# Teach Further Maths

'Teach Further Maths' is a suite of Maths PowerPoint presentations for Teachers and Students of Further Mathematics A Level, AS Level or equivalent. 68 high quality, fully animated colour further maths PowerPoint presentations, consisting of over 3000 slides - a comprehensive teaching resource. PowerPoints covering all of the major topics from the syllabi - Polar Coordinates, Matrices, Differential Equations etc...) Complete further maths A level lessons ready to deliver

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'Teach Further Maths' is a suite of Maths PowerPoint presentations for Teachers and Students of Further Mathematics A Level, AS Level or equivalent. 68 high quality, fully animated colour further maths PowerPoint presentations, consisting of over 3000 slides - a comprehensive teaching resource. PowerPoints covering all of the major topics from the syllabi - Polar Coordinates, Matrices, Differential Equations etc...) Complete further maths A level lessons ready to deliver

#### Trig. Ratios of Any Angle

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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.

#### Modelling with Second Order Differential Equations (A-Level Further Maths)

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A ‘Teach Further Maths’ Resource To be able to model simple harmonic motion using 2nd order differential equations. To be able to model damped (and forced) oscillations using 2nd order differential equations. (38 Slides)

#### Solving Linear Equations using Algebra Tiles

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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.

#### Differential Equations Bundle

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7 presentations covering various aspects of first and second order differential equations, including their use in modelling. Covers all of the core A-Level Further Maths content for differential equations + more!

#### Proof by Mathematical Induction

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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

#### Numerical Methods for 1st Order Differential Equations (A-Level Further Maths)

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A ‘Teach Further Maths’ Resource 57 Slides To be able to solve first order differential equations of the form dy/dx = f(x) using the following ‘step by step’ methods: 1. Euler’s method 2. The Mid-Point method. 3. The Improved Euler method.

#### Further Vectors 1 (A-Level Further Maths)

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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.

#### Further Vectors 4 (A-Level Further Maths)

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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.

#### Further Vectors 3 (A-Level Further Maths)

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A 'Teach Further Maths' Resource: 51 Slides To be able to find the Equation of a Plane in Scalar Product form. To be able to find the Equation of a Plane in Cartesian form. To be able to find the Equation of a Plane in Parametric form. To be able to find the Perpendicular Distance from a Point to a Plane.

#### Parabolas, Ellipses and Hyperbolas (A-Level Further Maths)

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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.

#### Numerical Methods

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A 'Teach Further Maths' Resource 59 Slides To be able to solve equations of the form f(x) =0 using the method of interval bisection. To be able to solve equations of the form f(x) =0 using the method of linear interpolation. To be able to solve equations of the form f(x) =0 using the Newton-Raphson method. To be able to solve equations of the form dy/dx = f(x) using Euler's 'Step by Step' Method.

#### Eigenvalues and Eigenvectors

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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.

#### First Order Differential Equations

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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.

#### Polar Coordinates 2

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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.

#### Finding the Centre of Rotation for 90 Degree Rotations

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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

#### Improper Integrals 1 (A-Level Further Maths)

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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.