Algebra and Series

Rational expressions

• Simplifying
• Addition and subtraction
• Exam Questions

Functions

Notation

• f(x) notation

Domain and Range

• Domain and Range 1
• Domain and Range 2

Combining Functions

• Combination of functions
  • Examples : 1 | 2

Inverse Functions

• The inverse of a function
  • Examples : 1 | 2 | 3
• Graphical relationship between f(x) and its inverse
  • Examples : 1 | 2
• Exam Questions

Transformations of Graphs (Revision of C1 work)

• Learn these base graphs
  • Basic graphs used in transformations
• Translations
  • y = f(x ± a ) and y= f(x) ± a
    • Why does the transformation do this?
• Reflections
  • y = - f(x) and y = f(-x)
    • Why does the transformation do this?
• Stretches
  • y = a f(x)
    • Why does the transformation do this?
  • y = f (ax)
    • Why does the transformation do this?
• Exam Questions on transformations
  • Exam questions

Modulus Functions

• The modulus function
• Graph y=|f(x)|
• Graph y=f(|x|)
  • Exam Questions
• Modulus Equations
  • Equations 1
  • Equations 2
  • Equations 3
• Modulus Inequalities
  • Inequalities 1
  • Inequalities 2
  • Inequalities 3

The Exponential Function e^x

• Exponential function (e^x )
  • Sketching graphs 1 | 2 | 3

Natural Log Functions

• The natural logarithmic function, ln x

Trigonometry

Secant, Cosecant and Cotangent

• Definitions of Secant, cosecant and cotangent
  • graphs

Inverse trig. functions

• arcsin x
• arccos x
• arctan x
  • Examples : 1 | 2 | 3

Identities

• Pythagorean type: sin²x + cos²x ≡1 ; 1 + tan²x ≡ sec²x ; 1 + cot²x ≡ cosec²x
  • Introduction and Proof
• Examples : 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8

 

• Addition type: sin(A±B), cos(A±B) and tan(A±B)
  • Addition Formulae (compound angles)
  • Using the formulae to get exact values:
    • Examples : 1 | 2
  • Proving identities :
    • Examples : 1 | 2

 

• Double angle type for sin2A, cos2A and tan2A
  • Double angle formulae
    • Examples : 1 | 2 | 3
  • Half angles
    • Half angles (1)
    • Half angles (2)
  • Applications - Triple angles
    • cos 3θ
    • sin 3θ

 

• Factor Formulae
  • Factor Formulae (1)
  • Factor Formulae (2)
  • Factor Formulae (3)

 

• A cos x ± B sin x and A sin x ± B cos x type
  • A cos x ± B sin x and A sin x ± B cos x

Equations using:

• the identities : sin²x + cos²x ≡1 ; 1 + tan²x ≡ sec²x ; 1 + cot²x ≡ cosec²x
  • Examples: 1 | 2 | 3

 

• the identities for sin2A, cos2A and tan2A
  • Examples: 1 | 2 | 3

 

• the identities for A cos x ± B sin x and A sin x ± B cos x
  • Examples : 1 and 2
• Exam Questions

Miscellaneous Exam Practice

• Exam Questions

Differentiation

Using the Formula Book

• exponential function e^x, natural log ln x and trig types sin x, cos x, tan x

The Chain Rule

• The chain rule
  • polynomial to a rational power types
  • exponential types
  • natural log types
  • trigonometric types (1)
  • trigonometric types (2)

The Product Rule

• The product rule

The Quotient Rule

• The quotient rule
  • example

A Special Result

• Using the result dy/dx = 1 ÷ dx/dy

Miscellaneous Exam Practice

• Methods
• Applications - tangents, normals and stationary points
• Exponential Rates of change

Numerical methods

Solution of Equations by:

• Graphical methods
• Change of sign
• Iteration
  • How it works
• Exam Questions