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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^{n}C_{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 i
^{2}=-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.

Click on a statement above for suggested resources and activities from Transum.