Study VCE Methods by chapter

Study VCE Methods by chapter. Find starred focus sections, worked examples and original questions based on exam skills. All free.

Functions and Relations

  • 1A Set notation and sets of numbers
  • 1B Identifying and describing relations and functions
  • 1C Types of functions and implied domains
  • 1D Sums and products of functions
  • 1E Composite functions
  • 1F Inverse functions
  • 1G Power functions
  • 1H Applications of functions
  • Review Chapter 1 Review

Coordinate Geometry

  • 2A Linear equations
  • 2B Linear literal equations and simultaneous linear literal equations
  • 2C Linear coordinate geometry
  • 2D Applications of linear functions
  • 2E The geometry of simultaneous linear equations with two variables
  • 2F Simultaneous linear equations with more than two variables
  • Review Chapter 2 Review

Transformations

  • 3A Translations
  • 3B Dilations
  • 3C Reflections
  • 3D Combinations of transformations
  • 3E Determining transformations
  • 3F Using transformations to sketch graphs
  • 3G Transformations of power functions with positive integer index
  • 3H Determining the rule for a function from its graph
  • 3I A notation for transformations
  • Review Chapter 3 Review

Polynomial Functions

  • 4A Quadratic functions
  • 4B Determining the rule for a parabola
  • 4C The language of polynomials
  • 4D Division and factorisation of polynomials
  • 4E The general cubic function
  • 4F Polynomials of higher degree
  • 4G Determining the rule for the graph of a polynomial
  • 4H Solution of literal equations and systems of equations
  • Review Chapter 4 Review

Exponential and Logarithmic Functions

  • 5A Exponential functions
  • 5B The exponential function f(x) = eˣ
  • 5C Exponential equations
  • 5D Logarithms
  • 5E Graphing logarithmic functions
  • 5F Determining rules for graphs of exponential and logarithmic functions
  • 5G Solution of exponential equations using logarithms
  • 5H Inverses
  • 5I Exponential growth and decay
  • Review Chapter 5 Review

Circular Functions

  • 6A Measuring angles in degrees and radians
  • 6B Defining circular functions: sine, cosine and tangent
  • 6C Further symmetry properties and the Pythagorean identity
  • 6D Graphs of sine and cosine
  • 6E Solution of trigonometric equations
  • 6F Sketch graphs of y = a sin n(t - ε) and y = a cos n(t - ε)
  • 6G Sketch graphs of y = a sin n(t - ε) + b and y = a cos n(t - ε) + b
  • 6H Addition of ordinates for circular functions
  • 6I Determining rules for graphs of circular functions
  • 6J The tangent function
  • 6K General solution of trigonometric equations
  • 6L Applications of circular functions
  • Review Chapter 6 Review

Further Functions

  • 7A More power functions
  • 7B Composite functions and inverse functions
  • 7C Sums and products of functions and addition of ordinates
  • 7D Function notation and identities
  • 7E Families of functions and solving literal equations
  • Review Chapter 7 Review

Differentiation

  • 9A The derivative
  • 9B Rules for differentiation
  • 9C Differentiating xⁿ where n is a negative integer
  • 9D The graph of the derivative function
  • 9E The chain rule
  • 9F Differentiating rational powers
  • 9G Differentiation of eˣ
  • 9H Differentiation of the natural logarithm function
  • 9I Derivatives of circular functions
  • 9J The product rule
  • 9K The quotient rule
  • 9L Limits and continuity
  • 9M When is a function differentiable?
  • Review Chapter 9 Review

Applications of Differentiation

  • 10A Tangents and normals
  • 10B Rates of change
  • 10C Stationary points
  • 10D Types of stationary points
  • 10E Absolute maximum and minimum values
  • 10F Maximum and minimum problems
  • 10G Families of functions
  • 10H Newton's method
  • Review Chapter 10 Review

Integration

  • 11A Estimating the area under a graph
  • 11B Antidifferentiation: indefinite integrals
  • 11C The antiderivative of (ax+b)ʳ
  • 11D The antiderivative of e^(kx)
  • 11E The fundamental theorem of calculus and the definite integral
  • 11F Finding the area under a curve
  • 11G Integration of circular functions
  • 11H Miscellaneous exercises
  • 11I The area of a region between two curves
  • 11J Applications of integration
  • 11K The fundamental theorem of calculus
  • Review Chapter 11 Review

Discrete Random Variables

  • 13A Sample spaces and probability
  • 13B Conditional probability and independence
  • 13C Discrete random variables
  • 13D Expected value, variance and standard deviation
  • Review Chapter 13 Review

The Binomial Distribution

  • 14A Bernoulli sequences and the binomial probability distribution
  • 14B The graph, expectation and variance of a binomial distribution
  • 14C Finding the sample size
  • 14D Proofs for the expectation and variance
  • Review Chapter 14 Review

Continuous Random Variables

  • 15A Continuous random variables
  • 15B Mean and percentiles for a CRV
  • 15C Measures of spread
  • 15D Properties of mean and variance
  • 15E Cumulative distribution functions
  • Review Chapter 15 Review

The Normal Distribution

  • 16A The normal distribution
  • 16B Standardisation and the 68-95-99.7% rule
  • 16C Determining normal probabilities
  • 16D Solving problems using the normal distribution
  • 16E The normal approximation to the binomial distribution
  • Review Chapter 16 Review

Sampling and Estimation

  • 17A Populations and samples
  • 17B The exact distribution of the sample proportion
  • 17C Approximating the distribution of the sample proportion
  • 17D Confidence intervals for the population proportion
  • Review Chapter 17 Review