The resource covers: Formulate a problem involving the solution of 3 linear simultaneous equations in 3 unknowns as a problem involving the solution of a matrix equation, or vice versa* Prove de Moivre’s theorem for a positive integer exponent Understand the cases that may arise concerning the consistency or inconsistency of 3 linear simultaneous equations, relate them to the singularity or otherwise of the corresponding matrix Solve consistent systems, and interpret geometrically in terms of lines and planes – to express trigonometrical ratios of multiple angles in terms of powers of trigonometrical ratios of the fundamental angle Understand the terms ‘characteristic equation’, ‘eigenvalue’ and ‘eigenvector’, as applied to square matrices Find eigenvalues and eigenvectors of 2 × 2 and 3 × 3 matrices express a square matrix in the form QDQ^–1, where D is a diagonal matrix of eigenvalues and Q is a matrix whose columns are eigenvectors, and use this expression Use the fact that a square matrix satisfies its own characteristic equation.

The resource covers: Formulate a problem involving the solution of 3 linear simultaneous equations in 3 unknowns as a problem involving the solution of a matrix equation, or vice versa* Prove de Moivre’s theorem for a positive integer exponent Understand the cases that may arise concerning the consistency or inconsistency of 3 linear simultaneous equations, relate them to the singularity or otherwise of the corresponding matrix Solve consistent systems, and interpret geometrically in terms of lines and planes – to express trigonometrical ratios of multiple angles in terms of powers of trigonometrical ratios of the fundamental angle Understand the terms ‘characteristic equation’, ‘eigenvalue’ and ‘eigenvector’, as applied to square matrices Find eigenvalues and eigenvectors of 2 × 2 and 3 × 3 matrices express a square matrix in the form QDQ^–1, where D is a diagonal matrix of eigenvalues and Q is a matrix whose columns are eigenvectors, and use this expression Use the fact that a square matrix satisfies its own characteristic equation.

Formulate hypotheses concerning the difference of population means, and apply, as appropriate – a paired sample t-test – a test using a normal distribution

Formulate hypotheses and apply a hypothesis test concerning the population mean using a small sample drawn from a normal population of unknown variance, using a t-test Calculate a pooled estimate of a population variance from two samples Formulate hypotheses concerning the difference of population means, and apply, as appropriate – a 2-sample t-test – a paired sample t-test – a test using a normal distribution Determine a confidence interval for a population mean, based on a small sample from a normal population with unknown variance, using a t-distribution Determine a confidence interval for a difference of population means, using a t-distribution or a normal distribution, as appropriate.

Sign Test PPT Paired Sign Test PPT One Sample Wilcoxon Sign Rank Test PPT Wilcoxon-Matched-Pairs Sign-Rank Test PPT Wilcoxon Rank-Sum Test PPT

Sign Test PPT Paired Sign Test PPT One Sample Wilcoxon Sign Rank Test PPT Wilcoxon-Matched-Pairs Sign-Rank Test PPT Wilcoxon Rank-Sum Test PPT

Use a Wilcoxon matched-pairs signed-rank test as appropriate, to test for identity of populations.

Use a a single-sample Wilcoxon signed-rank test to test a hypothesis concerning a population median

Use a single-sample sign test to test a hypothesis concerning a population median

Use a Wilcoxon rank-sum test, as appropriate, to test for identity of populations.

Use a paired-sample sign test as appropriate, to test for identity of populations.