Name
Exam 1 - Math 1030-008 - October 5, 2007
NOTICE: There are problems on both sides of each sheet of this exam!!
You will have 50 minutes to complete this exam. Please write legibly, justify your anwers, and
circle your answers. Remember: You must show all of your work. No work means no
partial credit!!
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1) Of the 57 students in Darci’s class, 21 snowboard, 25 ski, and 25 ice skate. Moreover, 3 participate
in all three activities, 7 ski and iceskate only, 10 ski and snowboard only, and 14 iceskate only.
(a) Draw a Venn diagram to illustrate this information. Use the symbols S, I, and SB to represent
the set of people who ski, iceskate, and snowboard, respectively.
(b) Use your diagram to answer the following:
·How many people in Darci’s class do not ski, iceskate, or snowboard?
·How many people in Darci’s class snowboard only?
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2) Draw a Venn diagram to determine whether the argument is valid. Then discuss the truth of
the premises and determine whether the argument is sound.
· Premise 1: Anyone who has taken Math 1030 went to college.
· Premise 2: Britt did not take Math 1030.
· Conclusion: Britt did not go to college.
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3) Suppose you drive a car with an average gas mileage of 35 miles per gallon. If you plan to take
a 2500-mile cross-country trip,
·How much should you budget (in dollars) for gasoline if the price of gasoline averages $3.00 per
gallon?
·How far do you go in kilometers?
·If 1 gallon = 3.785 L, how many cubic inches of gasoline do you use for your trip?
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4) You are recarpeting your living room. Your living room is 24 feet long by 20 feet wide. How
many square inches do you need to carpet your living room? square centimeters?
5) If the temperature outside is 86 degrees Fahrenheit, find the temperature in Celsius and Kelvin.
Use the conversions:
◦
F = 1.8C + 32 and ◦ C = K − 273.15
(1)
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6) Jay’s salary grew from $20,000 in 2000 to $28,000 in 2003. Erica’s salary grew from $25,000 to
$35,000 in the same period. Whose salary grew more in absolute terms? in relative terms? Explain.
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7) The final cost of your new shoes is $107.69. The local sales tax rate is 6.2%. What is the labeled
(pre-tax) cost?
8) Find the absolute and relative errors in the following scenario: The label on a bag of dog food
says ’30 pounds’, but the true weight is only 29 pounds.
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EXTRA CREDIT
The planet Neptune has a diameter of 48,400 km and an average distance to the sun of 4497 million
km. Using a scale ratio of 1 to 10 billion, calculate the scaled size and scaled distance from the sun
for Neptune.
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