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

By Roger Porkess

The highly-acclaimed MEI sequence of textual content books, aiding OCR's MEI dependent arithmetic specification, has been up-to-date to compare the necessities of the recent standards, for first instructing in 2004.

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13 The general quadratic curve You are now able to relate any quadratic curve to that of y = x 2. 5 (i) (ii) (iii) Write the equation y = 1 + 4x – x 2 in the form y = a[(x + p)2 + q]. Show how the graph of y = 1 + 4x – x 2 can be obtained from the graph of y = x 2 by a succession of transformations, and list the transformations in the order in which they are applied. Sketch the graph. SOLUTION (i) 32 / a[(x + p)2 + q] If 1 + 4x – x 2 then –x 2 + 4x + 1 / ax 2 + 2apx + a(p 2 + q) Comparing coefficients of x 2: a = –1.

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 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.

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