Pearson Edexcel Further Maths A Level Questions & Answers

What is Leibnitz's Theorem? - ANSWERSThe nth derivative of y where y=uv is equal to the sum from k=0 to n of (nCk)(u^k)*(v^n-k) What is L'Hospital's Rule? - ANSWERSIf lim(x—>a)f(x)=lim(x—>a)g(x)=0 or +-infinity, then lim(x—>a)f(x)/g(x) = lim(x—>a)f'(x)/g'(x) What are the Weierstrass Substitutions? - ANSWERSt=tan(x/2) and dx=2dt/(1+t^2) How to approximate differentials using step length? - ANSWERSFor first orders, (dy/dx)0 = (y1 - y0)/h Euler's method, (dy/dx)0 = (y1 - y-1)/2h For second orders, (d^2y/dx^2)0 = (y1 - 2y0 + y-1)/h^2 What is Simpson's Rule? - ANSWERS∫f(x)dx = (h/3)((endpoint y values) + 4(y1 + y3 + ...) + 2(y2 + y4 + ...)) Define impulse - ANSWERSForce over time/ change in momentum When two objects collide what can be said for the impulse experienced by each? - ANSWERSIt is equal What are the formulae for work done? - ANSWERSForce * distance when horizontal, mass * g * height when vertical Define power - ANSWERSEnergy per time/ force * velocity What is the formula for the tension in a spring? - ANSWERSλx/l What is the formula for work done to extend a spring? - ANSWERSλx^2/2l What is the formula for the coefficient of restitution? - ANSWERSSpeed of separation/ speed of approach