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These are the statements describing what students need to learn:

[Higher Level only statements are in blue]

• operations with numbers in the form a × 10^k where 1 ≤ a < 10 and k is an integer
• arithmetic sequences and series. Use of the formulae for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for sums of arithmetic sequences.
  
  Applications.
  
  Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life.
• geometric sequences and series. Use of the formulae for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for the sums of geometric sequences
  
  Use of sigma notation for the sums of geometric sequences.
  
  Applications.
• financial applications of geometric sequences and series: compound interest and annual depreciation
• laws of exponents with integer exponents. Introduction to logarithms with base 10 and e. Numerical evaluation of logarithms using technology
• simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side (LHS to RHS) proof. The symbols and notation for equality and identity
• laws of exponents with rational exponents.
  Laws of logarithms
  Change of base of a logarithm.
  Solving exponential equations, including using logarithms
• Sum of infinite convergent geometric sequences.
• the binomial theorem including the expansion of (a+b)ⁿ,n ∈ N. Use of Pascal's triangle and ⁿC_r
• Counting principles, including permutations and combinations. Extension of the binomial theorem to fractional and negative indices, ie (a+b)ⁿ, n ∈ Q
• Partial fractions
• Complex numbers: the number i, where i²=-1. Cartesian form z=a+bi; the terms real part, imaginary part, conjugate, modulus and argument. The complex plane.
• Modulus–argument (polar) form: z=r(cosθ+isinθ)=rcisθ. Euler form: z=re^iθ Sums, products and quotients in Cartesian, polar or Euler forms and their geometric interpretation.
• Complex conjugate roots of quadratic and polynomial equations with real coefficients. De Moivre’s theorem and its extension to rational exponents. Powers and roots of complex numbers.
• Proof by mathematical induction. Proof by contradiction. Use of a counterexample to show that a statement is not always true.
• Solutions of systems of linear equations (a maximum of three equations in three unknowns), including cases where there is a unique solution, an infinite number of solutions or no solution.

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