A2 Pure Mathematics (C3 and C4) by Roger Porkess

By Roger Porkess

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

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Y Not to scale O x x = –1 (i) (ii) (iii) (iv) Give the co-ordinates of the vertex and the value of y when x = 0. Find the values of the constants a, b such that 2 – 6x – 3x 2 = a(x + 1)2 + b. Copy the sketch and draw in the reflection of the curve with equation y = 2 – 6x – 3x 2 in the line y = 2. Write down the equation of the new curve and give the co-ordinates [MEI] of its vertex. 35 9 The diagram shows the graph of y = f(x). The curve passes through the origin and has a maximum point at (1, 1).

C3 3 Still glides the stream and shall forever glide; The form remains, the function never dies. William Wordsworth Why fly to Geneva in January? Several people arriving at Geneva airport from London were asked the main purpose of their visit. Their answers were recorded. The language of functions 3 Functions David Joanne Skiing Jonathan Returning home Louise To study abroad Paul Shamaila Business Karen This is an example of a mapping. The language of functions A mapping is any rule which associates two sets of items.

2 gf fgh (viii) (fh)2 (ii) (iii) (iv) (v) (vi) fh ghf h2 (ix) Exercise 3D fg hf (vii) g2 (i) C3 3 Find the inverses of the following functions. f(x) = 2x + 7 (ii) f(x) = 4 – x 4 (iii) f(x) = –––– (iv) f(x) = x 2 – 3 x у 0 2–x The function f is defined by f(x) = (x – 2)2 + 3 for x у 2. (i) 3 (i) (ii) 4 Sketch the graph of f(x). On the same axes, sketch the graph of f –1(x) without finding its equation. Express the following in terms of the functions f: x → g: x → x + 4. (i) x→ x+4 (ii) x →x + 8 (iii) x→ x+8 (iv) x→ x and x+4 5 The functions f, g and h are defined by 3 h(x) = 2 – x.

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