1. Some of the steps in Raya s solution to 2.5(6.25x + 0.5) = 11 is shown. Statement Reason 1. 2.5(6.25x + 0.5) = 11 1. Given 2. 2. 3. 3. Subtraction Property of Equality 4. x = 0.624 4.? Select the correct reason for line 4 of Raya s solution. A) Closure Property B) Distributive Property C) Addition Property of Equality D) Division Property of Equality E) Symmetric Property of Equality 2. Alfred s Motors charges $50 plus $2 per hour to rent a scooter and $12 plus $1.50 per hour to rent a helmet. Write an equation to model the total cost, c, of renting the items for h hour. 3. There are three consecutive integers that have a sum of 87. What are those numbers? 4. Find three consecutive even integers such that the twice the largest number is six less than three times the smallest number. 5. Matthew has 20 DVDs. Susie has 12 less than 3 of the number of DVDs that Matthew has. How many DVDs does Susie 4 have? 6. The length of a rectangle is three less than twice the width, and the perimeter is 36 inches. What is the rectangle's area? 7. Macey s reading assignment over the weekend is to read a certain amount of pages. She has read 9 pages so far, which accounts for three-eighths of the assignment. Write an equation to find how many pages she needs to read over the weekend. How many pages is this? 8. John is considering accepting one of two sales positions. ABC Company offers a yearly sale of $45,000. XYZ Company offers a yearly salary of $38,000 plus a 2% annual commission on sales. For what amount of sales s is the salary at XYZ Company greater than the salary at ABC Company? A) s > 7000 B) s > 35,000 C) s > 70,000 D) s > 350,000 9. Jennifer scored a 56, 75, and 91 on her first 3 Algebra tests. Her next test is her final, which counts double. Write and solve an equation that Theresa could use to determine the minimum grade she must score on her final to have a mean score of 80. 10. Janice ran 15 miles in 2 hours. What is the unit rate in miles per minute? 11. Shawn jogs n blocks, each of which are d meters long, in t minutes. What are the units for the expression nd t average speed for his jog? A) Blocks B) Meters C) Minutes D) Meters per minute 12. A certain cooking oil has a density of 0.91 grams per milliliter. Which of the following series of calculations correctly determines the mass, in kilograms, of 15 liters of this oil? A) 15 L B) 15 L C) 15 L D) 15 L 0.91 g 1 kg 1000 ml 1 ml 1000 g 1000 ml 1000 ml 1000 ml 0.91 g 1000 g 1 ml 1 kg 1mL 1000 g 0.91 g 1 kg 0.91 g 1 ml 1 kg 1000 g
13. A zip line starts 35 feet above the gorund and has one landing platform. The line is secured into the ground. Find the height of the platform. 14. Find the value of x. 15. Joshua purchased a Dragonball Z poster that is 120 cm by 100 cm. Daniel loved the design so much that he would like to make a replica of this by drawing it at 1 of the poster s size to keep in his folder. 4 a. What are the dimensions that Daniel should use? b. Find the ratio of the perimeters of the smaller poster to the larger poster. c. Find the ratio of the areas of the smaller poster to the larger poster. 16. The out-of-pocket costs to an employee for health insurance and medical expenses for one year are shown in the table below. Employee s Annual Health Care Costs Type of Cost Definition Cost to Employee Premium Deductible Co-payment Total amount employee pays insurance for the policy Amount of medical expenses employee pays before insurance company pays for anything Percentage of medical expenses after the first $500 that employee has to pay $3,626 According to the plan outlined in the table, total annual health care costs, C, depend on the employee s medical expenses for that year. If x represents the total medical expenses of an employee on this plan and x 500, which of the following equations can be used to determine this employee s total health care costs for that year? A) C = 3,626 500 + 0.20(x 500) B) C = 3,626 500 + 0.20x C) C = 3,626 + 500 + 0.20(x 500) D) C = 3,626 + 500 + 0.20x 17. Use the following table to answer part a and b. x 6 12 15 24 y 2 4 5 8 a. Tell whether the relationship is a direct variation. If so, identify the constant of variation. b. Tell whether the given ordered pairs satisfy a linear function. 18. Use the following table to answer part a and b. x 3 1 3 9 y 5 1 4 13 a. Tell whether the relationship is a direct variation. If so, identify the constant of variation. b. Tell whether the given ordered pairs satisfy a linear function. $500 20%
19. In a technical drawing class, students are analyzing the side view of a house that has been positioned on a coordinate grid, as shown below. Which of the following equations best represents the line that contain PQ? A) y = 5 x + 14.4 2 B) y = 5 x + 27 2 C) y = 2 x + 14.4 5 D) y = 2 x + 27 5 20. Aidan and Brett leave their homes at the same time and walk at a constant speed to a nearby park. Aidan s speed is modeled by the equation y = 0.07x + 1.47, where y represents the remaining distance to the park and x represents the time in minutes since he left home. The table describes Brett s speed. Time Since Leaving Home (in minutes), x 0 9.5 22.5 Distance from the Park (in miles), y 1.35 0.78 0 a. Who is walking faster? b. Who will arrive at the park first? 21. Russ bought 3 medium and 2 large submarine sandwiches for a total of $29.95. Stacy bought 4 medium and 1 large submarine sandwiches for a total of $28.45. Which statement shows the cost of each medium and each large submarine sandwich? A) Each medium sandwich costs $5.69 and each large sandwich costs $6.89. B) Each medium sandwich costs $5.69 and each large sandwich costs $6.39. C) Each medium sandwich costs $5.39 and each large sandwich costs $6.89. D) Each medium sandwich costs $5.39 and each large sandwich costs $6.39. 22. In a basketball game, Marlene made 18 field goals. Each of the field goals were worth either 2 points or 3 points, and Marlene scored a total of 39 points from field goals. a. Let x represent the number of two-point field goals and y represent the number of three-point field-goals. Write a system of equations in terms of x and y to model the situation. b. How many three-point field goals did Marlene make in the game? 23. The product of two numbers is 323 the and difference between them is 2. a. Write a system of equations to model this. b. What are the two numbers? 24. Fabulously Fit offers memberships for $35 per month plus $50 enrollment fee. The Fitness Studio offers memberships for $40 per month plus a $35 enrollment fee. In how many months will the fitness clubs cost the same? What will the cost be? 25. Your math test has 85 questions and is worth 500 points. The test consists of multiple choice questions, each worth 4 points and open-ended questions worth 12 points each. How many of each type are there? 26. Sandra has $2.80 in her coin purse. The money is in quarters and nickels. If there are a total of 20 coins, how many quarters and nickels does Sandra have in her coin purse? 27. Bianca buys 4 band shirts and 3 pairs of pants for $159, and Gianna buys the 3 of the same shirts and 2 pairs of the same pants for $113. How much does it cost to buy 5 band shirts and 5 pairs pants?
28. The solution to the system of equations x + y = 1 and x y = 7 is (x, y) = ( 3,4). This is NOT a solution to which of the following equations? [ ] x + y 2(x + y) = 1 2( 7) [ ] 3(x + y) + x y = 3(1) 7 [ ] x + y + 5(x y) = 5(1) 7 [ ] 4(x + y) + x y = 1 4( 7) [ ] x + y x + y = 1 + 7 29. The graph shows the number of acres, in millions, of farmland in the United States from 1975 to 2008. Which statement describes the average rate of change of the graph? A) The number of acres of farmland in the United States decreases by 0.21 million each year. B) The amount of farmland in the United States decreases by 4.8 million acres each year. C) The time it takes the farmland in the United States to decrease by 160 acres is 33 years. D) Every 5 years, the amount of farmland of farmland in the United States decreases by 20 acres. 30. The height of a fireworks rocket in meters can be approximated by h = 5t 2 + 30t, where h is the height in meters and t is the time in seconds. Find the maximum height and how long it takes the rocket the reach the maximum height. Then find the time it takes the rocket to reach the ground after it has been launched. 31. A tee box is 48 feet above its fairway. When a golf ball is hit from the tee box with an initial velocity of 32 ft/s, the quadratic equation 0 = 16t 2 + 32t + 48 gives the time t in seconds when a gold ball is at height 0 feet on the fairway. Find the maximum height and how long it takes the golf ball to reach the maximum height. Then find the time it takes the golf ball to reach the ground after it has been hit. 32. Morgan drops a rock from a bridge that is 30 meters above the river. The height of the tock in meters, h, after t seconds is modeled by the function shown. h(t) = t 2 2t + 30 Find the approximate number of seconds it will take for the rock to hit the water. Round your answer to the nearest whole number. A) 0 B) 5 C) 10 D) 30 33. Consider the function f(x) = 2x 2 + 4x 30. Classify each statement. a. The vertex of the graph of f(x) is (1, 32). [ ] True [ ] False b. The zeros of f(x) are x = 3 and x = 5. [ ] True [ ] False c. The graph of f(x) opens down. [ ] True [ ] False d. The axis of symmetry is x = 1. [ ] True [ ] False e. The y-interept of f(x) is 30. [ ] True [ ] False 34. A pine cone drops from the top of a slash pine tree. The height of the pine cone after x seconds is given by f(x) = 125 15x 2. Select all the correct interpretations of the coordinates of the point at the maximum of the function f(x). [ ] the time when the pine cone is at the highest point [ ] the height of the pine cone when it drops off the slash pine [ ] the distance of the pine cone from the slash pine when it hits the ground [ ] the time it takes the pine cone to hit the ground [ ] the time when the pine cone drops off the slash pine
35. Cora is using successive approximations to estimate a positive solution to f(x) = g(x), where f(x) = x 2 + 13 and g(x) = 3x + 14. The table shows her results for different input values of x. x f(x) g(x) 0 13 14 1 14 17 2 17 20 3 22 23 4 29 26 3.5 25.25 24.5 Use Cora s process to find the positive solution, to the nearest tenth, of f(x) = g(x). 36. Town A and Town B both had a population of 15,000 people in the year 2000. The population of Town A increased by 2.5% each year. The population of Town B decreased by 3.5% each year. a. Write a function A(t), the population of Town A t years after 2000. b. Write a function B(t), the population of Town B t years after 2000. c. Find the approximate population of Town A in 2005. d. Find the approximate population of Town B in 2005. 37. The table shows the balance b, in dollars, of Daryl s savings account t years after he made an initial deposit. What is an explicit formula for the geometric sequence that represents this situation? Time, t Balance, b (years) (dollars) 1 $1218 2 $1236.27 3 $1254.81 4 $1273.64 A) b(t) = 1.015(1218) t 1 B) b(t) = 1218(1.015) t C) b(t) = 1218 + 1.015(t 1) D) b(t) = 1218(1.015) t 1 38. The value V A of stock A t months after it is purchased is modeled by the function V A (t) = t 2 + 1.50. The value V B of stock B t months after it is purchased by the function V B (t) = 10(1.25) t. Based on the model, for which t-values is the value of stock B greater than the value of stock A? [ ] t = 5 [ ] t = 6 [ ] t = 7 [ ] t = 11 [ ] t = 12 39. For some exponential function f(x), f(0) = 12, f(1) = 18, and f(2) = 27. How does f(x) change when x increases by 1? A) f(x) grows by a factor of 2 3 B) f(x) grows by a factor of 3 2 C) f(x) increases by 6 D) f(x) increases by 9 40. The value of a stock over time is shown in the table. Write an exponential function that models the value V, in dollars, after t years. Time, t Value, V (years) (dollars) 0 18.00 1 16.20 2 14.58 3 13.12 4 11.81 5 10.63 41. The table shows the value, in dollars, of three cars after they are purchased. Which car s value decreases by a constant percent? Year Car A Car B Car C 0 $21,000 $18,000 $25,000 1 $18,000 $15,625 $22,500 2 $15,000 $13,250 $20,250 A) Car A B) Car B C) Car C D) Cars B and C
42. The table shows the population of two cities. Which city s population is changing at a constant rate per year? Year City A City B 2009 700,000 570,000 2010 697,500 580,000 2011 694,500 590,000 2012 690,500 600,000 A) A B) B C) Both A and B D) Neither A nor B 43. For which of these functions does the function value change at a constant rate per unit change in x? x f(x) g(x) h(x) 1 6 1 31 2 12 2 25 3 20 4 19 4 30 8 13 5 42 16 7 A) f(x) B) g(x) C) h(x) D) g(x) and h(x) 44. For which of these functions does the function value change at a constant factor per unit change in x? x f(x) g(x) h(x) 1 512 18 65 2 128 16 33 3 32 14 17 4 8 12 9 5 2 10 5 A) f(x) B) g(x) C) h(x) D) f(x) and g(x) 45. The population A of town A and the population B of town B t years after 2000 is described in the table. Time, t (years) Town A population A(t) Town B Population B(t) 0 1500 1500 1 1800 1725 2 2100 1984 3 2400 2281 4 2700 2624 5 3000 3017 6 3300 3470 7 8 a. Write a function for A(t). b. Write a function for B(t). c. Use the functions to complete the table, rounding to the nearest person. 46. The table below shows the values for the function y = f(x). x y 4 7 1 2 0 3 3 4 6 5 Complete the table for the function y = f( 1 5 x). x y
47. Given that y = 1 x + 15 is the line of the best fit obtained from a scatter plot, what is the residual of (5,21)? 2 48. A random sample of 300 students were surveyed of which core teacher they favored. If there are 40% more girls than boys who were surveyed, complete the two-way table to show the possible breakdown. Math English Science Total Boys 45 Girls 77 65 Total 190 300 49. The incomplete table summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. If there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.) Left Right Boys Girls Total 18 22 A) 0.410 B) 0.357 C) 0.333 D) 0.250 50. A random sample of 200 teenagers participated in a taste test. Each teenager sampled four choice of fruit drink (labeled A, B, C, and D ), and then were asked to pick a favorite. The table shows the results of this taste test. A B C D Total Boys 45 25 30 20 120 Girls 25 10 30 15 80 Total 70 35 60 35 200 Based on the information given, which of the statements are true? [ ] 40% of the participants were girls. [ ] 70% of the participants preferred A. [ ] 20 of the boys preferred D. 120 [ ] 10 of the participants who preferred B were girls. 35 [ ] The proportion of boys who preferred C is equal to the proportion of girls who preferred C.