Curve for the random variable x with mean and

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Unformatted text preview: e maximum point; (iii) the coordinates of the point of inflexion. (9) (b) Use your answers to part (a) to sketch a graph of the curve for 0 ≤ x ≤ 4, clearly indicating the features you have found in part (a). (3) (c) (i) On your sketch indicate by shading the region whose area is given by the following integral: ∫ 2 0 (ii) x( x − 4) 2 dx. Explain, using your answer to part (a), why the value of this integral is greater than 0 but less than 40. (3) (Total 15 marks) 85. A fair coin is tossed eight times. Calculate (a) the probability of obtaining exactly 4 heads; (2) (b) the probability of obtaining exactly 3 heads; (1) (c) the probability of obtaining 3, 4 or 5 heads. (3) (Total 6 marks) 61 86. An arithmetic sequence has 5 and 13 as its first two terms respectively. (a) Write down, in terms of n, an expression for the nth term, an. (b) Find the number of terms of the sequence which are less than 400. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 87. 3 2 Given the matrix A = − 1 0 find the values of the real number k for which det(A – kI) = 0 1 0 where I = 0 1 . Working: Answers: ....…………………………………….......... (Total 4 marks) 62 88. r rr r The vector n = 2 i – j +3 k is normal to a plane which passes through the point (2, 1, 2). Find an equation for the plane. Find a if the point (a, a – 1, a – 2) lies on the plane. Working: Answers: ....…………………………………….......... (Total 4 marks) 89. The random variable X is distributed normally with mean 30 and standard deviation 2. Find p(27 ≤ X ≤ 34). Working: Answers: ....…………………………………….......... (Total 4 marks) 63 90. For which values of the real number x is | x + k | = | x | + k, where k is a positive real number? Working: Answers: ....…………………………………….......... (Total 4 marks) 91. The area between the graph of y = ex and the x-axis from x = 0 to x = k (k > 0) is rotated through 360° about the x-axis. Find, in terms of k and e, the volume of the solid generated. Working: Answers: ....…………………………………….......... (Total 4 marks) 64 92. The rectangle box shown in the diagram has dimensions 6 cm × 4 cm × 3 cm. H G E F 3cm D C 4cm A 6cm B ˆ Find, correct to the nearest one-tenth of a degree, the size of the angle AHC . Working: Answers: ....…………………………………….......... (Total 4 marks) 65 93. The roots α and β of the quadratic equation x2 – kx + (k + l) = 0 are such that α2 + β2 = 13. Find the possible values of the real number k. Working: Answers: ....…………………………………….......... (Total 4 marks) 94. Express 3x − 4 in partial fractions. x2 − x Working: Answers: ....…………………………………….......... (Total 4 marks) 66 95. Find the largest domain for the function f : x a 1 4 ...
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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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