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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
Matrix Solution of Simultaneous Equations 2
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Matrix Solution of Simultaneous Equations 2

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A ‘Teach Further Maths’ Resource: 50 Slides To be able to interpret geometrically the solution (and failure of solution) of 3 simultaneous linear equations: Students should be able to interpret, on analysis of the 3 equations, whether the 3 planes meet in a point meet in a line (forming a sheaf) form a prism are all parallel are such that 2 of the 3 planes are parallel. Students should be familiar with the terms ‘dependent‘, ‘consistent’ and ‘inconsistent’.
Eigenvalues and Eigenvectors (A-Level Further Maths)
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Eigenvalues and Eigenvectors (A-Level Further Maths)

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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.
Finding the Centre of Rotation for 90 Degree Rotations
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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
Solving Linear Equations using Algebra Tiles
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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.
Matrices and Linear Transformations (A-Level Further Maths)
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Matrices and Linear Transformations (A-Level Further Maths)

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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.
Further Vectors 4 (A-Level Further Maths)
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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.
Inverse Matrices and Determinants
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Inverse Matrices and Determinants

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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.
Second Order Differential Equations (A-Level Further Maths)
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Second Order Differential Equations (A-Level Further Maths)

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A ‘Teach Further Maths’ Resource. 78 slides To understand what is meant by a ‘second order differential equation’. To be able to solve some second order differential equations using the auxiliary equation. To be able to solve some second order differential equations by finding a complementary function and a particular integral.
Roots of Polynomials
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Roots of Polynomials

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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.
Further Vectors 2 (A-Level Further Maths)
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Further Vectors 2 (A-Level Further Maths)

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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.
Roots of Polynomials (A-Level Further Maths)
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Roots of Polynomials (A-Level Further Maths)

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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.
Finding the Centre of Rotation for 90 Degree Rotations
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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
Polar Coordinates 2 (A-Level Further Maths)
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Polar Coordinates 2 (A-Level Further Maths)

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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.
DeMoivre's Theorem and Applications 2
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DeMoivre's Theorem and Applications 2

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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.
Inverse Trigonometric Functions (A-Level Further Maths)
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Inverse Trigonometric Functions (A-Level Further Maths)

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A ‘Teach Further Maths’ Resource 46 Slides To sketch graphs of inverse trigonometric functions. To be able to differentiate inverse trigonometric functions. To recognise integrals which integrate to inverse trigonometric functions. To integrate more complicated expressions To know a special form of integral
Further Vectors 3 (A-Level Further Maths)
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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.
Further Vectors 1 (A-Level Further Maths)
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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.