Year 13 Further Maths (FP2,M2, M3) 2017/2018

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Dwayne Murphy
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1 Half Term 1 5 th September 12 th September 19 th September 26 th September 3 rd October 10 th October 17 th October FP2-Inequalities The manipulation and solution of algebraic inequalities and inequations, including those involving the modulus sign. FP2-Series Summation of simple finite series using the method of differences FP2-Series Euler s relation e iθ = cosθ + isinθ De Moivre s theorem and its application to trig identities and to roots of a complex number Loci and regions in the Argand diagram Elementary transformations from the z-plane to the wplane. M1-Dynamics of a The concept of a force. Newton s laws of Motion. Simple applications including the motion of two connected particles M1-Dynamics of a Momentum and impulse. The impulsemomentum principle. The principle of conservation of momentum applied to two particles colliding directly. M2-Centre of Mass Centre of mass of a discrete mass distribution in one and two dimensions. M2-Centre of Mass Centre of mass of uniform plane figures, and simple cases of composite plane figures. Simple cases of equilibrium of a plane lamina. M2-Work and Energy Kinetic and potential energy, work and power. The workenergy principle. The principle of conservation of mechanical energy. M2-Collisions Momentum as a vector. The impulsemomentum principle in vector form. Conservation of linear momentum. M2-Collisions Direct impact of elastic particles. Newton s law of restitution. Loss of mechanical energy due to impact. Successive impacts of up to three particles or two particles and a smooth plane surface

2 FP2 Ch1 PPQ Hwk FP2 Ch2 PPQ Hwk M2 Ch3 PPQ Hwk M1 Jan 2012 M2 Ch2 PPQ Hwk M2 Ch4 PPQ Hwk Half Term 2 31 st October 7 th November 14 th November 21 st November 28 th November 5 th December 12 th December Review of FP2 to date Polar coordinates (r,θ), r 0. Use of the formula 1/2 r 2 dθ for area.

3 M2-Statics of Rigid Bodies Moment of a force. Equilibrium of rigid bodies FP2 Ch3 PPQ Hwk M2-Statics of Rigid Bodies M2-Kinematics of a Motion in a vertical plane with constant acceleration, eg under gravity. Simple cases of motion of a projectile. M2-Kinematics of a Velocity and acceleration when the displacement is a function of time M2-Kinematics of a Differentiation and integration of a vector with respect to time. S2-Binomial Distribution Using factorial notation to find the number of arrangements of some objects. Using the binomial theorem to find probabilities. FP2 Ch7 PPQ Hwk S2-Binomial Distribution When a binomial distribution is a suitable model. Using tables of cum distribution function to find probabilities. Simple formulae to find mean and variance. M2 Ch5 PPQ Hwk M2 Ch1 PPQ Hwk Half Term 3 2 nd January 9 th January 16 th January 23 rd January 30 th January 6 th February 13 th February

4 FP2-Maclaurin and Taylor series Third and higher order derivatives. Derivation and use of Maclaurin series. FP2-Maclaurin and Taylor series Derivation and use of Taylor series. FP2-Maclaurin and Taylor series Use of Taylor series method for series of solutions of differential equations. FP2-First Order Differential Equations Further solution of first order differential equations with separable variables FP2-First Order Differential Equations First order linear differential equations of the form dy/dx + Py = Q where P and Q are functions of x. FP2-First Order Differential Equations Differential equations reducible to the above types by means of a given substitution. FP2-First Order Differential Equations S2-Poisson Distribution S2-Poisson Distribution S2-Continuous random variables. S2-Continuous random variables. S2-Continuous uniform distribution S2-Continuous uniform distribution S2-Normal Distributions Relating the exponential series and the Poisson Using simple formulae to find the mean and variance. Using tables of the Poisson cumulative distribution function. Checking the suitability of the model. Approximating the binomial and Poisson Concept of continuous random variable and its probability density function. Continuous distribution function. Mean and variance of a probability density function. Mode, median and quartiles of a continuous random variable. Rectangular Properties of a continuous uniform Choosing the right model. Using a continuity correction Approximating a binomial distribution by a normal FP2 Ch6 PPQ Hwk FP2 Ch4 PPQ Hwk

5 Half Term 4 27 th February 6 th March 13 th March 20 th March 27 th March 3 rd April The linear second order differential equation a (d 2 y/dx 2 ) + b (dy/dx) + cy = f(x) where a,b and c are real constants and the particular integral can be found by inspection or trial. Differential equations reducible to the above types by means of a given substitution. S2-Normal Distributions Choosing the appropriate approximation. S2-Populations and samples Populations, censuses and samples Ads and disads S2-Populations and samples Simple random sampling Sampling distribution of a statistic S2-Hypothesis testing Concept and significance of a hypothesis test. One and two-tailed tests. S2-Hypothesis testing Hypothesis tests for binomial and poisson. Hypothesis tests for binomial and poisson using critical regions. S2-Hypothesis testing M2 Jan 2012 M1 Jan 2011 M2 Jan 2011 FP2 Ch5 PPQ Hwk

6 Half Term 5 24 th April 1 st May 8 th May 15 th May 22 nd May

7 Revision Revision Revision Revision Revision FP2 Jan 2012 FP2 Jan 2011 FP2 Jan 2010

8 Half Term 6 5 th June 12 th June 19 th June 26 th June 3 rd July 10 th July 17 th July

AS and A level Further mathematics contents lists

AS and A level Further mathematics contents lists Contents Core Pure Mathematics Book 1/AS... 2 Core Pure Mathematics Book 2... 4 Further Pure Mathematics 1... 6 Further Pure Mathematics 2... 8 Further