A ‘Teach Further Maths’ Resource 70 Slides To be able to recognise the equations for simple parabolas, ellipses and hyperbolas. To be able to sketch their graphs. To be able to perform simple transformations on these curves. To be able to find the equations of the asymptotes for simple hyperbolas.

A ‘Teach Further Maths’ Resource 12 slides Lesson Objectives: To understand what is meant by an ‘improper integral’. To be able to evaluate simple improper integrals.

A 'Teach Further Maths' Resource 57 Slides To find the cube roots of unity. To illustrate these cube roots on an Argand Diagram. To solve problems relating to the cube roots of unity. To find the nth roots of unity. To illustrate these nth roots on an Argand Diagram. To find the nth roots of any number.

A ‘Teach Further Maths’ Resource To understand and use the Mean Value Theorem for integration. To understand the term ‘Root Mean Square Value’ and know how to calculate it for certain functions. (37 Slides)

A ‘Teach Further Maths’ Resource To be able to derive the formulae for volumes of revolution about the coordinates axes To be able to calculate volumes of revolution about the coordinates axes. To be able to calculate more complicated volumes of revolution about the coordinates axes. (69 Slides)

A 'Teach Further Maths' Resource 43 Slides To be able to find the distance between 2 points in 3 dimensions. To be able to derive and use a useful formula for a point dividing a line in a given ratio. To understand when 2 (or more) vectors are parallel. To be able to find vector equation of a line in vector form. To be able to find vector equation of a line in Cartesian form. To be able to convert vector equations from vector form to Cartesian form and vice versa. To understand what direction ratios are.

A 'Teach Further Maths Resource: 55 Slides To be able to find angle between a line and a plane To be able to find angle between 2 planes. To be able to find the equation of the line of intersection of 2 planes.

A 'Teach Further Maths' Resource 73 slides To be able to convert Polar form to Cartesian form. To be able to convert Cartesian form to Polar form. To use integration to find areas bound by Polar curves. To be able to find equations of tangents at the pole. To be able to find equations of tangents parallel (or perpendicular) to the initial line.

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 To be able to derive and use reduction formulae for integration. (47 Slides)

A ‘Teach Further Maths’ Resource 57 Slides To find the cube roots of unity. To illustrate these cube roots on an Argand Diagram. To solve problems relating to the cube roots of unity. To find the nth roots of unity. To illustrate these nth roots on an Argand Diagram. To find the nth roots of any number.

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.

An excellent resource that shows alternative approaches to solving simple trig. ratio problems. Each problem is solved using (i) the CAST diagram (ii) a graphical approach (iii) a quick method. The PowerPoint begins with an explanation of how the CAST diagram works. These slides are aimed at the more inquisitive student and are not compulsory.

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.

A 'Teach Further Maths' Resource 45 Slides To recall the concept of a ‘limit’. To be able to use MacLaurin’s series expansions to find certain limits. To know and use two special limits

A 'Teach Further Maths' Resource 41 slides Lesson Objectives: To be able to reduce various relations to linear laws.

A 'Teach Further Maths' Resource 66 Slides To understand ‘scalar product’ and be able to calculate it. To be able to find the angle between two vectors using the scalar product To use the scalar product to show whether two lines are perpendicular or not. To be able to prove whether or not two lines intersect and, if they do, find their point of intersection. To understand what is meant when we say that 2 lines are ‘skew’. To be able to prove whether or not 2 lines are skew. To be able to solve simple vector problems involving scalar product and other simple vector properties.

A 'Teach Further Maths' Resource 54 Slides To understand what is meant by the ‘inverse’ of a matrix. To understand what is meant by the ‘determinant’ of a matrix. To be able to find the determinant of a 2x2 or 3x3 matrix. To be able to find the inverse of a 2x2 or 3x3 matrix. To be able to consider determinants of 2x2 matrices and 3x3 matrices geometrically.

Pupils often find it difficult to visualise the centre of rotation for 90 degree rotations. So instead of the trial and error approach that they often employ, try this instead. I wrote this short PowerPoint presentation to demonstrate how it works. There are 3 examples and it finally makes use of the often redundant set square! Do let me know how it goes. Thanks Paul

This is always very popular with my pupils and could certainly be edited to suit any topic in any subject. I usually use this particular resource as a revision aid.