Unformatted text preview: ECON 1078 Midterm 2 Practice Exam **Note—this practice exam has 2 more long answer problems than the real exam will. Accordingly, give yourself 1 hour and 15 minutes to complete this practice exam. When you calculate your final score, note the total number of points possible on this practice exam is 120. To find your percentage grade, calculate the total number points correct divided by 120. The real exam will have only 6 long answer problems. True/False (2 points each) 1) ! + 5 ln 7 = ln(!)!!! ! T / F 2) The distance between points (!!,!!") and (5, −20) is 89 T / F ! 3) The graph of ! ! = −(!) is identical to the graph of ! ! = (!!!) T / F 4) If ! ! = (! − 1)(! + 1) while ! ! = ! ! − 1 then f(g(x)) must equal g(f(x)) T / F 5) $H is invested in an account increasing at r% annually. The total in the account at t years ! is given by the formula (! + !"")! T / F 6) ! !!
! ! ! ! ! (! ) = ! !! ! ! !! ! ! ! !! (where b is a constant) T / F 7) If f(x) and g(x) are inverses, then the range of g(x) is equal to the domain of f(x) T / F 8) The minimum of function A(Q) = 3Q2 + 4Q – 7 occurs at
2/3 T / F 9) !" = (2! )!! 10) !"#! ! !! ! ! T / F T / F = 1251! Multiple Choice (4 points each) 1) Which of the following is a possible equation for the graph below? (note, the curve intersects the x axis at
1, 3 and 4) a) b) 1/6(x
4)(x+1)(x
3) c) d) 2) Given 4lnx + 5lnx3 = lnx2, x must equal: a) 1 b) c) d) 3) Compute the following sum: ! !
! !! ! !! (3! + 2!) 4) If a) b) c) d) 60 ! !" = 16! ·4!!! , then x equals: a) b) c) d)
7/3 5) The equation for a circle with center ( 2 , 3 ) and passing through point ( 0 , 3 ) is : a) b) c)(! − 2)! + (! − 3)! = 4 d) Long Answer (80 points total) 1) Given a(x) = x + 2, b(x) = x
4 + 2 and c(x) = x2, find b(c(a(x))) and c(a(b(x))), simplifying as much as possible. (10 points) 2) Express the following sum using summation notation (use j as your index): 1 – 12 + 23 – 34 + 45 – 56 + 67 (8 points) 3) If f(x) = (x
3), h(x) = (
x3 – 3x + 4) and f(x)g(x) = h(x), find g(x). (express any remainder in the appropriate form) (8 points) 4) Sketch the graph of = 6 −
! ! !! . For full credit graph the most basic function, graph each shift sequentially on a new graph and state what you are doing in each step (full sentences not required). (12 points) 5) There are female and male students in the chemistry department. Where t is the number of years since 1970, the equation c(t) = 250 + 30 t gives the total number of students and m(t) = 170 + 10 t gives the number of male students. Find the equation representing the number of female students at time t, f(t), then show that c(t) = m(t) + f(t) on a graph showing the values at t=30. How many female, male and total students are there in the department in the year 2000 (ie. when t=30)? (10 points) 6) The function f(x) is defined by the following table: a) b) c) d) Find the equations for f(x) and f
1(x) (the inverse in terms of x) Find domain, D, for f(x) and f
1(x) Find f(4) and f
1(4) Sketch f(x) and f
1(x) on one graph (make sure to label axes, functions, tic
marks and line y = x for reference) e) Will these functions intersect in quadrant I (right, top quadrant)? (12 points) 7. In 1990 your parents owned (completely) a house worth $750,000 and a car worth $35,000. Up until 2010 the house appreciated 1% per year, while the car depreciated 10% per year. In 2010, what was the total value of their assets based solely on these two investments? Realizing a car is poor investment choice, your parents sell the car for exactly its value in 2010 and deposit all the money they get into a high interest account earning 8% per year up till 2015. How much money will be in the account in 2015? (8 points) 8) An import company has a monopoly importing silicon from Uganda to sell I the US. The price it pays per ton Q is given by P = 1/3 Q + β1 while the price it receives is given by P =
1/2 Q + β2. In addition, the company pays γ per ton in shipping costs. Express the company’s profit function as a quadratic function of Q (simplifying as much as possible), then find the profit maximizing shipment in tons (assuming (β2 –β1 –γ) < 1). (12 points) ...
View
Full Document
 Spring '11
 koki

Click to edit the document details