Topics covers; Know conditions for an exponential distribution to be used as a model. Know the probability density function, f(x), and the cumulative distribution function, F(x), for an exponential distribution Calculate probabilities for an exponential distribution using F(x) or integration of f(x) Know proofs of mean, variance and standard deviation for an exponential distribution. Understand that the lengths of intervals between Poisson events have an exponential 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 Please leave a review as it will really help me to improve my resources

A selection of presentations and activities that introduce vectors by getting the students to draw basic column vectors and discovering parallel and perpendicular vectors. This leads on to scalar product and finding the angle between 2 vectors. The other large presentation shows students how to write an equation of a line in parametric form. It includes activities like finding intersection points. It also covers skew lines and finding the closest distance between a point and a line. 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 it with my free SMART 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 I have added ‘AS level maths 13 – Circles’ for free download Kinematics covers; Understand and use fundamental quantities and units in the S.I. system: length, time, mass Understand and use derived quantities and units: velocity, acceleration, force, weight Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration Understand, use and interpret graphs in kinematics for motion in a straight line Displacement against time and interpretation of gradient velocity against time and interpretation of gradient and area under the graph Understand, use and derive the formulae for constant acceleration for motion in a straight line Use calculus in kinematics for motion in a straight line

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.

This resource pack contains a wide range of matrix work. It contains, How to find the inverses of 2x2 and 3x3 matrices Equations of lines and planes Area of triangles and parallelograms Volumes of Parallelepipeds, pyramids and prisms Scalar and Vector Products Linear Independence Intersection of 2 planes and the angle between them Intersection of 3 planes including a jigsaw activity Eigenvectors and Eigenvalues including invariant lines and points 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 it with my free SMART 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 I have added ‘AS level maths 13 – Circles’ for free download Please leave a review to help me improve or add anything else that is needed Graphs of functions and transformations covers; Understand and use graphs of functions Sketch curves defined by simple equations including polynomials. y=a/x and y=a/x² (including their vertical and horizontal asymptotes) Interpret algebraic solution of equations graphically Use intersection points of graphs to solve equations. Understand and use proportional relationships and their graphs. Understand the effect of simple transformations on the graph of y=f(x) including sketching associated graphs: * y=af(x) * y=f(x)+a * y=f(x+a) * y=f(ax)

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 Conic sections covers; Sketching graphs of curves with equations CONIC EQUATIONS including intercepts with axes and equations of asymptotes of hyperbolas. Single transformations of curves involving translations, stretches parallel to coordinate axes and reflections in the coordinate axes and the lines y= ±x.

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 Rational inequalities covers; Solving inequalities such as (ax+b)/(cx+d)<ex+f algebraically. Graphs of rational functions of form (ax+b)/(cx+d) Asymptotes, points of intersection with coordinate axes or other straight lines Associated inequalities. Graphs of rational functions of form (ax^2+bx+c)/(dx^2+ex+f) , including cases when some of these coefficients are zero Asymptotes parallel to coordinate axes.

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 Graph theory Planar, Eulerian and networks covers; Understand and use Euler’s formula for connected planar graphs Identify or prove properties of a graph including that a graph is Eulerian, semi-Eulerian or Hamiltonian Understand and use the language of networks including: ‘node’, ‘arc’ and ‘weight’.

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 Graph theory Complete graphs, adjacency matrices covers; Understand and use the language of graphs including: ‘vertex’, ‘edge’, ‘trail’, ‘cycle’, ‘connected’, ‘degree’, ‘subgraph’, ‘subdivision’, ‘multiple edge’ and ‘loop’ Understand and use simple graphs, simple-connected graphs and trees. Understand and use complete graphs and bipartite graphs, including adjacency matrices and the complement of a graph

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 Polar coordinates covers; Understand and use polar coordinates and be able to convert between polar and Cartesian coordinates Sketch curves with r given as a function of θ, including use of trigonometric functions

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 Sampling, data representation, averages and spread covers; Understand and use the terms ‘population’ and ‘sample’ Use samples to make informal inferences about the population Understand and use sampling techniques, including simple random sampling and opportunity sampling Select or critique sampling techniques in the context of solving a statistical problem, including understanding that different samples can lead to different conclusions about the population. Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency Connect to probability distributions Interpret measures of central tendency and variation, extending to standard deviation Be able to calculate standard deviation, including from summary statistics

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 as it will really help me to improve my resources Trigonometry Addition rule, Double angles, Harmonic form and Small angles covers; Understand and use double angle formulae Use of formulae for sin⁡(A ± B) , cos⁡(A ± B) and tan⁡(A ± B) Understand geometrical proofs of these formulae Understand and use expressions for a cos θ + b sin θ in the equivalent forms of rcos(θ±α) or rsin(θ±α) Understand and use the standard small angle approximations of sine, cosine and tangent * sin⁡θ≈θ * cos⁡θ≈1-θ^2/2 * tan⁡θ≈θ where θ is in radians Construct proofs involving trigonometric functions and identities

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

TThese 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 – Continuous random variables covers; Understand and use a probability density function, f(x), for a continuous distribution and understand the differences between discrete and continuous distributions Find the probability of an observation lying in a specified interval Find median and quartiles for given probability density function, f(x) Find mean, variance and standard deviation for given CRV function, f(x). Know the formulae: * E(X)=∫x f(x) dx * E(X^2 )=∫x^2 f(x) dx * Var(X)=E(X^2 )-E(X)^2 Understand expectation of linear functions of CRVs and know the formulae: * E(aX+b)=aE(X)+b * Var(aX+b)=a^2 Var(X) Know the formula E(g(X))=∫g(x) f(x) dx Find the mean, variance and standard deviation of functions of a continuous random variable such as E(5X^3 ), E(18X^(-3) ), Var(6X^(-1) ) Know that if X and Y are independent (discrete or continuous) random variables then E(X+Y)=E(X)+E(Y) and Var(X+Y)=Var(X)+Var(Y)

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 Network Flow Augmentation Algorithm topics covers; Use flow augmentation from an initial flow to find a maximum flow through a network with only upper capacities State the maximum flow through a network in the context of the problem Find a flow pattern corresponding to the maximum flow through a network. Be able to use flow augmentation from an initial flow to find a maximum flow through a network with lower and upper capacities.

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 Topics covers; Mid-ordinate rule and Simpson’s rule for integration. Euler’s step by step method for solving first order differential equations Euler’s improvement: y_(r+1)=y_(r-1)+2hf(xr,yr), x_(r+1)=x_r+h

Hyperbolic functions covers; Use the domains and ranges of the hyperbolic functions. Understand the definitions of hyperbolic functions sechx, cosechx and cothx, including their domains and ranges. Use the domains and ranges of the inverse hyperbolic functions. Differentiate and integrate hyperbolic functions. Be able to derive logarithmic formulae for sech, cosech and coth Understand and use the identities; * sech² θ=1-tanh² θ * cosec² θ=coth² θ-1 * cosh2θ=cosh² θ+sinh² θ * sinh2θ=2sinhθcoshθ Construct proofs involving hyperbolic functions and identities 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

Random Variables Cumulative Density Functions covers; Know the formula E(g(X))=∑g(x)p Find the mean, variance and standard deviation for functions of a discrete random variable such as E(5X³), E(18/X³ ), Var(6X ) Understand and use a cumulative distribution function, F(x). Know the relationship between f(x) and F(x). Understand the rectangular distribution. Know the conditions for the rectangular distribution to be used as a model. Calculate probabilities from a rectangular distribution. Know proofs of mean, variance and standard deviation for a rectangular 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

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