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

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This publication 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 speedy 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 in your assessments!

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Additional resources for A2-Level Mathematics Edexcel: Complete Revision & Practice

Example text

Dy - ^sin 2 x + cos 2 xh = = -21 . sin 2 x sin x dx Don’t forget your easy C2 trig identities as well as the ones covered in Section 2. sin x , and cot x = 1 , then y = cos x = cot x. 5) Linking this back to the question, since tan x = cos x tan x sin x dy 1 1 2 And since cosec x = , then = = −cosec x. QED* sin x dx sin 2 x There’s more of this trig stuff on the next page. This was just a taste of things to come... *Quite Exciting Differentiation The second rule of maths club is — you do not talk about maths club...

Y (2 marks) π 2π x Use the double angle formula for cos to show that 1 + cos x 2 x = cos 2 . 75 in the interval 0 ≤ x ≤ 2p. 2 6 A curve has the equation: a) b) Find c) d) Determine the nature of each of the stationary points. Find (3 marks) (4 marks) y = e2x − 5ex + 3x. dy . dx (2 marks) d2y . dx 2 (2 marks) Show that the stationary points on the curve occur when x = 0 and x = ln 23 . (4 marks) (4 marks) 45 7 The UK population, P, of an endangered species of bird has been modelled over time, t years, by the function: The time t = 0 is set as the beginning of the year 2010.

Or was it a bridge... Learn the method for Integrating Parametrics 1) Normally, to find the area under a graph, you can do a simple integration. But if you’ve got parametric equations, things are more difficult — you can’t find 2) There’s a sneaky way to get around this. Suppose your parameter’s t, then 3) Both y and dx are written in terms of t, so you can multiply them dt together to get an expression you can integrate with respect to t. Example # # y dx if y isn’t written in terms of x. y dx = # y dx dt dt This comes from the chain rule (see p26) — if you think of dx as dx , 1 then dx = dx # dt .

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