Teach Further Maths  Quality Further Maths PowerPoints for Teachers
What is 'Teach Further Maths'?
'Teach Further Maths' is a suite of Maths PowerPoint presentations for Teachers and Students of 'AS' Level and 'A' Level (or equivalent) Further Mathematics.
 45 high quality, fully animated colour further maths presentations, consisting of over 1800 slides  a comprehensive teaching resource.
 Many of the major topics from FP1, FP2, FP3 and FP4 (e.g. Polar Coordinates, Matrices, Differential Equations etc...)
 Complete further maths 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).
 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 45 presentations will take care of a full 'A' Level Further Pure Mathematics course (e.g. AQA FP1, FP2 and FP3 Module are all complete)
Although the 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 45 presentations will take care of a full 'A' Level Further Pure Mathematics course (e.g. AQA FP1, FP2 and FP3 Module are all complete)
Although the 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.
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.
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.)
1. 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) 
2. Calculus
· To be able to find the gradient of a curve at any point from first principles.
(31 Slides) 
3. 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) 
4. 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. (35 Slides) 
5. Improper Integrals 1
· To understand what is meant by an ‘improper integral’.
· To be able to evaluate simple improper integrals. (12 Slides) 
6. Linear Laws
· To be able to reduce various relations to linear laws.
(41 Slides) 
7. 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) 
8. 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. (39 Slides) 
9. 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) 
10. 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) 
11. 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’. (36 Slides) 
12. Improper Intergrals 2
· To know what is meant by an ‘improper integral’.
· To know how to find further improper integrals. (23 Slides) 
13. Inequalities Involving Rational Expressions
· To recall how to solve simple inequalities.
· To be able to solve inequalities involving rational expressions. (41 Slides) 
14. 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) 
15. 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) 
16. 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) 
17. 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. (72 Slides) 
18. 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) 
19. 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) 
20. 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) 
21. 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) 
22. 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) 
23. 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)

24. 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. (29 Slides) 
25. Polar Coordinates 3
· To use the skills learnt so far to solve exam style polar geometry questions.
(20 Slides) 
26. 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)

27. 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) 
28. 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. (42 Slides) 
29. 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) 
30. 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) 
31. Graphical Solution of Inequalities
· To be able to inequalities involving rational expressions using a graphical method.
(34 Slides) 
32. 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) 
33. 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) 
34. 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.
(56 Slides) 
35. 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) 
36. 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. (16 Slides) 
37. 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) 
38. 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. (56 Slides) 
39. 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) 
40. 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)

41. Loci in the Complex Plane
· To be able to sketch loci on an Argand Diagram.
(52 Slides) 
42. 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) 
43. 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 (53 Slides) 
44. 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. (48 Slides) 
45. Solving Hyperbolic Equations
· To be able to solve hyperbolic equations.
(13 Slides) 
Purchase Single Further Maths PowerPoint Presentations:
Your selected presentation(s) will be sent to your chosen email address, once payment is received.
We may contact you to verify your presentation choices/email address in advance.
We may contact you to verify your presentation choices/email address in advance.
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.
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.
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 included in Packages:
Package 1
1. Asymptotes and Some Rational Functions 1
2. Calculus. 3. Complex Numbers 1. 4. Matrices 1. 5. Improper Integrals 1. 6. Linear Laws. 7. Roots of Quadratics. 8. 1st Order Differential Equations. 9. Polar Coordinates 1. 
Package 2
1. Exact Values of Trig. Ratios.
2. Matrices 2. 3. Inequalities involving Rational Expressions. 4. Linear Laws and Logarithms. 5. Asymptotes and Rational Functions 2 6. Complex Numbers 2. 7. Improper Integrals 2. 8. Polar Coordinates 2. 9. 2nd Order Differential Equations. 
Package 3
1. Composite Geometric Transformations using Matrices.
2. Trig. General Solutions. 3. Series. 4. Complex Roots of Polynomials. 5. Hyperbolic Functions. 6. Inverse Trig. Functions. 7. Roots of Polynomial Equations. 8. More 1st and 2nd Differential Equations 1. 9. Polar Coordinates 3. 
Package 4
1. Graphical Solution of Inequalities.
2. Numerical Methods. 3. Parabolas, Ellipses and Hyperbolas. 4. DeMoivre's Theorem 1. 5. Differentiation of Hyperbolic Functions. 6. Exponential Form of a Complex Number. 7. Length of a Curve. 8. The Method of Differences. 9. MacLaurin's Series. 
Package 5
1. Area of Surface of Revolution.
2. DeMoivre's Theorem 2. 3. Integration with Hyperbolic Functions. 4. Loci in the Complex Plane. 5. Proof by Mathematical Induction. 6. Solving Hyperbolic Equations. 7. Limits of MacLaurin's Series. 8. More 1st and 2nd Differential Equations 2. 9. Numerical Methods for 1st Order Differential Equations. 
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Note that, if purchasing any of the packages, they will be sent to you on a cellophane wrapped, high quality, full colour, thermally printed DVD disc, with glossy case cover.
P&P cost will be £4.50 (UK, Europe, USA, ...)
Purchases made will be nonrefundable (although excellent customer service will be provided to ensure that you are entirely satisfied with the product).
Please do view the FAQs page for important information about using the presentations.
If you have any other queries/questions, then please do ask (see contact page).
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Enjoy 'Teach Further Maths'!

Teach Further Maths by P. A. Hunt 