These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources Roots of polynomials covers; Understand and use the relationship between roots and coefficients of polynomial equations up to quartic equations Form a polynomial equation whose roots are a linear transformation of the roots of a given polynomial equation of at least cubic degree

These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources Route inspection problem covers; Solve Route Inspection problems Route inspection algorithm

These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources Volume of revolution covers; Derive formulae for and calculate volumes of revolution

These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; A complete set of notes for students Model examples Probing questions to test understanding Class questions including answers Individual whiteboard work Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources Statistics – Poisson distribution covers; Understand conditions for a Poisson distribution to model a situation. Understand terminology X~Po(λ) Know Poisson formula and calculate Poisson probabilities using the formula or equivalent calculator function Know mean, variance and standard deviation of a Poisson distribution. Use the result that, if X~Po(λ) then the mean and variance of X are equal Understand the distribution of the sum of independent Poisson distributions.

Type one errors and type two errors covers; Calculate probability of making Type I error from tests based on a normal distribution Understand the power of a test. Calculations of P(Type II error) and power for a test for tests based on a normal, Binomial or a Poisson distribution These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources

Complex Numbers covers; Understand de Moivre’s theorem and use it to find multiple angle formulae and sums of series Use de Moivre’s theorem for both finite and infinite trigonometric series. Know and use the definition e^iθ=cosθ+isinθ and the form z=re^iθ Find the n distinct nth roots of re^iθ for r≠0 and know that they form the vertices of a regular n-gon in the Argand diagram. Use complex roots of unity to solve geometric problems These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources

Yates’ correction covers; Knowledge of when and how to apply Yates’ correction. Know and be able to use the fact that Yates’ correction is used in a contingency table when there is only 1 degree of freedom (ie in a contingency table with 2 rows and 2 columns, which may occur after pooling has taken place) Know and be able to use the formula These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources

Calculus inverse trigonometric and hyperbolic functions covers; Differentiate inverse trigonometric and hyperbolic functions Integrate functions of the form * (a²-x²)^(-1/2) * (a²+x²)^(-1) * (x²+a²)^(-1/2) * (x²-a²)^(-1/2) Be able to choose trigonometric and hyperbolic substitutions to integrate associated functions. Integrate using partial fractions (extend to quadratic factors ax²+c in the denominator) These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources

Reduction formula covers; Understand how reduction techniques can be used to repeatedly reduce the complexity of the integrand to enable a given integral to be calculated Understand how integration by parts may be applied to produce reduction formulae Understand how other techniques of integration may be used to find reduction formulae Use reduction formulae to evaluate integrals. These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources

Differential equations integrating factor covers; Find and use an integrating factor to solve differential equations of form dy/dx+P(x)y=Q(x) and recognise when it is appropriate to do so Recognise when a given differential equation may be rearranged into the form to allow an integrating factor to be used Find an integrating factor by inspection or by using the formula Solve more difficult differential equations by transforming them into this form by means of a suitable given substitution. These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first Please leave a review as it will really help me to improve my resources

Coupled differential equations covers; Analyse and interpret models of situations with one independent variable and two dependent variables as a pair of coupled 1st order simultaneous equations and be able to solve them, for example predator-prey models Interpret a given context to form a pair of first order simultaneous differential equations Eliminate x or y to form and solve a second order differential equation Solve a pair of first order simultaneous differential equations to find the dependent variables as functions of the independent variable. These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first Please leave a review as it will really help me to improve my resources

Summations and Method of Differences covers; Understand and use formulae for the sums of integers, squares and cubes and use these to sum other series. Understand and use the method of differences for summation of series These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources

These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; A complete set of notes for students Model examples Probing questions to test understanding Class questions including answers Individual whiteboard work Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources Proof by induction covers; Construct proofs using mathematical induction; contexts include sums of series, divisibility, and powers of matrices

These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Hodder ed’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first Please leave a review as it will really help me to improve my resources Kuratowski’s theorem topics covers; Use Kuratowski’s theorem to prove a graph is planar Use Kuratowski’s theorem to prove a graph is not planar Identify the complete graph K₅ Identify the complete bipartite graph K₃,₃ Understand what is meant by a subgraph Understand what is meant by a subdivision.

These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Hodder ed’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first Please leave a review as it will really help me to improve my resources Introduction to Group Theory topics covers; Understand and use the language of groups including: * order * period * subgroup * proper * trivial * non-trivial Understand and use the group axioms: closure, identity, inverses and associativity Use of Cayley tables Understand and use Lagrange’s theorem. Recognise and use finite and infinite groups and their subgroups, including: groups of symmetries of regular polygons, cyclic groups and abelian groups. Identify and use the generators of a group Recognise and find isomorphism between groups of finite order

A presentation that shows learners the different graphs of the inverse and the reciprocal of trigonometric functions. Also shows examples of how these are used to solve trigonometric equations. SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try this free SMART resource.

This powerpoint show demonstrates how to complete the bubble sort algorithm. This is only a powerpoint show so it cant be edited

Please leave a review of this free resource These PowerPoints form full lessons of work that together cover the new A level Maths course for all exam boards. Together all the PowerPoints include; A complete set of notes for students Model examples Probing questions to test understanding Class questions including answers Individual whiteboard work Links to exercises in ‘The Textbook by CGP’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Please leave a review to help me improve or add anything else that is needed Circles covers; Understand and use the coordinate geometry of the circle including using the equation of a circle in the form (x-a)^2 +(y-b)^2 =r^2 Completing the square to find the centre and radius of a circle; use of the following properties: The angle in a semicircle is a right angle The perpendicular from the centre to a chord bisects the chord The radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point.

These PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson I have added ‘Further Maths 5 - Matrices Transformation’ and ‘Further Maths 23 - Network Flows’ for free download Please leave a review as it will really help me to improve my resources Vector equations of lines and scalar product covers; Understand and use the vector and Cartesian forms of an equation of a straight line in 3-D Calculate the scalar product and use it to calculate the angle between two lines. Check whether vectors are perpendicular by using the scalar product Find the intersection of two lines. Calculate the perpendicular distance between two lines, from a point to a line.