Type one errors and type two errors covers; Calculate probability of making Type I error from tests based on a normal distribution Understand the power of a test. Calculations of P(Type II error) and power for a test for tests based on a normal, Binomial or a Poisson 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

Complex Numbers covers; Understand de Moivre’s theorem and use it to find multiple angle formulae and sums of series Use de Moivre’s theorem for both finite and infinite trigonometric series. Know and use the definition e^iθ=cosθ+isinθ and the form z=re^iθ Find the n distinct nth roots of re^iθ for r≠0 and know that they form the vertices of a regular n-gon in the Argand diagram. Use complex roots of unity to solve geometric problems 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

Yates’ correction covers; Knowledge of when and how to apply Yates’ correction. Know and be able to use the fact that Yates’ correction is used in a contingency table when there is only 1 degree of freedom (ie in a contingency table with 2 rows and 2 columns, which may occur after pooling has taken place) Know and be able to use the formula 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

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

Improper Integrals covers; Identify why a given integral is improper Understand and clearly demonstrate the limiting processes involved, using correct notation Identify when and why an improper integral does not have a finite value Identify the point(s) where the integrand is undefined Evaluate improper integrals where the integrand is undefined at a value in between the limits of integration. 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

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

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

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

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

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

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

t-distribution t-statistic covers; Test for the mean of a normal distribution with unknown variance using a t-statistic with appropriate degrees of freedom Construct confidence intervals, symmetric or otherwise, from small samples, for the mean of a normal distribution with unknown variance using the t-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

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

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