MATH 112 Fall 2021 Final Exam: Multiple Choice Questions

MATH 112 Name:______________________________ Fall 2021 Final Exam (Multiple-Choice) 12/22/21 Time Limit: 2 hours There are two sections to this exam: Multiple Choice and Written. This section is the multiple choice part, and this section contains 4 pages (including this cover page) and 20 problems. Check to see if any pages are missing. Enter your name above and section number below. Put an “X” in the circle for your section below: o Section 001 MW 8:00 -9:15 Jayer Fernandes o Section 002 TR 8:00-9:15 Son Tu o Section 003 MW 9:30-10:45 Andrew Krenz o Section 004 TR 9:30-10:45 Bryan Oakley o Section 005 MW 11:00-12:15 Peter Wei o Section 006 TR 11:00-12:15 Enkhzaya Enkhtaivan o Section 007 MW 1:00-2:15 Johnnie Han o Section 008 TR 1:00-2:15 Evan Sorensen o Section 009 MW 2:30-3:45 Jenny Yeon o Section 010 TR 2:30-3:45 James Tang o Section 011 MW 4:00-5:15 Jake Malloy • Completely fill in the B5 General Purpose Answer Sheet with a No. 2 PENCIL . Enter and mark the corresponding bubbles to your last name, first name (as much as you are able), and student identification number. • Under “Special Codes” mark the columns A&B with the number of the exam’s version below (e.g. 11 or 22). Then mark columns D, E and F with the THREE NUMBER CODE of YOUR SECTION (as given above). • You may NOT use textbooks, course notes, cell phone, or calculator during this exam. • No justification is necessary for this portion of the exam. Only CORRECT answers will receive credit. The written section still requires work and justification. VERSION 11

DO NOT WRITE ON THIS PAGE! IT IS FOR INSTRUCTOR USE ONLY! Item: Value: 1-20 20 points 21 a) b) c) d). e) f) 7 points each 22 a) b) c) 3 points each 23 a) b) 5 points each 24 a) b) c) d) a) 3 pts b) 4 pts c) 1 pt d) 1 pt 25 a) b) c) d) e) 2 points each

1. (1 point) True or False? √81 = ±9 (A) True. (B) False. (C) It depends. Sometimes it’s true and sometimes it’s false. 2. (1 point) Find the vertex of the parabola ࠵? = 1 + 6࠵? + 3࠵? , . (A) (-3,10) (B) (3,46) (C) (1,-2) (D) (-1, 2) (E) (-1,-2) 3. (1 point) Find the remainder when ࠵? - + ࠵? , − 3࠵? − 2 is divided by ࠵? − 2 . (A) 12 (B) 0 (C) -4 (D) 4 (E) 24 4. (1 point) Compute: ࠵?࠵? 2 3 √4 5 6 (A) 3 7 (B) − 3 7 (C) √࠵? 5 (D) - √࠵? 5 (E) -5 5. (1 point) If ࠵?(࠵?) = √࠵? , + 16 with a domain of ࠵? ≥ 0 , then ࠵? >3 (5) is (A) √41 (B) 3 √-3 (C) 3 (D) -3 (E) 1 3 6. (1 point) Which of the following functions is odd ? (A) ࠵?(࠵?) = 2 − |4࠵?| (B) ࠵?(࠵?) = ࠵?10 |D| (C) ℎ(࠵?) = 3 >D F (D) ࠵?(࠵?) = ࠵? H + 5 (E) None of these functions are odd functions. 7. ( 1 point) Which of the following intervals is the solution to the inequality −2|࠵? − 1| − 4 ≤ 2 ? (A) [−2,4] (B) (−∞, −3] ∪ [3, ∞) (C) (−∞, −2] ∪ [4, ∞) (D) (−∞, ∞) (E) There are no solutions.

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8. (1 point) Which of the graphs below illustrates the solution of the system O 2࠵? + 3࠵? + 4࠵? = 0 4࠵? + 6࠵? + 8࠵? = 1 6࠵? + 9࠵? + 12࠵? = 2 ? (A) (B) (C) (D) 9. (1 point) For which of the following relations is ࠵? not a function of ࠵? ? (A) (B) (C ) ࠵? = √࠵? , − 1 (D). ࠵? = 10 ± 3 D (E) All of the above are functions. ࠵? ࠵? 1 -1 2 -1 3 -1 4 -1

10. (1 point) The function ࠵?(࠵?) = √࠵? is shifted right 3 units, reflected across the ࠵? -axis, stretched vertically by a factor of 2 and shifted down 4 units. The formula for the function ࠵? obtained by performing these transformations on ࠵? is (A) ࠵?(࠵?) = −2√࠵? − 3 − 4 (B) ࠵?(࠵?) = −√2࠵? − 3 − 4 (C) ࠵?(࠵?) = 2√−࠵? + 3 − 4 (D ) ࠵?(࠵?) = √−2࠵? − 3 − 4 (E) ࠵?(࠵?) = √−2࠵? + 3 − 4 11. (1 point) Of all the polynomials below, the polynomial with complex coefficients of least degree that has 1, 2 − 2࠵?, 4࠵? as zeroes with 1 having a multiplicity of 3 is (A) (࠵? − 1) H (࠵? − 2 + 2࠵?)(࠵? − 2 − 2࠵?)(࠵? − 4࠵?)(࠵? + 4࠵?) (B) (࠵? + 1) H (࠵? + 2 − 2࠵?)(࠵? + 2 + 2࠵?)(࠵? + 4࠵?)(࠵? − 4࠵?) (C) 3(࠵? − 1)(࠵? − 2 + 2࠵?)(࠵? − 4࠵?) (D) (࠵? − 1) H (࠵? − 2 + 2࠵?)(࠵? − 4࠵?) (E) 3(࠵? − 1)(࠵? − 2 + 2࠵?)(࠵? − 2 − 2࠵?)(࠵? − 4࠵?)(࠵? + 4࠵?) 12. (1 point) Simplify ࠵? 3RH . (A) ࠵? (B) −࠵? (C) 1 (D) -1 (E) All of these. 13. ( 1 point) Simplify √−29 . A) ࠵?√29 B) −࠵?√29 C) −29࠵? D) √29 E) 29࠵? 14. (1 point) For each of the systems of equations below, the system with no solutions is (A) S 2࠵? − ࠵? = 1 6࠵? − 3࠵? = 2 (B) S 3࠵? + 4࠵? = −1 −15࠵? − 20࠵? = 0 (C) S ࠵? + ࠵? = 6 −3࠵? − 3࠵? = 7 (D) Each of (A), (B), and (C) has at least one solution. (E) Each of (A), (B), and (C) has no solutions. 15. (1 point) The slope of any line perpendicular to the line 2࠵? + 3࠵? = 4 is (A) , H (B) − , H (C) H , (D) − H , (E) -4

16. (1 point) The rational function ࠵?(࠵?) = -D U >3 D>, has (A) A horizontal asymptote at ࠵? = 4 and a hole at ࠵? = 2 . (B ) A vertical asymptote at ࠵? = 2 and a slant asymptote at ࠵? = 4࠵? + 7 . (C ) A hole at ࠵? = 2 and a slant asymptote at ࠵? = 4࠵? + 8 . (D) A vertical asymptote at ࠵? = 2 and a slant asymptote at ࠵? = 4࠵? + 8 . (E ) A horizontal asymptote at ࠵? = 4 and a vertical asymptote at ࠵? = 2 . 17. ( 1 point) A pond is being filled with water at a constant rate with a pump. Initially, at time ࠵? = 0 hours, there are 200 gallons of water in the pond. At time ࠵? = 5 , there are 700 gallons in the pond. Which of the following is a linear function ࠵? that models the volume of water in the pond in gallons at time ࠵? hours? (A) ࠵?(࠵?) = 100࠵? + 200 (B) ࠵?(࠵?) = 200࠵? + 100 (C) ࠵?(࠵?) = 3 3RR ࠵? + 200 (D) ࠵?(࠵?) = 3 ,RR ࠵? + 100 (E) ࠵?(࠵?) = 200࠵? + 700 18. (1 point) The graphs of ࠵? and ࠵? are shown below. Which of the following is the graph of ࠵? + ࠵? ?

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(A) (B) (C ) (D) 19. (1 point) How long will it take $1000 to quadruple (i.e. becomes 4 times larger) if it is invested at 4% interest compounded semi-annually? Answers are provided in years . (A) XY H XY 3.R7 (B) XY - XY 3.R- (C) XY - , XY 3.R, (D) XY - .R- (E) XY - .R[

20. (1 point) Select the formula for function ࠵?(࠵?) graphed below. (A) ࠵?(࠵?) = ࠵? >\ − 3 (B) ࠵?(࠵?) = ln(࠵? − 3) (C) ࠵?(࠵?) = 3࠵? >\ − 4 (D) ࠵?(࠵?) = ln (3 − ࠵?) (E) ࠵?(࠵?) = ln(3 − ࠵?) − 2

MATH 112 Name:____________________________________ Fall 2021 Final Exam (Written) 12/22/21 Time Limit: 2 hours There are two sections to this exam: Multiple-Choice and Written. This section is the written portion, and this portion of the exam contains 5 pages(including this cover page) and 8 problems. Check to see if pages are missing. Enter your name above and section number below. Put an “X” in the circle for your section below: o Section 001 MW 8:00 -9:15 Jayer Fernandes o Section 002 TR 8:00-9:15 Son Tu o Section 003 MW 9:30-10:45 Andrew Krenz o Section 004 TR 9:30-10:45 Bryan Oakley o Section 005 MW 11:00-12:15 Peter Wei o Section 006 TR 11:00-12:15 Enkhzaya Enkhtaivan o Section 007 MW 1:00-2:15 Johnnie Han o Section 008 TR 1:00-2:15 Evan Sorensen o Section 009 MW 2:30-3:45 Jenny Yeon o Section 010 TR 2:30-3:45 James Tang o Section 011 MW 4:00-5:15 Jake Malloy You may NOT use textbooks, course notes, cell phones, or calculators during this exam. You are required to show your work on each problem on this exam, and the following rules apply. • Organize your work in a reasonable, neat, and coherent way. Work that is jumbled, disorganized, and lacks clear reasoning will receive little or no credit. • Unsupported answers will not receive full credit. Any answer must be supported by calculations, explanation, and/or algebraic work to receive full credit. Partial credit may be given to well-argued, incorrect/partial solutions also. • If your require more space, use the extra stapled pages. Clearly indicate when you do this below the problem. Do NOT un-staple the pages ! • Make sure your explanations are clear and answer the question asked when asked to explain things!

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21 . (42 points) Solve the following equations, systems, or inequalities, finding all real and complex solutions. For inequalities, put your final answers in interval notation. a) (7 points) 2࠵? , + 5 = 2࠵? b) (7 points) |4࠵? − 3| ≥ 17 c) (7 points) S 2࠵? + ࠵? , = 26 ࠵? − ࠵? = 1

(d) (7 points) D_, D ‘ >D > 0 (e) (7 points) ࠵? ,D − 3 = 2࠵? D (f) (7 points) ln(2࠵?) + ln 2࠵? − 3 , 6 = 0

22. (9 points) A farmer has 40 yards of fencing and wants to fence off a rectangular field that borders a straight river. He does not need any fence along the river (see the figure below). (a) (3 points) Find a quadratic function ࠵?(࠵?) that describes the total area (in square yards) that can be enclosed by a width of ࠵? yards. (b) (3 points) What are the dimensions of the field of largest area that he can fence? How do you know? (c) (3 points) What is the largest possible area that he can enclose? How do you know? 23. (10 points) For ࠵?(࠵?) = 5 − ࠵? and ࠵?(࠵?) = √1 − ࠵? , compute the following combinations and state their domains: a) (5 points) (࠵? + ࠵?)(࠵?) b) (5 points) (࠵? ∘ ࠵?)(࠵?)

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24. (9 points) A boat on a river travels downstream with the flow of the current between two points, 5 miles apart, in 1 hour (see the figure below). The return trip of the boat (traveling at the same speed) against the current takes 2 hours. (a) (3 points) Determine a system of two equations in the variables ࠵? and ࠵? that describe the trips up and downstream. Clearly identify what your variables represent, keeping up with appropriate units in your descriptions. (b) (4 points) Solve the system of equations you obtained for ࠵? and ࠵? . (c) (1 point) What is the speed of the boat in still water, in appropriate units ? (d) (1 point) What is the speed of the current, in appropriate units ?

25. (10 points) The number of grams of a precious metal that can be taken from a mine doubles every 5 hours. Suppose that initially 3 grams have been mined at time ࠵? = 0 . (a) (2 points) Find an exponential function ࠵? = ࠵?(࠵?) that models the number of grams that have been mined after ࠵? hours. (b) (2 points) How many grams have been mined after 20 hours? (c) (2 points) Find the average rate of change of the number of grams mined between ࠵? = 0 hours and ࠵? = 20 hours. Make sure to include the correct units in your answer! (d) (2 points) Find ࠵? = ࠵? >3 (࠵?) . (e) (2 points) Compute ࠵? >3 (24) and interpret the meaning of this quantity in the context of the problem.

MATH 112 Exam Final Fall 2021 Version 11 Yellow

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