MthSc 17 Test Spring 1 Student s Printed Name: CUID: Instructor: Section # : You are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook, notes, cell phone, laptop, PDA, or any technology on either portion of this test. All devices must be turned off while you are in the testing room. During this test, any communication with any person (other than the instructor or his designated proctor) in any form, including written, signed, verbal, or digital, is understood to be a violation of academic integrity. No part of this test may be removed from the testing room. Read each question very carefully. In order to receive full credit for the free response portion of the test, you must: 1. Show legible and logical (relevant) justification which supports your final answer.. Use complete and correct mathematical notation.. Include proper units, if necessary. 4. Give exact numerical values whenever possible. You have 9 minutes to complete the entire test. On my honor, I have neither given nor received inappropriate or unauthorized information at any time before or during this test. Student s Signature: Do not write below this line. Free Response Problem Possible Points Points Earned Free Response Problem Possible Points 1 4 6b 6 5 6c 5 a 4 7 6 b 8 5 4 6 9 1 5 1 Free Response 6 6a 6 Multiple Choice 4 Points Earned Test Total 1 Page 1 of 1
MthSc 17 Test Spring 1 Multiple Choice. There are 14 multiple choice questions. Each question is worth points and has one correct answer. The multiple choice problems will count as 4% of the total grade. Use a number pencil and bubble in the letter of your response on the scantron sheet for problems 1 14. For your own record, also circle your choice on your test since the scantron will not be returned to you. Only the responses recorded on your scantron sheet will be graded. You are NOT permitted to use a calculator on any portion of this test. 1. Write + + + " ( pts.) + " using sigma notation. 5 k + 1 a) k= 1 7 5 k b) k= 1 7 5 k c) k= 1 + 7 5 + k d) k= 1 7 The figure shows the areas of the regions bounded by the graph of f and the x-axis. Use the graph to answer the next two questions.. Evaluate the integral f (x) dx. a) -1 b) 7 c) - d) 14. Which of the following expressions does NOT represent the total area bounded by the graph of f and the x-axis between x = - and x =? a) f (x)dx + f (x)dx b) f( x) dx c) f( x) dx f( x) dx d) f( x) dx Page of 1
MthSc 17 Test Spring 1 4. Below is the graph of f x = 4x +. Use geometry to find the area of the region bounded by f x and the x-axis on the interval 1,. a) 1 b) 4 c) d) 5. The velocities (in/sec) of a remote controlled race car moving along a dirt path for 8 seconds are given in the following table. Estimate the distance traveled by the car using a right Riemann sum approximation to the displacement on,8 with n = 4. Time (sec) Velocity (in/sec) 1 4 5 6 7 8 1 1 17 7 1 5 a) 154 in b) 17 in c) 16 in d) 85 in 6. Estimate the area under the curve of f x = x on the interval, using a left ( pts.) Riemann sum approximation and rectangles. a) 18 b) 7 c) 6 d) 9 Page of 1
MthSc 17 Test Spring 1 7. Let f (x) be an even function where f (x)dx =. Let g(x) be an odd function where g(x)dx = 1. Find f (x) g(x) dx. a) 6 b) c) 4 d) 1 " 8. Use a graph and area to evaluate 1 x dx. a) 5π b) 5π c) 1π d) 1π 9. Find d dx x sin tdt. π a) xsin x b) 1 sin 4 x x c) 1 4 cos4 π 1 4 cos4 x d) sin x sin π 1. Evaluate the integral a) 7 b) -7 c) -4 d) 4 1 (4 x+ 1) dx. Page 4 of 1
MthSc 17 Test Spring 1 11. Find the integral ( + ) sec ( + 4 ) x a) tan ( 4 ) x x x dx. + x x + x + C b) tan( 4 ) x + x + C 1 tan x + 4 x + C c) ( ) x + sec x + 4 x + C d) ( ) 1. Evaluate ( 1) k= k (k 5). a) 4 b) c) 5 d) 1 Use f x dx =, f x dx = 4, 1. Find f x dx. and g x dx = 7 to answer the next two questions. a) 7 b) 1 c) 1 d) 7 14. Find g x f x dx. a) 5 b) 9 c) 9 d) The Free Response section follows. PLEASE TURN OVER YOUR SCANTRON while you work on the Free Response questions. You are welcome to return to the multiple choice section at any time. Page 5 of 1
MthSc 17 Test Spring 1 Free Response. The Free Response questions will count as 6% of the total grade. Read each question carefully. In order to receive full credit you must show legible and logical (relevant) justification which supports your final answer. Give answers as exact answers. You are NOT permitted to use a calculator on any portion of this test. 1. (4 pts.) Consider the graph of f x = 6 x. Estimate the area under the graph of f x on the interval 1,5 using midpoint rectangles. Draw the rectangles on the graph and use f x, not the graph, to find the function values.. a. Find the average value for the function f x = 6x 11 on the interval,5. b. ( pts.) Find the x-values that satisfy the Mean Value Theorem for Integrals for f x = 6x 11 on the interval,5. Page 6 of 1
MthSc 17 Test Spring 1 x if x <. Let f x = x which is defined piecewise as f (x) =. x if x a. (4 pts.) Find the total area bounded by the graph of f( x ) and the x-axis between x = and x = 4. It may help to shade the associated areas on the graph but the shading will not be graded. b. ( pts.) Evaluate f x dx. 4. (6 pts.) Evaluate the following integral. If you use substitution, clearly define u and du. 4 ( 4x + 5) dx 1 Page 7 of 1
MthSc 17 Test Spring 1 Version A 5.1 6.1 5. Compute the definite integral (x + ) dx as the limit of a right Riemann Sum by completing parts a. e. You may need one or more of the following common sums: k = n n + 1 ; k = n n + 1 n + 1 6 ; k = n n + 1 a. (1 pt.) Let n be the number of subintervals into which the interval is to be divided. State Δx, the width of each subinterval, in terms of n. b. ( pts.) Find an expression for the height of the k-th rectangle at the right endpoint of the k-th subinterval. The expression should be in terms of k and n. c. ( pts.) Find an expression for the area of the k-th rectangle, in terms of k and n. d. (4 pts.) State the right Riemann Sum for the function on the given interval. Simplify the Riemann Sum. State your final answer in terms of n only. e. (1 pts.) Find the limit of the Riemann Sum (found in part d) as the number of rectangles are increased to infinity. i.e. Find the exact value of the definite integral. Page 8 of 1
MthSc 17 Test Spring 1 Version A 5.1 6.1 6. Find the following integrals. Be sure to combine like terms, simplify coefficients, do not leave negative exponents in the final answer, etc. If you use substitution, clearly define u and du. a. (6 pts.) x 7 + x dx 1 b. (6 pts.) x sin(x )dx c. (5 pts.) 9x ( x x +1) dx 4 Page 9 of 1
MthSc 17 Test Spring 1 Version A 5.1 6.1 7. (6 pts.) The velocity of an object moving along a line is given by v(t) = 6t 18 m/s. Find the total distance traveled over the interval t 5 seconds. Be sure to include units with your answer. 8. (5 pts.) The population of a prairie dog community grows at a rate of P t dogs/month for t. The initial value of the population was P( ) = 55. What is the population of prairie dogs at months? Be sure to include units with your answer. ( ) = 1 5 t prairie 9. (1 pt.) Check to make sure your Scantron form meets the following criteria. If any of the items are NOT satisfied when your Scantron is handed in and/or when your Scantron is processed one point will be subtracted from your test total. My scantron: is bubbled with firm marks so that the form can be machine read; is not damaged and has no stray marks (the form can be machine read); has 14 bubbled in answers; has MthSc 17 and my Section number written at the top; has my Instructor s name written at the top; has Test No. written at the top; has Test Version A both written at the top and bubbled in below my CUID; and shows my correct CUID both written and bubbled in. Page 1 of 1