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1 Page 1 of 15 Name: Date: Winter Break 2018 Review Instructions: Please remember to use all appropriate resources (including class notes, online Digits lessons, handouts, etc.). Please do not guess. At some point, you will be required to explain your work and answers. 1. A small college opened in In the linear model below, x represents the number of years after 1999, and y represents the student population. Interpret the slope. An additional year of the college being open is associated with an additional 749 students. An additional year of the college being open is associated with an additional 576 students. An additional year of the college being open is associated with an additional 173 students. An additional year of the college being open is associated with an additional 403 students. 2. Heidi drove to visit her friend one summer. The miles she traveled are shown on the graph below. What is the unit rate of miles driven per hour? 25 miles per hour 50 miles per hour 100 miles per hour 75 miles per hour 3. Which of the following best describes the solution to the equation below? no real solutions
2 Page 2 of 15 infinite real solutions exactly one real solution, exactly one real solution, 4. Which of the following best describes the solution to the equation below? exactly one real solution, exactly one real solution, infinite real solutions no real solutions 5. The table below shows the cost for a factory to produce mid-sized cars. Number of Cars Produced Cost 0 $ $15, $25, $30, $40, Based on the information in the table, how much does it cost the factory to produce each car? $10, $15, $2, $5, Tabitha is renting a ballroom for an upcoming dinner reception. The rental fee for the ballroom includes a base price plus the cost of dinner per person. The table below shows the cost of the ballroom rental in relation to the number of people attending the dinner reception. No. of Attendees Total Rental Cost $355 $460 $565 What is the base price for the ballroom rental? $7 $105
3 Page 3 of 15 $50 $ The number shown above belongs to which of the following subsets of the real numbers? I. Whole Numbers II. Irrational Numbers III. Rational Numbers IV. Integers V. Natural Numbers I, IV, and V I, III, IV, and V IV only I and V 8. Nathan is a recreational cyclist. He can travel 10 miles in one hour on his bicycle. Which graph represents the number of miles Nathan can travel in x hours? W. X.
4 Page 4 of 15 X Y Z W Y. Z. 9. A company policy requires that, for every 50 employees, there must be 3 supervisors. If there are 258 supervisors at the company, how many employees does the company have? 2,150 3,870 4,300 5, Which of the following relations is a function? (1, 0), (-3, 3), (8, 1), (-3, 5) (1, 4), (-3, 2), (8, 1), (-7, 2) (8, 1), (-3, 4), (1, 1), (8, 2) (1, 4), (-3, 6), (1, 3), (-7, 2) 11. Which of the following represents a function? x y x y
5 Page 5 of 15 x y x y At what position on the number line is the red dot located? 13. John is creating a Thanksgiving display at the store where he works, using only canned pumpkin and canned green beans. He needs to maintain a ratio of pumpkin to green beans of 5 to 1. If he wants to use a total of 108 cans, how many cans of green beans should he use? 18 cans 19 cans 17 cans 5 cans 14. Which of the following best describes the solution to the equation below?
6 Page 6 of 15 no real solutions exactly one real solution, exactly one real solution, infinite real solutions 15. Which situation is best represented by the function in the graph? the number of vacation days used by an employee in a year a car s speed traveling at a constant rate the length of a candle not used over a period of time the speed of a ship in a stormy sea
7 Page 7 of Which of the following graphs is decreasing for all values of x? W. X. Y. Z. X W Z Y 17. Compare the rates of change of the following items.
8 Page 8 of 15 The rate of change of item I is greater than the rate of change of item II. The rate of change of item I is equal to the rate of change of item II. The rate of change of item II is greater than the rate of change of item I. 18. Use the number line above to correctly compare the following numbers. 19. Which of the following best describes the equation below? linear both linear and nonlinear neither linear nor nonlinear nonlinear 20. Which value of x makes the following equation true? (x + 7) = x Compare the rates of change of the following items.
9 Page 9 of 15 The rate of change of item I is greater than the rate of change of item II. The rate of change of item II is greater than the rate of change of item I. The rate of change of item I is equal to the rate of change of item II. 22. Which of the following best describes the equation below? both linear and nonlinear neither linear nor nonlinear nonlinear linear y = -8x Which of the following is an irrational number? 24. Shawn is typing a paper for class. He can type pages in of an hour. How many pages can Shawn type in one hour?
10 Page 10 of Which of the following best describes the ordered pairs listed below? both a relation and a function function only relation only neither a relation nor a function (-3, -4), (1, -8), (-3, -14), (6, -13) 26. Which value of x makes the following equation true? (x - 4) - 12 = 2(x - 6) Lydia is an architect. She has to design a courtyard garden inside a new hotel. On her blueprint, which is the size of the actual garden, the width of the garden is 29 inches. What is the width of the actual garden? 493 inches 850 inches 391 inches 754 inches 28. Yesterday, a local radio station played 94 songs prior to 10 a.m. The station also played 9 songs per hour for the remainder of the day.
11 Page 11 of 15 If a person listened to the radio station yesterday afternoon for x hours, which of the following equations can be used to find the number of songs the person listened to? y = 94x + 9 y = 9x y = 9x + 94 y = x Which of the following tables represents a proportional relationship? x y x y x y x y A school is having a canned food drive. Each class is challenged to collect 150 cans. If there are c classes in the school, which equation could be used to find the total number of cans, T, the school will collect if each class meets the challenge? 31. Which of these is a number that can be expressed as a nonrepeating, nonterminating decimal? a rational number a fraction a negative integer an irrational number
12 Page 12 of The graph below shows the average miles per gallon Marie's new car gets driving on the highway. What is the unit rate of the graph? 1.5 miles per gallon 20 miles per gallon 15 miles per gallon 30 miles per gallon 33. Which of the following best describes the solution to the equation below? no real solutions exactly one real solution, exactly one real solution, infinite real solutions 34. Two freight trains are delivering cargo. One freight train is delivering coal, and the other freight train is delivering grain. Their respective distances traveled after x hours is represented in the table and graph below. Time (Hours) Coal Freight Train Distance Traveled (Miles)
13 Page 13 of Which freight train is traveling at a faster speed? The grain freight train is traveling at a faster speed. There is not enough information to determine the speed of the trains. Both freight trains are traveling at the same speed. The coal freight train is traveling at a faster speed. 35. Which of the following best describes the equation below? nonlinear neither linear nor nonlinear linear both linear and nonlinear y = 3x Which value of x makes the following equation true? (x - 4) = -2x Compare the rates of change of the following items.
14 Page 14 of 15 Item II decreases faster. Item I decreases faster. The items decrease at the same rate. 38. Identify the missing symbol. > = < 39. Amy runs a bakery. She makes a different amount of cake mix each day. She varies the amount of sugar, s, based on the amount of flour, f. The table below lists the amounts of these ingredients. Amount of Flour, f (in pounds) Amount of Sugar, s (in pounds) Which equation represents the proportional relationship between the amount of flour and the amount of sugar? Answers 1. C 2. B 3. B 4. B 5. D 6. D 7. B
15 Page 15 of C 9. C 10. B 11. B 12. A A 15. A 16. B 17. B 18. B 19. D 20. A 21. B 22. C 23. D 24. B D 27. C 28. C 29. A 30. B 31. D 32. C 33. D 34. B 35. C 36. D 37. A 38. D 39. A 40. A 41. D
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