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P2 Tutorials

P2 Tutorials

Algebra and Functions

Algebraic Long Division

  1. Algebraic long division
  2. Converting Improper algebraic fractions to mixed fractions

Factor and Remainder Theorems

  1. How to solve a cubic equation
  2. Exam Questions - Factor theorem
  3. The remainder theorem
  4. Exam Questions - Remainder theorem

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

Logarithmic and Exponential Functions

Exponential Functions and Logarithms

  1. Exponential functions: what they are and their graphs
  2. What do we mean by a log?
  3. Rules of logs
  4. Logarithms - Change of Base
  5. Simplifying and expanding
  6. Converting between Logarithmic and Power (Exponential) equations
  7. Modelling exponential growth and decay
  8. Exponential and log equations
  9. Simultaneous equations
  10. Solving inequalities
  11. Exam Questions - Logarithms

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

Modelling Curves of the form y=kxn and y=kax

  1. Modelling curves - Converting to linear form

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

Identities & Equations – Pythagorean Type

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

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

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

Identities – Half angle type

  1. Examples using half angle identities

Identities – Triple angle type

  1. Identity for cos 3θ and sin 3θ

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

Exam Questions – Mixed trigonometry

  1. Exam Questions - Mixed trigonometry

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: 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 dx/dy

  1. The reciprocal function of dy/dx

Parametric Functions

  1. Differentiation: Parametric functions
  2. Tangents and normals
  3. Stationary points
  4. Exam Questions - Parametric functions

Implicit Functions

  1. Implicit functions
  2. Implicit functions with product rule
  3. Tangents and normals
  4. Stationary points
  5. Exam Questions - Implicit functions

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. Integrals Using Trigonometric Identities
  4. sin2x and cos2x types
  5. Exam Questions - Trigonometric types

Numerical Integration

  1. Simpson's Rule
  2. Exam Questions - Simpson's Rule

Numerical Solution of Equations

Solution of Equations by Numerical methods

  1. Graphical methods
  2. Change of sign
  3. Iteration
  4. Exam Questions - Iteration
  5. Newton-Raphson Method NEW!!
  6. Newton-Raphson method for locating a root in a given interval
  7. Exam Questions - Newton-Raphson