An introduction to Complex Numbers

Further complex numbers, Loci and the Argand Diagram

Matrices;

Add, subtract and multiply conformable matrices.

Multiply a matrix by a scalar.

Understand and use zero and identity matrices.

Use matrices to represent linear transformations in 2-D.

Successive transformations.

Single transformations in 3-D.

Find invariant points and lines for a linear transformation.

Topic assessments on Complex Numbers and Matrices

- Spiritual
- Moral
- Social
- Cultural

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

Complex Numbers

Hyperbolic functions

Polar coordinates

Each topic is assessed through a 50 minute formal test in class.

- Spiritual
- Moral
- Social
- Cultural

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

Vectors:

Equations of lines

The scalar product

Equations of planes

Further lines and planes

Calculus:

Volumes of revolution

Each topic is assessed through a 50 minute formal test.

- Spiritual
- Moral
- Social
- Cultural

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

Momentum and impulse

Work, energy and power

Elastic collisions in one dimension

Each topic is assessed through a 50 minute test under formal conditions

- Spiritual
- Moral
- Social
- Cultural

Roots of equations

Understand and use the relationships between the roots and coefficients of polynomial equations up to quartic equations.

Form a polynomial equation whose roots are a linear transformation of the roots of a given polynomial equation (of at least cubic degree).

Know that non-real roots of polynomial equations with real coefficients occur in conjugate pairs.

Solve cubic or quartic equations with real coefficients.

Sequences and series 1:

Summing series

Understand and use formulae for the sums of integers, squares and cubes and use these to sum other series.

Sequences and series 2:

Induction

Construct proofs using mathematical induction.

Contexts include sums of series, divisibility and powers of matrices.

Each topic is assessed through a 50 minute formal assessment task.

- Spiritual
- Moral
- Social
- Cultural

Poisson and binomial distributions (part 1)

Discrete probability distributions

Poisson and binomial distributions (part 2)

Chi squared tests

Each topic will be tested through a 50 minute assessment

- Spiritual
- Moral
- Social
- Cultural