Operations with numbers in the form a × 10k 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 used 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 used the first n terms of the sequence. Use of sigma notation for the sums of geometric sequences. Applications.

Financial applications of geometric sequences and series: • compound interest • annual depreciation.

Laws of exponents with integer exponents. Introduction to logarithms with base 10 and e. Numerical evaluation of logarithms using technology.

Approximation: decimal places, significant figures. Upper and lower bounds of rounded numbers. Percentage errors. Estimation.

Amortization and annuities using technology.

Use technology to solve: • Systems of linear equations in up to 3 variables be • Polynomial equations

Laws of logarithms: loga xy = loga x + logay x loga = loga x … logay y loga xm = mloga x for a, x, y >

Simplifying expressions, both numerically and algebraically, involving rational exponents.

The sum of infinite geometric sequences.

Complex numbers: the number i such that i2 = … 1. Cartesian form: z = a + bi; the terms real part, imaginary part, conjugate, modulus and argument. Calculate sums, differences, products, quotients, by hand and with technology. Calculating powers of complex numbers, in Cartesian form, with technology. The complex plane. Complex numbers as solutions to quadratic equations of the form ax + bx + c = 0, a ≠ 0, with real coefficients where b2 … 4ac < 0.

Modulus–argument (polar) form: z = r cosθ + isinθ = rcisθ. Exponential form: iθ z = re . Conversion between Cartesian, polar and exponential forms, by hand and with technology. Calculate products, quotients and integer powers in polar or exponential forms. Adding sinusoidal functions with the same frequencies but different phase shift angles. Geometric interpretation of complex numbers.

Definition of a matrix: the terms element, row, column and order for m × n matrices. Algebra of matrices: equality; addition; subtraction; multiplication by a scalar for m × n matrices. Multiplication of matrices. Properties of matrix multiplication: associativity, distributivity and non-commutativity. Identity and zero matrices. Determinants and inverses of n × n matrices with technology, and by hand for 2 × 2 matrices. Awareness that a system of linear equations can be written in the form Ax = b. Solution of the systems of equations using inverse matrix.

Eigenvalues and eigenvectors. Characteristic polynomial of 2 × 2 matrices. Diagonalization of 2 × 2 matrices (restricted to the case where there are distinct real eigenvalues). Applications to powers of 2 × 2 matrices.