Queensland Year 11 Specialist (Units 3 & 4) topics

Below are the topics that sit within Queensland Year 11 Specialist (Units 3 & 4) mathematics. When you click on a certain topic, you will be take to all the subtopics.

• Trigonometric functions
  Sub Topics:

  • Trigonometric functions
  • The reciprocal trigonometric functions
  • Angle sum and difference identities
  • The inverse trigonometric functions
  • Solution of equations.
  • Sums and products of sines and cosines
• Cartesian and parametric equations
  Sub Topics:

  • Circles
  • Ellipses and hyperbolas
  • Parametric equations
• Mathematical induction
  Sub Topics:

  • Revision of proof techniques
  • Mathematical induction
• Vectors
  Sub Topics:

  • Introduction to vectors
  • Resolution of a vector into rectangular components
  • Polar form of a vector
  • Scalar product of vectors
  • Vector projections
  • Collinearity
  • Geometric proofs
• Vector equations
  Sub Topics:

  • Vector functions
  • Position vectors as a function of time
  • Vector equations of lines
  • Intersection of lines and skew lines
  • Vector product
  • Vector equations of planes
  • Distances, angles and intersections
  • Equations of spheres
• Systems of linear equations
  Sub Topics:

  • Simultaneous linear equations with two variables
  • Simultaneous linear equations with more than two variables
  • Using augmented matrices for systems of equations
• Applications of matrices
  Sub Topics:

  • Revision of matrix algebra
  • Inverses and determinants for 2×2 matrices andapplications to transformations.
  • Using matrix algebra for systems of linear equations in two variables
  • Inverses and determinants for n×n matrices
  • Using matrix algebra for systems of linear equations in more than two variables
  • Dominance matrices
  • Leslie matrices
• Vector calculus
  Sub Topics:

  • Summary of differentiation and anti-differentiation
  • Position vectors as a function of time
  • Vector calculus
  • Velocity and acceleration for motion along a curve
  • Motion in a straight line
  • Projectile motion
  • Circular motion
• Complex numbers
  Sub Topics:

  • Starting to build the complex numbers
  • Modulus, conjugate and division
  • The polar form of a complex number
  • Basic operations on complex numbers in polar form
  • Solving quadratic equations over the complex numbers
  • Solving of polynomials over the complex numbers
  • Roots of complex numbers
  • Sketching subsets of the complex plane
• Techniques of integration
  Sub Topics:

  • Finding definite integrals and using the modulus function
  • Derivatives of inverse trigonometric functions
  • Anti-derivatives involving inverse trigonometric functions
  • Integration by substitution
  • Definite integrals by substitution
  • Using trigonometric identities for integration
  • Partial fractions
  • Integration by parts
  • Further techniques and miscellaneous exercises
• Applications of integration
  Sub Topics:

  • The fundamental theorem of calculus
  • Area of a region between two curves
  • Volumes of solids of revolution
  • The exponential probability distribution
  • Simpson’s rule
• Rates of change and differential equations
  Sub Topics:

  • Implicit differentiation
  • An introduction to differential equations
  • Differential equations involving a function of the independent variable
  • Differential equations involving a function of the dependent variable
  • Applications of differential equations
  • The logistic differential equation
  • Separation of variables
  • Related rates
  • Differential equations with related rates
  • Slope field for a differential equation.
• Modelling motion
  Sub Topics:

  • Motion in a straight line
  • Differential equations of the form v=f(x) and a=f(v)
  • Other expressions for acceleration
  • Simple harmonic motion
  • Force
  • Newton’s laws of motion
  • Resolution of forces and inclined planes
  • Connected particles
  • Variable forces
• Statistical inference
  Sub Topics:

  • Linear combinations of random variables
  • Linear combinations of independent normal random variables
  • The distribution of the sample mean for a normal random variable
  • The distribution of the sample mean for other random variables
  • Confidence intervals for the population mean