Queensland Year 11 Specialist (Units 1 & 2) topics

Below are the topics that sit within Queensland Year 11 Specialist (Units 1& 2) mathematics. When you click on a certain topic, you will be take to all the subtopics.

• Algebra
  Sub Topics:

  • Indices
  • Standard form
  • Solving linear equations and simultaneous linear equations
  • Solving problems with linear equations
  • Solving problems with simultaneous linear equations
  • Substitution and transposition of formulas
  • Algebraic fractions
  • Literal equations
• Number Systems and Sets
  Sub Topics:

  • Set notation
  • Sets of numbers
  • Surds
  • Natural numbers
  • Problems involving sets
• Trigonometric Ratios and Applications
  Sub Topics:

  • Reviewing trigonometry
  • Exact values of sine, cosine and tangent
  • The sine rule
  • The cosine rule
  • Angles of elevation, angles of depression and bearings
  • Angles in the four quadrants
• Further Algebra
  Sub Topics:

  • Polynomial identities
  • Quadratic equations
  • Applying quadratic equations to rate problems
  • Partial fractions
  • Simultaneous equations
• Vectors in the Plane
  Sub Topics:

  • Introduction to vectors
  • Components of vectors
  • Polar form of a vector
  • Scalar product of vectors
  • Vector projections
  • Applications of vectors - displacement and velocity
  • Applications of vectors - relative velocity
  • Applications of vectors - forces and equilibrium
• Principles of counting
  Sub Topics:

  • Basic counting methods
  • Factorial notation and permutations
  • Permutations with restrictions
  • Permutations of like objects
  • Combinations
  • Combinations with restrictions
  • Pascals triangle
  • The pigeonhole principle
  • The inclusion-exclusion principle
  • Applications to probability
• Number and Proof
  Sub Topics:

  • Direct proof
  • Proof by contrapositive
  • Proof by contradiction
  • Equivalent statements
  • Disproving statements
  • Mathematical induction
• Geometry in the plane and proof
  Sub Topics:

  • Points, lines and angles
  • Triangles and polygons
  • Congruence and proofs
  • Pythagoras theorem
  • Ratios
  • Introduction to similarity
  • Proofs involving similarity
  • Areas, volumes and similarity
  • Geometric proofs using vectors
  • The golden ratio
• Circle Geometry
  Sub Topics:

  • Angle properties of circles
  • Tangents
  • Chords in circles
• Graphing techniques
  Sub Topics:

  • The modulus function
  • Reciprocals of polynomial functions
  • Rational functions
  • Graphing rational functions using calculus
• Trigonometric functions
  Sub Topics:

  • Defining the trigonometric functions
  • Symmetry properties and the Pythagorean identity
  • Solution of equations involving sine and cosine
  • Transformations of the graphs of sine and cosine
  • The tangent function
  • General solution of trigonometric equations
  • Reciprocals of trigonometric functions
  • Graphing the reciprocal trigonometric functions
  • Applications of trigonometric functions
• Trigonometric identities
  Sub Topics:

  • Reciprocal trigonometric functions and the Pythagorean identity
  • Angle sum and difference identities
  • Simplifying a cos x + b sin x
  • Sums and products of sines and cosines
• Complex numbers
  Sub Topics:

  • Starting to build the complex numbers
  • Multiplication and division of complex numbers
  • Argand diagrams
  • Solving equations over the complex numbers
  • Polar form of a complex number
  • De Moivres theorem
• Matrices
  Sub Topics:

  • Matrix notation
  • Addition, subtraction and multiplication by a real number
  • Multiplication of matrices
  • Identities, inverses and determinants for 2 x 2 matrices
  • Solution of simultaneous equations using matrices
  • Inverses and determinants for n x n matrices
  • Simultaneous linear equations with more than two variables
• Transformations of the plane
  Sub Topics:

  • Linear transformations
  • Geometric transformations
  • Rotations and general reflections
  • Composition of transformations
  • Inverse transformations
  • Transformations of straight lines and other graphs
  • Area and determinant
  • General transformations
• Further graphing techniques
  Sub Topics:

  • Locus of points
  • Parabolas
  • Ellipses
  • Hyperbolas
  • Parametric equations
  • Polar coordinates
  • Graphing using polar coordinates
  • Further graphing using polar coordinates