UNIT 2 End-of-Unit Test REVIEW

Transcription

1 Name: Date: Page 1 of 7 UNIT 2 End-of-Unit Test REVIEW 1. The Bridgeport Bluefish management discovered that the profit they make on their concession stands may be found by using the formula P = 5A 500, where P represents the profit (in dollars) and A represents the attendance at the game. a. Use the formula to find the profit if the attendance is 1,100 fans. Show your work. b. Use the formula to find the attendance if the profit is $2200. c. Find a value for the attendance (A) for which the profit (P) is zero. Explain what this means in the real world situation.

2 Name: Date: Page 2 of 7 2. University of Connecticut (UCONN) defeated Louisville University in the finals of the NCAA Women s Basketball Tournament in 2009 by a score of 82 to 61. There are three ways to score points in college basketball: You can score a free throw, which is worth 1 point. Let a represent the number of free throws made. You can score a 2-point basket. Let b represent the number of 2-pointers scored. You can score a 3-point basket. Let c represent the number of 3-pointers scored. a. Write a formula for determining the final score, S, if you know a, b, and c. b. UCONN won the championship game by scoring a total of 82 points. UCONN scored 30 baskets worth 2 points during the game and 5 baskets worth 3 points. Find the number of free throws UCONN scored. Show all work and put your final answer in a sentence. c. Louisville scored a total of 61 points. They made 9 free throws and 20 baskets worth 2- points during the game. In the equation, 61 = 3c , c represents the number of 3- point baskets Louisville scored. Solve this equation for c.

3 Name: Date: Page 3 of 7 3. Chad was driving through Vermont when he was pulled over going faster than the 55 mph speed limit. The police officer told him that he would have to pay for all of the paperwork fees as well as for every mph over the speed limit. Chad could calculate his fine by using the formula F = (x 55), where F represents the total cost of the fine (in dollars), and x represents the speed Chad was driving. a. How much would Chad s fine be if he was caught driving 74 mph? Show your work and put your answer in a sentence. b. How fast was Chad driving if his speeding ticket was $655? Show your work and put your answer in a sentence. c. What is the real world meaning of 30 in the formula above? d. What is the real world meaning of 25 in the formula above? e. Would it be sensible to use the formula to compute a fine if the driver is going 45 mph on the highway? Why or why not? f. Would it be sensible to use the formula to compute a fine if the driver is going 57 mph on the highway? Why or why not?

4 Name: Date: Page 4 of 7 Pedro and Janelle are given the task by their families of getting the rubbish ready for pickup each week during the summer vacation. Pedro is paid $8 per week while Janelle is paid $21 at the beginning of the summer and $5 each week. Let w represent the number of weeks they get the rubbish ready for pick-up. g. Write an expression for the amount of money Pedro will earn by working w weeks. h. Write an expression for the amount of money Janelle will earn by working w weeks. i. Write an equation to find the value of w when they earn the same amount. j. Solve the equation you wrote in part (c). k. If you worked every week for the 14 weeks of summer vacation, which method of payment would you prefer? Explain your choice.

5 Name: Date: Page 5 of 7 5. Solve the following equations. Show all your work. a. 10x 9.4 = 2x b. x x = 90 3x c. 3(x 5) + 4x = 9x + 18 d. 5x 4(x 3) = x e.!! x + 8 = 26 f. Explain the justification for each step in your solution to equation (d).

6 Name: Date: Page 6 of 7 6. Kathy was asked to simplify the expression 6x + (7 + 2x). She decided to change the order of 7 + 2x. She wrote it as 2x + 7 instead. Her new expression was 6x + (2x + 7). What property allowed Kathy to change the order of the terms? 7. Kathy then changed 6x + (2x + 7) to (6x + 2x) + 7. She liked this because her like terms were grouped together. What property allowed her to group the 6x and 2x terms together? 8. The formula A = P + Prt is used to find the amount of money (A) owed on a simple interest loan, where P is the principal (the amount borrowed), r is the rate of interest, and t is the time (in years). a. Use the formula to find A when P = $2000, r = 0.03, and t = 6 years. b. Use the formula to find t when P = $7000, r = 0.06 and A = $9940. c. Solve the formula A = P + Prt for t. 9. Solve the equation for y: 3x + 6y = 12.

7 Name: Date: Page 7 of Translate each real world situation into an inequality using the appropriate inequality symbol <, >,, or. a. In order to be president your age (a) must be at least 35 years. b. At Killingly High School a student must have less than 8 absences (a) in order to pass a course. c. The amount of money (m) that Sondra can spend on the prom is no more than $ Solve for x and graph the solution on the number line. 4x + 8 8x Oscar and his band want to record and sell CDs. There will be a set-up fee of $500, and each CD will cost $4.25 to burn. The recording studio requires bands to make a minimum purchase of $1265. What is the minimum number of CD s the band can burn to meet the minimum purchase of $1265. Define your variables, and write and solve an inequality to solve this problem.