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 Sequence and series covers; Understand and work with arithmetic sequences and series, including the formulae for nth term and the sum to n terms Understand and work with geometric sequences and series including the formulae for the nth term and the sum of a finite geometric series The sum to infinity of a convergent geometric series, including the use of |r|<1 Modulus notation Understand and use sigma notation for sums of series Use sequences and series in modelling Work with sequences including; * Those given by a formula for the nth term * Those generated by a simple relation of the form x_(n+1)= f(x_n ) * Increasing and decreasing sequences Periodic sequences

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 ‘A2 level maths 13 - Composite functions’ for free download Please leave a review as it will really help me to improve my resources Statistics – Normal distribution covers; Understand and use the Normal distribution as a model; find probabilities using the Normal distribution Link to histograms, mean, standard deviation, points of inflection and the binomial distribution Select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate

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 ‘A2 level maths 13 - Composite functions’ for free download Please leave a review as it will really help me to improve my resources Statistics – Hypothesis tests for Normal and Bivariant data covers; Conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context Understand and apply correlation coefficients as measures of how close data points lie to a straight line and be able to interpret a given correlation coefficient using a given p-value or critical value

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

Arc length and Surface area covers; Arc length and area of surface of revolution for curves expressed in Cartesian or parametric coordinates Understand and use the formula for the arc length of a curve in Cartesian form Understand and use the formula for the arc length of a curve defined parametrically Understand and use the formula for the area of surface of revolution for a curve expressed in Cartesian form Understand and use the formula for the area of surface of revolution for a curve expressed in parametric form. 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

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

This large presentation introduces the modulus function and its graph. It covers how to sketch a modulus graph and also has questions for students to do. It then moves into solving modulus functions both algebraically and using the graphs. 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 Trigonometry covers; Understand and use the definitions of sine, cosine and tangent for all arguments The sine and cosine rules The area of a triangle in the form (1/2) ab sin⁡C Understand and use the sine, cosine and tangent functions Their graphs, symmetries and periodicity

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)

Matrices covers; Inverse and determinant of a 3x3 Matrix Plane geometry Find eigenvalues and eigenvectors of 2×2 and 3×3 matrices Find and use the characteristic equation. Understand the geometrical significance of eigenvalues and eigenvectors Diagonalisation of matrices Write a matrix in the form UDU^(-1) and understand Mⁿ=UDⁿ U^(-1) 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

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 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 ‘A2 level maths 13 - Composite functions’ for free download Please leave a review as it will really help me to improve my resources Mechanics – Vectors, Kinematics and Projectiles covers; Use vectors in three dimensions Use vectors to solve problems in kinematics Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces Understand, use and derive the formulae for constant acceleration for motion in 2 dimensions using vectors Use calculus in kinematics for motion in 2 dimensions using vectors Model motion under gravity in a vertical plane using vectors Projectiles

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 Matrices, invariant points and lines, inverse matrices and determinants covers; Add, subtract and multiply conformable matrices Multiply a matrix by a scalar. Understand and use zero and identity matrices. Find invariant points and lines for a linear transformation Calculate determinants of 2×2 matrices Understand and use singular and non-singular matrices; properties of inverse matrices Calculate and use the inverse of non-singular 2×2 matrices.

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 Travelling salesman problem covers; Find and interpret upper bounds and lower bounds for the Travelling Salesman problem Evaluate, modify and refine models which use networks Using adjacency matrices to solve travelling salesman problem

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 Game theory for zero sum games covers; Understand, interpret and construct pay-off matrices Find play-safe strategies and the value of the game Prove the existence or non-existence of a stable solution Identify and make use of dominated strategies Find optimal mixed strategies for a game including use of graphical methods

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

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