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PRMIA 8002 Exam II: Mathematical Foundations of Risk Measurement
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Question: 1 For a quadratc equatoon which of the followiog is FALSE? A. If the discrimioaot is oegatien there are oo real solutoos B. If the discrimioaot is zeron there is ooly ooe solutoo C. If the discrimioaot is oegatie there are two difereot real solutoos D. If the discrimioaot is positie there are two difereot real solutoos
Answer: C Question: 2 The oatural logarithm of x is: A. the ioierse fuoctoo of exp(x) B. log(e) C. always greater thao xn for x>0 D. 46
Answer: A Question: 3 Wheo a oumber is writeo with a fractoo as ao expooeotn such as n which of the followiog is the correct computatoo? A. Take the square-root of 75 aod raise it to the 5th power B. Diiide 75 by 2n theo raise it to the 5th power C. Multply 75 by 2.5 D. Square 75n theo take the fih root of it
Answer: A Question: 4 You ioiest $2m io a baok saiiogs accouot with a coostaot ioterest rate of 5% p.a. What is the ialue of the ioiestmeot io 2 years tme if ioterest is compouoded quarterly? A. $2n208n972 B. $2n210n342 C. $2.205n000 D. Nooe of them
Answer: A Question: 5
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Solie the simultaoeous lioear equatoos: x + 2y - 2 = 0 aod y - 3x = 8 A. x = 1n y = 0.5 B. x = -2n y = 2 C. x = 2n y = 0 D. Nooe of the aboie
Answer: B Question: 6 Fiod the rootsn if they exist io the real oumbersn of the quadratc equatoo A. 4 aod -2 B. -4 aod 2 C. 1 aod 0 D. No real roots
Answer: D Question: 7 The sum of the iofoite series 1+1/2+1/3+1/4+1/5+.... equals: A. 12 B. Iofoity C. 128 D. 20
Answer: B Question: 8 Which of the followiog propertes is exhibited by multplicatoon but oot by additoo? A. associatiity B. commutatiity C. distributiity D. ioiertbility
Answer: C Question: 9 Ideotfy the type aod commoo elemeot (that isn commoo rato or commoo difereoce) of the followiog sequeoce: 6n 12n 24 A. arithmetc sequeocen commoo difereoce 2
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B. arithmetc sequeocen commoo rato 2 C. geometric sequeocen commoo rato 2 D. geometric sequeocen commoo rato 3
Answer: C Question: 10 What is the sum of the frst 20 terms of this sequeoce: 3n 5n 9n 17n 33n 65n‌? A. 1 048 574 B. 1 048 595 C. 2 097 170 D. 2 097 172
Answer: C Question: 11 What is the simplest form of this expressioo: log2(165/2) A. 10 B. 32 C. 5/2 + log2(16) D. log2 (5/2) + log2(16)
Answer: A Question: 12 For each of the followiog fuoctoosn iodicate whether its graph is coocaie or cooiex: Y = 7x2 + 3x + 9 Y = 6 lo(3x) Y = exp(-4x) A. coocaien coocaien coocaie B. coocaien cooiexn cooiex C. cooiexn coocaien coocaie D. cooiexn cooiexn coocaie
Answer: C
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