C3 Tutorials – MEI A Level Maths

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

Algebra and Functions

Working with Functions

  1. f(x) notation
  2. Domain and range
  3. Exam Questions - Domain and range
  4. Combination of functions
  5. The inverse of a function
  6. Graphical relationship between f(x) and its inverse
  7. Exam Questions - Inverse functions

Even and Odd and Periodic Functions

  1. Even and odd and periodic functions

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

Sketching Curves

Graph Transformations and Asymptotes

    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)

    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

    The Product and Quotient Rules

    1. The product rule
    2. The quotient rule

    More Standard Differentials

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

    The Reciprocal Function of dy/dx

    1. The reciprocal function of dy/dx

    Exam Questions – Differentiation

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

    Implicit Functions

    1. Implicit functions
    2. Tangents and normals
    3. Stationary points
    4. Exam Questions - Implicit functions

    Connected Rates of Change

    1. Connected rates of change
    2. Using three connected rates of change
    3. Connected rates of change cone type problems
    4. Exam Questions - Connected rates of change

    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)

    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

    Integration by Substitution

    1. Integration by substitution
    2. Square root types
    3. Integration of trigonometric functions by substitution
    4. Integration of exponential types by substitution
    5. Integration by substitution using limits
    6. Integration of trigonometric functions by substitution with limits
    7. Exam Questions - Integration by substitution

    Integration by Parts

    1. Integration by parts
    2. Integration by parts (ln types)
    3. Integration by parts using limits
    4. Proof of the formula - Integration by parts
    5. Exam Questions - Integration by parts

    Mixed Examples & Exam Question – Integration

    1. Integration - General Methods
    2. Mixed Examples - Integration
    3. Exam Questions - Integration

    Numerical Solution of Equations

    Solution of Equations by Numerical methods

    1. Graphical methods
    2. Change of sign
    3. Bisection method for locating a root in a given interval
    4. Linear interpolation method for locating a root in a given interval
    5. Iteration
    6. Exam Questions - Iteration
    7. Newton-Raphson method for locating a root in a given interval
    8. Exam Questions - Newton-Raphson