Excellent PowerPoint Teaching Resources for Teachers of Further Maths A Level
What is '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.
 50 high quality, fully animated colour further maths PowerPoint presentations, consisting of over 2000 slides  a comprehensive teaching resource.
 PowerPoints covering many of the major topics from modules FP1, FP2, FP3 and FP4 (e.g. Polar Coordinates, Matrices, Differential Equations etc...)
 Complete further maths A level lessons ready to deliver in the class room or for tutoring at home.
 Written by a very experienced classroom practitioner.
 Includes demonstrations, proofs, worked examples, exercises, examstyle questions and actual exam questions (used with permission).
 Material from all of the major examination boards (OCR, MEI, AQA, EDEXCEL, WJEC, SQA, CCEA...)
 Ideal for use with interactive whiteboards.
 No need for internet/network connection.
A selection of some of the most outstanding and inspiring mathematicians in history.
Which topics does 'Teach Further Maths' cover?
There is extensive coverage of the key topics met on most further mathematics syllabi: Complex numbers, Calculus etc...
For some exam boards, the 50 presentations will take care of a full ALevel Further Pure Mathematics course (e.g. AQA FP1, FP2 and FP3 Module are all complete)
Although these PowerPoint presentations do not yet form an exhaustive list for all exam boards, there will be more presentations added, as they are completed.
Overall, regardless of your exam board, you will no doubt regard 'Teach Further Maths' as an essential and much valued teaching tool.
For some exam boards, the 50 presentations will take care of a full ALevel Further Pure Mathematics course (e.g. AQA FP1, FP2 and FP3 Module are all complete)
Although these PowerPoint presentations do not yet form an exhaustive list for all exam boards, there will be more presentations added, as they are completed.
Overall, regardless of your exam board, you will no doubt regard 'Teach Further Maths' as an essential and much valued teaching tool.
Screenshots from 'Teach Further Maths':
A small sample of what to expect from 'Teach Further Maths':
Pricing for Individual Further Maths PowerPoint Presentations:
If you do not wish to purchase all of the PowerPoint presentations, then you can simply choose the presentations that you prefer.
Individual PowerPoint presentations will be uploaded to an email address of your choosing, once payment has been made.
Individual PowerPoint presentations will be uploaded to an email address of your choosing, once payment has been made.
Single User Licence: For use on one single computer at one location. Suitable for student home use or private tutoring at home.
(PLEASE NOTE THAT A SINGLE USER LICENCE IS NOT SUITABLE FOR SCHOOL USE. )
Single Site Licence: For use on multiple computers at one location. Suitable for school staff use.
Extended Site Licence: Same as single site licence but also includes use at home by staff/students and VLE use.
(PLEASE NOTE THAT A SINGLE USER LICENCE IS NOT SUITABLE FOR SCHOOL USE. )
Single Site Licence: For use on multiple computers at one location. Suitable for school staff use.
Extended Site Licence: Same as single site licence but also includes use at home by staff/students and VLE use.
Topics Available as Individual Further Maths PowerPoint Presentations (Including Learning Objectives):
(Please that the number of slides stated is an approximate guide only.)
F1. Asymptotes and Rational Functions
· To understand what is meant by an ‘asymptote’.
· To know how to find the equations of horizontal asymptotes. · To know how to find the equations of vertical asymptotes. · To be able to sketch the graphs of some rational functions. (32 Slides) 
F2. Calculus
· To be able to find the gradient of a curve at any point from first principles.
(31 Slides) 
F3. Complex Numbers 1
· 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. (37 Slides) 
F4. First Order Differential Equations
· 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. (37 Slides) 
F5. Improper Integrals 1
· To understand what is meant by an ‘improper integral’.
· To be able to evaluate simple improper integrals. (12 Slides) 
F6. Linear Laws
· To be able to reduce various relations to linear laws.
(41 Slides) 
F7. Matrices
· 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. (64 Slides) 
F8. Inequalities Involving Rational Expressions
· To recall how to solve simple inequalities.
· To be able to solve inequalities involving rational expressions. (41 Slides) 
F9. Polar Coordinates 1
· 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. (42 Slides) 
F10. Roots of Quadratics
· To understand and use the relationship between the roots and coefficients of a quadratic equation.
· To find quadratic equations with related roots. (61 Slides) 
F11. Linear Laws and Logarithms
· To recall the laws of logarithms.
· To be able to use logarithms to reduce certain relations to linear laws. (25 Slides) 
F12. Matrix Transformations
· To be able to use algebra to solve simple transformations problems.
· To be able to find matrices associated with common matrix transformations. · To be able to describe transformations represented by certain matrices. (64 Slides) 
F13. More Asymptotes and Rational Functions
· 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. (46 Slides) 
F14. Polar Coordinates 2
· 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. (73 Slides) 
F15. Second Order Differential Equations
· 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. (78 Slides) 
F16. Complex Numbers 2
· 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 ModulusArgument form. · To multiply and divide complex numbers written in modulusargument form. (55 Slides) 
F17. Exact Values of Trigonometric Ratios
·
To be able to deduce trig. ratios of 30, 45 and
60 degrees respectively.
· To know the relationships sin θ = cos (90θ) and cos θ = sin(90θ). · To be able to write trig. ratios as trig. ratios of acute angles. · To understand what is meant by ‘odd functions’ and ‘even functions’. (39 Slides) 
F18. Improper Integrals 2
· To know what is meant by an ‘improper integral’.
· To know how to find further improper integrals. (23 Slides) 
F19. Roots of Polynomials
· 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 (65 Slides)

F20. Graphical Solution of Inequalities
· To be able to inequalities involving rational expressions using a graphical method.
(34 Slides) 
F21. Composite Geometric Transformations Using Matrices
· To recall the rules of simple transformations.
· To be able to find matrices representing simple composite transformations. · To know that composite transformation matrices are premultiplied. · To be able to describe simple composite transformations represented by some matrices. (28 Slides) 
F22. Trigonometry (General Solutions)
· To be able to find the general solution of simple trigonometric equations in degrees.
· To be able to find the general solution of simple trigonometric equations in radians. (34 Slides) 
F23. Numerical Methods
· 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 NewtonRaphson method. · To be able to solve equations of the form using Euler’s ‘step by step’ method.
(59 Slides) 
F24. Hyperbolic Functions
· To understand what is meant by hyperbolic functions.
· To be able to sketch graphs of hyperbolic functions. · To be able to establish hyperbolic identities. · To understand Osborn’s Rule. (31 Slides) 
F25. Inverse Trigonometric Functions
· 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 the result (47 Slides)

F26. More 1st and 2nd Order Differential Equations 1
· To be able to solve certain first order differential equations using a complementary function and a particular integral.
· To use a change of variable to solve some first and second order differential equations. (30 Slides) 
F27. Polar Coordinates 3
· To use the skills learnt so far to solve exam style polar geometry questions.
(20 Slides) 
F28. Complex Roots of Polynomials with Real Coefficients
· 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. (33 Slides) 
F29. Series
· 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 . To be able to solve series questions requiring algebraic manipulation.
(47 Slides) 
F30. Matrices and Linear Transformations
·
To understand what is meant by a
‘transformation’ and 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. (73 Slides) 
F31. De Moivre's Theorem and Applications 1
· To recall how to multiply and divide complex numbers in ModulusArgument 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. (43 Slides) 
F32. Differentiation of Hyperbolic Functions
· 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. (36 Slides) 
F33. Exponential Form of a Complex Number
· To write a complex number in exponential form.
· To multiply and divide complex numbers in exponential form. (18 Slides) 
F34. Length of a Curve
· To find the length of a curve when the curve is given in Cartesian form.
· To find the length of a curve when the curve is given in Parametric form. (20 Slides) 
F35. Inverse Matrices and Determinants
· 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. (54 Slides) 
F36. Matrix Solution of Simultaneous Equations
· 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. (24 Slides) 
F37. MacLaurin's Series
· To be able to use MacLaurin’s Series to find series expansions.
· To be able to find the Ranges of Validity for certain series. (38 Slides) 
F38. Parabolas, Ellipses and Hyperbolas
· 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. (70 Slides) 
F39. The Method of Differences
· To understand the Method of Differences.
· To be able to use the Method of Differences to prove results for the summation of certain series. (17 Slides) 
F40. Loci in the Complex Plane
· To be able to sketch loci on an Argand Diagram.
(52 Slides) 
F41. Area of Surface of Revolution
· To find the area of surface of revolution for curves given in Cartesian form.
· To find the area of surface of revolution for curves given in Parametric form. (22 Slides) 
F42. De Moivre's Theorem and Applications 2
· 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. (57 Slides) 
F43. Integration with Hyperbolic Functions
· To recall the derivatives of hyperbolic functions.
· To be able to integrate hyperbolic functions. · To recognise integrals which integrate to inverse hyperbolic functions. (35 Slides) 
F44. Limits of MacLaurin's Series
· To recall the concept of a ‘limit’.
· To be able to use MacLaurin’s series expansions to find certain limits. · To know and use the special limits (45 Slides)

F45. More 1st and 2nd Order Differential Equations 2
· To understand the chain rule when using first and second order derivatives.
· Use a substitution in conjunction with the chain rule to solve certain second order differential equations. (38 Slides) 
F46. Numerical Methods for 1st Order Differential Equations
· To be able to solve first order differential equations of the form
using the following ‘step by step’ methods:
· Euler’s Method · The MidPoint Method · The Improved Euler Method (57 Slides) 
F47. Proof by Mathematical Induction
· 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. (49 Slides) 
F48. Solving Hyperbolic Equations
· To be able to solve hyperbolic equations.
(13 Slides) 
F49. Eigenvalues and Eigenvectors
· 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. (54 Slides) 
F50. Diagonalisation of a Matrix
·
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. (40 Slides) 

Purchase Single Further Maths PowerPoint Presentations:
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Value Package Prices:
For multiple presentation purchases, the following moneysaving packages are available (on DVDROM disc).
There are 5 packages of 9 presentations per package (see below).
Note that if you buy any 4 packages, we will give you the 5th absolutely FREE.
There are 5 packages of 9 presentations per package (see below).
Note that if you buy any 4 packages, we will give you the 5th absolutely FREE.
Single User Licence: For use on one single computer at one location. Suitable for student home use or private tutoring at home.
(PLEASE NOTE THAT A SINGLE USER LICENCE IS NOT SUITABLE FOR SCHOOL USE. )
Single Site Licence: For use on multiple computers at one location. Suitable for school use.
Extended Site Licence: Same as single site licence but also includes use at home by staff/students and VLE use.
(PLEASE NOTE THAT A SINGLE USER LICENCE IS NOT SUITABLE FOR SCHOOL USE. )
Single Site Licence: For use on multiple computers at one location. Suitable for school use.
Extended Site Licence: Same as single site licence but also includes use at home by staff/students and VLE use.
Topics included in Packages:
Package 1
1. Asymptotes and Some Rational Functions 1
2. Calculus. 3. Complex Numbers 1. 4. 1st Order Differential Equations. 5. Improper Integrals 1. 6. Linear Laws. 7. Matrices. 8. Inequalities involving Rational Expressions. 9. Polar Coordinates 1. 10. Roots of Quadratics. 
Package 2
1. Linear Laws and Logarithms
2. Matrix Transformations. 3. Asymptotes and Rational Functions 2. 4. Polar Coordinates 2. 5. 2nd Order Differential Equations. 6. Complex Numbers 2. 7. Exact Values or Trig. Ratios. 8. Improper Integrals 2. 9. Roots of Polynomials 10.Graphical Solution of Inequalities. 
Package 3
1. Composite Geometric Transformations using Matrices.
2. Trig. General Solutions. 3. Numerical Methods. 4. Hyperbolic Functions. 5. Inverse Trigonometric Functions. 6. More 1st and 2nd Order Differential Equations 1. 7. Polar Coordinates 3. 8. Complex Roots of Polynomials with Real Coefficients. 9.Series. 10. Matrices and Linear Transformations. 
Package 4
1. DeMoivre's Theorem 1.
2. Differentiation of Hyperbolic Functions. 3. Exponential Form of a Complex Number. 4. Length of a Curve. 5. Inverse Matrices and Determinants. 6. Matrix Solution of Simultaneous Equations. 7. MacLaurin's Series. 8. Parabolas, Ellipses and Hyperbolas. 9. The Method of Differences. 10. Loci in the Complex Plane. 
Package 5
1. Area of Surface of Revolution.
2. DeMoivre's Theorem 2. 3. Integration with Hyperbolic Functions. 4. Limits of MacLaurin's Series. 5. More 1st and 2nd Order Differential Equations 2. 6. Numerical Methods for 1st Order Differential Equations. 7. Proof by Mathematical Induction. 8. Solving Hyperbolic Equations. 9. Eigenvalues and Eigenvectors. 10. Diagonalisation of a Matrix. 
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NEW! MATHS TRUMPS (another great Smart Solutions product written by the author of 'Teach Further Maths')

Teach Further Maths by P. A. Hunt 