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Teach Further Maths

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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

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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

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Series
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Series

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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.
DeMoivre's Theorem and Applications 1
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DeMoivre's Theorem and Applications 1

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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.
Complex Roots of Polynomials with Real Coefficients
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Complex Roots of Polynomials with Real Coefficients

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A 'Teach Further Maths Resource' 33 Slides To understand that, for a polynomial with real coefficients, any complex roots occur in conjugate pairs. To use this condition in solving various problems about complex roots of polynomials.
Differentiation of Hyperbolic Functions
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Differentiation of Hyperbolic Functions

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A 'Teach Further Maths' Resource 36 Slides To be able to differentiate hyperbolic functions. To be able to sketch graphs of hyperbolic functions. To be able to differentiate inverse hyperbolic functions. To be able to sketch graphs of inverse hyperbolic functions. To write inverse hyperbolic functions in logarithmic form.
Composite Geometric Transformations Using Matrices
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Composite Geometric Transformations Using Matrices

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A 'Teach Further Maths' Resource 28 Slides To recall the rules of simple transformations. To be able to find matrices representing simple composite transformations. To know that composite transformation matrices are pre-multiplied. To be able to describe simple composite transformations represented by some matrices.
Diagonalisation of a Matrix
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Diagonalisation of a Matrix

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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.
Numerical Methods for 1st Order Differential Equations
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Numerical Methods for 1st Order Differential Equations

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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.
Polar Coordinates 1
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Polar Coordinates 1

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A 'Teach Further Maths' Resource 42 slides Lesson Objectives: To understand what is meant by ‘Polar Coordinates’. To be able to plot Polar Coordinates. To be able to sketch curves given in Polar form. To understand that some simple polar curves can be sketched without plotting points.
More Asymptotes and Rational Functions
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More Asymptotes and Rational Functions

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A 'Teach Further Maths' Resource 46 slides Lesson Objectives: To be able to sketch curves for certain rational functions. Find the regions for which certain rational functions actually exist. Find stationary points without the use of calculus.
Modelling with First Order Differential Equations
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Modelling with First Order Differential Equations

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A ‘Teach Further Maths’ Resource To be able to model certain situations using 1st order differential equations. To be able to model certain situations using coupled 1st order differential equations. (64 Slides)
Modelling with Second Order Differential Equations
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Modelling with Second Order Differential Equations

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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)
Matrix Transformations in 3D
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Matrix Transformations in 3D

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A ‘Teach Further Maths’ Resource To be able to carry out reflections about one of the coordinate axes in 3 dimensions. To be able to carry out rotations about one of the coordinate axes in 3 dimensions. (40 Slides)
Further Vectors 6
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Further Vectors 6

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A ‘Teach Further Maths’ Resource To be able to find the vector product of two vectors. To understand various properties of the vector product. To be able to use the vector product to find perpendicular vectors. To be able to find certain areas and volumes using the vector product. (52 Slides)
Further Vectors 7
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Further Vectors 7

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A ‘Teach Further Maths’ Resource To be able to find the equation of a line using the vector product. To be able to the distance between a point and a line using the vector product. To be able to find the shortest distance between two skew lines using the vector product. To be able to use the vector product to deduce whether or not two lines intersect. To be able to interpret the vector product geometrically. (36 Slides)
The Mean Value Theorem
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The Mean Value Theorem

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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)
L’Hôpital’s Rule
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L’Hôpital’s Rule

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A ‘Teach Further Maths’ Resource To be able to use L’Hôpital’s Rule to evaluate certain limits of indeterminate form. (36 Slides)
Further Numerical Integration
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Further Numerical Integration

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A ‘Teach Further Maths’ Resource To be able to approximate the area under a curve using the Mid-Ordinate Rule. To be able to approximate the area under a curve using Simpson’s Rule. (51 Slides)
Factorising Determinants
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Factorising Determinants

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A ‘Teach Further Maths’ Resource To know and use the basic rules for simplifying determinants. To be able to factorise determinants. (57 Slides)
Inequalities Involving Cubics and Quartics
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Inequalities Involving Cubics and Quartics

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A ‘Teach Further Maths’ Resource To be able to apply the Rational Root Theorem to identify factors of polynomials. To be able to use Descartes’ Rule of Signs to identify the nature (signs) of roots of polynomials. To be able to solve inequalities involving cubic and quartic functions. (41 Slides)