Queensland Year 11 Methods (unit 3 & 4) topics

Below are the topics that sit within Queensland Year 12 Methods (units 3 & 4) mathematics. When you click on a certain topic, you will be take to all the subtopics.

• Functions and relations
  Sub Topics:

  • Set notation and sets of numbers
  • Identifying and describing relations and functions
  • Implied domains and types of functions
  • Combining functions
  • Power functions
  • Applications of functions
• Coordinate geometry and transformations
  Sub Topics:

  • Linear coordinate geometry
  • Translations
  • Dilations and reflections
  • Combinations of transformations
  • Using transformations to sketch graphs
  • Transformations of power functions
  • Determining the rule for a function from its graph
• Polynomial functions
  Sub Topics:

  • Quadratic functions
  • Determining the rule for a parabola
  • The language of polynomials
  • Division and factorisation of polynomials
  • The general cubic function
  • Polynomials of higher degree
  • Determining the rule for the graph of a polynomial
  • Solution of literal equations and systems of equations
• Trigonometric functions
  Sub Topics:

  • Measuring angles in degrees and radians
  • Defining sine, cosine and tangent
  • Further symmetry properties and the Pythagorean identity
  • Graphs of sine and cosine
  • Solution of trigonometric equations
  • Sketch graphs ofy=asinn(t±ε) andy=acosn(t±ε)
  • Sketch graphs ofy=asinn(t±ε)±bandy=acosn(t±ε)±b
  • Determining rules for graphs of trigonometric functions
  • The tangent function
  • Applications of trigonometric functions
• Exponential and logarithmic functions
  Sub Topics:

  • Revision of exponential functions
  • The exponential functionf(x)=ex.
  • Revision of exponential equations
  • Logarithms and the logarithm laws
  • Graphing logarithmic functions
  • Determining rules for graphs of exponential andlogarithmic functions
  • Solving equations involving exponential and logarithmic functions
  • Applications of exponential functions
  • Applications of logarithmic functions
• Refresher on differentiation
  Sub Topics:

  • The derivative
  • Rules for differentiation
  • Differentiating x^n where n is a negative integer
  • The graph of the derivative function
• Further differentiation and applications
  Sub Topics:

  • The chain rule
  • Differentiating rational powers
  • Differentiation of e^x
  • Differentiation of the natural logarithm function
  • Differentiation of trigonometric functions
  • The product rule
  • The quotient rule
  • Tangents and normals
  • Rates of change
  • Motion in a straight line
  • Stationary points
  • Types of stationary points
• Anti-differentiation
  Sub Topics:

  • Anti-differentiation of polynomial functions
  • Anti-differentiation of power functions
  • The anti-derivative of (ax+b)^r
  • The anti-derivative of e^kx
  • Anti-differentiation of trigonometric functions
  • Further anti-differentiation techniques
  • Applications of anti-differentiation to motion in astraight line
• Integration
  Sub Topics:

  • Estimating the area under a graph
  • Finding the exact area: the definite integral
  • Signed area
  • Integration of more families of functions
  • Further integration techniques
  • The area of a region between two curves
  • Applications of integration
• The second derivative and applications
  Sub Topics:

  • The second derivative and acceleration
  • Using the second derivative in graph sketching
  • Absolute maximum and minimum values
  • Optimisation problems
• Trigonometry using the sine and cosine rules
  Sub Topics:

  • Reviewing trigonometry
  • The sine rule
  • The cosine rule
  • The area of a triangle
  • Angles of elevation, angles of depression and bearings
  • Problems in three dimensions
  • Angles between planes and more complex 3D problems
• Refresher on probability and discrete random variables
  Sub Topics:

  • Sample spaces and probability
  • Conditional probability and independence
  • Discrete random variables
  • Expected value, variance and standard deviation
• Bernoulli sequences and the binomial distribution
  Sub Topics:

  • Introduction to Bernoulli sequences and the binomial distribution
  • The graph, expectation and variance of abinomial distribution
  • Finding the sample size
• Continuous random variables
  Sub Topics:

  • Introduction to continuous random variables
  • Mean and median for a continuous random variable
  • Measures of spread
  • Cumulative distribution functions
• The normal distribution
  Sub Topics:

  • The normal distribution
  • Standardisation
  • Determining normal probabilities
  • Solving problems using the normal distribution
  • The normal approximation to the binomial distribution
• Sampling and estimation
  Sub Topics:

  • Populations and samples
  • The exact distribution of the sample proportion
  • Approximating the distribution of the sample proportion
  • Confidence intervals for the population proportion