Practice Final Exam, Math 10311 2 3 4 5 6Last Name:First Name:ID: Section:Math 1031December , 2004There are 22 multiple machine graded questions and 6 write-outproblems .NO GRAPHIC CALCULATORS are permitted. GOOD LUCK !2MC1. Consider the parabola y = −3(x + 5)2. The coordinates of its vertex are:a) (1, 1)b) (0, 0)c) (5, 0)d) None of the aboveMC2. What is the relation between the two lines defined by the equations3x − 2y = 0 and 6y − 9x = 1a) They are the sameb) They are perpendicular to each otherc) The lines are parallel to each otherd) The lines intersect at the origine) None of the aboveMC3. Let f(x) =√x2+ 1 defined for x > 0. The inverse function, f−1, is:a)1√x2+1b) xc) x2d)√x2− 1e) None of the above3MC4. Let f(x) =√x2− 1, then the domain of f is:a) x > 0b) x < −1c) x > 1d) x > 2e) None of the aboveMC5. Let f(x) =√x2+ 1 and g(x) = x3, then (fog)(2) =a)√65b) 8c)√5d) 0e) None of the aboveMC6. Let f(x) =√x3− 2 and g(x) = 1 − x , then (fog)(1) is:a) 10b) x3− x − 1c) Not definedd) 0e) 1MC7. The solution set of the equation3x2−6x2−2= 3 isa) x = −1b) all real numbers4c) all real numbers except x =√2d) x =√2e) None of the aboveMC8. A DVD player is sold for $210 after 10% discount. The original price ofthe player was:a) $300b) $220c) $231d) $1000e) None of the aboveMC9. You are given a quadratic equationx2− 3x + c = 0in which c is a constant that you don‘t know. Suppose that one of the solutions isx = 2. The other solution is then:a) x = 4b) x = −3c) x = 1d) 0e) The answer cannot be determined because c is unknown.MC10. The solution of the inequality (x + 1)(x2− 1) ≥ 0 is:a) x > 1b) x > −15c) x ≤ −1 or x ≥ 1d) x < 0e) None of the aboveMC11. Since f(x) = 3x+ 2xis an increasing function, it is invertible. Thenf−1(5) =a) 0b) 200c) 243 + 32d) 1e) None of the aboveMC12. The solution set of the inequality (1 − x2)8+ 1 > 0 is:a) all real numbersb) x > 1c) x > −1d) x < −1e) all real numbers except 1MC13. The value of the expresion32/33/4is:a)√3b) 27c) 81d)19e) None of the above6MC14. Let f(x) = x(x2− 1). The number of turning points of the function is:a) 0b) 1c) 2d) 3e) None of the aboveMC15. The unique solution of the equation ex= e − ln(x) is:a) x = ln(e − 1)b) x = 2.716c) x = 1d) x = 0e) None of the aboveMC16.In how many ways you can arrange 2 different mathematics texts, threedifferent English texts and four different history texts on a bookshelf when books inthe same subject must be kept together?a) 6b) 288c) 864d) 1728e) 5184MC17. In how many ways can 2 passangers be seated in a van with 3 passangerseats?a) 67b) 3c) 9d) 4e) None of the aboveMC18. A fair coin is tossed and a card is drawn at random from a standarddeck of 52 cards. The probability that the coin shows a head and that the card is aking is:a) 1/2b) 4/52c) 1d) 2/52e) None of the aboveMC19. Two fair dice are rolled. What is the probability their sum is odd?a)14b) 0.6c) −1d)12e) None of the aboveMC20.Suppose that x and y are two real, positive numbers such that xy =19. Iflog3(x) = −1, then log13(y) =a) 0b) 18c) 3d) −1e) None of the aboveMC21.You play a game in which, first, you roll a die and second you flip a coinonce, if the number on the die is odd and twice if the number on the die is even.You are paid a dollar for each head and you have to pay one dollar for each tail youobtain. What is your expected gain?a) 0b) 1c) 3d) −1e) None of the aboveMC22. Scientists are trying to determine whether two different diseases whichaffect chickens are actually related. After they tested a large number of chickensthey obtained the following informations. Out of all the chickens 60% have thedisease A but only 10% of these are affected by disease B. Of those 40% who don‘thave the disease A, only 20% have the disease B. What is the probability that arandomly selected chicken has the disease A, given that it has the disease B?a) 0.4b) 0.2c) 0.3d)1519e) None of the above9Pb23. Consider the following equation, which defines a line in the plane.6x + 3y − 8 = 0What is the equation of the line perpendicular to the given line and which passesthrough the origin?10Pb24. 20 liters of saline solution has a concentration of 10% salt. How manyliters of solution have to be replaced by pure salt to obtain a 50% solution?11Pb25. Bob invests $2000 in an account with continuously compounded interest.After two years the balance is $2800. What was the annual interest rate?12Pb26. A certain radioactive material has a half-life of 100 years. Find out howlong will it take for a chunk of this material to be reduced to 30% of its initialamount.13Pb27. Let f(x) = −x2+ 6x − 5.a) Sketch the graph of this function.b) What is the range of the function?c) For what values of x is this function increasing?14Pb28. At a certain pastry shop they bake three types of muffins, namely choco-late, strawbery ,and banana muffins. In an average day the probability that themuffins are not fresh are 0.5 for chocolate muffins, 0.2 for strawberry muffins and0.1 for banana muffins. If you randomly select a muffin from a basket containingequal numbers of chocolate, strawberry and banana muffins , what is the probabilityyou selected a strawberry muffin given that the muffin is