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
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(The order of delivery over the 2 years may differ from this depending on the needs of the individual teaching group)
Core Pure - Series, Roots of Polynomials, Volumes of Revolution
Decision - Graphs and Networks, Algorithms on Graphs
Each topic will be tested through a 50 minute assessment
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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 will be tested through a 50 minute assessment
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Momentum and impulse
Work, energy and power
Elastic collisions in one dimension
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Vectors:
Equations of lines
The scalar product
Equations of planes
Further lines and planes
Calculus:
Volumes of revolution
Each topic will be tested through a 50 minute assessment
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Complex Numbers
Hyperbolic functions
Polar coordinates
Mock Exam
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New Description
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