51ºÚÁÏ

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' 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 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 49 Slides To understand the method of Mathematical Induction. To use Induction to prove results for summation of series. To use Induction to prove results from other areas. Last updated 23 Jan 2016, created 23 Jan 2016

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 53 Slides To be able to sketch loci on an Argand Diagram.

A 'Teach Further Maths Resource 65 slides To know the relationship between the roots of a polynomial equation and its coefficients. To be able to find polynomial equations with related roots. To know and use the result for the sums of the squares of roots.

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 41 slides Lesson Objectives: To be able to reduce various relations to linear laws.

A 'Teach Further Maths Resource 65 slides To know the relationship between the roots of a polynomial equation and its coefficients. To be able to find polynomial equations with related roots. To know and use the result for the sums of the squares of roots.

A 'Teach Further Maths' Resource 37 slides Lesson Objectives: To understand what is meant by an ‘imaginary number’. To be able to calculate with powers of i. To understand what is meant by a ‘complex number’. To be able to solve any quadratic equation. To know the condition for a quadratic equation to have complex conjugate solutions. To understand what is meant by an ‘Argand Diagram’. To be able to perform simple arithmetic with complex numbers. To be able to equate real and imaginary parts to solve some problems involving complex numbers.

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 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 18 Slides To write a complex number in exponential form. To multiply and divide complex numbers in exponential form.

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 24 Slides To be able to solve linear simultaneous equations by finding the inverse of a matrix. To appreciate that the determinant can be used to determine the existence (or not) of a unique solution for a system of linear simultaneous equations.

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.

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.

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

I wrote this for those pupils who have difficulty with the traditional methods of solving linear equations, and it has gone down rather well so far. I found that some pupils didn't even need to use a set of algebra tiles. They were happy to simply visualise what was happening in the PowerPoint presentation whilst solving their equations. I hope it works for you.