10 marks 246 note radians are used throughout this

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Unformatted text preview: ), then translating the graph of y = f(x). (b) Describe fully each of these transformations, which together map the graph of y = f(x) onto the graph of y = g(x). Working: Answers: (a) ………………………………………….. (b) .................................................................. .................................................................. (Total 3 marks) 177 254. If f(x) = ln(2x – 1), x > 1 , find 2 (a) f′ (x); (b) the value of x where the gradient of f(x) is equal to x. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 178 255. A machine fills bottles with orange juice. A sample of six bottles is taken at random. The bottles contain the following amounts (in ml) of orange juice: 753, 748, 749, 752, 750, 751. Find (a) the sample standard deviation; (b) an unbiased estimate of the population standard deviation from which this sample is taken. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 179 256. If f ( x) = x , for x ≠ –1 and g(x) = (f ° f)(x), find x +1 (a) g( x ) (b) (g ° g)(2). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 180 257. The position vectors of points P and Q are: p = 3i + 2j + k q = i + 3j – 2k (a) Find the vector product p × q. (b) Using your answer to part (a), or otherwise, find the area of the parallelogram with two sides OP and OQ . Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 181 258. Find the coordinates of the point of intersection of the line L with the plane P where: x + 3 y –1 z –1 = = 2 –1 2 P :2x + 3y – z = – 5 L: Working: Answers: ………………………………………….. (Total 3 marks) 182 259. A girl walks to school every day. If it is not raining, the probability that she is late is raining, the probability that she is late is 1 . If it is 5 2 . The probability that it rains on a particular day is 3 1 . 4 On one particular day the girl is late. Find the probability that it was raining on that day. Working: Answers: ………………………………………….. (Total 3 marks) 260. Solve, by any method, the following system of equations: 3x – 2y + z = –4 x + y –z = –2 2x + 3y = 4 Working: Answers: ………………………………………….. (Total 3 marks) 183 1 of the students travel to school by bus. Five students are chosen at random. Find 3 the probability that exactly 3 of them travel to school by bus. 261. In a school, Working: Answers: ………………………………………….. (Total 3 marks) ∫ 262. Find 1n x dx . Working: Answers: ………………………………………...
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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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