2015 Algebra 1 Semester Exam Review. Write an equation to represent the graph below. Which ray on the graph best represents a slope of 55 mph?

Transcription

1 2015 Algebra 1 Semester Exam Review 1. Write an equation to represent the graph below In the distance formula d = rt, r represents the rate of change, or slope. Which ray on the graph best represents a slope of 55 mph? 3. Which coordinate points represent the x- and y-intercepts of the graph shown below?

2 4. The table below shows ordered pairs of a linear function. What are the x- and y-intercepts for the graph of this linear function? 5. Mr. Czar wants to order some candy bars for the math team s annual fund-raiser. The graph below shows the total cost for an order of fewer than 5 boxes of candy bars, including the standard fee for shipping and handling. What is the approximate cost of each box of candy? 6. The cost of renting a car for 1 day at Cars Plus is $20 plus 10 cents per mile driven. The cost of renting a car for 1 day at Need-A-Car is $20 plus 15 cents per mile driven. In a graph of the cost of a car rental, what does the cost per mile driven represent? 7. The total cost, y, of riding rides at the county fair can be determined by using the linear equation, which describes the cost of each ride, x, and the price of admission. Write an equation to represent an increase in the cost of each ride of $0.25 and a decrease in the price of admission by $ Jeri can row a boat at a speed of 8 miles per hour with the current. The number of miles, m, she rows with the current in h hours can be represented by the function m = 8h. What is the dependent quantity in this function? 9. An ice-cream vendor made a table showing the relationship between the daily high temperature and the number of ice-cream cones sold per day. What is the dependent quantity in this relationship?

3 10. The table shows the number of slices of pepperoni placed on each size of pizza at Pepe s Pizza Shop. Size of Pizza Radius of Pizza (inches) Number of Pepperoni Slices Single 2 6 Small 4 18 Medium 6 30 Large 8 42 Extra Large Let r represent the radius of the pizza and let n represent the number of slices of pepperoni. Identify an equation that represents the relationship between the radius and the number of slices of pepperoni. 11. The table below shows the relationship between p, the number of cell phones a company produces, and d, the number of cell phones that are defective. Write an equation that can be used to describe This relationship. 12. Given that y is a function of x, which of the following tables best represents a function? A B C D 13. Describe a situation that can be represented by the function f (x), where f (x) = 12x + 5.

4 14. A math club decided to buy T-shirts for its members. A clothing company quoted the following prices for the T-shirts. Which equation best describes the relationship between the total cost, c, and the number of T-shirts, s? A c = 6.75s B c = 7.00s C c = 2s 20 D c = s 15. What is the equation of the line that passes through the point (9, 2) and has a y-intercept of (0, 5)? 16. Which function includes the data set {(2, 4), (6, 6), (12, 9)}? A y = 2x B y = C y = 2x 9 D y = The owner of a candle store purchases his candles from a local distributor. The graph below shows the relationship between n, the number of candles ordered, and c, the total cost of the candle order. Which conclusion can be drawn about this relationship? A B C D An order of 50 candles will cost less than $20. An order of 100 candles will cost more than $60. An order of 150 candles will cost less than $70. An order of 200 candles will cost more than $90.

5 18. The graph below shows the relationship between the value of a car in dollars and the age of the car in years. According to the graph, which of the following statements appears to be true? A B C D The value of the car decreased by $1,000 per year. The value of the car decreased by $2,000 per year. The value of the car decreased more from Year 9 to Year 10 than in any other year. The value of the car decreased more from Year 0 to Year 1 than in any other year. 19. Mr. Wilson asked his class to sketch a graph that would represent the following activity: Start 3 meters away from me and slowly walk away for 8 seconds. Then stand still for 3 seconds and walk quickly toward me for 4 seconds. Sketch a graph that best represents this activity. 20. Which statement is true for the graph below? A Ms. Goodlett will earn $500 if she sells $5000 worth of merchandise. B Mr. Murphy will not earn any money if he does not sell any merchandise. C Mr. Lefeber will earn $1000 if he sells $1000 worth of merchandise. D Ms. Cho will earn $700 if she sells $5000 worth of merchandise.

6 21. The graph below represents Cheyenne s bicycle trip from her house to a friend s house. On which segment of the graph does it appear that Cheyenne was riding her bicycle at the slowest pace? 22. Which situation could this graph best represent? A A boy ran for 10 minutes, rested on a bench for 15 minutes, and then ran for 10 more minutes. B A boy ran for 10 minutes, walked for 15 minutes, and then ran for 10 C more minutes. A boy ran for 10 minutes, rested on a bench for 15 minutes, and then walked for 10 more minutes. D A boy walked for 10 minutes, ran for 15 minutes, and then walked for 10 more minutes. 23. Monica collected data on the ages and heights of a random sample of sixth-, seventh-, and eighth-grade students at her school. If she plots the data on a scatterplot, what relationship will she most likely see between age and height? 24. The graph below shows the relationship between the distance in miles a delivery truck traveled and the number of hours each delivery took. Which best describes the relationship shown on the graph?

7 25. Auto-Check Motors charged Mr. Jones $84.00 for an automotive part plus $68.00 per hour that a mechanic worked to install the part. The total charge was $ For about how long did the mechanic work to install the part on Mr. Jones s car? 26. An artist studies human proportions in order to make realistic drawings. He observes that a person s kneeling height, y, is of the person s standing height, x. Write an equation that best represents this relationship. 27. A small business purchased a van to handle its delivery orders. The graph below shows the value of this van over a period of time. Which of the following best describes this situation? A The van was purchased for $1,600. B The van decreases in value by $1,600 per year. C The van increases in value by $1,600 per year. D The van has no value after 5 years. 28. A chemist started an experiment with 5 grams of a chemical. The chemical was used at a rate of 0.01 gram per minute. Write an equation to describe the relationship between c, the amount of chemical remaining in grams, and t, the time in minutes.

8 29. Rita put some hummingbird feeders in her backyard. The table shows the number of hummingbirds that Rita saw compared to the number of feeders. A h = 2f + 1 B f = 2h + 1 C h = f + 2 D f = h Mr. Ross is purchasing a table and chairs for $1350, including tax and interest. He will pay for the furniture with monthly payments of $75. If Mr. Ross has made m payments, write an equation that best describes r, the amount of the remaining balance. 31. The number of hours Abe practices golf each week, g, is 2 more than the number of hours he runs, r. Write an equation to represent the number of hours he runs each week. 32. Tyler wants to buy a video-game system for $375. He can pay for the system in 12 months if he pays $75 now and $25 each month. How will the number of monthly payments be affected if Tyler pays $75 now and $30 each month? 33. The graph of a linear function is shown below. If the line is translated 2 units down, write an equation to describe the new line.

9 34. Troy borrowed money from his father so that he could buy a used car. The table shows the remaining balance, b, of Troy s loan after each payment. Write a function to describe this relationship. 35. The steps to a solution process are shown below. Step 1: 2(3x 1) = 3x + 1 Step 2: 6x 2 = 3x + 1 Step 3: Step 4: x = 1 Write an equation to represent the missing step of the solution process Joan went to a department store to buy a sweater that was on sale for 25% off the original price, p. Write an equation to determine s, the sale price of the sweater, not including tax. Simplify the expression 6 3(5x + 2) 10x The cost of renting a DVD at a certain store is described by the function f(x) = 4x + 3 in which f(x) is the cost and x is the time in days. If Lupe has $12 to spend, what is the maximum number of days that she can rent a single DVD if tax is not considered? A recycling center pays $0.35 per pound of glass that it receives. If students at Falcon High School want to raise $500 in a glass-recycling project, what is a reasonable number of pounds of glass they must collect?

10 40. In 2004 a married couple could have calculated their estimated income tax, t, for that year using the equation t = 0.25c 6525, in which c represents their combined taxable income. If a married couple had a combined taxable income between $60,000 and $64,000, what is a reasonable amount for their income tax? A $6,525 B $8,975 C $13,869 D $15, The tables below show the amount of data in kilobytes that was downloaded by a computer over time. Which of the following tables best represents a linear function? A. B. C. D. 42. Which of the following situations might be represented by this graph? A The amount of weight (in pounds) gained during the first four years of a person s life B The temperature (in degrees Celsius) of an ice cube melting on a counter C The distance traveled (in miles) of a car traveling at a constant rate D The area of a square as the length of the side increases 43. Which graph best represents the relationship between the height of a burning candle and the amount of time that passes as the candle burns? A B C D

11 44. At Vicky s Grocery Store the cost of a bag of ice varies directly with the weight of the ice. If a 7-pound bag of ice costs $0.86, what is the cost of a 20-pound bag of ice? 45. The amount of chlorine, y, needed for a swimming pool varies directly with the amount of water, x, needed to fill the pool. If 16 units of chlorine are needed for every 1250 gallons of water, which of the following represents the equation of direct variation? A y = x C y = x B y = x D y = x 46. On a certain day the exchange rate of Mexican pesos for U.S. dollars was approximately 10 pesos for 1 dollar. If an exchange of 4,000 pesos was made that day, what was the approximate value of the exchange in dollars? 47. A florist plans to sell bouquets for $25 each. He wants to use only roses and carnations in each bouquet and needs to charge the following amount for each type of flower. $1.50 per rose $1.25 per carnation Which of these combinations of roses and carnations will result in bouquets that the florist can sell for exactly $25 each? I. 18 roses and 2 carnations II. 6 roses and 10 carnations III. 10 roses and 8 carnations IV. 5 roses and 14 carnations 48. Sawyer dropped one marble at a time into a cylinder containing water. The data set he collected is shown in the scatterplot below. Assuming the cylinder will not overflow, what will be the height of the water after a total of 10 marbles is added?

12 Determine whether the sequence is arithmetic. Identify the common difference and write the explicit and recursive from , 480, 420, 360, Arithmetic? Yes or No Common Difference Explicit Recursive 50. 4, 8, 12, 16, Arithmetic? Yes or No Common Difference Explicit Recursive 51. Rhonda has 25 coins in her pocket. All of the coins are either dimes or nickels. If Rhonda has a total of $2.30, how many dimes does she have? 52. Sam is ordering pizza. Tony s Pizza charges $7 for a large cheese pizza plus $.75 for each additional topping. Maria s Pizza charges $8 for a large pizza plus $.50 for each additional topping. For what number of toppings will the cost of a large pizza be the same at either restaurant? 53. The sum of two numbers is 67. The smaller number is 3 less than the larger number. What are the two numbers? 54. A chemist is mixing one solution that is 32% sodium and another solution that is 12% sodium. How many liters of each type should the chemist use to produce 50 liters of the solution that is 20% sodium? 55. Solve the following for b. 56. Solve the following for h.