Fall 2011-2012 IM I Exam B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following equations is linear? a. y = 2x - 3 c. 2. What is the y-intercept of? a. 0 c. 2 b. 3 d. 1 3. Simplify (x - 6)(x + 6) a. x² - 36 c. x² - 12x - 36 b. x² - 12x + 36 d. x² + 36 4. Simplify: 5. Find the values of x, y, and z. The diagram is not to scale. 37 18 60 x z y 6. 7. Given the equation 0 = -2x² + 6, find the solution(s). a. - 1.73, 1.73 c. 0, -3 b. no solution d. -3
8. In 2000 Bob planted a tree that was feet tall. In 2005 the tree was feet tall. Assuming the growth of the tree is linear, how many feet can we expect the tree to grow in 2006? 9. Which equation describes the data below? x y -2 6 0-2 3 16 4 30 10. A superball is dropped from a height of 15 feet and bounces to 70% of its previous height after each bounce. The equation, where h is the height off the floor at a given point in time and n is the number of bounces, can be used to approximate the maximum height of the ball at any given bounce. How many bounces will it take for the ball to be less than one foot off the floor? a. 9 c. 10 b. 7 d. 8 11. In business the breakeven point is where Income (I) equals Expenses (E). Ralph makes and sells CD s. He use the equation E = $946 + 1.5d to determine his cost each month. He sells his CD s for $7.00 each. How many CD s must he sell each month to breakeven? a. 631 c. 172 b. 171 d. 135 12.. Find the value of x for p to be parallel to q. The diagram is not to scale. 3 4 5 6 1 2 p q a. 119 b. 18 c. 126 d. 133
13. The equation y = -4x - 2, defines a function of x. If x = 1, what is y? a. 6 c. 2 b. -2 d. -6 14. Simplify: 15. A taxi ride cost $24.20. The taxi driver gets $5.20 plus $1.00 per mile. How far did the taxi travel on this trip? a. 19 miles c. 24 miles b. 24.2 miles d. 5.2 miles 16. The value of a particular car is related to the previous year s value by the function. Which statement best describes the change in the car s value from one year to the next? a. The value is decreasing by 92%. c. The value is increasing by 8%. b. The value is decreasing by 8%. d. The value is increasing by 92%. 17. Given a quadratic in the form y = ax² + c, what is the minimum point? a. 0 c. ( 0, c ) b. c d. ( 0, 0 ) 18. Given the following equation, which could be the value of x? a. -2 c. 1 b. -3 d. -4 19. Given -2x² + 4 = 36, find the solution(s). a. no solution c. 4, -4 b. 4 d. -4.47, 4.47 20. Line r is parallel to line t. Find m 5. The diagram is not to scale.
r 7 142 1 3 t 4 5 2 6 a. 142 b. 38 c. 28 d. 138 21. Simplify (x - 2)² a. x² + 4x + 4 c. x² - 4x + 4 b. x² + 4 d. x² - 4 22. Given the following table, determine what type of equation it represents: x 0 1 2 3 4 y 2 3 5 9 17 a. Other c. Exponential b. Linear d. Quadratic 23. Given 0 = 2x² + 6x, find the solution(s). a. 0, 3 c. 0, 6 b. 0, -3 d. -3 24. Mr. Hanson recorded the typing speeds (in words per minute) of 25 students and their weeks of experience. The line of best fit for the data is y = 4.4x + 18.9, where x is the number of weeks of experience of a student and y is the student s typing speed. What is the meaning of the rate of change for this set of data? a. the typing speed of a student with no c. the average typing speed of the experience students b. the highest typing speed recorded d. the improvement in typing speed per week for the average student 25. Tim kicks a ball off the ground. After t seconds, its height, h (in feet), is given by the formula. What is the maximum height reached by the ball? a. 64 feet c. 48 feet b. 80 feet d. 16 feet 26. An object is blasted upward at an initial velocity, v o, of 256 ft/s. The height, h, of the object is a function of time, t (in seconds), and is given by the formula. How long will it take the object to hit the ground after takeoff?
a. 7.5 seconds c. 15 seconds b. 4 seconds d. 16 seconds 27. The height, h, in feet of an object thrown into the air with an initial upward velocity of 65 feet per second is given by the formula, where t is the time in seconds. What is the height of the object after 3 seconds? a. 45 feet c. 62 feet b. 51 feet d. 66 feet 28. Given the following table, determine what type of equation it represents: x 0 1 2 3 4 y 2-4 -6-4 2 a. Quadratic c. Other b. Linear d. Exponential 29. Find the slope of a line that contains the points ( -2, -4) and (1,3) 2 30. Simplify: 31. Debbie recorded the time it took seven children of different ages to run one lap around the track. Age of Child (years) Time (seconds) 4 225 8 185 10 138 11 130 14 112 14 106 18 52 Using a linear equation of best fit, which is closest to the length of time it should take Debbie s 12-yearold niece to run one lap?
a. 200 sec c. 140 sec b. 127 sec d. 170 sec 32. The dashed line on each graph represents. On which graph is? a. 5 y c. 5 y 4 4 3 3 2 2 1 1 5 4 3 2 1 1 1 2 3 4 5 x 2 3 4 5 5 4 3 2 1 1 1 2 3 4 5 x 2 3 4 5 b. 5 y d. 5 y 4 4 3 3 2 2 1 1 5 4 3 2 1 1 1 2 3 4 5 x 2 3 4 5 5 4 3 2 1 1 1 2 3 4 5 x 2 3 4 5 33. Which is equivalent to the expression? 34. An i-phone cost $360 and depreciates at a rate of $90 per year. Which linear equation represents the value, V, of the phone at the end of t years? a. V = 90t-360 c. V = 4(90) - 360 b. V = 360-90t d. V = 360t + 90 35. Given a quadratic in the form y = ax², what is the vertex?
a. x = 0 c. not enough information is given b. ( 0, 0 ) d. x = 0, a 36. Given the equation, which is true for ( x, -9 )? a. x = 3 c. x = -2 b. x = -3 d. x = 6 37. Enrique wants to buy a car. He currently has saved $360. He needs a total of $3,000 for his car. He earns $125 per week but can only save $90 each week towards his car. Which equation can he use to determine the number of weeks, w, he needs to continue to work before he has the $3,000 he needs to purchase his car? a. 3,000 = 90w + 360 c. 3,000 = 360-125w b. 3,000 = 360-90w d. 3,000 = 125w - 360 38. Which is a factored form of the following expression? 39. Determining where y = 0 for a linear function will specifically tell you: a. the x-intercept c. any point on the graph b. how quickly it rises or falls d. the slope 40. 41. Given ax 2 + bx + c, what does the b do to the graph. a. it determines the y-intercept c. it determines the width b. it causes a horizontal shift d. it causes a vertical shift 42. What is the slope of the graph:
y 5 4 3 2 1 5 4 3 2 1 1 1 2 3 4 5 x 2 3 4 5 a. -2 c. 2 43. Given ax 2 + bx + c, what does the a do to the graph. a. it determines the y-intercept c. it causes a horizontal shift b. it causes a vertical shift d. it determines the width 44. Which of the following equations is a quadratic? 45. Given, find the x-intercept(s). a. -9 c. 3 b. 0, 3 d. -9, 0 46. What is the slope of the line? b. 2 d. 47. b. (-3c) 3 d. 48. Find the distance between points P(8, 6) and Q(1, 5) to the nearest tenth. a. 14.2 b. 8 c. 7.1 d. 50
49. Given the following table, determine what type of equation it represents: x 0 1 2 3 4 y 2-4 -10-16 -22 a. Exponential c. Quadratic b. Other d. Linear 50. Simplify: 51. Which of the following equations is exponential decay? 52. Find the value of the variable if and The diagram is not to scale. 1 2 3 4 l 5 6 7 8 m a. 2 b. 1 c. 1 d. 4 53. 54. Simplify (x + 2)² a. x² + 4 c. x² + 4x + 4
b. x² - 4x - 4 d. x² - 4 55. If find the values of x, EF, and FG. The drawing is not to scale. E F G a. x = 8, EF = 9, FG = 9 c. x = 10, EF = 27, FG = 45 b. x = 8, EF = 13, FG = 15 d. x = 10, EF = 13, FG = 15 56. Find the midpoint of 10 y P 5 10 5 5 10 x 5 10 Q a. ( 1, 1) b. ( 2, 2) c. ( 1, 2) d. ( 2, 1) 57. Line b has a slope of 3 and goes through the point (2, 1). Which is one form of the equation for line b? 58. Simplify: 59. Simplify:
60. The equation C = 320n + 5,400, where C = average cost and n = the number of years since 2000, represents the average cost of a classic 1967 Mustang Boss beginning in the year 2000 thru 2009. What does the 320 represent in the equation? a. The yearly decrease in value c. The yearly increase in value b. The value in 1967 d. The value in 2000 61. Simplify: 62. Which equation fits the following table: x y 3 4 6 6 9 8 12 10 63. Simplify: 64. Which of the following equations is a exponential growth? 65. Simplify: 66.
67. Katrina s dad put some money into a college savings account for her when she was born. Her dad intends to let the interest accumulate in the account until she goes to college. The rule gives the account balance after x years. Katrina decides she would rather have a down payment on a house instead of going to college. She needs about $34,000 down to purchase the house she wants. How old will she be when she has enough money in her college fund? a. 26 years old c. 25 years old b. 27 years old d. 24 years old 68. Given the equation y = x² + 8x, what is the vertex? a. ( 0, 0 ) c. ( 0, -8 ) b. ( -4, -16 ) d. ( 4, -16 ) 69. If and then what is the measure of The diagram is not to scale. a. 92 b. 54 c. 76 d. 38 70. Which point is the midpoint of? A B C D E 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 a. B b. D c. C d. not B, C, or D 71. In 2002 movie tickets sold for an average price of $5.25 each. In 2009 the average price was $6.57 each. If the price continues to increase in a linear fashion, what can you expect the average price to be in 2011? a. $6.95 c. $6.40 b. $6.57 d. $7.00 72. Given the equations y = 2x² and y = 2x² + 3, how are they different. a. The second one has a vertical shift c. The second one is narrower than the first b. They are the same width d. The second one has a horizontal shift 73. Given the equations y = 2x² and y = -2x² + 3x, how are they the same.
a. The first opens down, the second up c. They are both the same width b. The second has a horizontal shift d. The first opens up the second down 74. An object is dropped from a tall building. Suppose the distance it travels is given by the formula, where d represents the distance in feet and t represents time in seconds. About how long does it take the object to fall 580 feet? a. 4 seconds c. 7 seconds b. 5 seconds d. 6 seconds 75. What is true about the equation? a. r = 2 c. no solution b. r = -1 d. r = -3 76. For the line y = mx + b, where m < 0 and b > 0, what change would occur if m is multiplied by -1 and b remains the same? a. The slope would become positive. c. The slope would become negative. b. The line would be parallel to the d. The line would be perpendicular to the original. original. 77. The balance in Mr. Smith s savings account at the end of each year is calculated by the equation. Mr. Smith made a deposit to open the account 4 years ago. He has not made any additional deposits or withdrawals since. The balance at the end of 2 years was $1,929.71. What is the balance at the end of 4 years? a. $2,188.73 c. $2,143.69 b. $1,929.70 d. $1,922.51 78. A dead tennis ball is dropped from a height of 15 feet and bounces to 70% of its previous height after each bounce. The equation, where h is the height off the floor at a given point in time and n is the number of bounces, can be used to approximate the maximum height of the ball at any given bounce. About what is the maximum height of the ball on its 3rd bounce? a. 8 c. 7 b. 6 d. 5 79. Which angles are corresponding angles?
none of these 80. Given the equation, y = 3x + 12, what value of x will make y = 0? a. -4 c. 3 b. 4 d. -3 81. For the line graphed below, the x-intercept is changed to 1 and the slope remains the same. How will the graph of the line change? 5 4 3 2 1 y 5 4 3 2 1 1 1 2 3 4 5 x 2 3 4 5 a. It will intersect the original. c. It will be the same as the original. b. It will be parallel to the original. d. It will be perpendicular to the original. 82. Lexi is training for an Ironman competition. To train for the roadrace portion, she cycles 360 miles each week. She averages 60 miles each day she rides. The equation M = 360-60d gives the number of miles, M, left to ride after d days. Which graph shows the number of miles Lexi has left to ride after d days? a. miles c. miles 325 300 275 250 225 200 175 150 125 100 75 50 25 325 300 275 250 225 200 175 150 125 100 75 50 25 1 2 3 4 5 6 7 days 1 2 3 4 5 6 7 days
b. 325 300 275 250 225 200 175 150 125 100 75 50 25 miles d. 325 300 275 250 225 200 175 150 125 100 75 50 25 miles 1 2 3 4 5 6 7 days 1 2 3 4 5 6 7 days 83. Given the equations y = 2x² and y = -2x² + 3, how are they different. a. The first opens up the second down c. The first opens down, the second up b. The second has a horizontal shift d. They are both the same width 84. Katrina s dad put some money into a college savings account for her when she was born. Her dad intends to let the interest accumulate in the account until she goes to college. The rule gives the account balance after x years. When Katrina is 18 she decides she wants to go to college. About how much money will she have in her college fund? a. $20,000 c. $17,000 b. $18,000 d. $19,000 85. What would the x-intercepts be for the equation y = x(3x - 6)? a. -2 c. 0 b. 0, 2 d. 0, -2 Short Answer 86. Tony is working on building a punkin chunkin machine for the annual contest. After he practices, he figures out that the rule gives the height of the pumpkin ( in feet ) t seconds after he launches it. a. Explain what the 12 and the 50 in the rule tell you about the path of Tony s pumpkin. What does the 12 mean? What does the 50 mean? b. Assuming that nobody touches the pumpkin before it hits the ground, how long is the pumpkin in the air? (Round your answer to two decimal places) Show and explain
your work. c. What is the maximum height the pumpkin reaches and at what time will that occur? (Round your answer to two decimal places) Show you work or explain your reasoning. A maximum height of occurs at seconds after the pumpkin is launched. d. At what time(s) is the pumpkin at least 25 feet above the ground? (Round your answer to two decimal places) Show your work or explain your reasoning. Jordan s family has rented a suite at a Carolina Panthers football game for her birthday party. The suite cost $300.00 to rent. In addition, they must pay $16 per ticket for each person coming to the game/birthday party. 87. a) Display the (number of people, cost of party) data in the following table and properly label and scale the graph. # of people 0 1 2 3 4 5 Cost of party
b) If C is the cost of the party and n is the number of people going to the party/game, write an equation to represent the cost of the party. c) Write your equation from b) as a NOW/NEXT equation. NEXT = starting at d) Which variable from b) represents the independent variable and which represents the dependent variable. Explain your reasoning. independent variable dependent variable reasoning: e) Use or adapt your equation from b) to answer the following. Show your work. i) How much did it cost if 10 people came to the party? ii) If Jordan s parents spent $492, how many people came to the party?
iii) How many people can come to the party if the cost must be less than $636? 88. A simple one-celled bacterium divides into two identical bacteria every hour. a. If 2 of these bacteria are present in a sample now, how many will be present after 4 hours. (assuming none of them die)? Show and explain your work. Number present: b. Write a Now-Next rule that shows how to use the number of bacteria present at any time to predict the number that will be present an hour later. Next = starting @ c. Write a rule that includes exponents and begins y =... that can be used to calculate the number of bacteria present after any number of hour periods. y = d. Use the rules from Parts b or c to complete the following table: Number of Hour Time Periods 0 1 2 3 4 Number of Bacteria Present e. How many bacteria will be present in the sample after 12 hours? Explain or show your work. Number present: f. Mark an appropriate scale on the y-axis shown, and correctly label each axis. Plot the points from your table in Part d.
y 1 2 3 4 5 6 7 8 9 x g. Describe the way y changes as x increases.