DEPARTMENT OF MATHEMATICS AND STATISTICS QUEEN S UNIVERSITY AT KINGSTON MATH 121/124 - APR 2014 A. Ableson, T. Day, A. Hoefel
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1 Page 1 of 18 STUDENT NUMBER: DEPARTMENT OF MATHEMATICS AND STATISTICS QUEEN S UNIVERSITY AT KINGSTON MATH 121/124 - APR 2014 A. Ableson, T. Day, A. Hoefel INSTRUCTIONS: Answer all questions, writing clearly in the space provided. If you need more room, there are blank pages at the end of the exam. If you use these pages, you must provide clear directions to the marker, e.g. Continued on page 17. Show all your work and explain how you arrived at your answers, unless explicitly told to do otherwise. Only CASIO FX-991, Gold Sticker or Blue Sticker calculators are permitted. Write your student number clearly at the top of each page. You have three hours to complete the examination. Wherever appropriate, include units in your answers. When drawing graphs, add labels and scales on all axes. HAND-IN Answers recorded on question paper. PLEASE NOTE: Proctors are unable to respond to queries about the interpretation of exam questions. Do your best to answer exam questions as written. FOR MARKER S USE ONLY Section I II III IV V Possible Grade Section VI VII VIII IX/X Total Possible Grade This material is copyrighted and is for the sole use of students registered in MATH 121/124 and writing this examination. This material shall not be distributed or disseminated. Failure to abide by these conditions is a breach of copyright and may also constitute a breach of academic integrity under the University Senate s Academic Integrity Policy Statement.
2 Page 2 of 18 STUDENT NUMBER: Section I. Multiple Choice (10 questions, 2 marks each) Each question has four possible answers, labeled (A), (B), (C), and (D). Choose the most appropriate answer. Write your answer in the space provided, using UPPERCASE letters. Illegible answers will be marked incorrect. You DO NOT need to justify your answer. (1) Consider the differential equation dp dt differential equation? = 100(50 P). What are the equilibria for this (A) P = 0 (B) P = 50 (C) P = 0 and P = 50 (D) This differential equation has no equilibria. (2) A surface is defined by z = (x 2 + 1)sin(y) + xy 2. By setting one variable constant, we generate a plane that intersects the surface. Which of the following planes will intersect the surface in a sine curve? (A) x = 0. (B) x = 1. (C) y = 0. (D) y = 1. (3) Four functions are given below. For which function does doubling both x and y result in a doubling of f? (A) f(x,y) = x 0.25 y 0.25 (B) f(x,y) = x 0.5 y 0.5 (C) f(x,y) = x 0.75 y 0.75 (D) f(x,y) = x 1.00 y 1.00
3 Page 3 of 18 STUDENT NUMBER: (4) Consider the function f(x,y) = 7 x 2 +y 2. Which of the following is a graph of this function? A B C D (5) Consider the region between y = x 3 and the x-axis on the interval from x = 0 to x = 1. Which of the following integrals represents the volume generated by rotating this region around the y axis? (A) (B) (C) (D) π(x 3 ) 2 dx π(1 2 (x 3 ) 2 ) dx π( 3 y) 2 dy π(1 2 ( 3 y) 2 ) dy
4 Page 4 of 18 STUDENT NUMBER: (6) The productivity of a wheat field (P) is measured under various levels of fertilizer (F) and rainfall (R). Results are shown in the table below. R F Which of the following is a possible linear approximation for the wheat field productivity for environments similar to F = 200, R = 12? (A) P(F,R) F 100R. (B) P(F,R) F 50R. (C) P(F,R) (F 200) 100(R 12). (D) P(F,R) (F 200) 50(R 12). (7) Consider the contour diagram for f(x,y) shown below, with the point P indicated. In which direction is the gradient at P directed? P y 5 4 x (A) Roughly in the direction of 1, 1 (B) Roughly in the direction of 1, 1 (C) Roughly in the direction of 1, 1 (D) Roughly in the direction of 1, 1
5 Page 5 of 18 STUDENT NUMBER: (8) A large ship is being towed by two tug boats. The larger tug exerts a force which is 50% greater than the smaller tug; the larger tug is pulling at an angle of 25 degrees north of east. Which direction must the smaller tug pull to ensure that the ship travels due east? (A) Between 0 and 20 degrees south of east. (B) Between 20 and 30 degrees south of east. (C) Between 30 and 40 degrees south of east. (D) Between 30 and 50 degrees south of east. (9) Which of the following functions is a solution to the differential equation dy dx = x y? (Assume y > 0.) (A) y = x (B) y = x+1 (C) y = x 2 (D) y = x 2 +1 (10) Which of the following describes the second derivatives at the point Q on the contour diagram below? Q (A) f yy is positive; f xy is positive. (B) f yy is positive; f xy is negative. (C) f yy is negative; f xy is positive. (D) f yy is negative; f xy is negative. y x
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DEPARTMENT OF MATHEMATICS AND STATISTICS QUEEN S UNIVERSITY AT KINGSTON MATH 121/124 - APR 2014 A. Ableson, T. Day, A. Hoefel
Page 1 of 18 DEPARTMENT OF MATHEMATICS AND STATISTICS QUEEN S UNIVERSITY AT KINGSTON MATH 121/124 - APR 2014 A. Ableson, T. Day, A. Hoefel INSTRUCTIONS: Answer all questions, writing clearly in the space
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