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The highly-acclaimed MEI sequence of textual content books, assisting OCR's MEI established arithmetic specification, has been up to date to compare the necessities of the hot requisites, for first educating in 2004.
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Extra info for A2 Pure Mathematics (C3 and C4)
The diagram shows a sketch of the graph of y = f(x), where f(x) = 6x – x 2. Use this graph to sketch (i) (ii) (iii) y y = f(x – 2) y = –12 f(x) y = 2f(x – 1) (3, 9) y = f(x) indicating clearly where these graphs cross the x axis and the co-ordinates of the highest point. 4 O 6 x The diagram shows the graph of y = f(x). y (1, 1) 1 y = f(x) 0 1 2 x Sketch the graph of each of these functions. (i) (iii) (v) y = f(2x) y = 2f(x – 1) x y=f ––1 2 ( ) (iv) y = f(x + 2) y = 3f(x) (vi) y = f(3x + 1) (ii) 29 5 C3 3 Starting with the curve y = cos x, show how transformations can be used to sketch these curves.
The function F(x) is defined by F(x) = b – c sin x, 0° р x р 360°, where b and c are constants, with c Ͼ 0. (a) (b) Find the range of F(x) in terms of b and c. Show that the graph of y = F(x) crosses the x axis if –c Ͻ b Ͻ c. Given that b = –12 c, find the co-ordinates of the points where the graph crosses the x axis, and sketch the graph. 2 Sketch the curves of y = f(x) and y = –f(x) for each of the following functions. (i) x2 (ii) sin x (iii) x 3 – 6x 2 + 11x – 6 Describe the relationship between the graphs of y = f(x) and y = –f(x) in these cases.
A) Decide which mappings fall into each category, and for those which do not have inverse functions, explain why. (b) For those which have inverse functions, how can the functions and their inverses be written down algebraically? 39 Functions C3 3 (i) (ii) (iii) (iv) Temperature measured in Celsius → temperature measured in Fahrenheit. Marks in an examination → grade awarded. Distance measured in light years → distance measured in metres. Number of stops travelled on the London Underground → fare.