By Hugh Neill, Douglas Quadling, Julian Gilbey
Written to check 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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Hence find the other point where the two curves meet. 17 Find the value of the constant p if the three curves y = x 2 + 3x + 14 , y = x 2 + 2x + 11 and y = px 2 + px + p have one point in common. 18 The straight line y = x -1 meets the curve y = x 2 - 5x - 8 at the points A and B. The curve y = p + qx - 2x 2 also passes through the points A and B. Find the values of p and q. 19 The line y = lOx - 9 meets the curve y = x 2 . Find the coordinates of the points of intersection. / 50. PuRE MATHEMATICS 1 20 Suggest a possible equation for each of the graphs shown below.
Find the length of AB and the coordinates of the midpoint of AB. (OCR) 14 (a) Find the equation of the line l through the point A(2,3) with gradient -! (b) Show that the point P with coordinates (2 + 2t,3- t) will always lie on l whatever the value of t . (c) Find the values of t such that the _length AP is 5 units. (d) Find the value of t such that OP is perpendicular to l (where 0 is the origin). Hence find the length of the perpendicular from 0 to l. 15 P and Q are the points of intersection of the line ::+~=1 a b I (a>O, b>O) with the x- and y-axes respectively.
I 3 (a) y = x 2 (d) y I (b) y=x 3 I = 4x-• (e) y (c) y = -2x 2 l 4 = x -, (f) y=x' -x _l 3 5 Sketch these graphs, including negative values of x where appropriate. • (a) y=x' (d) y=x _l 3 3 (b) y=x 4 (e) y 4 (c) y=xs 4 = x' 6 Draw sketch graphs with these equations. (b) y=x+x-2 (a) y=x2+x-1· (d) y=x-2 -x- 1 (e) y=x -2 -x -3 (f) y=x _l 2 · -I (c) y=x 2 -x (f) y=x -2 -x -4 7 Of the following functions, one is even and two are odd. Determine which is which. _ CHAPTER 3: FuNCTIONS AND GRAPHS 41 8 State the values of the following.
Advanced Level Mathematics: Pure Mathematics 1 by Hugh Neill, Douglas Quadling, Julian Gilbey