H1 a find the speed of each vehicle 2 b i find

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Unformatted text preview: 100 1 Total 70 Find (a) the sample standard deviation; (b) an unbiased estimate of the standard deviation of the population from which this sample is taken. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 101 145. Find the coefficient of x7 in the expansion of (2 + 3x)10, giving your answer as a whole number. Working: Answers: ....………………………………….......... (Total 3 marks) 146. The system of equations represented by the following matrix equation has an infinite number of solutions. 2 1 2 −1 2 1 − 9 x 7 3 y = 1 − 3 z k Find the value of k. Working: Answers: ....…………………………………….......... (Total 3 marks) 102 147. In a game a player rolls a biased tetrahedral (four-faced) die. The probability of each possible score is shown below. Score 1 2 3 4 Probability 1 5 2 5 1 10 x Find the probability of a total score of six after two rolls. Working: Answers: ....…………………………………….......... (Total 3 marks) 103 148. Find a vector that is normal to the plane containing the lines L1, and L2, whose equations are: L1: r = i + k + λ (2i + j – 2k) L2: r = 3i + 2j + 2k + µ (j + 3k) Working: Answers: ....…………………………………….......... (Total 3 marks) 149. The sum of the first n terms of an arithmetic sequence is Sn = 3n2 – 2n. Find the nth term un. Working: Answers: ....…………………………………….......... (Total 3 marks) 104 150. The plane 6x – 2y + z = 11 contains the line x – 1 = y +1 z − 3 . Find l. = 2 l Working: Answers: ....…………………………………….......... (Total 3 marks) 151. The probability distribution of a discrete random variable X is given by x P(X = x) = k 2 , for x = 0,1, 2, ...... 3 Find the value of k. Working: Answers: ....…………………………………….......... (Total 3 marks) 105 152. The velocity, v, of an object, at a time t, is given by v = ke −t 2 , where t is in seconds and v is in m s–1. Find the distance travelled between t = 0 and t = a. Working: Answers: ....…………………………………….......... (Total 3 marks) 153. Mr Blue, Mr Black, Mr Green, Mrs White, Mrs Yellow and Mrs Red sit around a circular table for a meeting. Mr Black and Mrs White must not sit together. Calculate the number of different ways these six people can sit at the table without Mr Black and Mrs White sitting together. Working: Answers: ....…………………………………….......... (Total 3 marks) 106 154. Find the coordinates of the point which is nearest to the origin on the line L: x = 1 – λ, y = 2 – 3λ, z = 2. Working: Answers: ....…………………………………….......... (Total 3 marks) 155. Given that x > 0, find the solution of the following system of equations: 8x 3 = 3 y xy – y = x2 + 9 4 (Total 3 marks) 156. A rectangle is drawn so that its...
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