1. Of all the topics we have covered in unit 2, what has stood out to you as something most relevant to your life? Explain why.

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1 v1 Math 54 Practice Exam 2 Name THIS IS NOT THE REAL TEST. THE PURPOSE OF THIS PRACTICE EXAM IS TO REFRESH YOUR MEMORY ABOUT THE CONCEPTS DISCUSSED IN UNIT 2, AND GIVE YOU AN IDEA OF THE LENGTH AND LEVEL OF DIFFICULTY OF THE QUESTIONS THAT WILL BE ON THE TEST. 1. Of all the topics we have covered in unit 2, what has stood out to you as something most relevant to your life? Explain why. 2. In model trains, O scale means the models are made using a 1:48 scale. In the U.S., real train tracks have rails that are 4 ft 8 in apart. a. If miniature train track was made using O scale, how far apart should the rails be? Round to the nearest hundredth of an inch. b. The word gauge refers to how far apart the model rails are. For some reason, O gauge track does not exactly use O scale, and O gauge rails are 1.25 inches apart. Find the relative difference of the rail spacing on O gauge track compared to what it should be (refer to part a) if it followed O scale. Round to the nearest tenth of a percent. 1

2 3. To be completely accurate, a model railroad needs to scale down speed in addition to size. Rail speed limits depend on track quality, but the highest speed limit in the U.S. is 200 mph. What should the highest speed be for a 1:48 O scale train in feet per second? Round to the nearest tenth. 4. Whatever happened to 1 pound bags of coffee? My favorite brands of coffee are Eight O Clock and Dunkin Donuts, but it is hard to compare because they come in different size bags. Compare the following: Eight O Clock Coffee comes in an 11 oz bag for $5.99 Dunkin Donuts Coffee comes in a 12 oz. bag for $6.69 Find the unit price for each bag of coffee to determine the best deal. 5. The median price of a house in San Diego in the year 2000 was $199,000. In 2014, the median home price in San Diego was $430,000. Compute the relative difference in the median home price in San Diego between the years 2000 and Round to the nearest tenth of one percent. 2

3 6. A polygraph test is sometimes used to detect if someone is lying, but it is generally not admissible in court because of its dubious accuracy. A polygraph test is given to 98 people, and the test is wrong for 24 of them. What is the empirical probability that the polygraph test is wrong for a randomly chosen person? What is the probability that it is right? Express each answer as a simplified fraction. 7. What is the difference between theoretical and empirical probability? For questions 7 and 8, determine whether the type of reasoning used is inductive or deductive. Explain how you decided. 8. Leanne was concerned that if she continued to be late for work, she would lose her job. 9. Paul knew that Leanne had been late the past 8 workdays, so he didn t save a seat for her at the morning meeting. 10. Explain what a counterexample is. 3

4 11. A greeting card company can sell cards for $2.75 each, so the revenue can be calculated using the formula R = 2.75x. The company s total cost consists of a fixed overhead of $12,000 plus 35 cents per card, so the total cost can be calculated using the formula C = 0.35x a. Write the algebraic equation needed to determine when the company will break even (when the revenue will equal the cost). b. Solve the equation from part a. c. Write the algebraic inequality needed to indicate that the revenue is greater than the cost. d. Solve the inequality from part c. e. What does your answer from part d tell you about when the company will make a profit? 4

5 12. The following table shows the total paid on a car loan, given the number of months since the loan was taken out. Only the first five months are shown. Months Total Paid 0 $1, $1, $2, $2, $2, $2, a. How much was paid after 0 months? What does this represent? b. What are the independent and dependent variables? c. Write a formula for the total amount paid after m months. 13. Is the area of a two-inch square 2 in 2? Explain. 5

6 Problem Solving Show all your work, and give your answer in a complete sentence. 14. Erin is buying floor tile to put in a room that is 10 ft by 15 ft. She has chosen tiles that are 18 in by 18 in. Assuming that she needs to buy 10% extra to be safe, how many tiles will she need to buy? 15. A riding lawn mower can mow a strip of grass at the rate of 4 miles per hour. How many feet can it mow per second? (Round to nearest foot/sec) How many minutes would it take to mow a strip 1500 yards long? 16. In a deck of cards, 13 are diamonds, 13 are spades, 13 are clubs, and 13 are hearts. A single card is drawn from the deck. Find the probability of getting a heart. 17. Convert the unit of mass. 721 g = kg 18. Write the ratio in lowest terms. 21 years to 9 years 6

7 19. Find the unit cost of each package of napkins to determine the best buy. (Round to four decimal places.) a. $2.35 for 400 napkins b. $0.80 for 100 napkins c. Which is the better buy. Explain why. 20. Write the rate as a unit rate rounded to the nearest hundredth. April pays $2.40 for 5 pounds of bananas. 21. The class size at a certain school increased from 33 to 73. What was the percent increase? Round to the nearest whole percent. 22. Bill's daughter is 26 years younger than he is. Write an expression for his daughter's age if Bill is B years old. 7

8 23. Solve the equation. 12 = 3y Solve the inequality. 11 7(n + 4) 2n 25. Solve the proportion. 3 5 = 4xx 11 8

9 English Measures and Equivalents Length Weight 12 inches (in) = 1 foot (ft) 3 feet = 1 yard (yd) 5280 feet = 1 mile (mi) 16 ounces (oz) = 1 pound (lb) 2000 pounds = 1 ton (T) Liquid Volume Time 3 teaspoons (tsp) = 1 tablespoon (tbs) 8 fluid ounces (oz) = 1 cup 2 cups (c) = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) 60 seconds (sec) = 1 minute (min) 60 minutes = 1 hour (hr) 24 hours = 1 day 7 days = 1 week 52 weeks = 1 year 365 days = 1 year Metric System Kilo Hecto Deka Base Unit Deci Centi Milli km hm dam Length Meter (m) dm cm mm kg hg dag Weight Gram (g) dg cg mg kl hl dal Volume Liter (L) dl cl ml Conversions between Systems Length Weight Volume 2.54 cm = 1 in 1 m = 3.28 ft 1.61 km = 1 mi 28.3 g = 1 oz 2.2 lb = 1 kg 1.06 qt = 1 L 3.79 L = 1 gal 9