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This booklet 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 punctiliously. 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 in your assessments!
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Additional resources for A2-Level Mathematics Edexcel: Complete Revision & Practice
Y a) Find dy at the point (2, 1). dx b) Hence find the equation of the tangent to the curve at (2, 1), in the form y = ax + b, where a and b are constants. x (5 marks) 3 Use the quotient rule to show that, for the function f(x) = sec x: f´(x) = sec x tan x. (2 marks) (4 marks) C3 Section 4 — Differentiation 34 C3 Section 4 — Practice Questions 4 Differentiate the following with respect to x. a) b) 3e 5 A sketch of the function f(x) = 4ln 3x is shown in the diagram. ^e x + e 2xh . 2x + 1 (3 marks) − ln (1 − x ) + 2x .
T = 0 ﬁ x = –1, y = 0 t = – 21 ﬁ x = 4( 41 ) – 1 = 0, y = (– 21)3 + 21 = 83 t = 2 ﬁ x = 4(4) – 1 = 15, y = 23 – 2 = 6 So the graph crosses the line 8y = 3x + 3 at the points (–1, 0), (0, 83 ), (15, 6). y-coordinates? y not... You quite often get given a sketch of the curve that the parametric equations define. Don’t forget that the sketch can be useful for checking your answers — if the curve crosses the x-axis twice, and you’ve only found one x-coordinate for when y = 0, you know something’s gone a bit pear-shaped and you should go back and sort it out, sunshine.
Exam Questions dy for each of the following functions. Simplify your answer where possible. dx y = ln(3x + 1) sin(3x + 1). 1 Find a) b) y = c) d) y = 2 cosec (3x) 2 The curve shown below has the equation x = x2 + 3 . cos 3x (4 marks) (4 marks) y = sin3 (2x2) (3 marks) (2 marks) y 2 + 3y . y a) Find dy at the point (2, 1). dx b) Hence find the equation of the tangent to the curve at (2, 1), in the form y = ax + b, where a and b are constants. x (5 marks) 3 Use the quotient rule to show that, for the function f(x) = sec x: f´(x) = sec x tan x.