C3 Tutorials – AQA A Level Maths


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

Contents for C3 AQA

Algebra and Functions
Working with Functions
Graph Transformations and Asymptotes
Modulus Functions, Equations and Inequalities
Trigonometry
Sec, Cosec and Cot
Inverse Trigonometric Functions
Identities and Equations – Pythagorean Type
Logarithmic and Exponential Functions
The Exponential Function and Natural Log Functions
Differentiation
Standard Differentials
The Chain Rule
The Product and Quotient Rules
More Standard Differentials
The Reciprocal Form of dy/dx
Exam Questions – Differentiation
Integration
Common Functions
Trigonometric Functions
By Substitution
By Parts
Standard integrals involving inverse trigonometric functions
Volumes of Revolution
Numerical Integration
Numerical Solution of Equations
Solution of Equations by Numerical Methods

Algebra and 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

Up to Contents

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

Up to Contents

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

Up to Contents

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

Up to Contents

Inverse trigonometric functions

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

Up to Contents

Identities & Equations – Pythagorean Type

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

Up to Contents

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

Up to Contents

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)

Up to Contents

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

Up to Contents

The Product and Quotient Rules

  1. The product rule
  2. The quotient rule

Up to Contents

More Standard Differentials

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

Up to Contents

The Reciprocal Function of dy/dx

  1. The reciprocal function of dy/dx

Up to Contents

Exam Questions – Differentiation

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

Up to Contents

Integration

Integration – Common Functions

  1. Integration:(ax+b)n types
  2. Exam Questions - Integration:(ax+b)n types
  3. Integrating exponential functions ex, eax and e(ax+b)
  4. Exam Questions - Integrating exponential functions ex, eax and e(ax+b)
  5. Integrating reciprocal functions 1/x and 1/(ax+b)
  6. Exam Questions - Integrating reciprocal functions 1/x and 1/(ax+b)
  7. Integrals of the form : f '(x)/f(x)
  8. Integrals of the form : f'(x)ef(x)

Up to Contents

Integrals of Trigonometric Functions

  1. Integrals of sin x, cos x, sec² x
  2. Integrals of the form sin(ax+b), cos(ax+b), sec² (ax+b) types
  3. Exam Questions - Trigonometric types

Up to Contents

Integration by Substitution

  1. Integration by substitution
  2. Square root types
  3. Integration of exponential types by substitution
  4. Integration by substitution using limits
  5. Exam Questions - Integration by substitution

Up to Contents

Integration by Parts

  1. Integration by parts
  2. Integration by parts (ln types)
  3. Integration by parts using limits
  4. Exam Questions - Integration by parts

Up to Contents

Standard Integrals Involving Inverse Trigonometric Functions

  1. Integrals of the form 1/(a2+x2) and 1/√(a2-x2)

Up to Contents

Applications of Integration – Volumes of revolution

  1. Volume of revolution about the x-axis
  2. Exam Questions - Volume of revolution about the x-axis
  3. Volume of revolution about the x-axis generated between curves
  4. Volume of Revolution about the y-axis
  5. Exam Questions - Volume of Revolution about the y-axis
  6. Volume of Revolution about the y-axis generated between curves

Up to Contents

Numerical Integration

  1. Trapezium rule
  2. Exam Questions - Trapezium rule
  3. Simpson's Rule
  4. Exam Questions - Simpson's Rule
  5. Mid-ordinate Rule

Up to Contents

Numerical Solution of Equations

Solution of Equations by Numerical methods

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

Up to Contents