inequalities

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Logarithmic and Exponential Functions

The Exponential Function ex and Natural Log Functions

  1. The exponential function ex
  2. Sketching exponential graphs based on transformations
  3. The natural logarithmic function, ln x
  4. Exam Questions - Natural log functions

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Trigonometry

Sec θ, Cosec θ and Cot θ

  1. Trig functions sec θ, cosec θ and cot θ
  2. Graphs of sec θ, cosec θ and cot θ

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Inverse trigonometric functions

  1. Inverse trigonometric functions - arcsin x, arccos x, arctan x
  2. Examples using Inverse trigonometric functions

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Identities & Equations – Pythagorean Type

  1. sin²x + cos²x ≡1 , 1 + tan²x ≡ sec²x , 1 + cot²x ≡ cosec²x
  2. Solving equations using Pythagorean identities

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Identities – Addition type

  1. sin(A±B), cos(A±B) and tan(A±B)
  2. Using the Addition formulae to get exact values
  3. Proving identities using the addition formulae
  4. Identities - Addition type - Equations

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Identities & Equations – Double angle type

  1. Identities for sin2A, cos2A and tan2A
  2. Examples using double angle identities
  3. Solving equations using double angle identities
  4. Exam Questions - Double Angles

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Identities – Half angle type

  1. Examples using half angle identities

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Identities – Triple angle type

  1. Identity for cos 3θ and sin 3θ

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Identities – Factor Formulae

  1. Proving identities using the factor formulae

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Identities & Equations – Harmonic Formulae

  1. Harmonic Identities Rsin(x ± α), Rcos(x ± α)
  2. Equations using harmonic identities
  3. Harmonic identities - Max and Min
  4. Exam Questions - Harmonic identities and equations

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Exam Questions – Mixed trigonometry

  1. Exam Questions - Mixed trigonometry

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Differentiation

Standard Differentials

  1. Exponential function ex
  2. The natural log function, ln(x)
  3. The trig functions sin(x), cos(x) and tan(x)

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The Chain Rule

  1. Chain rule: Polynomial to a rational power
  2. Chain rule: Exponential types
  3. Chain rule: Natural log types
  4. Chain rule: Trigonometric types

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The Product and Quotient Rules

  1. The product rule
  2. The quotient rule

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More Standard Differentials

  1. The trig functions, sec(x), cosec(x) and cot(x)

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The Reciprocal Function of dy/dx

  1. The reciprocal function of dy/dx

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Exam Questions – Differentiation

  1. Exam Questions - Differentiation methods
  2. Exam Questions - Differentiation: tangents, normals and stationary points
  3. Exam Questions - Exponential rates of change

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Numerical Solution of Equations

Solution of Equations by Numerical methods

  1. Graphical methods
  2. Change of sign
  3. Iteration
  4. Exam Questions - Iteration

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