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
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.
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
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.
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.
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
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.
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.
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.
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