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Unformatted text preview: low shows part of the graph of f(x). The maximum point on the curve is P(3, 2). y 4 P(3, 2) 2 –1 1 2 3 4 5 6 x –2 –4 –6 –8 –10 –12 469 (a) Write down the value of (i) h; (ii) k. (2) (b) Show that f(x) can be written as f(x) = –x2 + 6x – 7. (1) (c) Find f′(x). (2) The point Q lies on the curve and has coordinates (4, 1). A straight line L, through Q, is perpendicular to the tangent at Q. (d) (i) Calculate the gradient of L. (ii) Find the equation of L. (iii) The line L intersects the curve again at R. Find the x-coordinate of R. (8) (Total 13 marks) 699. Points A, B, and C have position vectors 4i + 2j, i – 3j and – 5i – 5j. Let D be a point on the x-axis such that ABCD forms a parallelogram. (i) Find BC . (ii) (a) Find the position vector of D. (4) (b) Find the angle between BD and AC . (6) 470 The line L1 passes through A and is parallel to i + 4j. The line L2 passes through B and is parallel to 2i + 7j. A vector equation of L1 is r = (4i + 2j) + s(i + 4j). (c) Write down a vector equation of L2 in the form r = b + tq. (1) (d) The lines L1 and L2 intersect at the point P. Find the position vector of P. (4) (Total 15 marks) 700. A packet of seeds contains 40 % red seeds and 60 % yellow seeds. The probability that a red seed grows is 0.9, and that a yellow seed grows is 0.8. A seed is chosen at random from the packet. (a) Complete the probability tree diagram below. 0.9 0.4 Grows Red Does not grow Grows Yellow Does not grow (3) 471 (b) (i) Calculate the probability that the chosen seed is red and grows. (ii) Calculate the probability that the chosen seed grows. (iii) Given that the seed grows, calculate the probability that it is red. (7) (Total 10 marks) 701. A company offers its employees a choice of two salary schemes A and B over a period of 10 years. Scheme A offers a starting salary of $11 000 in the first year and then an annual increase of $400 per year. (a) (i) Write down the salary paid in the second year and in the third year. (ii) Calculate the total (amount of) salary paid over ten years. (3) Scheme B offers a starting salary of $10 000 dollars in the first year and then an annual increase of 7 % of the previous year’s salary. (b) (i) Write down the salary paid in the second year and in the third year. (ii) Calculate the salary paid in the tenth year. (4) (c) Arturo works for n complete years under scheme A. Bill works for n complete years under scheme B. Find the minimum number of years so that the total earned by Bill exceeds the total earned by Arturo. (4) (Total 11 marks) 702. Let f(x) = 1 + 3 cos(2x) for 0 ≤ x ≤ π, and x is in radians. (a) (i) Find f′(x). (ii) Find the values for x for which f′(x) = 0, giving your answers in terms of π. (6) 472 The function g(x) is defined as g(x) = f(2x) – 1, 0 ≤ x ≤ (b) π . 2 (i) The graph of f may be transformed to the graph of g by a stretch 1in the x-direction with scale factor followed by another transformation. Describe fully this other transform...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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