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

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 Mean value of a function covers; Understand and evaluate the mean value of a function

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 Linear Relationships covers; Use logarithmic graphs to estimate parameters in relationships of the form 〖y=ax〗^n and 〖y=kb〗^x , given data for x and y

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

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 Differentiation of trigonometric and exponential functions and points of inflection covers; Understand and use the derivative of sin⁡x and cos⁡x The second derivative and its connection to convex and concave sections of curves and points of inflection Differentiate e^kx, a^kx , sin⁡kx , cos⁡kx , tan⁡kx and related sums, differences and constant multiples Understand and use the derivative of ln⁡x Apply differentiation to find points of inflection

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 - Conditional probability covers; Understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables Understand and use the conditional probability formula P(A│B)=P(A∩B)/P(B) Modelling with probability, including critiquing assumptions made and the likely effect of more realistic assumptions

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 ‘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 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

Topics covers; Modulus of functions and associated inequalities Graphs of y=|f(x)| and y=1/(f(x)) for given y=f(x) Understand the concept of an oblique asymptote Conic functions extended to composite transformations including rotations 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

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

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

Differential Equations First and Second Order covers; Find both general and particular solutions to differential equations. Solve differential equations of form y’’+ay’+by=0 where a and b are constants by using the auxiliary equation. Solve differential equations of 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 (in cases where f(x) is a polynomial, exponential or trigonometric function). Understand and use the relationship between the cases when the discriminant of the auxiliary equation is positive, zero and negative and the form of solution of the differential equation Use differential equations in modelling in kinematics and in other contexts. 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