Problem Review
Quizzes 1 - 3:
1. Consider an argument in which Premise 1 is ”All fruit is fat-free” and Premise 2
is ”Avocados are fat-free.” If X represents avocados, which Venn diagram correctly
represents the two premises?
2. You are given two pieces of information: (1) the price of gasoline in dollars per gallon
is $3.80 per gallon and (2) the gas mileage of a car is 18 miles per gallon. What is
the cost of driving this car in dollars per mile?
3. Use the Venn diagram to answer the following questions.
a. How many woman at the party are aged under 30 ?
b. How many people are at the party?
4. Is the following deductive argument valid or not, and is it sound or not?
Premise: All U.S. presidents are men.
Premise: George Washington was a man.
Conclusion: George Washington was a U.S. president.
5. A 45-minute bike ride at a moderate pace consumes about 600 Calories. What is
your average power output, in watts, during a 20-minute bike ride?
(1 Calorie = 4184 Joules, 1 watt = 1
Joule
)
sec
6. You currently earn $1000 per month, but you expect your earnings to rise 10% per
year. How much will you earn in five years?
Exam 1:
7. Suppose the price value of a home changed from $250,000 to $200,000 over three
years. By what precent did the value of the home change per year?
8. Carry out the following unit conversions.
a. Convert 19 gallons to quarts. (1 gallon = 4 quarts)
b. Convert 160 kilometers to miles. (1 mile = 1.6093 kilometers)
c. Convert 27000 cubic centimeters to cubic meters. (1 meter = 100 centimeters)
d. Convert $3.60 per gallon to Canadian dollars per liter. ($ 0.91 = Canadian dollar,
1 gallon = 3.785 L)
9. Which is worth more: 200 Japanese yen or 30 Mexican pesos? (1 US Dollar = 102.3
Japanese yen and 1 US Dollar = 13.33 Mexican pesos) Covert both to US Dollars.
10. Find the absolute change and the relative change of the population. The population
of the United States increased from 249 million in 1990 to 308 million in 2010.
11. You purchase a bicycle with a retail (pre-tax) price of $678. The local sales tax rate
is 5.4%. What is the final price?
Quizzes 4 - 7:
12. Bob goes to a club or concert every two weeks and spends an average of $60 each
time. What is his annual spending?
13. If you deposit $5,000 now at an APR of 2.8% compounded monthly, how much will
you have in 20 years? Round to the nearest whole dollar.
14. Find the savings plan balance after 10 years with an APR of 6.9% and monthly
payments of $350. Assume monthly compounding, and round to the nearest whole
dollar.
15. (From Notes in Section 4D) Suppose the a loan of $7000 at an APR = 6% is taken
and you want to pay it off in 3 years. The exact payments can be calculated with
P × APR
n
i
PMT = h
APR (−nY )
1− 1+ n
What is the monthly payment? How much in total deposits are made?
16. Suppose a credit card has a balance of $2300, with an annual interest rate of 21%.
You decide to pay off the balance after 1 year, assuming you make no other credit
card purchases. How much should you pay each month?
17. A new company’s revenues are growing 21% per year. What is the exact doubling
time for the revenue?
18. The half-life of a drug in the bloodstream is 7 hours. What fraction of the original
drug dose remains in 24 hours? The original dosage is 60 milligrams. How much (in
milligrams) of the dose remains in 24 hours?
19. Find the slope and express it as a rate of change (be sure to include units.) Express
the function in an equation. What was the population for t = 5?
Population (thousands)
80
60
40
20
2
4
6
8
Time (years)
Exam 2:
20. A demand function for pineapples starts at 80 pineapples sold for $2 and ends at 50
pineapples sold for $5. What is the rate of change?
21. (3 pts) A city’s population starts at 100,000 people and grows 3% per year for 7
years. In the general exponential equation, Q = Q0 × (1 + r)t , what is the growth
rate r?
22. Write a function in the form y = mx + b. Identify the independent variable and dependent variable. Then answer the following questions. You drive along the highway
at a constant speed of 85 miles per hour. How far do you travel in 1.5 hours? in 2.2
hours?
Sections 9C and 10A:
23. A privately owned forest that had 1 million acres of old growth is being clear cut at
a rate of 7% per year. Create an exponential function of the form Q = Q0 × (1 + r)t
or Q = Q0 × (1/2)(t/Thalf ) . Then answer when the forest will have 897,000 acres of
old growth.
24. The half-life of Carbon-14 is 5700 years. A preserved piece of wood is found at an
archeological dig site and has 12.3% of its original carbon. How old is the piece of
wood?
25. What is the grade of a road on a hill that rises 2 feet for every run of 20 feet?
26. A can of soup with a diameter of 3 inches and a height of 4 inches is rescaled by a
factor of 3. What is the surface area and volume of the new can?