A2-Level Mathematics Edexcel: Complete Revision & Practice by CGP Books

By CGP Books

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This ebook is stuffed with transparent revision notes and examination perform questions for A2 Maths scholars. It covers the C3, C4, S2 and M2 modules for the Edexcel examination, and it’s effortless to learn and revise from - everything’s defined easily and carefully. each few pages there are quickly warm-up questions, a few exam-style questions and on the finish of every module there are perform examination papers (answers on the back). There’s additionally a sprinkling of jokes to lighten the temper. It’s precisely what you must organize to your assessments!

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2 Example If f(x) = ex + 2ex, find f’(x) for x = 0. 1) Let’s break down the function into its two bits and differentiate them separately: 2 y = ex and 2) This is the tricky bit. Use the chain rule from the last page: u = x2 and y = eu y = 2ex 5) This bit’s easy. If y = 2ex then dy = 2ex too. dx 3) Both u and y are now easy to differentiate: du = 2x and dy = eu du dx 2 dy du dy 4) = × = 2x ∙ eu = 2x ∙ ex dx dx du When y = kf(x) where k is a constant, then dy/dx is just kf ’(x). 6) Put the bits back together and you end up with f’(x) = 2xex + 2ex.

Dx 2) To find dv for the product rule, we need the chain rule twice: dx v = u12, where u1 = tan (3x). dv = 2u = 2 tan (3x), and du1 = 3 sec2 (3x) (which is an easy chain rule solution itself). So dv = 6 tan (3x) sec2 (3x). 1 dx du1 dx dy 3) Now we can put this result in the product rule formula to get : dx dy = (ex ∙ 6 tan (3x) sec2 (3x)) + (tan2 (3x) ∙ ex) = ex tan (3x)[6 sec2 (3x) + tan (3x)]. Job done. dx du dv dx dx u v Differentiate Again for d2y/dx2, Turning Points, Stationary Points etc.

C) After how many years will the motorbike’s value have fallen below £500? d) Sketch a graph showing how the value of the motorbike varies with age, labelling all key points. Feeling confident? Thought so. Let’s see how you handle these exam-style problems — they’re a wee bit more problematic... Exam Questions 1 a) Given that 6ex = 3, find the exact value of x. b) Find the exact solutions to the equation: e2x − 8ex + 7 = 0. c) d) Solve the equation: giving your answers as exact values of x. 2 The sketch below shows the function y = eax + b, where a and b are constants.

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