Download PDF by Roger Porkess: A2 Pure Mathematics (C3 and C4)

By Roger Porkess

ISBN-10: 0340888512

ISBN-13: 9780340888513

ISBN-10: 1444142755

ISBN-13: 9781444142754

The highly-acclaimed MEI sequence of textual content books, helping OCR's MEI established arithmetic specification, has been up-to-date to check the necessities of the recent standards, for first educating in 2004.

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Extra info for A2 Pure Mathematics (C3 and C4)

Example text

This can only be the case if the mapping is one-to-one. So the condition for a function f to have an inverse function is that, over the given domain and co-domain, f represents a one-to-one mapping. This is a common situation, and many inverse functions are self-evident as in the following examples, for all of which the domain and co-domain are the real numbers. ● f : x → x – 1; f –1 : x → x + 1 g : x → 2x; g –1 : x → –12 x h: x → x 3; h –1: x → 3 x Some of the following mappings are functions which have inverse functions, and others are not.

Given also that g(x) = g(–x) for all x, sketch the graph of g(x) for –2 р x р 2.

Given that f(x) = (x – 2)2 + 1 sketch the curves with the following equations on separate diagrams. Label each curve and give the co-ordinates of its vertex and the equation of its axis of symmetry. (a) y = f(x) (b) y = –f(x) (c) y = f(x + 1) + 2 [MEI] 5 Write the expression 2x 2 + 4x + 5 in the form a(x + b)2 + c where a, b and c are numbers to be found. Use your answer to write down the co-ordinates of the minimum point on the graph of y = 2x 2 + 4x + 5. [O & C] 34 6 The circle with equation x 2 + y 2 = 1 is stretched with scale factor 3 parallel to the x axis and with scale factor 2 parallel to the y axis.

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A2 Pure Mathematics (C3 and C4) by Roger Porkess

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