Teach Further Maths — Superb PowerPoints for Teachers of A-Level Maths & Further Maths

Euler, Newton, Gauss, Fermat, Pascal — a selection of outstanding mathematicians in history

A selection of some of the most outstanding and inspiring mathematicians in history

What is 'Teach Further Maths'?

'Teach Further Maths' is a suite of high quality, fully animated colour A-Level Further Maths PowerPoint presentations, consisting of over 3000 slides.

Written for teachers by a very experienced classroom practitioner, examiner and published maths author (Paul Hunt), the presentations include demonstrations, proofs, worked examples, exercises, exam-style questions and actual exam questions (used with permission).

'Teach Further Maths' is perfect for the current specifications and includes complete coverage of the compulsory content from all of the main examination boards — Edexcel, AQA, OCR and MEI.

Each presentation is designed to be used directly in the classroom, saving teachers significant preparation time whilst delivering exceptional quality lessons.

3000+ Slides

An extensive suite of presentations covering every compulsory topic for all major exam boards.

Fully Animated

High quality colour animations bring mathematical concepts to life in the classroom.

Written by an Examiner

Includes actual exam questions (used with permission) and exam-style practice throughout.

All 4 Major Exam Boards

Complete compulsory content coverage for Edexcel, AQA, OCR and MEI.

Try Before You Buy

A free sample presentation is available — see Free Sample Presentation.

Screenshots from 'Teach Further Maths'

A small sample of what to expect:

DeMoivre's Theorem & Applications 2

Improper Integrals

2nd Order Differential Equations

Matrix Solution of Simultaneous Equations

Compulsory A-Level Further Mathematics Content by Exam Board

Teach Further Maths includes full, detailed coverage of every topic from the compulsory content that teachers are required to deliver. All 4 of the main exam boards are completely catered for.

Topic	Content	Edexcel	AQA	OCR 'A'	MEI
Proof
Proof	Construct proofs by mathematical induction	✓	✓	✓	✓
Complex Numbers
Complex Numbers	Solve any quadratic with real coefficients	✓	✓	✓	✓
Complex Numbers	Solve cubic or quartic equations with real coefficients	✓	✓	✓	✓
Complex Numbers	Add, subtract, multiply and divide complex numbers; real part, imaginary part, modulus and argument	✓	✓	✓	✓
Complex Numbers	Understand and use the complex conjugate; non-real roots of polynomials occur in conjugate pairs	✓	✓	✓	✓
Complex Numbers	Use and interpret Argand diagrams	✓	✓	✓	✓
Complex Numbers	Convert between Cartesian form and Modulus-Argument form	✓	✓	✓	✓
Complex Numbers	Multiply and divide complex numbers in modulus-argument form	✓	✓	✓	✓
Complex Numbers	Construct and interpret simple loci in an Argand diagram	✓	✓	✓	✓
Complex Numbers	Know and use both forms of Euler's formula	✓	✓	✓	✓
Complex Numbers	Understand and use De Moivre's Theorem; multiple angle formulae and sums of series	✓	✓	✓	✓
Complex Numbers	Find the nth roots of any complex number; vertices of a regular n-sided polygon in the Argand diagram	✓	✓	✓	✓
Complex Numbers	Use complex roots of unity to solve geometric problems	✓	✓	✓	✓
Matrices
Matrices	Add, subtract and multiply conformable matrices; multiply a matrix by a scalar	✓	✓	✓	✓
Matrices	Understand and use zero and identity matrices	✓	✓	✓	✓
Matrices	Matrix multiplication is associative but not commutative	✓	✓	✓	✓
Matrices	Matrices representing linear transformations in 2D including simple shears; successive transformations; 3D transformations	✓	✓	✓	✓
Matrices	Find invariant points and lines for a linear transformation	✓	✓	✓	✓
Matrices	Find the determinant of 2×2 and 3×3 matrices	✓	✓	✓	✓
Matrices	Determinant of a 2×2 matrix as area scale factor; interpretation of sign	✓	✓	✓	✓
Matrices	Calculate the inverse of 2×2 and 3×3 non-singular matrices	✓	✓	✓	✓
Matrices	Solve 3 simultaneous linear equations using the inverse matrix	✓	✓	✓	✓
Matrices	Interpret geometrically the solution and failure of 3 simultaneous equations	✓	✓	✓	✓
Matrices	Factorisation of determinants using row and column operations	N/A	✓	N/A	N/A
Matrices	Find eigenvalues and eigenvectors of 2×2 and 3×3 matrices; characteristic equation	N/A	✓	N/A	N/A
Matrices	Diagonalise matrices	N/A	✓	N/A	N/A
Further Algebra
Further Algebra	Relationship between roots and coefficients of polynomial equations up to quartics	✓	✓	✓	✓
Further Algebra	Form a polynomial equation whose roots are a linear transformation of the roots of a given polynomial	✓	✓	✓	✓
Further Algebra	Formulae for sums of integers, squares and cubes; sum other series	✓	✓	✓	✓
Further Algebra	Method of differences for summation of series including use of partial fractions	✓	✓	✓	✓
Further Algebra	Find the Maclaurin series of a function including its general term	✓	✓	✓	✓
Further Algebra	Recognise and use Maclaurin series; ranges of validity	✓	✓	✓	✓
Further Algebra	Evaluation of limits using Maclaurin series (L'Hôpital's Rule also included)	✓	✓	✓	✓
Further Algebra	Inequalities involving polynomial equations (cubic and quartic)	N/A	✓	N/A	N/A
Further Algebra	Solving rational inequalities algebraically	N/A	✓	N/A	N/A
Further Algebra	Modulus of functions and associated inequalities	N/A	✓	N/A	N/A
Further Algebra	Graphs of rational functions; asymptotes and points of intersection	N/A	✓	N/A	N/A
Further Algebra	Sketching curves of parabolas, ellipses and hyperbolas	N/A	✓	N/A	N/A
Further Algebra	Transformations of curves: translations, stretches, reflections and composite transformations	N/A	✓	N/A	N/A
Further Calculus
Further Calculus	Evaluate improper integrals (undefined integrand or infinite interval)	✓	✓	✓	✓
Further Calculus	Derive formulae for and evaluate volumes of revolution	✓	✓	✓	✓
Further Calculus	Understand and evaluate the mean value of a function	✓	✓	✓	✓
Further Calculus	Integrate using partial fractions (including quadratic factors in the denominator)	✓	✓	✓	✓
Further Calculus	Differentiate inverse trigonometric functions	✓	✓	✓	✓
Further Calculus	Integrate functions using appropriate trigonometric substitutions	✓	✓	✓	✓
Further Calculus	Arc length and surface area of revolution (Cartesian and parametric)	N/A	✓	N/A	N/A
Further Calculus	Derivation and use of reduction formulae for integration	N/A	✓	N/A	N/A
Further Vectors
Further Vectors	Vector and Cartesian form of an equation of a straight line in 3D	✓	✓	✓	✓
Further Vectors	Vector and Cartesian forms of an equation of a plane	✓	✓	✓	✓
Further Vectors	Scalar product; angles between lines and planes	✓	✓	✓	✓
Further Vectors	Intersections of lines and planes; distances from points to lines and planes	✓	✓	✓	✓
Further Vectors	Parallel, skew or intersecting lines in 3D	✓	✓	✓	✓
Further Vectors	Distance between parallel lines and shortest distance between skew lines	✓	✓	✓	✓
Further Vectors	Vector product to find perpendicular vectors; areas of triangles	✓	✓	✓	✓
Polar Coordinates
Polar Coordinates	Understand and use polar coordinates; convert between polar and Cartesian	✓	✓	✓	✓
Polar Coordinates	Sketch curves with simple polar equations	✓	✓	✓	✓
Polar Coordinates	Find the area enclosed by a polar curve	✓	✓	✓	✓
Hyperbolic Functions
Hyperbolic Functions	Definitions, domains, ranges and graphs of hyperbolic functions	✓	✓	✓	✓
Hyperbolic Functions	Inverse hyperbolic functions: definitions, domains and ranges	✓	✓	✓	✓
Hyperbolic Functions	Differentiate and integrate hyperbolic functions	✓	✓	✓	✓
Hyperbolic Functions	Logarithmic forms of the inverse hyperbolic functions	✓	✓	✓	✓
Hyperbolic Functions	Integrate using appropriate hyperbolic substitutions	✓	✓	✓	✓
Hyperbolic Functions	Construct proofs involving hyperbolic functions and identities	✓	✓	✓	✓
Differential Equations
Differential Equations	Integrating factor to solve first order linear differential equations	✓	✓	✓	✓
Differential Equations	General and particular solutions to differential equations	✓	✓	✓	✓
Differential Equations	Differential equations in modelling (kinematics and other contexts)	✓	✓	✓	✓
Differential Equations	Second order DEs using the auxiliary equation	✓	✓	✓	✓
Differential Equations	Second order DEs: complementary function and particular integral	✓	✓	✓	✓
Differential Equations	Discriminant of auxiliary equation and form of solution	✓	✓	✓	✓
Differential Equations	Simple harmonic motion	✓	✓	✓	✓
Differential Equations	Damped oscillations using second order differential equations	✓	✓	✓	✓
Differential Equations	Coupled first order simultaneous equations (e.g. predator-prey models)	✓	✓	✓	✓
Numerical Methods
Numerical Methods	Mid-ordinate rule and Simpson's rule for integration	N/A	✓	N/A	N/A
Numerical Methods	Euler's method and Mid-Point Method for first order DEs	N/A	✓	N/A	N/A
Numerical Methods	Improved Euler Method for first order differential equations	N/A	✓	N/A	N/A

A-Level Further Mathematics Presentations

68 presentations in total, covering all compulsory content. Slide counts are approximate guides only.

Asymptotes and Rational Functions

Horizontal and vertical asymptotes
Sketching graphs of rational functions

32 slides

Complex Numbers 1

Imaginary numbers and powers of i
Complex numbers and quadratic equations
Argand diagrams; arithmetic with complex numbers

37 slides

First Order Differential Equations

Separation of variables
Family of solution curves
Integrating factor method

37 slides

Improper Integrals 1

Evaluating simple improper integrals

12 slides

Matrices

Matrix terminology and operations
Square, identity and zero matrices

64 slides

Inequalities Involving Rational Expressions

Solving inequalities with rational expressions

41 slides

Polar Coordinates 1

Plotting and sketching polar curves

42 slides

Roots of Quadratics

Roots and coefficients of quadratic equations
Finding equations with related roots

61 slides

Matrix Transformations

Matrices associated with common transformations
Describing transformations from matrices

64 slides

F10

More Asymptotes and Rational Functions

Sketching further rational functions
Stationary points without calculus

46 slides

F11

Polar Coordinates 2

Converting between polar and Cartesian
Integration to find polar areas
Tangents at the pole

73 slides

F12

Second Order Differential Equations

Auxiliary equation method
Complementary function and particular integral

78 slides

F13

Complex Numbers 2

Modulus-Argument form
Dividing complex numbers
Solving equations using real and imaginary parts

55 slides

F14

Improper Integrals 2

Further improper integrals

23 slides

F15

Roots of Polynomials

Roots and coefficients of polynomial equations
Equations with related roots

65 slides

F16

Graphical Solution of Inequalities

Graphical method for rational inequalities

34 slides

F17

Composite Geometric Transformations Using Matrices

Composite transformation matrices

28 slides

F18

Numerical Methods

Interval bisection; linear interpolation
Newton-Raphson; Euler's method

59 slides

F19

Hyperbolic Functions

Definitions, graphs and identities
Osborn's Rule

31 slides

F20

Inverse Trigonometric Functions

Graphs and differentiation
Integration to inverse trig functions

47 slides

F21

More 1st and 2nd Order Differential Equations 1

CF and PI for first order DEs
Change of variable

30 slides

F22

Polar Coordinates 3

Exam-style polar geometry questions

20 slides

F23

Complex Roots of Polynomials with Real Coefficients

Complex roots occur in conjugate pairs

33 slides

F24

Series

Sigma notation; formulae for Σr, Σr², Σr³
Algebraic manipulation of series

47 slides

F25

Matrices and Linear Transformations

Linear transformations and their matrices
Invariant points and lines; transpose

73 slides

F26

De Moivre's Theorem and Applications 1

Powers of complex numbers
Trigonometric identities

43 slides

F27

Differentiation of Hyperbolic Functions

Derivatives and graphs of hyperbolic functions
Inverse hyperbolic functions in logarithmic form

36 slides

F28

Exponential Form of a Complex Number

Exponential form; multiplying and dividing

18 slides

F29

Inverse Matrices and Determinants

Inverse and determinant of 2×2 and 3×3 matrices
Geometric interpretation of determinants

54 slides

F30

Matrix Solution of Simultaneous Equations 1

Solving simultaneous equations via inverse matrix

28 slides

F31

Maclaurin's Series

Series expansions and ranges of validity

38 slides

F32

Parabolas, Ellipses and Hyperbolas

Equations, sketches and transformations
Asymptotes of hyperbolas

70 slides

F33

The Method of Differences

Proving summation results

17 slides

F34

Loci in the Complex Plane

Sketching loci on an Argand diagram

52 slides

F35

De Moivre's Theorem and Applications 2

Cube and nth roots of unity
nth roots of any complex number

57 slides

F36

Integration with Hyperbolic Functions

Integrating hyperbolic functions
Integrals leading to inverse hyperbolic functions

35 slides

F37

Limits of Maclaurin's Series

Using series to find limits; L'Hôpital's Rule

45 slides

F38

More 1st and 2nd Order Differential Equations 2

Chain rule with first and second derivatives
Substitution to solve second order DEs

38 slides

F39

Numerical Methods for 1st Order DEs

Euler's Method; Mid-Point Method; Improved Euler Method

58 slides

F40

Proof by Mathematical Induction

Induction for series summation and other results

49 slides

F41

Solving Hyperbolic Equations

Techniques for solving hyperbolic equations

13 slides

F42

Eigenvalues and Eigenvectors

Characteristic equation; eigenvalues and eigenvectors
Normalised and orthogonal eigenvectors

54 slides

F43

Diagonalisation of a Matrix

Diagonal and symmetric matrices
Diagonalising a matrix; powers of symmetric matrices

40 slides

F44 NEW

Further Vectors 1

Distance in 3D; dividing a line in a given ratio
Vector equations of lines (vector and Cartesian form)

43 slides

F45 NEW

Further Vectors 2

Scalar product; angles between vectors
Intersection and skew lines

66 slides

F46 NEW

Further Vectors 3

Equation of a plane (scalar, Cartesian, parametric)
Perpendicular distance from a point to a plane

51 slides

F47 NEW

Further Vectors 4

Angles between lines and planes; intersection of planes

55 slides

F48 NEW

Matrix Solution of Simultaneous Equations 2

Geometric interpretation of 3 simultaneous equations
Sheaf, prism, parallel and consistent/inconsistent cases

50 slides

F49 NEW

Volumes of Revolution

Formulae and calculations for volumes of revolution

69 slides

F50 NEW

Mean Value Theorem

Mean value theorem for integration; Root Mean Square

37 slides

F51 NEW

Partial Fractions and Integration

Partial fractions with quadratic denominators
Integration using partial fractions

47 slides

F52 NEW

A Geometric View of Determinants

Geometric interpretation of 2×2 and 3×3 determinants

30 slides

F53 NEW

Matrix Transformations in 3D

Reflections and rotations about coordinate axes in 3D

40 slides

F54 NEW

Further Vectors 5

Distance between parallel lines and skew lines

33 slides

F55 NEW

Further Vectors 6

Vector product; perpendicular vectors; areas and volumes

52 slides

F56 NEW

Further Vectors 7

Equation of a line using vector product
Distances and shortest distance between skew lines

36 slides

F57 NEW

De Moivre's Theorem and Applications 3

Summing series using De Moivre's Theorem

39 slides

F58 NEW

De Moivre's Theorem and Applications 4

Geometric problems using De Moivre's Theorem

57 slides

F59 NEW

Modelling with 1st Order Differential Equations

Modelling with first order and coupled first order DEs

64 slides

F60 NEW

Modelling with 2nd Order Differential Equations

Simple harmonic motion; damped and forced oscillations

38 slides

F61 NEW

Reduction Formulae

Deriving and using reduction formulae for integration

47 slides

F62 NEW

Factorising Determinants

Rules for simplifying and factorising determinants

57 slides

F63 NEW

Further Numerical Integration

Mid-Ordinate Rule and Simpson's Rule

51 slides

F64 NEW

Inequalities Involving Cubic and Quartic Polynomials

Rational Root Theorem; Descartes' Rule of Signs

41 slides

F65 NEW

Modulus of Functions and Associated Inequalities

Transformation rules and inequalities with modulus function

57 slides

F66 NEW

L'Hôpital's Rule

Evaluating limits of indeterminate form

36 slides

F67

Length of a Curve

Arc length in Cartesian and parametric form

20 slides

F68

Area of Surface of Revolution

Surface area in Cartesian and parametric form

22 slides

Packages

There are 4 standard packages of 12 presentations each, plus a bumper Package 5 containing the remaining 20 presentations that complete the full compulsory core content for all major exam boards.

Package 1

F1. Asymptotes and Rational Functions 1
F2. Complex Numbers 1
F3. First Order Differential Equations
F4. Improper Integrals 1
F5. Matrices
F6. Inequalities (Rational Expressions)
F7. Polar Coordinates 1
F8. Roots of Quadratics
F9. Matrix Transformations
F10. Asymptotes and Rational Functions 2
F11. Polar Coordinates 2
F12. Second 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
F18. Numerical Methods
F19. Hyperbolic Functions
F20. Inverse Trigonometric Functions
F21. More 1st and 2nd Order DEs 1
F22. Polar Coordinates 3
F23. Complex Roots of Polynomials
F24. Series

Package 3

F25. Matrices and Linear Transformations
F26. De Moivre'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 1
F31. Maclaurin's Series
F32. Parabolas, Ellipses and Hyperbolas
F33. Method of Differences
F34. Loci in the Complex Plane
F35. De Moivre's Theorem 2
F36. Integration with Hyperbolic Functions

Package 4

F37. Limits of Maclaurin's Series
F38. More 1st and 2nd Order DEs 2
F39. Numerical Methods for 1st Order DEs
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 ★

F49. Volumes of Revolution
F50. Mean Value Theorem
F51. Partial Fractions & Integration
F52. A Geometric View of Determinants
F53. Matrix Transformations in 3D
F54. Further Vectors 5
F55. Further Vectors 6
F56. Further Vectors 7
F57. De Moivre's Theorem 3
F58. De Moivre's Theorem 4
F59. Modelling with 1st Order DEs
F60. Modelling with 2nd Order DEs
F61. Reduction Formulae
F62. Factorising Determinants
F63. Further Numerical Integration
F64. Inequalities (Cubic & Quartic)
F65. Modulus of Functions & Inequalities
F66. L'Hôpital's Rule
F67. Length of a Curve
F68. Area of Surface of Revolution

Pricing

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Note: A Single User Licence is not suitable for school use — even if only one teacher intends to use the presentations.

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Sort code	23-08-01
Account number	83908895
IBAN	GB30 TRWI 2308 0183 9088 95
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