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: Understand de Moivre’s theorem, for a positive or negative integer exponent, in terms of the geometrical effect of multiplication and division of complex numbers Prove de Moivre’s theorem for a positive integer exponent Use de Moivre’s theorem for a positive or negative rational exponent – to express trigonometrical ratios of multiple angles in terms of powers of trigonometrical ratios of the fundamental angle – to express powers of sinθand cos θ in terms of multiple angles – in the summation of series – in finding and using the nth roots of unity

The resource covers: Understand de Moivre’s theorem, for a positive or negative integer exponent, in terms of the geometrical effect of multiplication and division of complex numbers Prove de Moivre’s theorem for a positive integer exponent Use de Moivre’s theorem for a positive or negative rational exponent – to express trigonometrical ratios of multiple angles in terms of powers of trigonometrical ratios of the fundamental angle – to express powers of sinθand cos θ in terms of multiple angles – in the summation of series – in finding and using the nth roots of unity

The resource covers: Find an integrating factor for a first order linear differential equation, and use an integrating factor to find the general solution Recall the meaning of the terms ‘complementary function’ and ‘particular integral’ in the context of linear differential equations, and recall that the general solution is the sum of the complementary function and a particular integral Find the complementary function for a first or second order linear differential equation with constant coefficients Recall the form of, and find, a particular integral for a first or second order linear differential equation in the cases where a polynomial or ae^bx or a cos px + b sin px is a suitable form, and in other simple cases find the appropriate coefficient(s) given a suitable form of particular integral. Use a given substitution to reduce a differential equation to a first or second order linear equation with constant coefficients or to a first order equation with separable variables. Use initial conditions to find a particular solution to a differential equation, and interpret a solution in terms of a problem modelled by a differential equation

The resource covers: Understand de Moivre’s theorem, for a positive or negative integer exponent, in terms of the geometrical effect of multiplication and division of complex numbers Prove de Moivre’s theorem for a positive integer exponent Use de Moivre’s theorem for a positive or negative rational exponent – to express trigonometrical ratios of multiple angles in terms of powers of trigonometrical ratios of the fundamental angle – to express powers of sinθand cos θ in terms of multiple angles – in the summation of series – in finding and using the nth roots of unity

The resource covers: Find an integrating factor for a first order linear differential equation, and use an integrating factor to find the general solution Recall the meaning of the terms ‘complementary function’ and ‘particular integral’ in the context of linear differential equations, and recall that the general solution is the sum of the complementary function and a particular integral Find the complementary function for a first or second order linear differential equation with constant coefficients Recall the form of, and find, a particular integral for a first or second order linear differential equation in the cases where a polynomial or ae^bx or a cos px + b sin px is a suitable form, and in other simple cases find the appropriate coefficient(s) given a suitable form of particular integral. Use a given substitution to reduce a differential equation to a first or second order linear equation with constant coefficients or to a first order equation with separable variables. Use initial conditions to find a particular solution to a differential equation, and interpret a solution in terms of a problem modelled by a differential equation

The resource covers: Find an integrating factor for a first order linear differential equation, and use an integrating factor to find the general solution Recall the meaning of the terms ‘complementary function’ and ‘particular integral’ in the context of linear differential equations, and recall that the general solution is the sum of the complementary function and a particular integral Find the complementary function for a first or second order linear differential equation with constant coefficients Recall the form of, and find, a particular integral for a first or second order linear differential equation in the cases where a polynomial or ae^bx or a cos px + b sin px is a suitable form, and in other simple cases find the appropriate coefficient(s) given a suitable form of particular integral. Use a given substitution to reduce a differential equation to a first or second order linear equation with constant coefficients or to a first order equation with separable variables. Use initial conditions to find a particular solution to a differential equation, and interpret a solution in terms of a problem modelled by a differential equation

Use integration to find surface areas of revolution about one of the axes for curves with equations in Cartesian coordinates, including the use of a parameter.

Approximating area under a curve using area of rectangles and use rectangles to estimate or set bounds for the area under a curve or to derive inequalities or limits concerning sums

Derive and use reduction formulae for the evaluation of definite integrals

Integration hyperbolic functions and inverses

The resource covers: Integration hyperbolic functions and inverses Derive and use reduction formulae for the evaluation of definite integrals Approximating area under a curve using area of rectangles and use rectangles to estimate or set bounds for the area under a curve or to derive inequalities or limits concerning sums Use integration to find arc lengths for curves with equations in Cartesian coordinates, including the use of a parameter, or in polar coordinates Use integration to find surface areas of revolution about one of the axes for curves with equations in Cartesian coordinates, including the use of a parameter.

The resource covers: Integration hyperbolic functions and inverses Derive and use reduction formulae for the evaluation of definite integrals Approximating area under a curve using area of rectangles and use rectangles to estimate or set bounds for the area under a curve or to derive inequalities or limits concerning sums Use integration to find arc lengths for curves with equations in Cartesian coordinates, including the use of a parameter, or in polar coordinates Use integration to find surface areas of revolution about one of the axes for curves with equations in Cartesian coordinates, including the use of a parameter.

The resource covers: Integration hyperbolic functions and inverses Derive and use reduction formulae for the evaluation of definite integrals Approximating area under a curve using area of rectangles and use rectangles to estimate or set bounds for the area under a curve or to derive inequalities or limits concerning sums Use integration to find arc lengths for curves with equations in Cartesian coordinates, including the use of a parameter, or in polar coordinates Use integration to find surface areas of revolution about one of the axes for curves with equations in Cartesian coordinates, including the use of a parameter.

The resource covers Maclaurin’s series

The resource covers the differentiation of parametric equations

The resource covers differentiation of inverse trigonometric functions

The resource covers the differentiation of implicit functions

The resource covers the differentiating hyperbolic functions and inverses

The resource covers : Differentiating hyperbolic functions and inverses Differentiation implicit functions Differentiating parametric equations Differentiating inverse of trigonometric functions Maclaurin series