Download Advanced Level Mathematics: Pure Mathematics 1 by Hugh Neill, Douglas Quadling, Julian Gilbey PDF

By Hugh Neill, Douglas Quadling, Julian Gilbey

Written to compare the contents of the Cambridge syllabus. natural arithmetic 1 corresponds to unit P1. It covers quadratics, features, coordinate geometry, round degree, trigonometry, vectors, sequence, differentiation and integration.

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X 2 +2x+2 (b) x 2 -8x-3 (c) x 2 +3x-7 (d) 5-6x+x 2 (e) x 2 +14x+49 (f) 2x 2 +12x-5 (g) 3x 2 -12x+3 (h) 7 - 8x - 4x 2 (i) 2x 2 +5x-3 (a) 5 Use the completed square form to factorise the following expressions. of x for which this occurs.

13 and 3. 14 different scales have been used on the two axes. If equal scales had been used the elongation in both figures would have been more obvious. 1 Sketch the graph of f(x) = 3x 2 - 1 ''" , 2x -1. You can factorise the expression as f(x) = (3x +l)(x -1), but to apply the factor method you need to write it as f(x) = 3(x + j-)(x-1). +. y=3x 2 -2x-l So the graph passes through (-~ ,0) and (1,0). The constant 3 tells you that the graph faces upwards and is elongated. x This is enough information to give a good idea of the shape of the graph, from which you can draw a sketch like Fig.

Y=2(x-l)(x-4), or y = 2x 2 - •x A If\ Since the point (3,-4) Jies on this curve, -4=a(3-1)(3-4),giving -4=-2a,so a=2. The equation of the curve is therefore Fig. 18 lOx + 8 . Exercise 3E 1 Sketch the following graphs. 2 (a) y=(x-2)(x-4) (b) y=(x+3)(x-l) (c) y=x(x-2) (d) y = (x + 5)(x + 1) (e) y=x(x+3) (f) y = 2(x + l)(x-1) Sketch the following graphs. (x 2 ~ x -12) (g) y = - x 2 (h) y=-(x 2 -7x+12) (i) y = llx - 4x 2 (a) y = x 2 - 2x - 8 - 4x - 4 - 6 2 4 Find the equation, in the form y = x + bx + c , of the parabola which (a) crosses the x~axis at the points (2,0) and (5,0), (b) crosses the x-axis at the points (-7,0) and (-iO,O), (c) passes through the points (-5,0) and (3,0), (d) passes through the points (-3,0) and (1,-16).

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