Superb PowerPoint Teaching Resources for Teachers of ALevel Further Maths
"...student friendly and should be in every school in the UK!"
A selection of some of the most outstanding and inspiring mathematicians in history.
What is 'Teach Further Maths'?
Written for teachers, 'Teach Further Maths' is a suite of high quality, fully animated colour ALevel Further Maths PowerPoint presentations, consisting of over 2000 slides.
Written by a very experienced classroom practitioner, examiner and published maths author (Paul Hunt), the presentations include demonstrations, proofs, worked examples, exercises, examstyle questions and actual exam questions (used with permission).
'Teach Further Maths' is perfect for the new 2017 specifications and already includes most of the compulsory content from all of the main examination boards.
Written by a very experienced classroom practitioner, examiner and published maths author (Paul Hunt), the presentations include demonstrations, proofs, worked examples, exercises, examstyle questions and actual exam questions (used with permission).
'Teach Further Maths' is perfect for the new 2017 specifications and already includes most of the compulsory content from all of the main examination boards.
Which topics does 'Teach Further Maths' cover?
There is extensive coverage of the compulsory content that teachers now have to deliver (see the table below for details of compulsory ALevel Further Mathematics content for each of Edexcel, AQA, OCR and MEI).
Included means that the content is already written and can be purchased.
Not Included at present means that the content is not yet written and so is unavailable to purchase until a later date.
N/A means that the content is not applicable (i.e. not compulsory content) to that particular exam board.
(However, the content may be applicable to the noncompulsory syllabus)
In Progress means that the content is currently being written and should be available in the very near future (early September)
Included means that the content is already written and can be purchased.
Not Included at present means that the content is not yet written and so is unavailable to purchase until a later date.
N/A means that the content is not applicable (i.e. not compulsory content) to that particular exam board.
(However, the content may be applicable to the noncompulsory syllabus)
In Progress means that the content is currently being written and should be available in the very near future (early September)
Screenshots from 'Teach Further Maths':
A small sample of what to expect from 'Teach Further Maths':
Can I try before I buy?
Not as such, but we do offer a completely free Sample presentation (from the ALevel Mathematics specification) so that you can experience the high quality of presentations that 'Teach Further Maths' offers you.
Compulsory ALevel Further Mathematics content by exam board
Topic 
Content 
Edexcel 
AQA 
OCR 'A' 
MEI 
Proof 
Construct proofs by mathematical induction 
Included 
Included 
Included 
Included 
Complex Numbers 
Solve any quadratic with real coefficients 
Included 
Included 
Included 
Included 
Complex Numbers 
Solve cubic or quartic equations with real coefficients 
Included 
Included 
Included 
Included 
Complex Numbers 
Add, subtract, multiply and divide complex numbers; understand the terms 'real' part and 'imaginary' part, 'modulus' and 'argument' 
Included 
Included 
Included 
Included 
Complex Numbers 
Understand and use the complex conjugate; know that nonreal roots of polynomials equations with real coefficients occur in conjugate pairs 
Included 
Included 
Included 
Included 
Complex Numbers 
Use and interpret Argand diagrams 
Included 
Included 
Include 
Included 
Complex Numbers 
Convert between Cartesian form and ModulusArgument form of a complex number 
Included 
Included 
Included 
Included 
Complex Numbers 
Multiply and divide complex numbers in modulusargument form 
Included 
Included 
Included 
Included 
Complex Numbers 
Construct and interpret simple loci in an Argand diagram. 
Included 
Included 
Included 
Included 
Complex Numbers 
Know and use both forms of Euler's formula (*) 
Included 
Included 
Included 
Included 
Complex Numbers 
Understand and use DeMoivre's Theorem and use it to find the multiple angle formulae and sums of series 
Included 
Included 
Included 
Included 
Complex Numbers 
Find the nth roots of any complex number and know that they form the vertices of a regular nsided polygon in the Argand diagram 
Included 
Included 
Included 
Included 
Complex Numbers 
Use complex roots of unity to solve geometric problems 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Matrices 
Add, subtract and multiply conformable matrices; multiply a matrix by a scalar 
Included 
Included 
Included 
Included 
Matrices 
Understand and use zero and identity matrices 
Included 
Included 
Included 
Included 
Matrices 
Know that matrix multiplication is associative but not commutative 
Included 
Included 
Included 
Included 
Matrices 
Find and use matrices to represent linear transformations in 2D (including simple shears); successive transformations; 3D transformations confined to simple cases only 
Included 
Included 
Included 
Included 
Matrices 
Find invariant points and lines for a linear transformation 
Included 
Included 
Included 
Included 
Matrices 
Find the determinant of 2 x 2 and 3 x 3 matrices. 
Included 
Included 
Included 
Included 
Matrices 
Know that the determinant of a 2 x 2 matrix is the area scale factor of the associated transformation and interpret the sign of the determinant in terms of the orientation of the image. 
In Progress 
In Progress 
In Progress 
In Progress 
Matrices 
Calculate the inverse of 2 x 2 and 3 x 3 nonsingular matrices 
Included 
Included 
Included 
Included 
Matrices 
Solve 3 simultaneous linear equations in 2 variables by use of the inverse matrix 
Included 
Included 
Included 
Included 
Matrices 
Interpret geometrically the solution and failure of solution of 3 simultaneous equations 
In Progress 
In Progress 
In Progress 
In Progress 
Matrices 
Factorisation of determinants using row and column operations 
N/A 
Not Included at present 
N/A 
N/A 
Matrices 
Find the eigenvalues and eigenvectors of 2 x 2 and 3 x 3 matrices; find and use the characteristic equation 
N/A 
Included 
N/A 
N/A 
Matrices 
Diagonalise matrices 
N/A 
Included 
N/A 
N/A 
Further Algebra 
Understand and use the relationship between roots and coefficients of polynomial equations up to quartic equations. 
Included 
Included 
Included 
Included 
Further Algebra 
Form a polynomial equation whose roots are a linear transformation of the roots of a given polynomial 
Included 
Included 
Included 
Included 
Further Algebra 
Understand and use formulae for sums of integers, squares and cubes and use these to sum other series 
Included 
Included 
Included 
Included 
Further Algebra 
Understand and use the method of differences for summation of series including use of partial fractions 
Included 
Included 
Included 
Included 
Further Algebra 
Find the MacLaurin series of a function, including its general term 
Included 
Included 
Included 
Included 
Further Algebra 
Recognise and use Maclaurin series for certain functions and be aware of their range of validity 
Included 
Included 
Included 
Included 
Further Algebra 
Evaluation of limits using MacLaurin series (L'Hopital's Rule not included) 
Included 
Included 
Included 
Included 
Further Algebra 
Inequalities involving polynomial equations (cubic and quartic) 
N/A 
Not Included at present 
N/A 
N/A 
Further Algebra 
Solving rational inequalities algebraically (**) 
N/A 
Included 
N/A 
N/A 
Further Algebra 
Modulus of functions and associated inequalities 
N/A 
Not Included at present 
N/A 
N/A 
Further Algebra 
Graphs of rational functions with linear numerator/denominator; asymptotes, points of intersection 
N/A 
Included 
N/A 
N/A 
Further Algebra 
Graphs of rational functions with quadratic numerator/denominator 
N/A 
Included 
N/A 
N/A 
Further Algebra 
Quadratic theory (not calculus) for rational functions with quadratic numerator/denominator; stationary points 
N/A 
Included 
N/A 
N/A 
Further Algebra 
Sketching curves of parabolas, ellipses and hyperbolas (***) 
N/A 
Included 
N/A 
N/A 
Further Algebra 
Single transformations of curves involving translations, stretches parallel to the coordinate axes and reflections in the lines y = x and y = x; Extend to composite transformations including rotations and enlargements 
N/A 
Included 
N/A 
N/A 
Further Calculus 
Evaluate improper integrals where either the integrand is undefined at a value in the interval of integration or the interval of integration extends to infinity 
Included 
Included 
Included 
Included 
Further Calculus 
Derive formulae for and evaluate volumes of revolution 
In Progress 
In Progress 
In Progress 
In Progress 
Further Calculus 
Understand and evaluate the mean value of a function 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Further Calculus 
Integrate using partial fractions (extend to quadratic factors in the denominator) 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Further Calculus 
Differentiate inverse trigonometric functions 
Included 
Included 
Included 
Included 
Further Calculus 
Integrate functions of the form (****) and choose appropriate trigonometric substitutions to integrate associated functions 
Included 
Included 
Included 
Included 
Further Calculus 
Arc length and surface of area of revolution for curves expressed in Cartesian or parametric form 
N/A 
Included 
N/A 
N/A 
Further Calculus 
Derivation of use of reduction formulae for integration 
N/A 
Not Included at present 
N/A 
N/A 
Further Calculus 
Know and use two special limits (*****) applied to improper integrals 
N/A 
Included 
N/A 
N/A 
Further Vectors 
Understand and use the vector and Cartesian form of an equation of a straight line in 3D 
Included 
Included 
Included 
Included 
Further Vectors 
Understand and use the vector and Cartesian forms of an equation of a plane. 
Included 
Included 
Included 
Included 
Further Vectors 
Calculate the scalar product and use it to express the equation of a plane, and to calculate the angle between two lines, the angle between two planes and the angle between a line and a plane. 
Included 
Included 
Included 
Included 
Further Vectors 
Find the intersection of a line and line; Find the intersection of a line and a plane; Calculate the distance from a point to a line and from a point to a plane. 
Included 
Included 
Included 
Included 
Further Vectors 
Be able to determine whether two lines in 3 dimensions are parallel, skew or intersect, and find the point of intersection if there is one. 
Included 
Included 
Included 
Included 
Further Vectors 
Be able to find the distance between two parallel lines and the shortest distance between two skew lines 
In Progress 
In Progress 
In Progress 
In Progress 
Further Vectors 
Be able to use the vector product to find a vector perpendicular to two given vectors 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Further Vectors 
Understand and use the equation of a straight line in the form (r  a) x b = 0; use vector products to find the area of a triangle 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Polar Coordinates 
Understand and use polar coordinates, and be able to convert between polar and Cartesian coordinates 
Included 
Included 
Included 
Included 
Polar Coordinates 
Sketch curves with simple polar equations where r is given as a function of theta 
Included 
Included 
Included 
Included 
Polar Coordinates 
Be able to find the area enclosed by a polar curve 
Included 
Included 
Included 
Included 
Hyperbolic Functions 
Understand and use the definitions of hyperbolic functions, including their domains and ranges, and be able to sketch their graphs 
Included 
Included 
Included 
Included 
Hyperbolic Functions 
Understand and use the definitions of inverse hyperbolic functions and their domains and ranges. 
Included 
Included 
Included 
Included 
Hyperbolic Functions 
Differentiate and integrate hyperbolic functions 
Included 
Included 
Included 
Included 
Hyperbolic Functions 
Derive and use logarithmic forms of the inverse hyperbolic functions. 
Included 
Included 
Included 
Included 
Hyperbolic Functions 
Integrate functions of the form (******) and choose appropriate hyperbolic substitutions to integrate associated functions 
Included 
Included 
Included 
Included 
Hyperbolic Functions 
Construct proofs involving hyperbolic functions and identities 
Included 
Included 
Included 
Included 
Differential Equations 
Find and use the integrating factor to solve differential equations of the form y'(x) +P(x)y=Q(x) and recognise when it is appropriate to do so 
Included 
Included 
Included 
Included 
Differential Equations 
Find both general and particular solutions to differential equations 
Included 
Included 
Included 
Included 
Differential Equations 
Use differential equations in modelling in kinematics and in other contexts 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Differential Equations 
Solve differential equations of the form y'' +ay' +by =0, where a and b are constants, by using the auxiliary equation 
Included 
Included 
Included 
Included 
Differential Equations 
Solve differential equations of the form y'' +ay' +by = f(x), where a and b are constants, by solving the homogeneous case and adding a particular integral to the complementary function. 
Included 
Included 
Included 
Included 
Differential Equations 
Understand and use the relationship between cases when the discriminant of the auxiliary equation is positive, negative and zero, and the form of solution of the differential equation 
Included 
Included 
Included 
Included 
Differential Equations 
Solve the equation for simple harmonic motion and relate the solution to motion 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at presen 
Differential Equation 
Model damped oscillations using second order differential equations and interpret their solutions 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Differential Equations 
Analyse and interpret models of situations with one independent variable and two dependent variables as a pair of coupled first order simultaneous equations and be able to solve them, for example predatorprey models 
Not Included at present 
Not Included at present 
Not Included at present 
Not Included at present 
Numerical Methods 
Midordinate rule and Simpson's rule for integration 
N/A 
Not Included at present 
N/A 
N/A 
Numerical Methods 
Euler's stepbystep method and The MidPoint Method for solving 1st order differential equation 
N/A 
Included 
N/A 
N/A 
Numerical Methods 
Improved Euler Method for solving 1st order differential equations 
N/A 
Included 
N/A 
N/A 
ALevel Further Mathematics
PowerPoint Presentations containing Compulsory Teaching content
(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. Complex Numbers 1

F3. First Order Differential Equations

F4. Improper Integrals 1

F5. Matrices

F6. Inequalities Involving Rational Expressions

F7. Polar Coordinates 1

F8. Roots of Quadratics

F9. Matrix Transformations

F10. More Asymptotes and Rational Functions

F11. Polar Coordinates 2

F12. Second Order Differential Equations

F13. Complex Numbers 2

F14. Improper Integrals 2

F15. Roots of Polynomials

F16. Graphical Solution of Inequalities

F17. Composite Geometric Transformations Using Matrices

F18. Numerical Methods

F19. Hyperbolic Functions


F22. Polar Coordinates 3· To use the skills learnt so far to solve exam style polar geometry questions.
(Formerly F27) (20 Slides) 
F23. Complex Roots of Polynomials with Real Coefficients

F24. Series

F25. Matrices and Linear Transformations

F26. De Moivre's Theorem and Applications 1

F27. Differentiation of Hyperbolic Functions

F28. Exponential Form of a Complex Number

F29. Inverse Matrices and Determinants

F30. Matrix Solution of Simultaneous Equations 1

F31. MacLaurin's Series

F32. Parabolas, Ellipses and Hyperbolas

F33. The Method of Differences

F34. Loci in the Complex Plane

F35. De Moivre's Theorem and Applications 2

F36. Integration with Hyperbolic Functions

F37. Limits of MacLaurin's Series

F38. More 1st and 2nd Order Differential Equations 2

F39. Numerical Methods for 1st Order Differential Equations

F40. Proof by Mathematical Induction

F41. Solving Hyperbolic Equations

F42. Eigenvalues and Eigenvectors

F43. Diagonalisation of a Matrix

F44. Further Vectors 1

F45. Further Vectors 2

F46. Further Vectors 3

F47. Further Vectors 4

F48. Matrix Solution of Simultaneous Equations 2

ALevel Further Mathematics
PowerPoint Presentations containing NonCompulsory Teaching content
FN1 Length of a Curve

FN2 Area of Surface of Revolution

ALevel Mathematics PowerPoint Presentations
P1 Calculus

P2 Linear Laws

P3 Linear Laws and Logarithms

· To be able to find the gradient of a curve at any point from first principles.
(31 Slides) 
To be able to reduce various relations to linear laws.
(41 Slides) 
· To recall the laws of logarithms.
· To be able to use logarithms to reduce certain relations to linear laws. (25 Slides) 
P4 Exact Values of Trigonometric Ratios

P5 Trigonometry (General Solutions)

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) 
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) 
Topics included in Packages:
Package 1
F1. Asymptotes and Some Rational Functions 1
F2. Complex Numbers 1. F3. 1st Order Differential Equations. F4. Improper Integrals 1. F5. Matrices. F6. Inequalities involving Rational Expressions F7. Polar Coordinates 1 F8. Roots of Quadratics F9. Matrix Transformations. F10. Asymptotes and Rational Functions 2. F11. Polar Coordinates 2. F12. 2nd Order Differential Equations. 
Package 2
F13. Complex Numbers 2.
F14. Improper Integrals 2. F15. Roots of Polynomials F16.Graphical Solution of Inequalities. F17. Composite Geometric Transformations using Matrices. F18. Numerical Methods. F19. Hyperbolic Functions. F20. Inverse Trigonometric Functions. F21. More 1st and 2nd Order Differential Equations 1. F22. Polar Coordinates 3. F23. Complex Roots of Polynomials with Real Coefficients. F24. Series 
Package 3
F25. Matrices and Linear Transformations.
F26. DeMoivre's Theorem 1. F27. Differentiation of Hyperbolic Functions. F28. Exponential Form of a Complex Number. F29. Inverse Matrices and Determinants. F30. Matrix Solution of Simultaneous Equations. F31. MacLaurin's Series. F32. Parabolas, Ellipses and Hyperbolas. F33. The Method of Differences. F34. Loci in the Complex Plane. F35. DeMoivre's Theorem 2. F36. Integration with Hyperbolic Functions 
Package 4
F37. Limits of MacLaurin's Series.
F38. More 1st and 2nd Order Differential Equations 2. F39. Numerical Methods for 1st Order Differential Equations. F40. Proof by Mathematical Induction. F41. Solving Hyperbolic Equations. F42. Eigenvalues and Eigenvectors. F43. Diagonalisation of a Matrix. F44. Further Vectors 1 F45. Further Vectors 2 F46. Further Vectors 3 F47. Further Vectors 4 F48. Matrix Solution of Simultaneous Equations 2 
Package 5
Remaining compulsory content topics denoted by 'Not Included at present' in the above table.
Available by September 2018. NOTE: Package 5 will be FREE (when available  see above) to institutions who purchase ALL of packages 1, 2 3 AND 4 via a site licence or an extended site licence. Note 1: Institutions who do not purchase all packages will not be eligible to receive package 5 for FREE. Note 2: This free offer is also unavailable to single user licence purchases. 
Value Package Prices:
There are 4 packages of 12 presentations per package (see above).
The more packages that are purchased, the more money you save compared to purchasing presentations individually.
Remember that if you do purchase all 4 packages on a site licence or an extended site licence, then you will receive the 5th package as soon as it is released (likely September next year) absolutely FREE.
The more packages that are purchased, the more money you save compared to purchasing presentations individually.
Remember that if you do purchase all 4 packages on a site licence or an extended site licence, then you will receive the 5th package as soon as it is released (likely September next year) absolutely FREE.
Licence Types:
Single User Licence: For use on one single computer at one location. Suitable for student home use or private tutoring.
(NOTE: 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.
(NOTE: USE BY ONE TEACHER AT ONE SCHOOL STILL REQUIRES A SITE LICENCE)
Extended Site Licence: Same as single site licence but also includes use at home by staff/students and VLE use.
Single User Licence: For use on one single computer at one location. Suitable for student home use or private tutoring.
(NOTE: 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.
(NOTE: USE BY ONE TEACHER AT ONE SCHOOL STILL REQUIRES A SITE LICENCE)
Extended Site Licence: Same as single site licence but also includes use at home by staff/students and VLE use.
Purchase A Single Package 
Purchase Any 2 Packages 
Purchase All 4 Packages 
NOTE: Purchase Orders are welcome.
Email SmartSolutions@europe.com with your purchase order number and we send you an invoice along with acceptable methods of payment.
Also, payment by BACS transfer is also welcome.
Email SmartSolutions@europe.com to request the relevant bank details.
Individual Presentations
If you only wish to purchase individual presentations, then you may still do so at the prices stated below.
Simply let us know the name and number of your desired presentations when you order.
Individual PowerPoint presentations will be uploaded to an email address of your choosing, once payment has been made.
(PLEASE ALLOW 1 WORKING DAY FOR YOUR PRESENTATIONS(S) TO BE UPLOADED TO YOU)
Simply let us know the name and number of your desired presentations when you order.
Individual PowerPoint presentations will be uploaded to an email address of your choosing, once payment has been made.
(PLEASE ALLOW 1 WORKING DAY FOR YOUR PRESENTATIONS(S) TO BE UPLOADED TO YOU)
Note that, if purchasing all 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).
We will always be happy to help and assist you in any way we can.
Enjoy 'Teach Further Maths'!

Teach Further Maths by P. A. Hunt 