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 Integration covers; Know and use the Fundamental Theorem of Calculus Integrate xⁿ (excluding x=-1), and related sums, differences and constant multiples Evaluate definite integrals Use a definite integral to find the area under a curve

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 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 – Discrete random variables and expectation covers; Understand DRVs with distributions given in the form of a table or function Evaluate probabilities for a DRV Evaluate measures of average and spread for a DRV to include mean, variance, standard deviation, mode or median Understand expectation and know the formulae: * E(X)=∑x p * E(X^2 )=∑^2 p * Var(X)=E(X^2)-E(X)^2 Understand expectation of linear functions of DRVs and know the formulae: * E(aX+b)=aE(X)+b * Var(aX+b)=a^2 Var(X) Know the discrete uniform distribution defined on the set {1, 2, …, n}. Understand when this distribution can be used as a model. Proof of mean and variance of discrete uniform distribution.

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 Inverse and reciprocal trigonometric functions covers; Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan Understand their relationships to sine, cosine and tangent Understand and use; * sec^2 θ = 1 + tan^2 θ * cosec^2 θ = 1 + cot^2 θ

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 Argand diagrams and complex roots covers; Construct and interpret simple loci in the Argand diagram such as |z-a|>r and arg⁡(z-a)=θ Know that non-real roots of polynomial equations with real coefficients occur in conjugate pairs. Solve any quadratic equation with real coefficients Solve cubic or quartic equations with real coefficients given sufficient information to deduce at least one root for cubics or at least one complex root or quadratic factor for quartics

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 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 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 Volume of revolution covers; Derive formulae for and calculate volumes of revolution

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

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

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

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

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

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

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

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 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