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

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

Maclaurin series and l’Hôpital’s rule covers; Find the Maclaurin series of a function including the general term Evaluation of limits using Maclaurin series or l Hopital rule The limits lim(x→∞)⁡(x^k e^(-x)) and lim(x→0)⁡(x^k lnx) where k>0, applied to improper 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 Please leave a review as it will really help me to improve my resources

Cubic and quartic inequalities covers; Inequalities involving polynomial equations (cubic and quartic) Understand how to manipulate inequalities correctly Consider critical values and give solution sets using correct interval or set notation Use a calculator find numerical solutions. 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 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.

Topics covers; Understand and use the formula for a polar curve defined as r = f(θ) for α ≤ θ ≤ β Use symmetry to simplify the evaluation of areas Find composite areas. 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 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 Radians and small angles covers; Work with radian measure, including use for arc length and area of sector Know and use exact values of sin and cos for and multiples thereof Know and use exact values of tan for and multiples thereof

A presentation showing learners how to use binomial expansion. The presentations starts with basic quadratic and cubics to allow the learners to spot the patterns it then moves onto harder questions such as finding coefficients. 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.

A presentation that show the learners how to solve differential equations by separating the variables. It also includes an activity that teaches the learners how to convert from worded questions into a differential equation. 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.

A presentation that shows students how the compound angles are found using basic trigonometry. The students can complete the activity sheet and all the solutions are on the presentation for the teacher to discuss the results of cos(A+B) and sin(A+B). The presentation also covers double angles and examples of how they are used to solve trig equations and trig identities. The other presentation shows students how to use harmonic form to solve equations of the form asinx+bcosx=c. 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 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 Quadratics covers; Using the discriminant of a quadratic function, including the conditions for real and repeated roots Completing the square Solution of quadratic equations including solving quadratic equations in a function of the unknown. Graphs of quadratics

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 Product, Quotient and Chain rule covers; Differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse 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 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 Integration covers; Integrate e^kx , 1/x , sin⁡kx , cos⁡kx and related sums, differences and constant multiples Use a definite integral to find the area between two curves Understand and use integration as the limit of a sum Carry out simple cases of integration by substitution and integration by parts Understand these methods as the inverse processes of the chain and product rules respectively

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 Numerical methods locating roots and Newton-Raphson covers; Locate roots of f(x)= 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well-behaved Understand how change of sign methods can fail Solve equations approximately using simple iterative methods; be able to draw associated cobweb and staircase diagrams Solve equations using the Newton-Raphson method and other recurrence relations of the form x_(n+1) = g(x_n ) Understand how such methods can fail Use numerical methods to solve problems in context

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 – Equilibrium, resolving, Statics, Dynamics covers; Understand and use Newton’s second law for motion in situations where forces need to be resolved (restricted to 2 dimensions) Resolving forces in 2 dimensions Equilibrium of a particle under coplanar forces Understand and use addition of forces Resultant forces Dynamics for motion in a plane Coefficient of friction Understand and use the F ≤ μR model for friction Motion of a body on a rough surface Limiting friction and statics