24 marks 803 a write the number 10 201 in base 8 4 b

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Unformatted text preview: ity that (a) only medical students are chosen; (b) all three law students are chosen. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 576 841. The probability density function f(x) of the continuous random variable X is defined on the interval [0, a] by 1x f ( x) = 8 27 2 8x for 0 ≤ x ≤ 3. for 3 < x ≤ a. Find the value of a. Working: Answer: ....…………………………………….......... (Total 6 marks) 842. Given that asin4x + bsin2x = 0, for 0 < x < π , find an expression for cos2 x in terms of a and b. 2 Working: Answer: ....…………………………………….......... (Total 6 marks) 577 843. Given that | z | = 2 5 , find the complex number z that satisfies the equation 25 − 15 = 1 − 8i. z z* Working: Answer: ....…………………………………….......... (Total 6 marks) 844. (a) (b) Express as partial fractions Hence or otherwise, find 2x + 4 . ( x 2 + 4)( x − 2) ∫ (x 2 2x + 4 dx . + 4)( x − 2) Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 578 845. An experiment is carried out in which the number n of bacteria in a liquid, is given by the formula n = 650 ekt, where t is the time in minutes after the beginning of the experiment and k is a constant. The number of bacteria doubles every 20 minutes. Find (a) the exact value of k; (b) the rate at which the number of bacteria is increasing when t = 90. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 579 2 846. Let f(x) = x + 5 x + 5 , x ≠ –2. x+2 (a) Find f′(x). (b) Solve f′(x) > 2. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 847. The normal to the curve y = k + ln x2, for x ≠ 0, k ∈ x 3x + 2y = b, where b ∈ , at the point where x = 2, has equation . Find the exact value of k. Working: Answer: ....…………………………………….......... (Total 6 marks) 580 848. Given that (A ∪ B)′ = ∅, P(A′|B) = 1 and P(A) = 6 , find P(B). 3 7 Working: Answer: ....…………………………………….......... (Total 6 marks) ˆ ˆ 849. The triangle ABC has an obtuse angle at B, BC = 10.2, A = x and B = 2x. (a) Find AC, in terms of cos x. (b) ˆ Given that the area of triangle ABC is 52.02 cos x, find angle C . Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 581 850. The sum of the first n terms of an arithmetic sequence {un} is given by the formula Sn = 4n2 – 2n. Three terms of this sequence, u2, um and u32, are consecutive terms in a geometric sequence. Find m. Working: Answer: ....……………...
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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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