A ‘Teach Further Maths’ Resource 22 slides Lesson Objectives: To know what is meant by an ‘improper integral’. To know how to find certain improper integrals.

A ‘Teach Further Maths’ Resource 37 slides Lesson Objectives: To understand what is meant by a linear, first order differential equation’. To recall how to solve some linear first order differential equations by separating variables. To know what is meant by a ‘Family of Solution Curves’. To know how to solve some linear first order differential equations using an integrating factor.

A ‘Teach Further Maths’ Resource 64 slides To understand simple matrix terminology e.g. ‘matrix’, ‘order’. To be able add, subtract and multiply compatible matrices. To be able to ascertain whether or not matrix multiplication is commutative/associative. To know and use the properties of ‘square’, ‘identity’ and ‘zero’ matrices.

A ‘Teach Further Maths’ Resource: 32 slides Lesson Objectives: To understand what is meant by an ‘asymptote’. To know how to find the equations of horizontal asymptotes. To know how to find the equations of vertical asymptotes. To be able to sketch the graphs of some rational functions.

A ‘Teach Further Maths’ Resource 55 slides Lesson Objectives: To understand what is meant by an Argand Diagram. To understand what is meant by the Modulus and Argument of a complex number. To be able to divide one complex number by another complex number. To solve equations using Real and Imaginary parts. To understand what is meant by Modulus-Argument form. To multiply and divide complex numbers written in modulus-argument form.

A ‘Teach Further Maths’ Resource 40 Slides To understand what is meant by ‘diagonal matrices’ and ‘symmetric matrices’. To understand what is meant by ‘diagonalising’ a matrix. To be able to deduce diagonalisability for simple 2x2 and 3x3 matrices. To be able to diagonalise a given symmetric matrix. To apply the method of diagonalisation to evaluate the power of a given symmetric matrix.

A ‘Teach Further Maths’ Resource 34 Slides To be able to find the general solution of simple trigonometric equations in degrees. To be able to find the general solution of simple trigonometric equations in radians.

A Teach Further Maths' Resource 73 Slides To understand what is meant by a ‘transformation’. To understand what is meant by a ‘linear transformation’. To be able to show that a given transformation is linear. To understand what is meant by an ‘inverse transformation’. To be able to find the inverse of a given linear transformation. To be able to find matrices that represent given linear transformations. To be able to find matrices that represent composite linear transformations. To understand what is meant by ‘invariant points’ and ‘invariant lines’. To be able to find invariant points/lines for a given transformation matrix. To be able to find matrices representing inverse linear transformations. To be able to find matrices representing inverse of composite linear transformations. To understand how to find the transpose of a matrix.

A ‘Teach Further Maths’ Resource 54 Slides To understand what is meant by ‘eigenvalues’ and ‘eigenvectors’. To understand how to find the ‘characteristic equation’. To be able to find eigenvalues and eigenvectors for given 2x2 and 3x3 matrices. Understand what is meant by the terms ‘normalised eigenvectors’, ‘orthogonal eigenvectors’ and ‘orthogonal matrices’. To be able to show that a given matrix is orthogonal.

A 'Teach Further Maths' Resource 34 slides Lesson Objectives: To be able to solve inequalities involving rational expressions using a graphical method.

A 'Teach Further Maths' Resource 22 slides Lesson Objectives: To know what is meant by an ‘improper integral’. To know how to find certain improper integrals.

A 'Teach Further Maths' Resource. 25 slides Lesson Objectives: To recall the laws of logarithms. To be able to use logarithms to reduce certain relations to linear laws.

A 'Teach Further Maths' Resource 34 Slides To be able to find the general solution of simple trigonometric equations in degrees. To be able to find the general solution of simple trigonometric equations in radians.

A 'Teach Further Maths' Reesource 38 Slides To be able to use MacLaurin’s Series to find series expansions. To be able to find the Ranges of Validity for certain series.

A 'Teach Further Maths' Resource 18 Slides To write a complex number in exponential form. To multiply and divide complex numbers in exponential form.

A 'Teach Further Maths' Resource 47 Slides To understand and use Sigma notation. To be able to derive and use the formula for ∑r. To be able to use the formulae for ∑r2 and ∑r3. To be able to solve series questions requiring algebraic manipulation.

A 'Teach Further Maths' Resource 31 Slides To understand what is meant by hyperbolic functions. To be able to sketch graphs of hyperbolic functions. To be able to establish hyperbolic identities. To understand Osborn’s Rule.

A ‘Teach Further Maths’ Reesource 38 Slides To be able to use MacLaurin’s Series to find series expansions. To be able to find the Ranges of Validity for certain series.

A ‘Teach Further Maths’ Resource 53 Slides To be able to sketch loci on an Argand Diagram.

A 'Teach Further Maths' Resource 43 Slides To recall how to multiply and divide complex numbers in Modulus-Argument form. To understand DeMoivre’s Theorem. To use DeMoivre’s Theorem to find powers of complex numbers. To use DeMoivre’s Theorem to establish trigonometric identities.