Formulas Mass Density = Volume Population Density People = Area Absolute change = New value Old value Relative change New value Old value = 100% Old value Absolute difference = Compared value Reference value Relative difference Compared valu e Reference value = 100% Reference value Absolute error = Measured value True value Relative error Measured value True value = 100% True value Version B KEY Page 1 of 15
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Student s Printed Name: XID: C Instructor: Section: No questions will be answered during this exam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the correct answer. You have 90 minutes (1.5 hours) to complete this test. General Directions: Any communication with any person (other than the instructor or a designated proctor) during this exam of any form, including written, signed, verbal, or digital, is understood to be a violation of academic integrity. All devices, such as computers, cell phones, cameras, and PDAs, must be turned off while the student is in the testing room. No smart watches allowed. You may use any scientific calculator except a TI-89 or a TI-NSpire CAS. No smart watches are allowed in the examination room. No part of this test may be removed from the examination room. 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. Question 1 2 3 4 Scantron Points 8 12 9 10 1 Earned Free Response Total 40 Multiple Choice Total 60 Test Score Version B KEY Page 3 of 15
Multiple Choice Portion There are 20 multiple choice questions. Each question is worth 3 points and has one correct answer. Use a number 2 pencil and bubble in the letter of your response on the Scantron sheet. 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. 1. Which of the Venn diagrams below best illustrates the following deductive argument? P: Some mammals are egg-laying animals. P: Tigers (X) are not egg-laying animals. C: Tigers are not mammals. Mammals A) B) X Mammals Egg-laying Animals Egg-laying Animals X C) D) Mammals X Mammals X Egg-laying Animals Egg-laying Animals E) Mammals X Egg-laying Animals 2. Which of the following is the smallest number? A) 2 million B) 167 thousandths C) 5 10 7 D).0000346 E) 1 billionth Version B KEY Page 4 of 15
3. In Highlands, NC, the average temperature in August is 78 F. Convert this temperature to degrees Celsius. Round your answer to the nearest tenth of a degree. A) 25.6 C B) 61.1 C C) 35.4 C D) 28.3 C E) 78.0 C 4. Given that a deductive argument is sound, what must be true about the argument s validity and the truth of the premises? A) The argument may or may not be valid and the premises may or may not be true. B) The argument must be valid and all of the premises must be true. C) The argument may or may not be valid and all of the premises must be true. D) The argument is not valid and at least one of the premises is not true. E) The argument must be valid and the premises may or may not be true. 5. A vessel has mass of 8560 g and volume of 150000 cm 3. Water has a density of 1 g/cm 3. Calculate the density of the vessel and determine if the vessel will float or sink in water. Round your answer to three decimal places. A) The density of the vessel is.057 g/cm 3, so the vessel will float in water. B) The density of the vessel is 1.752 g/cm 3, so the vessel will float in water. C) The density of the vessel is.057 g/cm 3, so the vessel will sink in water. D) The density of the vessel is.571 g/cm 3, so the vessel will float in water. E) The density of the vessel is 17.523 g/cm 3, so the vessel will sink in water. Version B KEY Page 5 of 15
6. The Gimli Glider ran out of fuel before reaching its destination, but the pilot was able to safely land the aircraft. The aircraft had 12,185 kg less fuel than it needed for the journey. Convert this measure of fuel into gallons. For airline fuel, 1 gal = 6.84 lbs. Round your answer to the nearest whole number. A) 5527 gallons B) 808 gallons C) 37805 gallons D) 3927 gallons E) 12341 gallons 7. In Belgium, one gallon of milk costs 3.39 (European Euros). Using the Currency Conversions on the Conversion Factor formula sheet, calculate this cost in U.S. Dollars. Round your answer to two decimal places. A) $3.81 B) $3.39 C) $3.01 D) $3.72 E) $3.78 8. Sears is having a store-wide Labor Day sale for 30% off everything in the store. If the original price of a vacuum cleaner is $90, what is the discounted price? Round your answer to two decimal places. A) $63.00 B) $27.00 C) $117.00 D) $87.30 E) $92.70 Version B KEY Page 6 of 15
9. In 2014, the Intel Core i7 5960X processor was rated at 238,310 million instructions per second. Express this processor speed in scientific notation. A) 2.3831 10 6 instructions per second B) 238310 10 6 instructions per second C) 23.831 10 10 instructions per second D) 2.3831 10 5 instructions per second E) 2.3831 10 11 instructions per second 10. Evaluate the following argument. Assume that all of the premises are TRUE. P: All rocks are minerals. P: Wheat (X) is not a mineral. C: Wheat is not a rock. A) The argument is sound, but not valid. B) The argument is a strong inductive argument. We should accept the conclusion. C) The argument is neither valid nor sound. D) The argument is valid and sound. E) The argument is valid, but not sound. 11. A shoebox is 6 inches by 12 inches by 5 inches. Calculate the volume of the shoebox in cubic centimenters (cm 3 ). Round your final answer to the nearest whole number. RECALL: Volume = length width height A) 914 cm 3 B) 5899 cm 3 C) 360 cm 3 D) 6122 cm 3 E) 142 cm 3 Version B KEY Page 7 of 15
12. The following number is expressed in scientific notation. Identify the exponent. 8.231 10 3 A) 10 3 B) 8 C) 10 D) 3 E) 8.231 13. Which of the categorical propositions below is BEST illustrated by the Venn diagram? Dogs Students A) Some dogs are students. B) No dogs are students. C) Some dogs are not students. D) All dogs are students. E) All students are dogs. 14. Anna and Paul decide to work on a homework problem on their own and then compare their answers. The true answer of the problem is 1.24679 10-6. Anna got an answer of 0.001243 10-3 whereas Paul got 0.12508 10-5. Whose answer is more accurate and with what absolute error? A) Anna s answer is more accurate with an absolute error of 3.79 10-9. B) Paul s answer is more accurate with an absolute error of 4.01 10-9. C) Paul s answer is more accurate with an absolute error of 1.12 10-11. D) Anna s answer is more accurate with an absolute error of 7.8 10-9. E) Anna s answer is more accurate with an absolute error of 1.25 10-9. Version B KEY Page 8 of 15
15. State the number of significant digits and the implied precision of the given number. 2,340,500,000 A) 4 significant digits, precise to the nearest hundred-thousands place B) 5 significant digits, precise to the nearest ones place C) 5 significant digits, precise to the nearest hundred-thousands place D) 10 significant digits, precise to the nearest ones place E) 10 significant digits, precise to the nearest hundred-thousands place 16. Perform the following operation, reporting your answer in scientific notation with the correct number of significant digits. (18.40 10 3 ) (.02431 10 2 ) A) 4.47 10 6 B) 4.473 10 5 C) 4.473 10 4 D) 4.47 10 4 E).4473 10 5 17. In 2000, 12.8% of vehicles sold were off-road vehicles. In 2010, that number decreased to 10.2%. Calculate and interpret the relative change in the number of off-road vehicles sold from 2000 to 2010. Round your answer to two decimal places, if necessary. A) In 2010, there were 25.49% fewer off-road vehicles sold than in 2000. B) In 2000, there were 20.31% more off-road vehicles sold than in 2010. C) In 2000, there were 2.6% more off-road vehicles sold than in 2010. D) In 2010, there were 2.6% fewer off-road vehicles sold than in 2000. E) In 2010, there were 20.31% fewer off-road vehicles sold than in 2000. Version B KEY Page 9 of 15
18. Which choice below BEST describes the relationship between the sets X and Y? X = {1, 2, 3, 4, 5, 6} Y = {3, 6, 9, 12} A) Sets X and Y are disjoint. B) Set Y is a subset of set X. C) Sets X and Y are overlapping. D) Sets X and Y are the same set, i.e. the sets have exactly the same members. E) Set X is a subset of set Y. 19. A bakery has 45 cookies to sell. A cookie may have nothing added or it may have walnuts or chocolate chips or both added. There are 10 cookies with both walnuts and chocolate chips. There are a total of 25 cookies containing chocolate chips. There are 7 cookies with nothing added. How many cookies have walnuts, but not chocolate chips? (HINT: Completing a Venn diagram may help you answer this question.) A) 23 B) 10 C) 3 D) 13 E) 15 20. A son s age is 24% of his father s age. The son is 12 years old. How old is his father? Round your answer to the nearest whole number, if necessary. A) His father is 40 years old. B) His father is 42 years old. C) His father is 60 years old. D) His father is 58 years old. E) His father is 50 years old. Version B KEY Page 10 of 15
Free Response Portion Show all necessary work. Verify that the answers carry the appropriate units. Partial credit may be given for work towards the correct solution. However, if answers are shown without necessary work, YOU MAY RECEIVE LITTLE OR NO CREDIT FOR THE CORRECT ANSWER. 1. Your refrigerator is rated at 650 watts. Your utility company charges 7 cents per kilowatt-hour. If the refrigerator runs 24 hours per day, how much does it cost to run the refrigerator for 30 days? Show all work and express your answer in dollars rounded to two decimal places. $0.07 1 kw - h 650 watts 30 days 24 hours day 1 kw 1000 watts = $32.76 1 point for given cost of electricity (in cents/kw-h or in $/kw-h) 1 point for given wattage of refrigerator 1 point for given number of days 2 points for number of hours/day 2 points for conversion factor: kw to watts (Full credit awarded for any correct conversion.) 1 point for calculation, following reasonable work ½ if units of any factor are missing or incorrect, up to a maximum of 2 points deducted ½ if answer not rounded correctly No deduction if work missing for conversion from cents to $. Answer: $ 32.76 Points earned on this question: Available points on this question: 8 Version B KEY Page 11 of 15
2. An International Pharmaceutical Association has 518 members. The members are either clinical psychologists or psychiatrists. Some are citizens of the United States, others are not. a. Complete the two-way table describing the members of the association. U.S. Citizens Non-U.S. Citizens Total Clinical Psychologists 70 129 199 Psychiatrists 130 189 319 Total 200 318 518 1 point per value in table In Version B only, problem statement says 521 members, so grader followed work to award as much partial credit to full credit possible. b. The Venn diagram below shows the relationship between the association members who are psychiatrists and the members who are U.S. citizens. Complete the Venn diagram. (Hint: You will need to place 4 numbers into the 4 regions of the Venn diagram.) Members of the Association Psychiatrists U.S. Citizens 189 130 70 129 1 point per value in Venn diagram c. How many U.S. Citizens (in the association) are not psychiatrists? 70 2 points per answer, no work required, all or nothing, following work above d. How many association members are Non-U.S. Citizens? 318 2 points per answer, no work required, all or nothing, following work above Points earned on this question: Available points on this question: 12 Version B KEY Page 12 of 15
3. Suppose the price of a Mercedes sedan is $40,000 and the price of a Lexus sedan is $50,000. Calculate the following price comparisons, showing all work and rounding to the nearest whole number. a. Find the absolute difference and relative difference in the sedan prices using the Lexus as the reference. Absolute Difference = $40,000 $50,000 = $10,000 Relative Difference = 40,000 50,000 100% = 20% 50,000 Absolute Difference: $10,000 Relative Difference: 20% b. Find the absolute difference and relative difference in the sedan prices using the Mercedes as the reference. Absolute Difference = $50,000 $40,000 = $10,000 Relative Difference = 50,000 40,000 100% = 25% 40,000 Absolute Difference: $10,000 Relative Difference: 25% Each abs. & rel. diff.: 1 point for work (units not required in work) 1 point for numeric answer ½ if answer rounded incorrectly ½ if missing units in answer, up to a maximum of 1 point deducted 1 if values switched in formula 2 if values switched in parts a. and b. (Used wrong reference in both.) No credit if incorrect formula is used. c. Complete the following interpretations of the price comparison by filling in the blank with the appropriate relative difference. The Lexus price is 25 % higher than the Mercedes. 1 point, following part b. Points earned on this question: Available points on this question: 9 Version B KEY Page 13 of 15
4. A light-year is the distance that light can travel in one year. It is approximately 9 trillion kilometers. (One trillion km = 10 12 km) Proxima Centauri is the nearest stellar neighbor to our Sun at 4.24 light years away from Earth. In 2018, a new NASA mission - Solar Probe Plus - will be launched. The probe will hit velocities as high as 200 kilometers per second. a. At the probe s maximum velocity of 200 km/sec, approximately how long would it take for the probe to reach Proxima Centauri? Show all work and express your answer in years rounded to the nearest whole number. 1 sec 200 km (4.24 9 1012 ) km 1 point for given velocity of probe 1 point for given distance to star 2 points for converting time: seconds to years (Full credit awarded for any correct conversion.) 1 point for calculation, following reasonable work ½ if units of any factor are missing or incorrect, up to a max of 2 points deducted ½ if answer not rounded correctly Answer: 6050 years b. At the probe s maximum velocity of 200 km/sec, it could travel from the Earth to the Moon in about 0.5 hours. Use this information to approximate the distance from the Earth to the Moon. Show all work and express your answer in km rounded to the nearest whole number. 200 km 1 sec 0.5 hours 3600 sec 1 hour = 360,000 km 1 point for given velocity of probe 1 point for given time to moon 2 points for converting time: seconds to hours (Full credit awarded for any correct conversion.) 1 point for calculation, following reasonable work 1 hour 3600 sec 1 day 24 hours 1 year 365 days = 6050 ½ if units of any factor are missing or incorrect, up to a max of 2 points deducted ½ if answer not rounded correctly Answer: 360,000 km Points earned on this question: Available points on this question: 10 Version B KEY Page 14 of 15
Scantron (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 20 bubbled in answers; has MATH 1010 and my Section number written at the top; has my Instructor s name written at the top; has Test No. 1 written at the top; has Test Version B both written at the top and bubbled in below my CUID; and shows my correct XID written in and then bubbled in with a zero in the first column followed by the eight digits. Version B KEY Page 15 of 15