Final - George Westinghouse College Prep
final
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Write a verbal expression for the algebraic expression.
____ 1. [pic]
|a. |4 times 5 |c. |4 divided by 5 |
|b. |four to the fifth power |d. |five to the fourth power |
____ 2. [pic]
|a. |2 times x squared minus 4 times x |
|b. |2 times x cubed increased by 4 times x |
|c. |the sum of 2 times x cubed and 4 times x |
|d. |2 times x cubed minus 4 times x |
____ 3. [pic]
|a. |9 times m to the fourth power decreased by 7 times n squared |
|b. |the difference of 9 times m to the fourth power and 7 times n squared |
|c. |9 times m to the fourth power increased by 7 times n squared |
|d. |the quotient of 9 times m to the fourth power and 7 times n squared |
____ 4. [pic]
|a. |the sum of three-fifths and two |
|b. |the difference of three-fifths and two |
|c. |the product of three-fifths and two |
|d. |the quotient of three-fifths and two |
Evaluate the expression.
____ 5. 54 – 3(8 – 4)
|a. |204 |c. |26 |
|b. |42 |d. |90 |
____ 6. Evaluate the following expression if a = 12, b = 5, and c = 4.
3c + bc – 2a
|a. |67 |c. |8 |
|b. |132 |d. |84 |
Write an algebraic expression for the verbal expression. Then simplify.
____ 7. three times the sum of c and d decreased by d
|a. |[pic] |
|b. |[pic] |
|c. |[pic] |
|d. |[pic] |
Evaluate the expression. Show each step.
____ 8. [pic]
|a. |[pic] |c. |[pic] |
| |[pic] | |[pic] |
| |[pic] | |[pic] |
| |[pic] | |[pic] |
| |[pic] | |[pic] |
| |[pic] | | |
|b. |[pic] |d. |[pic] |
| |[pic] | |[pic] |
| |[pic] | |[pic] |
| |[pic] | |[pic] |
| |[pic] | | |
Simplify the expression.
____ 9. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 10. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 11. Find the solution of the equation if the replacement set is [pic].
[pic]
|a. |63 |c. |81 |
|b. |35 |d. |51 |
Find the solution set for the inequality using the given replacement set.
____ 12. [pic]; [pic]
|a. |{11, 12} |c. |{11} |
|b. |{12} |d. |{11, 12, 13} |
____ 13. [pic]; [pic]
|a. |{7, 8, 9, 10, 11} |c. |{8, 9, 10, 11} |
|b. |{7, 9, 10, 11} |d. |{7, 8, 9, 10} |
Express each relation as a graph and a mapping. Then determine the domain and range.
____ 14. {(3, 1), (2, –5), (2, 4), (3, 3)}
|a. |[pic] |c. |[pic] |
| |[pic] | |[pic] |
| | | | |
| |D = {2, 3}; R = {–5, 1, 3, 4} | |D = {2, 3}; R = {–5, 1, 3, 4} |
|b. |[pic] |d. |[pic] |
| |[pic] | |[pic] |
| | | | |
| |D = {2, 3}; R = {–5, 1, 3, 4} | |D = {2, 3}; R = {–5, 1, 3, 4} |
____ 15. {(1, 1), (–2, 3), (2, 4), (3, 1)}
|a.|[pic][pic] |c.|[pic][pic] |
| | | | |
| |D = {–2, 1, 3}; R = {1, 3, 4} | |D = {–2, 1, 2, 3}; R = {1, 3, 4} |
|b.|[pic] |d.|[pic] |
| |[pic] | |[pic] |
| | | | |
| |D = {–2, 1, 2, 3}; R = {1, 3, 4} | |D = {–2, 1, 2, 3}; R = {1, 3, 4} |
Express each relation as a graph and a table. Then determine the domain and range.
____ 16. {(4, 0), (3, 2), (3, 0), (–3, –2), (4, –1)}
|a. |[pic] |c. |[pic] |
| |[pic] | |[pic] |
| |D = {–3, 3, 4}; R = {–2, –1, 0, 2} | |D = {–3, 3, 4}; R = {–2, –1, 0, 2} |
|b. |[pic] |d. |[pic] |
| |[pic] | |[pic] |
| |D = {–3, 3, 4}; R = {–2, –1, 0, 2} | |D = {–2, –1, 0, 2}; R = {–3, 3, 4} |
____ 17. Identify the graph that displays the speed of a baseball being pitched and then hit by the batter.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 18. Identify the graph that displays the altitude of a skydiver as he is taken up in a plane and then jumps.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 19. Identify the graph that displays the depth of water in a swimming pool after the drain is opened.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 20. Identify the graph that displays the height of a ping pong ball after it is dropped.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 21. During a snowy day, it snowed lightly for a while, stopped for a while, snowed heavily, and then stopped. Which graph represents the situation?
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
The following table shows car sales at a local car dealership for the first seven days of October.
|Day |1 |2 |3 |4 |5 |6 |7 |
|Sales |3 |4 |6 |7 |9 |10 |12 |
____ 22. Identify the independent and dependent variables in the October car sales table.
|a. |independent -- Sales |c. |independent -- Sales |
| |dependent -- Day | |dependent -- Day of the Week |
|b. |independent -- Salesman |d. |independent -- Day |
| |dependent -- Time of Day | |dependent -- Sales |
The following table shows the monthly charges for subscribing to the local newspaper.
|Number of Months |1 |2 |3 |4 |5 |
|Total Cost ($) |15.25 |30.50 |45.75 |61.00 |76.25 |
____ 23. Write the ordered pairs represented by the newspaper subscription table.
|a. |(1, 15.25), (2, 30.50), (3, 45.75), (4, 61.00), (5, 76.25) |
|b. |(1, 15), (2, 31), (3, 46), (4, 61), (5, 76) |
|c. |(15.25, 1), (30.50, 2), (45.75, 3), (61.00, 4), (76.25, 5) |
|d. |(2, 30.50), (3, 45.75), (4, 61.00), (5, 76.25) |
____ 24. Use the data in the newspaper subscription table to find the cost of the subscription for one year.
|a. |$167.75 |c. |$152.50 |
|b. |$183 |d. |$182.90 |
____ 25. Which relation is a function?
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 26. Which relation is a function?
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 27. Which relation is a function?
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 28. Which relation is a function?
|a. |{(5, 3), (2, 8), (–5, –1), (4, 7), (2, 1)} |
|b. |{(5, 3), (2, 8), (–5, –1), (4, 7), (5, 7)} |
|c. |{(–5, 3), (2, 8), (–5, –1), (4, 7), (2, 2)} |
|d. |{(5, 3), (2, 8), (–5, –1), (4, 7), (–2, 1)} |
____ 29. Which relation is a function?
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Identify the hypothesis and conclusion of the statement. Then write the statement in if-then form.
____ 30. David goes swimming when he finishes mowing the lawn.
|a. |H: he has finished mowing the lawn |
| |C: David is going swimming |
| |If he has finished mowing the lawn, then David is going swimming. |
|b. |H: David is going swimming |
| |C: he has finished mowing the lawn |
| |If David is going swimming, then he has finished mowing the lawn. |
|c. |H: David has finished all of his chores |
| |C: he is going swimming |
| |If David has finished all of his chores, then he is going swimming. |
|d. |H: he is going to play tennis |
| |C: David has finished mowing the lawn |
| |If he is going to play tennis, David has finished mowing the lawn. |
Find a counterexample for the statement.
____ 31. If you finish in the top 10% in medical school, then you will become a heart surgeon.
|a. |top 8% -- heart surgeon |c. |top 12% -- general practice |
|b. |top 8% -- pediatrician |d. |top 15% -- brain surgeon |
____ 32. If you graduate from high school in Florida, then you will attend the University of Florida.
|a. |graduated from high school in Florida -- attended the University of Kentucky |
|b. |graduated from high school in Florida -- attended the University of Florida |
|c. |graduated from high school in Tennessee -- attended the University of Georgia |
|d. |graduated from high school in Georgia -- attended the University of Florida |
____ 33. If x is an odd composite number, then x is divisible by 3.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 34. If [pic], then [pic].
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Translate the sentence into an equation.
____ 35. Four times the number x increased by 15 is 83.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 36. Eighty-five minus five times x is equal to ten.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 37. Fourteen minus four times y is equal to y increased by 4.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Translate the equation into a verbal sentence.
____ 38. [pic]
|a. |A number x minus 18 is 12. |c. |A number x divided by 18 is 12 |
|b. |A number x plus 18 is 12 |d. |A number x minus 12 is 18. |
____ 39. [pic]
|a. |Two-thirds of d increased by three-fifths is the same as twice d. |
|b. |Two-thirds of d decreased by three-fifths is the same as twice d. |
|c. |Two-thirds of d increased by three-fifths is the same as one-half d. |
|d. |The quotient of two-thirds and d plus three-fifths is the same as twice d. |
____ 40. [pic]
|a. |Eight plus x is the same as two. |
|b. |x minus eight is the same as two. |
|c. |Eight increased by x is the same as two. |
|d. |Eight minus x is the same as two. |
____ 41. [pic]
|a. |Three times c plus the difference of c and four is 127. |
|b. |Three times c plus the sum of c and four is 127. |
|c. |Three plus c plus the sum of c and four is 127. |
|d. |Three times c plus the product of c and four is 127. |
Solve the equation. Then check your solution.
____ 42. a – [pic] = [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 43. – [pic] + a = [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 44. [pic]
|a. |14 |c. |24 |
|b. |–14 |d. |–13 |
____ 45. [pic]
|a. |–62 |c. |18 |
|b. |19 |d. |–18 |
____ 46. [pic] + x = [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 47. [pic]
|a. |35 |c. |140 |
|b. |70 |d. |116 |
____ 48. 1.6a = –9.12
|a. |–7.52 |c. |–10.72 |
|b. |–5.7 |d. |10.72 |
Write an equation and solve each problem.
____ 49. Fifty-six is twelve added to four times a number. What is the number?
|a. |[pic]; 17 |c. |[pic]; 11 |
|b. |[pic]; 44 |d. |[pic]; 11 |
____ 50. Find three consecutive integers with a sum of 24.
|a. |[pic]; 9, 10, 11 |
|b. |[pic]; 6, 8, 10 |
|c. |[pic]; 7, 8, 9 |
|d. |[pic]; 21, 22, 23 |
____ 51. Find four consecutive odd integers with a sum of –32.
|a. |[pic]; –11, –13, –15, –17 |
|b. |[pic]; –10, –9, –7, –6 |
|c. |[pic]; –5, –3, –1, 1 |
|d. |[pic]; –11, –9, –7, –5 |
Solve the equation. Then check your solution.
____ 52. [pic]
|a. |–3 |c. |3 |
|b. |[pic] |d. |[pic] |
____ 53. [pic]k – 5 = –7 [pic]k
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 54. [pic]w [pic] = [pic] [pic]w
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 55. Graph [pic].
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 56. Use cross products to determine which pair of ratios forms a proportion.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Solve the proportion. If necessary, round to the nearest hundredth.
____ 57. [pic]
|a. |90 |c. |80 |
|b. |100 |d. |70 |
State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. Round to the nearest whole percent.
____ 58. original: 11
new: 33
|a. |increase; 200% |c. |decrease; 200% |
|b. |increase; 67% |d. |decrease; 67% |
Find the final price of the item.
____ 59. CD player: $89.95
discount: 15%
tax: 6%
|a. |$76.46 |c. |$101.46 |
|b. |$71.87 |d. |$81.05 |
____ 60. tennis racket: $47.50
discount: 25%
tax: 5%
|a. |$35.62 |c. |$33.84 |
|b. |$37.41 |d. |$49.88 |
The formula for the perimeter, P, of a rectangle is P = 2[pic] + 2w, where [pic] is the length and w is the width.
____ 61. Find the width of a rectangle which has a perimeter of 54 centimeters and a length of 18 centimeters.
|a. |9 square centimeters |c. |27 centimeters |
|b. |18 centimeters |d. |9 centimeters |
The circumference of a circle is given by the formula [pic], where r is the measure of the radius.
____ 62. Solve the formula for r.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Two trains leave Chicago at the same time, one traveling east and the other traveling west. The eastbound train travels at 50 miles per hour, and the westbound train travels at 40 miles per hour. Let t represent the amount of time since their departure.
[pic]
____ 63. Complete the table representing the situation.
|a. |[pic] |
|b. |[pic] |
|c. |[pic] |
|d. |[pic] |
Fumiko and Kenji leave home at the same time, traveling in opposite directions. Fumiko drives 50 miles per hour, and Kenji drives 55 miles per hour.
[pic]
____ 64. Complete the table representing the situation.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 65. Write an equation that could be used to determine when they will be 630 miles apart.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 66. In how many hours will they be 630 miles apart?
|a. |126 hours |c. |5.7 hours |
|b. |6.3 hours |d. |6 hours |
Two airplanes leave Denver, one traveling east at 700 miles per hour and one traveling west at 750 miles per hour. Let t represent the time since their departure.
[pic]
____ 67. Complete the table representing the situation.
|a. |[pic] |
|b. |[pic] |
|c. |[pic] |
|d. |[pic] |
____ 68. Jan and David began riding their bicycles in opposite directions. Jan travels at 10 miles per hour and David rides at 12 miles per hour. When will they be 11 miles apart?
|a. |[pic] hours |c. |[pic] hour |
|b. |[pic] hours |d. |[pic] hour |
The Nut House sells peanuts for $6.75 per pound and cashews for $9.50 per pound. On Saturday, they sold 32 pounds more peanuts than cashews. The total sales for both types of nuts was $1,012.25. Let p represent the number of pounds of peanuts sold.
[pic]
____ 69. Copy and complete the table representing the problem.
|a. |[pic] |
|b. |[pic] |
|c. |[pic] |
|d. |[pic] |
____ 70. Write an equation to represent the problem.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Ye Olde Coffee Shop sells Colombian Coffee for $9.25 per pound. Brazilian Coffee sells for $7.75 per pound. The management wishes to mix 6 pounds of Colombian Coffee with an amount of Brazilian Coffee so that the mixture sells for $8.25 per pound.
[pic]
____ 71. Write an equation to represent the problem.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Big Dog sells a beef-based dog food for $2.30 per pound and a lamb-based food for $3.80 per pound. They sell a mixture of the two kinds of food for $2.90 per pound. Let b represent the amount of beef food the company uses in 8 pounds of the mixture.
[pic]
____ 72. Copy and complete the table representing the problem.
|a. |[pic] |
|b. |[pic] |
|c. |[pic] |
|d. |[pic] |
Solve the equation for the given domain. Graph the solution set.
____ 73. y = 2x – 1 for x = {–3, –1, 1, 2, 3}
|a. |{(–3, –7), (–1, –3), (1, 1), (5, 5), (3, 5)} |
| |[pic] |
|b. |{(–3, –6), (–1, –3), (1, 1), (2, 3), (3, 5)} |
| |[pic] |
|c. |{(–3, –7), (–1, –3), (1, 1), (2, 3), (3, 5)} |
| |[pic] |
|d. |{(–3, –7), (–1, –3), (1, 1), (2, 3), (3, 5)} |
| |[pic] |
____ 74. 3x – y = –1 for x = {–1, 0, 1, 4}
|a. |{(–1, –2), (0, 1), (1, 4), (4, 13)} |c. |{(–1, –1), (0, 1), (1, 4), (4, 13)} |
| |[pic] | |[pic] |
|b. |{(–1, –2), (0, 1), (1, 4), (7, 15)} |d. |{(–1, –2), (0, 1), (1, 4), (4, 13)} |
| |[pic] | |[pic] |
Solve the equation.
____ 75. [pic]
|a. |2 |c. |–6 |
|b. |–2 |d. |–4 |
____ 76. [pic]
|a. |–2 |c. |6 |
|b. |–6 |d. |2 |
____ 77. A board is leaning against a building so that the top of the board reaches a height of 18 feet. The bottom of the board is on the ground 4 feet away from the wall. What is the slope of the board as a positive number?
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |undefined |
____ 78. A conveyor belt runs between floors of a building as pictured below. Find the slope of the belt as a positive number.
[pic]
|a. |undefined |c. |[pic] |
|b. |[pic] |d. |0 |
[pic]
Source: public_works/stormwater/rain/rainfall.htm
____ 79. For which one month period was the rate of change in rainfall amounts in Orlando the greatest?
|a. |May - June |c. |June - July |
|b. |Aug. - Sept. |d. |Feb. - March |
[pic]
Source: U.S. Bureau of Census
____ 80. For which 10-year period was the rate of change of the population of Green Bay the greatest?
|a. |1990 - 2000 |c. |1980 - 1990 |
|b. |1970 - 1980 |d. |1975 - 1985 |
____ 81. For which 10-year period was the rate of change of the population of Green Bay the least?
|a. |1990 - 2000 |c. |1980 - 1990 |
|b. |1970 - 1980 |d. |1975 - 1985 |
Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve.
____ 82. If y = –15 when x = –5, find x when y = 12.
|a. |y = –3x; –4 |c. |y = 3x; 4 |
|b. |y = 3x; 3 |d. |y = 2x; 4 |
Write a direct variation equation that relates the variables. Then graph the equation.
____ 83. Roasted cashews are $5.98 per pound. The total cost of p pounds is C.
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
____ 84. The total cost is C for n packages of popcorn priced at $1.50 per package.
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
____ 85. Movie tickets costs $7.50 each. The total cost of t tickets is C.
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
____ 86. Luis drives at a rate of 50 miles per hour. His total distance in t hours is d.
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
____ 87. The table below shows the distance traveled by a person driving at the rate of 60 miles per hour.
|Hours |1 |2 |3 |4 |5 |
|Distance (miles) |60 |120 |180 |240 |300 |
Write an equation to describe the relationship.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Write an equation of the line with the given slope and y-intercept
____ 88. slope: 0.8, y-intercept: 10
|a. |y = –0.8x + 10 |c. |y = 0.8x + 10 |
|b. |y = 0.8x – 10 |d. |y = [pic]x + 10 |
Write a linear equation in slope-intercept form to model the situation.
____ 89. An icicle is 12 inches long and melts at a rate of [pic] inch per hour.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 90. The temperature is 38° and is expected to rise at a rate of 3° per hour.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Mr. Collins is constructing a fence around his property. He already has 25 sections up and plans to add 8 sections each Saturday until he is finished.
____ 91. Graph the equation for the number of fence sections F standing after any number of Saturdays s.
|a. |[pic] |
|b. |[pic] |
|c. |[pic] |
|d. |[pic] |
Write an equation of the line that passes through the pair of points.
____ 92. [pic]
|a. |y = [pic]x + [pic] |c. |y = [pic]x – [pic] |
|b. |y = [pic]x – [pic] |d. |y = [pic]x + [pic] |
Write each equation in standard form.
____ 93. y + 3 = [pic](x + 9)
|a. |2x – 5y = 33 |c. |y = [pic]x + [pic] |
|b. |2x – 5y = –3 |d. |2x + 5y = 3 |
Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of the equation.
____ 94. (–5, –3), 5x – 4y = 8
|a. |y = [pic]x + [pic] |
|b. |y = [pic]x – [pic] |
|c. |y = [pic]x + [pic] |
|d. |y = [pic]x + [pic] |
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
____ 95.
|Video Rental Fines |
|[pic] |
|a. |negative; as the number of videos rented increases, the amount of fine increases. |
|b. |negative; as the number of videos rented increases, the amount of fine decreases. |
|c. |no correlation |
|d. |positive; as the number of videos rented increases, the amount of fine decreases. |
____ 96.
|Strawberries Picked |
|[pic] |
|Time (hours) |
|a. |positive; as time passes, the number of quarts picked decreases. |
|b. |negative; as time passes, the number of quarts picked decreases. |
|c. |no correlation |
|d. |positive; as time passes, the number of quarts picked increases. |
|United States Birth Rate |
|Year |
____ 97. Predict the birthrate in 2005. Round your answer to the nearest tenth, if necessary.
|a. |14.5 |c. |15.1 |
|b. |13.1 |d. |14.0 |
| |Domestic Traveler Spending in the U.S., 1987-1999 |
| |[pic] |
|[pic] | |
| |Year |
| |Source: The World Almanac, 2003 |
____ 98. Use the scatter plot that shows the domestic traveler spending. Predict the amount of spending for domestic travelers in 2010.
|a. |about $640,000,000 |c. |about $640 |
|b. |about $460,000,000,000 |d. |about $640,000,000,000 |
|Strawberries Picked |
|[pic] |
____ 99. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Use the points (1, 73) and (8, 41) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
|Average Cycling Speed |
|[pic] |
____ 100. Use the scatter plot that shows the average cycling speed as time passes. Use the points (5, 15) and (25, 10) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 101. Use the scatter plot that shows the average cycling speed as time passes. Predict the speed of the cyclist after 30 minutes.
|a. |about 6.2 miles per hour |c. |about 12.3 miles per hour |
|b. |about 8.8 miles per hour |d. |about 10.5 miles per hour |
Find the equation of the regression line.
____ 102. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Find y for the given value of x.
____ 103. The best-fit line is [pic]. [pic].
|a. |8.55 |c. |1.2 |
|b. |8.05 |d. |7.23 |
Find the graph of the function.
____ 104. [pic]
|a. | |c. | |
| |[pic] | |[pic] |
|b. | |d. | |
| |[pic] | |[pic] |
____ 105. [pic]
|a. | |c. | |
| |[pic] | |[pic] |
|b. | |d. | |
| |[pic] | |[pic] |
Solve the inequality. Graph the solution on a number line.
____ 106. [pic]
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
____ 107. [pic]
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
____ 108. [pic]
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
Solve the inequality.
____ 109. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 110. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 111. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Solve the compound inequality and graph the solution set.
____ 112. [pic] or [pic]
|a. |[pic] |
| |[pic] |
|b. |[pic] |
| |[pic] |
|c. |[pic] |
| |[pic] |
|d. |[pic] |
| |[pic] |
____ 113. Solve [pic].
|a. |d < –9 |c. |–9 < d < 7 |
|b. |d > 7 |d. |d < –9 or d > 7 |
____ 114. The levels of humidity in a hermit crab cage are kept within 5% of 75% humidity. What is the range of humidity levels in the cage?
|a. |{x | 70 ≤ x} |c. |{x | x ≤ 70 or x [pic] 80} |
|b. |{x | x ≤ 80} |d. |{x | 70 ≤ x ≤ 80} |
____ 115. At a track meet, the height of John’s high jump was within 6 inches of the track record of 76 inches. What is the range of heights for John’s jump?
|a. |{x | 70 ≤ x ≤ 82} |c. |{x | 70 ≤ x} |
|b. |{x | x ≤ 70 or x [pic] 82} |d. |{x | x ≤ 82} |
____ 116. In order to earn a grade of C on the midterm, a student must have a score that is within 6 points of the average score of 62 points. Which score would earn a C?
|a. |{x | 56 < x < 68} |c. |{x | 56 ≤ x ≤ 68} |
|b. |{x | x < 56 or x > 68} |d. |{x | x ≤ 56 or x [pic] 68} |
A student can buy notebooks for $0.40 each and pens for $0.25 each. Ben needs to have at least 8 notebooks. He has a total of $5.00 to spend.
____ 117. Write a system of inequalities to show how many notebooks and pens Ben can buy.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 118. The difference between Rosa’s age and her father’s age is less than 35. Rosa’s father is more than three times her age. Which of the following are possible ages for Rosa and her father?
|a. |5 and 40 |c. |10 and 30 |
|b. |7 and 28 |d. |14 and 38 |
Short Answer
119. Define a mathematical expression. Give an example of a verbal expression translated into a mathematical expression.
120. Define a variable to represent a real-life quantity, such as length in centimeters or money in cents. Then use the variable to write a mathematical expression to represent one of your daily activities. Describe in words what your expression represents, and explain your reasoning.
121. Define a variable to represent a real-life quantity, such as weight in pounds or capacity in quarts. Then use the variable to write a mathematical expression to represent one of your daily activities. Describe in words what your expression represents, and explain your reasoning.
122. In the square, x represents a positive whole number. Find the value of x such that the area is equal to half the perimeter of the square.
[pic]
123. The table shows annual expenditure estimates of a relief organization on different diseases.
[pic]
Write and solve an expression that could be used to determine the total expenditure on the following:
1. Five-year expenditure on HIV/AIDS and tuberculosis.
2. Seven-year expenditure on malaria and leprosy.
124. At a local fair, a stall for a dart game displays the following prize money for different scores. Each player has three chances and the prize money is awarded on the basis of total points.
[pic]
Write and solve an expression that can be used to find the total prize money for the following:
1. Eleven people who scored between [pic] and [pic].
2. Nine people who scored between [pic] and above 300.
Name the properties used.
125. Every month, Ben spends $350 on groceries, $150 on gasoline, and $250 on clothes. Write and evaluate an expression to predict how much money he will spend on these items over the next 12 months.
126. Lisa earns $7.15 per hour working after school. She needs at least $235 to buy a stereo system. Write and solve an inequality to find the minimum number of hours she must work to buy the stereo.
127. A gourmet jelly bean company packs 2565 jelly beans in 45 different packets every hour. Write and solve an equation to find how many jelly beans each packet holds, assuming each packet contains equal number of jelly beans.
Express the relation shown in each table, mapping, or graph as a set of ordered pairs. Then write the inverse of the relation.
128. [pic]
Determine whether the relation is a function.
129. [pic]
130. [pic]
131. {(5, 9), (4, 8), (–7, 4), (0, 4), (2, 4), (3, 9), (–3, 8)}
Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form.
132. Mark uses an umbrella when it rains.
133. A potted tree weighs 21 pounds. The pot weighs 3 pounds. If w represents the weight of the tree without the pot, write an equation to find the weight of the tree without the pot.
134. Jack’s school is 20 miles from his house. He has already traveled 13 miles. If d represents the distance he still needs to travel to reach his school, write an equation to represent this situation. Then use this equation to find the distance Jack still needs to travel to reach his destination.
135. Mary bought a coat on sale for $63.75. The original price for the coat was $85. Write and solve an equation to find the amount of money Mary saved.
136. Bryan eats three slices of a ten-slice pizza. He pays $3.30 as his share of the full price. Write and solve an equation to find the full price.
137. Eleven increased by three times a number equals 68. Write an equation for this situation and then find the number.
138. Fourteen decreased by twice a number equals –42. Write an equation for this situation and then find the number.
139. Forty-two is twelve added to five eighths of a number. Write an equation for this situation and then find the number.
140. Act 3 of the 2003 Leonid meteor shower was expected to last 24 hours. The margin of error for this prediction was 0.7 days. What was the range for the length of time that Act 3 could last?
141. In a random sample of 400 customers at a fast food restaurant, it was determined that 124 customers ordered a salad. If the restaurant typically has 1200 customers in a day, how many of these customers will probably order a salad?
142. In 1989, a poll of 1000 voters conducted by the staff of a senator found that 390 people approved of the job the senator was doing. The following year, a new poll of 1000 voters found that 335 people were happy with the senator’s performance. What is the percent of decrease of the senator’s approval rating? Round to the nearest whole percent.
143. In 2001, Bradley’s Pet Shop had a 210% increase in turtle sales over the previous year. If they sold 30 turtles in 2000, find the total number of turtles sold in 2001.
Write an equation and solve for the variable specified.
144. Twelve more than a number, s, equals another number, p, minus 4. Solve for s.
145. How many liters of a 26% vinegar solution should be added to a 60% vinegar solution to create 136 liters of a 49% vinegar solution?
Copy and complete the table representing the problem.
| |Liters |Total Amount of Vinegar |
|49% Vinegar |136 | |
|26% Vinegar |n | |
|60% Vinegar |136 − n | |
Also write an equation to represent the problem.
146. Find the x- and y-intercepts of the graph of [pic].
147. Trudy bought a $20 prepaid long distance phone card. For every minute that she talks, $0.25 is deducted from her card. The function [pic] represents the amount of money f(m) she has left after talking m minutes. Find the zero and explain what it means in the context of this situation.
Use the graph of computer prices for 1980–1987 to answer the following questions.
[pic][pic]
[pic]
Source:
148. In which years did computer prices fall the most? Explain two ways you could find this.
149. What is the difference between proportional and nonproportional relationships?
150. The table of ordered pairs shows the coordinates of the two points on the graph of a line.
|x |y |
|0 |6 |
|4 |10 |
Write an equation that describes the line.
151. A company manufactured 324,000 computers in 2002. The company’s output grows by 5,000 units per year.
|Year |Production (thousands) |
|2002 |324 |
|2003 |329 |
|2004 |334 |
Write a linear equation to find the company’s production, P, in year, t.
152. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that passes through [pic] with slope 4.
153. Line l passes through [pic] with slope [pic]. Write the point-slope form, slope-intercept form, and standard form of an equation for line l.
154. Write an equation of the line that is parallel to the graph of [pic] and passes through [pic].
155. The graph below shows the relationship between a long-distance truck driver’s driving times and the number of miles traveled.
[pic][pic]
[pic]
Is it reasonable to use the equation for line of fit to estimate the distance traveled for a driving time of 10 hours? Explain.
156. Olivia must earn 475 points out of 550 to receive a B in math. So far, she has earned 240 test points, 85, quiz point, and 40 homework points. How many points, p, must she score on her final exam to earn at least a B in math?
157. A school is having a raffle to raise money for a charity. Any homeroom that sells at least 175 tickets can help charity volunteers build a home. Ms. Blakely’s homeroom is keeping a table of the number of tickets sold each day. How many more tickets, t, do they need to sell to help build the home?
|Day |Tickets |
|1 |43 |
|2 |21 |
|3 |? |
|4 |? |
158. Isabella works part time to earn money. She wants to earn at least $275 to buy a new computer. If she earns $11 per hour, how many hours must she work to reach her target?
159. A machine can produce 200 jellybeans in an hour. If 15 jellybeans are packed in a single packet, how many packets of jellybeans can be packed in an hour? Define a variable and write an inequality to solve the problem. Interpret your solution.
160. Aaron’s point totals in the first four of five basketball games were 15, 18, 19, and 12. How many points, t, must he score to have a mean point total of more than 16?
161. A bank investment plan reads, “In one year, your balance will be greater than your original investment plus 8% of the investment.” Suppose Sandra invests $1200. How much money, x, can she expect to have at the end of the year?
162. The water temperature for a manufacturing process should be kept at 140°F. A computer program uses the inequality [pic], which describes the acceptable water temperatures, t, in Fahrenheit. What is the range of acceptable temperatures for the water?
163. Morgan is building a square dog kennel in his backyard. The perimeter of the kennel is to be at least 14 feet but not more than 48 feet. Find all the possible values for the length, s, of its sides.
164. Students tested the average acidity of the campus pond over a three-day period. On Monday and Tuesday, the pH values were 7.01 and 7.94. Find the range of pH values for Wednesday’s reading that will result in an average acidity greater than 6.8 and less than 7.3.
165. Solve [pic] and graph the solution set.
166. Compare and contrast the solution of [pic] and the solution of [pic].
A radio station is giving away tickets to a play. They plan to give away tickets to seats that cost $10 or $20. They plan to give away at least 20 tickets, and the total cost of all the tickets can be no more than $300.
167. Write two ways of giving away the tickets keeping the restrictions in mind.
Suppose a car dealer receives a profit of $500 for each mid-sized car m sold and $750 for each sport-utility vehicle s sold. The dealer must sell at least two mid-sized cars for each sport-utility vehicle and must earn at least $3500 per week.
168. Suppose a car dealer sells 2 sport-utility vehicles. How many mid-sized cars must be sold to earn at least $3500?
Essay
169. A carrom board is a square board with four corner pockets. Each pocket is at the same distance from the next consecutive pocket on the board. Suppose d represents the length of each side.
a. Explain how expressions can be used to find the perimeter of the carrom board.
b. Include two different verbal expressions and an algebraic expression other than 4d to represent the perimeter of the carrom board.
170. The table shows the points scored by teams A, B, C, and D in two rounds of a quiz show.
[pic]
a. Write an open-sentence to show the Reflexive Property using the above data.
b. Explain how properties can be used to compare data.
c. Include an example of the Transitive Property if another round was added in the quiz show.
171. The table shows the time taken by a southbound train to reach different stations.
[pic]
a. Write an expression to find the time to reach Springfield from Cleveland.
b. Explain how the Commutative and Associative Properties are useful in performing calculations.
c. Include an expression using the properties that could help you find the time to reach Fairview from Lexington.
172. An amusement park charges $8 for admission and $1.50 per ride. Diego has $25.
a. Write an open-sentence to find the maximum number of rides he can take with the given amount?
b. Explain the answer given in part a.
c. Give examples of real-world situations in which you would use inequalities and equations?
173. The table below gives the statistics for goals scored and shots on goal for a soccer championship, which can be represented as a set of ordered pairs. The number of goals are the first coordinates, and the shots on goal are the second coordinates.
[pic]
a. Explain how relations can be used to represent soccer statistics.
b. Include a graph of the relation of goals and the number of shots on goal for all the teams.
c. Describe the relationship between the quantities.
174. A company increases the salaries of its employees every year by 15%. The graph shows the salary of a particular employee as the number of years increase.
[pic]
The increase in salary of the employee is the function of the number of years passed. Explain how real-world situations can be modeled using graphs and functions.
175. The graph below shows the average annual rainfall of a region from the years 1998 to 2003.
[pic]
The average annual rainfall in 2002 is 30 inches which is 20 less than the average annual rainfall in 2003. An equation can be used to find the average annual rainfall in 2003. If a is the average annual rainfall for 2003, then [pic]. You can use a property of equality to find the value of a.
a. Explain how equations can be used to compare data.
b. Explain how to solve the equation given above.
c. Include a sample problem and related equation using the information in the graph.
176. The information below gives the power supply needed for different sizes of air conditioners.
Power of different sized air conditioners
••••••••••••3120 watts
••••••••••••••••••••••5050 watts
•••••••••••••••••••••••••••••••••9540 watts
••••••••••••••••••4590 watts
••••••••••••••••••••••••••••••••••••••••••14,300 watts
••••••••••••••••••••••••••••••••••••••••••••••20,000 watts
Electric power equals the product of voltage and current. If we assume that the voltage is supplied at a constant rate of 220 volts, the following equation can be used to find the current for different air conditioners.
[pic]
a. Explain how equations can be used to find the current flow for different sizes of air conditioners.
b. Write and explain an equation to find the current for an air conditioner that has 20,000 watts of power.
177. Elephant seals dive deep underwater and can stay submerged for many minutes, even though they are air-breathing mammals. They do this by slowing their metabolism, especially their heart rate.
The expression [pic] represents the average heart rate of an elephant seal, when it is submerged in water for x minutes. If the heart rate of a particular elephant seal is 90 beats per minute under water, the equation [pic] can be used to estimate the time for which the elephant seal can stay submerged in water.
a. Explain how equations can be used to estimate the time for which the elephant seal can stay submerged in water.
b. Include an explanation of how to solve the equation representing the average heart rate and the time for which the elephant seal can stay submerged in water.
178. The ingredients in the recipe given below will make 4 glasses of summer cooler mocktail.
[pic]
Cathy can use ratios and equations to find the amount of each ingredient needed to make enough mocktail for her party.
a. Explain how ratios are used in recipes.
b. Include an explanation of how to use a proportion to determine how much grenadine is needed if you use 3 scoops of ice cream, and a description of how to alter the recipe to get 7 glasses of mocktail.
179. Anthony threw a ball from the top of a 10-story building that was 165 feet tall. The speed of the ball was 85 feet per second. If we ignore the friction, the equation [pic] can be used to find the maximum height the ball can attain after being thrown from the top of the building. In this equation g represents the acceleration due to gravity (32 feet per second squared), h is the maximum height attained by the ball, and v is the speed of the ball.
a. Explain how equations can be used to find the maximum height the ball can attain after being thrown from the top of the building.
b. Include a list of steps you could use to solve the equation for h, the maximum height the ball can attain after being thrown from the top of the building.
180. The temperature C, in degrees, that is equivalent to a temperature of F degrees Fahrenheit is given by [pic]. The graph of this equation shows the temperature in Celsius for the corresponding temperatures in Fahrenheit.
[pic]
a. Explain how linear equations can be used in temperature conversion.
b. Explain how could you could use the conversion graph to find the normal body temperature in degrees Celsius, which is 98.6°F.
181. Write a function with a zero of [pic]. Explain how you know.
182. Mary charges a flat fee of $5 plus $2 per hour for baby-sitting.
[pic]
a. Explain how y-intercepts can be used to describe real-world costs.
b. Write a description of a situation in which the y-intercept of its graph is $7.50.
183. Megan wants to change her Internet Service Provider. She is considering three different plans.
Plan 1 charges a $15 monthly fee plus $0.08 per minute of use.
Plan 2 charges a $5 monthly fee plus $0.11 per minute of use.
Plan 3 charges a flat monthly fee of $49.95.
a. For each plan, write an equation that represents the monthly cost C for m minutes per month.
b. Graph each of the three equations on the same coordinate axes. Label each line.
c. Megan expects to use 500 minutes per month. In which plan do you think Megan should enroll? Explain.
184.
|Average Hourly Earnings (dollars) of U.S. Production Workers, 1991-2001 |
|Year |
a. Draw a scatter plot with years on the x-axis and earnings on the y-axis.
b. Draw a line of fit for the data.
c. Write the slope-intercept form of an equation for the line of fit.
d. Predict the hourly earnings for production workers in 2005.
185. Alan used his graphing calculator to find the best-fit line of a set of data. The correlation coefficient was -0.965. Explain what that means.
186. Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.
a. If both of them get $4.50 an hour, write an inequality to compare Peter’s and Cindy’s earnings.
b. What should Cindy’s per-hour income be so that she earns at least $14 a day? Write an inequality and an explanation of how to solve it.
187. Admission prices to Cinema I to see a movie are $9.50 for an adult and $6.50 for a child. The admission charge at Cinema II is $8.00 per person regardless of age.
a. Write an inequality showing that the prices are cheaper at Cinema I than at Cinema II.
b. If 6 adults and their children go together to see a movie, use the inequality to find how many children must attend for Cinema I to be the better deal.
188. A county government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
a. Write and solve an absolute value inequality to represent this situation.
b. Graph the solution.
c. A lifeguard measures the chlorine level in the pool and finds it is 1.0 ppm. Should he add more chlorine? Explain.
final
Answer Section
MULTIPLE CHOICE
1. ANS: B
Translate the algebraic expression into a verbal expression using key operation words.
| |Feedback |
|A |Is that a product? |
|B |Correct! |
|C |Is division indicated? |
|D |Which number is the exponent? |
PTS: 1 DIF: Basic REF: Lesson 1-1
OBJ: 1-1.2 Write verbal expressions for mathematical expressions.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2
TOP: Write verbal expressions for mathematical expressions
KEY: Write Expressions | Verbal Expressions
2. ANS: D
Translate the algebraic expression into a verbal expression using key operation words.
| |Feedback |
|A |What is the exponent? |
|B |What is the meaning of increased by? |
|C |Is addition involved in the expression? |
|D |Correct! |
PTS: 1 DIF: Basic REF: Lesson 1-1
OBJ: 1-1.2 Write verbal expressions for mathematical expressions.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2
TOP: Write verbal expressions for mathematical expressions
KEY: Write Expressions | Verbal Expressions
3. ANS: C
Translate the algebraic expression into a verbal expression using key operation words.
| |Feedback |
|A |Does decreased indicate addition? |
|B |Does the expression involve subtraction? |
|C |Correct! |
|D |Does the expression involve division? |
PTS: 1 DIF: Average REF: Lesson 1-1
OBJ: 1-1.2 Write verbal expressions for mathematical expressions.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2
TOP: Write verbal expressions for mathematical expressions
KEY: Write Expressions | Verbal Expressions
4. ANS: A
Translate the algebraic expression into a verbal expression using key operation words.
| |Feedback |
|A |Correct! |
|B |Is there subtraction in the expression? |
|C |Does the expression indicate multiplication? |
|D |Does the expression involve division? |
PTS: 1 DIF: Basic REF: Lesson 1-1
OBJ: 1-1.2 Write verbal expressions for mathematical expressions.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2
TOP: Write verbal expressions for mathematical expressions
KEY: Write Expressions | Verbal Expressions
5. ANS: B
Perform any operations within grouping symbols first. Then evaluate powers followed by multiplication and division from left to right, then addition and subtraction from left to right.
| |Feedback |
|A |Did you do multiplication before any addition or subtraction? |
|B |Correct! |
|C |Did you perform operations within parentheses first? |
|D |Be careful with addition and subtraction. |
PTS: 1 DIF: Average REF: Lesson 1-2
OBJ: 1-2.1 Evaluate numerical expressions by using the order of operations.
TOP: Evaluate numerical expressions by using the order of operations
KEY: Evaluate Expressions | Order of Operations
6. ANS: C
Replace the variables with their values. Then find the value of the numerical expression using the order of operations.
| |Feedback |
|A |Did you replace the variables carefully? |
|B |Be careful with the order of operations. |
|C |Correct! |
|D |Did you add before multiplying? |
PTS: 1 DIF: Average REF: Lesson 1-2
OBJ: 1-2.2 Evaluate algebraic expressions by using the order of operations.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP: Evaluate algebraic expressions by using the order of operations
KEY: Evaluate Expressions | Order of Operations
7. ANS: A
Translate the verbal expression to an algebraic expression. Use the properties learned so far to simplify the expression.
| |Feedback |
|A |Correct! |
|B |Did you use the Distributive Property correctly? |
|C |Did you try to add unlike terms? |
|D |Did you add unlike terms? |
PTS: 1 DIF: Average REF: Lesson 1-3
OBJ: 1-3.3 Use the Commutative and Associative Properties to simplify algebraic expressions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Recognize the Commutative and Associative Properties
KEY: Commutative Property | Associative Property
8. ANS: B
Use identity and equality properties along with the order of operations to evaluate the expression.
| |Feedback |
|A |Be careful with the order of operations. |
|B |Correct! |
|C |Did you evaluate the power correctly? |
|D |Did you forget to evaluate the power? |
PTS: 1 DIF: Average REF: Lesson 1-3
OBJ: 1-3.2 Use the properties of identity and equality. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2
TOP: Use the properties of identity and equality
KEY: Identity Property | Equality Property
9. ANS: D
Use the properties studied so far to simplify the expression.
| |Feedback |
|A |Did you use the Distributive Property carefully on both products? |
|B |Did you switch x and y? |
|C |Did you correctly use the Distributive Property on both products? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 1-3
OBJ: 1-3.3 Use the Commutative and Associative Properties to simplify algebraic expressions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Use the Commutative and Associative Properties to simplify algebraic expressions
KEY: Commutative Property | Associative Property
10. ANS: C
Use the properties studied so far to simplify the expression.
| |Feedback |
|A |Did you correctly use the Distributive Property? |
|B |Did you use the Distributive Property? |
|C |Correct! |
|D |Did you correctly use the properties? |
PTS: 1 DIF: Average REF: Lesson 1-3
OBJ: 1-3.3 Use the Commutative and Associative Properties to simplify algebraic expressions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Use the Commutative and Associative Properties to simplify algebraic expressions
KEY: Commutative Property | Associative Property
11. ANS: A
The solution set of an open-sentence is the set of elements from the replacement set that make the open-sentence true.
| |Feedback |
|A |Correct! |
|B |Did you add or subtract after replacing the variable? |
|C |Does that replacement make the equation true? |
|D |Be careful with division. |
PTS: 1 DIF: Basic REF: Lesson 1-5
OBJ: 1-5.1 Solve open-sentence equations. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP: Solve open-sentence equations KEY: Equations | Solve Equations
12. ANS: A
Replace the variable with each member of the replacement set. All values from the replacement set that make the inequality true are solutions.
| |Feedback |
|A |Correct! |
|B |Check all replacements again. |
|C |Do you have all the solutions in the replacement set? |
|D |Do you have too many solutions? |
PTS: 1 DIF: Basic REF: Lesson 1-5
OBJ: 1-5.2 Solve open-sentence inequalities. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2
TOP: Solve open-sentence inequalities KEY: Inequalities | Solve Inequalities
13. ANS: A
Replace the variable with each member of the replacement set. All values from the replacement set that make the inequality true are solutions.
| |Feedback |
|A |Correct! |
|B |Check all replacements again. |
|C |Make sure you check each member from the replacement set. |
|D |Did you check all replacements carefully? |
PTS: 1 DIF: Average REF: Lesson 1-5
OBJ: 1-5.2 Solve open-sentence inequalities. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2
TOP: Solve open-sentence inequalities KEY: Inequalities | Solve Inequalities
14. ANS: A
A relation is a set of ordered pairs. A relation can also be represented by a table, a graph, or a mapping.
| |Feedback |
|A |Correct! |
|B |Are you sure about the mapping? |
|C |Did you plot the points correctly? |
|D |Check the mapping again. |
PTS: 1 DIF: Average REF: Lesson 1-6
OBJ: 1-6.1 Represent relations of sets of ordered pairs, tables, mappings, and graphs.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Represent relations as sets of ordered pairs, tables, mappings, and graphs
KEY: Relations | Ordered Pairs | Tables | Mappings | Graphs
15. ANS: B
A relation is a set of ordered pairs. A relation can also be represented by a table, a graph, or a mapping.
| |Feedback |
|A |Are you sure about the domain? |
|B |Correct! |
|C |Did you plot the points correctly? |
|D |Are you sure about the mapping? |
PTS: 1 DIF: Average REF: Lesson 1-6
OBJ: 1-6.1 Represent relations of sets of ordered pairs, tables, mappings, and graphs.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Represent relations as sets of ordered pairs, tables, mappings, and graphs
KEY: Relations | Ordered Pairs | Tables | Mappings | Graphs
16. ANS: C
A relation is a set of ordered pairs. A relation can also be represented by a table, a graph, or a mapping.
| |Feedback |
|A |Did you plot all the points correctly? |
|B |Check your table again. |
|C |Correct! |
|D |Are you sure about the domain and range? |
PTS: 1 DIF: Average REF: Lesson 1-6
OBJ: 1-6.1 Represent relations of sets of ordered pairs, tables, mappings, and graphs.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Represent relations as sets of ordered pairs, tables, mappings, and graphs
KEY: Relations | Ordered Pairs | Tables | Mappings | Graphs
17. ANS: A
The ball leaves the pitcher with an initial speed which goes to zero when struck by the bat and then increases rapidly and then slows down.
| |Feedback |
|A |Correct! |
|B |Does the ball leave the pitcher with zero speed? |
|C |Does the ball change direction without stopping? |
|D |Does the ball change speed when it is hit? |
PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.2 Interpret graphs of relations.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7 TOP: Interpret graphs of functions
KEY: Interpret Graphs | Functions
18. ANS: A
The plane increases altitude steadily and levels off. The skydiver jump and descends rapidly at first, then opens his chute and slows as he drifts to the ground.
| |Feedback |
|A |Correct! |
|B |Does the plane go high enough? Does he fall straight down? |
|C |Was the plane already at high altitude? |
|D |Did he go up after he jumped? |
PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.2 Interpret graphs of relations.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7 TOP: Interpret graphs of functions
KEY: Interpret Graphs | Functions
19. ANS: B
The water level slowly and steadily decreases to zero.
| |Feedback |
|A |Does the water get deeper? |
|B |Correct! |
|C |Does the water level rise after it begins to drain? |
|D |Does the water level stay constant for a while and then drop to zero? |
PTS: 1 DIF: Basic REF: Lesson 1-6 OBJ: 1-6.2 Interpret graphs of relations.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7 TOP: Interpret graphs of functions
KEY: Interpret Graphs | Functions
20. ANS: D
The height of the ball decreases as the ball falls. It hits the floor and bounces up and down until the height stays at zero.
| |Feedback |
|A |Does the ball go up before it falls? |
|B |Does the ball bounce? |
|C |Was the ball thrown upward? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.2 Interpret graphs of relations.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7 TOP: Interpret graphs of functions
KEY: Interpret Graphs | Functions
21. ANS: A
The snow accumulates slowly for a while. The accumulation stops for a while, and then accumulates faster as it snows harder. As the snow stops, the accumulation levels off.
| |Feedback |
|A |Correct! |
|B |Was there only one period of snow accumulation? |
|C |Was the snow steady for the entire period? |
|D |Did melting occur during the period? |
PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.2 Interpret graphs of relations.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7 TOP: Interpret graphs of functions
KEY: Interpret Graphs | Functions
22. ANS: D
In the table, number of sales depends on the day of the first seven days of October. Therefore, Day is the independent variable and Sales is the dependent variable.
| |Feedback |
|A |Does the day depend on the number of sales? |
|B |Does the table involve a salesman? |
|C |Are days of the week mentioned in the table? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.3 Draw graphs of relations.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2 TOP: Draw graphs of functions
KEY: Graphs | Functions
23. ANS: A
An ordered pair is a set of numbers, or coordinates, written in the form (x, y).
| |Feedback |
|A |Correct! |
|B |Were you suppose to round the decimals? |
|C |Which variable is the independent variable? |
|D |Did you list all of the ordered pairs? |
PTS: 1 DIF: Basic REF: Lesson 1-6 OBJ: 1-6.3 Draw graphs of relations.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2 TOP: Draw graphs of functions
KEY: Graphs | Functions
24. ANS: B
Use the table to find the relationship between the independent and dependent variables. Use this relationship to find the cost for one year.
| |Feedback |
|A |How many months are in one year? |
|B |Correct! |
|C |How many months did you use? |
|D |Did you multiply correctly? |
PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.3 Draw graphs of relations.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2 TOP: Draw graphs of functions
KEY: Graphs | Functions
25. ANS: B
A function is a relation in which each element of the domain is paired with exactly one element of the range.
| |Feedback |
|A |How many elements of the range are paired with 3? |
|B |Correct! |
|C |Is there exactly one element of the range paired with each element of the domain? |
|D |How many range elements are paired with –5? |
PTS: 1 DIF: Basic REF: Lesson 1-7
OBJ: 1-7.1 Describe whether a relation is a function. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Determine whether a relation is a function KEY: Relations | Functions
26. ANS: A
A function is a relation in which each element of the domain is paired with exactly one element of the range.
| |Feedback |
|A |Correct! |
|B |Is there exactly one range element paired with each element of the domain? |
|C |How many range elements are paired with 5? |
|D |Did you look at the domain carefully? |
PTS: 1 DIF: Basic REF: Lesson 1-7
OBJ: 1-7.1 Describe whether a relation is a function. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Determine whether a relation is a function KEY: Relations | Functions
27. ANS: C
A function is a relation in which each element of the domain is paired with exactly one element of the range.
| |Feedback |
|A |Is there only one range element paired with each element of the domain? |
|B |How many range elements are paired with x = –2? |
|C |Correct! |
|D |What range elements are paired with x = 0? |
PTS: 1 DIF: Basic REF: Lesson 1-7
OBJ: 1-7.1 Describe whether a relation is a function. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Determine whether a relation is a function KEY: Relations | Functions
28. ANS: D
A function is a relation in which each element of the domain is paired with exactly one element of the range.
| |Feedback |
|A |Is there only one range element paired with each element of the domain? |
|B |How many range elements are paired with x = 5? |
|C |What range elements are paired with x = –5? |
|D |Correct! |
PTS: 1 DIF: Basic REF: Lesson 1-7
OBJ: 1-7.1 Describe whether a relation is a function. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Determine whether a relation is a function KEY: Relations | Functions
29. ANS: A
A function is a relation in which each element of the domain is paired with exactly one element of the range.
| |Feedback |
|A |Correct! |
|B |How many range elements are paired with x = 1? |
|C |Did you try the vertical line test? |
|D |Does the graph pass the vertical line test? |
PTS: 1 DIF: Basic REF: Lesson 1-7
OBJ: 1-7.1 Describe whether a relation is a function. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Determine whether a relation is a function KEY: Relations | Functions
30. ANS: A
The hypothesis is the part of the conditional following the word if, and the conclusion is the part of the conditional following the word then.
| |Feedback |
|A |Correct! |
|B |Can he only go swimming on days that he mows? |
|C |Does the statement involve chores? |
|D |Does the statement involve playing tennis? |
PTS: 1 DIF: Average REF: Lesson 1-8
OBJ: 1-8.1 Identify the hypothesis and conclusion in a conditional statement.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Identify the hypothesis and conclusion in a conditional statement
KEY: Conditional Statements | Hypothesis | Conclusion
31. ANS: B
A counterexample is a specific case in which a statement is false. It takes only one counterexample to show that a statement is false.
| |Feedback |
|A |Are the hypothesis and conclusion both true? |
|B |Correct! |
|C |Is the hypothesis true? |
|D |Is the hypothesis true? |
PTS: 1 DIF: Average REF: Lesson 1-8
OBJ: 1-8.2 Use a counterexample to show that an assertion is false.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7
TOP: Use a counterexample to show that an assertion is false
KEY: Counterexample | Deductive Reasoning
32. ANS: A
A counterexample is a specific case in which a statement is false. It takes only one counterexample to show that a statement is false.
| |Feedback |
|A |Correct! |
|B |Are the hypothesis and conclusion both true? |
|C |Is the hypothesis true? |
|D |Is the hypothesis true? |
PTS: 1 DIF: Average REF: Lesson 1-8
OBJ: 1-8.2 Use a counterexample to show that an assertion is false.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7
TOP: Use a counterexample to show that an assertion is false
KEY: Counterexample | Deductive Reasoning
33. ANS: A
A counterexample is a specific case in which a statement is false. It takes only one counterexample to show that a statement is false.
| |Feedback |
|A |Correct! |
|B |Are the hypothesis and conclusion both true? |
|C |Is the hypothesis true? |
|D |Is the hypothesis true? |
PTS: 1 DIF: Average REF: Lesson 1-8
OBJ: 1-8.2 Use a counterexample to show that an assertion is false.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7
TOP: Use a counterexample to show that an assertion is false
KEY: Counterexample | Deductive Reasoning
34. ANS: C
A counterexample is a specific case in which a statement is false. It takes only one counterexample to show that a statement is false.
| |Feedback |
|A |Are the hypothesis and conclusion both true? |
|B |Are the hypothesis and conclusion both true? |
|C |Correct! |
|D |Is the hypothesis true? |
PTS: 1 DIF: Average REF: Lesson 1-8
OBJ: 1-8.2 Use a counterexample to show that an assertion is false.
NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7
TOP: Use a counterexample to show that an assertion is false
KEY: Counterexample | Deductive Reasoning
35. ANS: A
Translate verbal sentences into equations by using key words and phrases you have learned to replace words with symbols.
| |Feedback |
|A |Correct! |
|B |What does increased by translate to in an equation? |
|C |Does increased by indicate multiplication? |
|D |Should you have divided? |
PTS: 1 DIF: Basic REF: Lesson 2-1
OBJ: 2-1.1 Translate verbal sentences into equations. NAT: NA 6
TOP: Translate verbal sentences into equations KEY: Verbal Sentences | Equations
36. ANS: B
Translate verbal sentences into equations by using key words and phrases you have learned to replace words with symbols.
| |Feedback |
|A |Is addition indicated by the sentence? |
|B |Correct! |
|C |What is being subtracted? |
|D |Are the parentheses needed? |
PTS: 1 DIF: Basic REF: Lesson 2-1
OBJ: 2-1.1 Translate verbal sentences into equations. NAT: NA 6
TOP: Translate verbal sentences into equations KEY: Verbal Sentences | Equations
37. ANS: D
Translate verbal sentences into equations by using key words and phrases you have learned to replace words with symbols.
| |Feedback |
|A |How do you translate increased by? |
|B |Be careful with the order of the subtraction. |
|C |Are the parentheses indicated by the sentence? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-1
OBJ: 2-1.1 Translate verbal sentences into equations. NAT: NA 6
TOP: Translate verbal sentences into equations KEY: Verbal Sentences | Equations
38. ANS: A
Using key words for operations, translate the equation into a number sentence.
| |Feedback |
|A |Correct! |
|B |Is there addition in the equation? |
|C |Is there division in the equation? |
|D |Carefully look at the equation again. |
PTS: 1 DIF: Basic REF: Lesson 2-1
OBJ: 2-1.2 Translate equations into verbal sentences. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Translate equations into verbal sentences KEY: Equations | Verbal Sentences
39. ANS: A
Using key words for operations, translate the equation into a number sentence.
| |Feedback |
|A |Correct! |
|B |What is meant by decreased by? |
|C |Are you sure about the right side of the equation? |
|D |What did you translate as the quotient? |
PTS: 1 DIF: Average REF: Lesson 2-1
OBJ: 2-1.2 Translate equations into verbal sentences. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Translate equations into verbal sentences KEY: Equations | Verbal Sentences
40. ANS: D
Using key words for operations, translate the equation into a number sentence.
| |Feedback |
|A |Is there addition in the equation? |
|B |Check the left side of the equation again. |
|C |What is meant by increased by? |
|D |Correct! |
PTS: 1 DIF: Basic REF: Lesson 2-1
OBJ: 2-1.2 Translate equations into verbal sentences. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Translate equations into verbal sentences KEY: Equations | Verbal Sentences
41. ANS: B
Using key words for operations, translate the equation into a number sentence.
| |Feedback |
|A |What did you translate as the difference? |
|B |Correct! |
|C |Are there three additions in the equation? |
|D |Are there two products in the equation? |
PTS: 1 DIF: Basic REF: Lesson 2-1
OBJ: 2-1.2 Translate equations into verbal sentences. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Translate equations into verbal sentences KEY: Equations | Verbal Sentences
42. ANS: B
To solve an equation means to find all the values of the variable that make the equation a true statement. One way to do this is to isolate the variable on one side of the equation. You can sometimes do this by adding the same number to both sides of the equation.
| |Feedback |
|A |Be careful with sign rules. |
|B |Correct! |
|C |How do you add fractions? |
|D |What did you add to both sides? |
PTS: 1 DIF: Average REF: Lesson 2-2
OBJ: 2-2.2 Solve equations with fractions by using addition. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with fractions by using addition
KEY: Solve Equations | Addition | Fractions
43. ANS: A
To solve an equation means to find all the values of the variable that make the equation a true statement. One way to do this is to isolate the variable on one side of the equation. You can sometimes do this by adding the same number to both sides of the equation.
| |Feedback |
|A |Correct! |
|B |What did you add to both sides? |
|C |How do you add fractions? |
|D |Be careful with sign rules. |
PTS: 1 DIF: Average REF: Lesson 2-2
OBJ: 2-2.2 Solve equations with fractions by using addition. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with fractions by using addition
KEY: Solve Equations | Addition | Fractions
44. ANS: B
To solve an equation means to find all the values of the variable that make the equation a true statement. One way to do this is to isolate the variable on one side of the equation. You can sometimes do this by subtracting the same number from both sides of the equation.
| |Feedback |
|A |Be careful with sign rules. |
|B |Correct! |
|C |Did you subtract a number from both sides? |
|D |Did you perform the subtraction correctly? |
PTS: 1 DIF: Basic REF: Lesson 2-2
OBJ: 2-2.4 Solve equations with integers by using subtraction. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with integers by using subtraction
KEY: Solve Equations | Subtraction | Integers
45. ANS: C
To solve an equation means to find all the values of the variable that make the equation a true statement. One way to do this is to isolate the variable on one side of the equation. You can sometimes do this by subtracting the same number from both sides of the equation.
| |Feedback |
|A |Did you subtract a number from both sides? |
|B |Did you perform the subtraction correctly? |
|C |Correct! |
|D |Be careful with sign rules. |
PTS: 1 DIF: Basic REF: Lesson 2-2
OBJ: 2-2.4 Solve equations with integers by using subtraction. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with integers by using subtraction
KEY: Solve Equations | Subtraction | Integers
46. ANS: D
To solve an equation means to find all the values of the variable that make the equation a true statement. One way to do this is to isolate the variable on one side of the equation. You can sometimes do this by subtracting the same number from both sides of the equation.
| |Feedback |
|A |Be careful with sign rules. |
|B |How do you subtract fractions? |
|C |What did you subtract from both sides? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-2
OBJ: 2-2.5 Solve equations with fractions by using subtraction.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with fractions by using subtraction
KEY: Solve Equations | Subtraction | Fractions
47. ANS: B
If an equation is true and each side is multiplied by the same number, the resulting equation is true.
| |Feedback |
|A |What did you multiply both sides by? |
|B |Correct! |
|C |Did you isolate the variable? |
|D |Did you multiply both sides by the correct number? |
PTS: 1 DIF: Average REF: Lesson 2-2
OBJ: 2-2.7 Solve equations with integers by using multiplication.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with integers by using multiplication
KEY: Solve Equations | Multiplication | Integers
48. ANS: B
If an equation is true and each side is multiplied or divided by the same number, the resulting equation is true.
| |Feedback |
|A |Did you add a number to both sides? |
|B |Correct! |
|C |Do you undo multiplication by subtracting? |
|D |How do you undo multiplication? |
PTS: 1 DIF: Basic REF: Lesson 2-2
OBJ: 2-2.11 Solve equations with decimals using multiplication and division.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with decimals by using multiplication and division
KEY: Solve Equations | Multiplication | Division | Decimals
49. ANS: C
First translate the verbal sentences into equations by using key words and phrases you have learned to replace words with symbols. Then to solve an equation with more than one operation, undo operations by working backward.
| |Feedback |
|A |Carefully read the sentence again. |
|B |Did you isolate the variable? |
|C |Correct! |
|D |Is subtraction indicated by the sentence? |
PTS: 1 DIF: Basic REF: Lesson 2-3
OBJ: 2-3.2 Solve consecutive integer problems. NAT: NA 1 | NA 2 | NA 6 | NA 8
TOP: Solve consecutive integer problems. KEY: Solve equations | Integers
50. ANS: C
First translate the verbal sentences into equations by using key words and phrases you have learned to replace words with symbols. Then to solve an equation with more than one operation, undo operations by working backward.
| |Feedback |
|A |Did you do the correct operation? |
|B |Are these consecutive integers? |
|C |Correct! |
|D |Did you isolate the variable? |
PTS: 1 DIF: Average REF: Lesson 2-3
OBJ: 2-3.2 Solve consecutive integer problems. NAT: NA 1 | NA 2 | NA 6 | NA 8
TOP: Solve consecutive integer problems. KEY: Solve equations | Integers
51. ANS: D
First translate the verbal sentences into equations by using key words and phrases you have learned to replace words with symbols. Then to solve an equation with more than one operation, undo operations by working backward.
| |Feedback |
|A |Did you do the correct operation? |
|B |Are these consecutive odd integers? |
|C |Check your calculation again. |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-3
OBJ: 2-3.2 Solve consecutive integer problems. NAT: NA 1 | NA 2 | NA 6 | NA 8
TOP: Solve consecutive integer problems. KEY: Solve equations | Integers
52. ANS: C
To solve equations with variables on each side, first use the Addition or Subtraction Property of Equality to write an equivalent equation that has all of the variables on one side. Simplify both sides of the equation, and use the Multiplication or Division Property of Equality to solve for the variable.
| |Feedback |
|A |Be careful with sign rules. |
|B |Be careful with sign rules. |
|C |Correct! |
|D |Which property did you use first? |
PTS: 1 DIF: Average REF: Lesson 2-4
OBJ: 2-4.1 Solve equations with integers with the variable on each side.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with integers with the variable on each side
KEY: Solve Equations | Variables | Integers
53. ANS: A
To solve equations with variables on each side, first use the Addition or Subtraction Property of Equality to write an equivalent equation that has all of the variables on one side. Simplify both sides of the equation, and use the Multiplication or Division Property of Equality to solve for the variable.
| |Feedback |
|A |Correct! |
|B |Be careful with sign rules. |
|C |Did you combine the variable fractions correctly? |
|D |Did you use the Addition or Subtraction Property correctly? |
PTS: 1 DIF: Average REF: Lesson 2-4
OBJ: 2-4.2 Solve equations with fractions with the variable on each side.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with fractions with the variable on each side
KEY: Solve Equations | Variables | Fractions
54. ANS: B
To solve equations with variables on each side, first use the Addition or Subtraction Property of Equality to write an equivalent equation that has all of the variables on one side. Simplify both sides of the equation, and use the Multiplication or Division Property of Equality to solve for the variable.
| |Feedback |
|A |Did you use the Addition or Subtraction Property correctly? |
|B |Correct! |
|C |Did you combine the variable fractions correctly? |
|D |Be careful with sign rules. |
PTS: 1 DIF: Average REF: Lesson 2-4
OBJ: 2-4.2 Solve equations with fractions with the variable on each side.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve equations with fractions with the variable on each side
KEY: Solve Equations | Variables | Fractions
55. ANS: B
Set f(x) = 0 and solve for x to find the minimum value. Then choose values for x that are greater and less than the minimum value to make a table of (x, y) values.
| |Feedback |
|A |Did you solve the equation [pic] to find the x-coordinate of the minimum point? |
|B |Correct! |
|C |Did you solve the equation [pic] to find the x-coordinate of the minimum point? |
|D |Did you solve the equation [pic] to find the x-coordinate of the minimum point? |
PTS: 1 DIF: Average REF: Lesson 2-5
OBJ: 2-5.2 Graph absolute value functions. NAT: NA 2 | NA 8
TOP: Graph absolute value functions. KEY: Absolute Value | Graphs
56. ANS: B
If the cross products are equal, the ratios are equal and form a proportion.
| |Feedback |
|A |Are the cross products the same? |
|B |Correct! |
|C |Did you multiply carefully? |
|D |Are the cross products the same? |
PTS: 1 DIF: Average REF: Lesson 2-6
OBJ: 2-6.1 Determine whether two ratios form a proportion. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Determine whether two ratios form a proportion KEY: Ratios | Proportions
57. ANS: C
To solve a proportion containing a variable, use cross products and other techniques to solve the equation.
| |Feedback |
|A |Did you multiply correctly? |
|B |How do you solve a proportion? |
|C |Correct! |
|D |Did you find the cross product correctly? |
PTS: 1 DIF: Average REF: Lesson 2-6 OBJ: 2-6.2 Solve proportions.
NAT: NA 1 | NA 3 | NA 8 | NA 9 | NA 2 TOP: Solve proportions
KEY: Proportions | Solve Proportions
58. ANS: A
First find the amount of change. Then find the percent of change by using the original number as the base.
| |Feedback |
|A |Correct! |
|B |Did you use the original number as the base? |
|C |Which is the greater number, the new or the original? |
|D |Which number is greater? |
PTS: 1 DIF: Average REF: Lesson 2-7
OBJ: 2-7.1 Find percents of increase and decrease. NAT: NA 2 | NA 6 | NA 8 | NA 9 | NA 3
TOP: Find percents of increase and decrease
KEY: Percent of Increase | Percent of Decrease
59. ANS: D
Find the amount of discount by multiplying the discount rate converted to a decimal. Subtract the amount of discount from the original price. Compute the tax on the discounted price.
| |Feedback |
|A |Did you forget to add the tax? |
|B |Did you subtract the tax? |
|C |Did you mix up the discount and the tax? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-7
OBJ: 2-7.2 Solve problems involving percents of change. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve problems involving percents of change KEY: Percent of Change | Solve Problems
60. ANS: B
Find the amount of discount by multiplying the discount rate converted to a decimal. Subtract the amount of discount from the original price. Compute the tax on the discounted price.
| |Feedback |
|A |Did you forget to subtract the tax? |
|B |Correct! |
|C |Did you subtract the tax? |
|D |Did you forget the discount? |
PTS: 1 DIF: Average REF: Lesson 2-7
OBJ: 2-7.2 Solve problems involving percents of change. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve problems involving percents of change KEY: Percent of Change | Solve Problems
61. ANS: D
Solve the formula for w. Then evaluate using the given values for P and [pic].
| |Feedback |
|A |Do you measure width in square units? |
|B |Did you divide by 2? |
|C |What is the formula for the width of the rectangle? |
|D |Correct! |
PTS: 1 DIF: Basic REF: Lesson 2-8
OBJ: 2-8.2 Use formulas to solve real-world problems. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Use formulas to solve real-world problems KEY: Formulas | Real-World Problems
62. ANS: D
Solve the formula for the specified variable using the properties of equality.
| |Feedback |
|A |Did you divide both sides of the equation by the same number? |
|B |Should you have added to both sides? |
|C |Did you do the division property correctly? |
|D |Correct! |
PTS: 1 DIF: Basic REF: Lesson 2-8
OBJ: 2-8.2 Use formulas to solve real-world problems. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Use formulas to solve real-world problems KEY: Formulas | Real-World Problems
63. ANS: A
Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using the given information.
| |Feedback |
|A |Correct! |
|B |How fast were the trains traveling? |
|C |Did the eastbound train travel longer? |
|D |Were the trains traveling at the same rate of speed? |
PTS: 1 DIF: Average REF: Lesson 2-9
OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems
64. ANS: D
Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using the given information.
| |Feedback |
|A |How fast was Kenji traveling? |
|B |Did Kenji travel for a longer period of time? |
|C |Did Kenji travel for a longer period of time? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-9
OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems
65. ANS: A
Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using the given information. The sum of the distances the two men travel is equal to the total distance.
| |Feedback |
|A |Correct! |
|B |Does the left side of the equation equal the total distance traveled? |
|C |Does the right side of the equation equal the total distance traveled? |
|D |Does the left side of the equation equal the total distance traveled? |
PTS: 1 DIF: Average REF: Lesson 2-9
OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems
66. ANS: D
Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using the given information. The sum of the distances the two men travel is equal to the total distance. Solve the equation for t.
| |Feedback |
|A |Did you subtract the distances of each man? |
|B |Did they travel at the same rate of speed? |
|C |What was the total distance traveled? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-9
OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems
67. ANS: D
Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using the given information.
| |Feedback |
|A |How fast were the planes traveling? |
|B |Did the westbound plane leave earlier? |
|C |Did the westbound plane leave earlier? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-9
OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems
68. ANS: D
Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using the given information. The sum of the distances the two bicycles travel is equal to the total distance. Solve the equation for t.
| |Feedback |
|A |Did you subtract the distances of each cyclist? |
|B |Did you use the Division Property of Equality correctly? |
|C |Did both cyclists travel at 10 miles per hour? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 2-9
OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems
69. ANS: A
Complete the table with expressions for price per pound and total price.
| |Feedback |
|A |Correct! |
|B |Are you sure about the price per pound? |
|C |Are the total prices correct? |
|D |Be careful placing the values into the table. |
PTS: 1 DIF: Average REF: Lesson 2-9 OBJ: 2-9.2 Solve mixture problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve mixture problems
KEY: Mixture Problems | Solve Problems
70. ANS: D
Complete the table and use the values in the total price column to write the equation for total price.
| |Feedback |
|A |Did they sell more cashews than peanuts? |
|B |Does your equation represent a total price? |
|C |What is the price per pound of peanuts? |
|D |Correct |
PTS: 1 DIF: Average REF: Lesson 2-9 OBJ: 2-9.2 Solve mixture problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve mixture problems
KEY: Mixture Problems | Solve Problems
71. ANS: B
Complete the table with expressions for price per pound, total price, and mixture. Use the total price column to write an equation for the problem.
| |Feedback |
|A |Should you subtract the price of the Brazilian Coffee? |
|B |Correct! |
|C |What is to be the price of the mixture? |
|D |How many pounds of Columbian Coffee is to be in the mixture? |
PTS: 1 DIF: Average REF: Lesson 2-9 OBJ: 2-9.2 Solve mixture problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve mixture problems
KEY: Mixture Problems | Solve Problems
72. ANS: B
Complete the table with expressions for price per pound, total price, and mixture.
| |Feedback |
|A |Do the number of pounds of beef and lamb equal the number of pounds of the mixture? |
|B |Correct! |
|C |What is the price per pound of the beef-based food? |
|D |What is the weight of the mixture? |
PTS: 1 DIF: Average REF: Lesson 2-9 OBJ: 2-9.2 Solve mixture problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve mixture problems
KEY: Mixture Problems | Solve Problems
73. ANS: C
A solution of an equation in two variables is an ordered pair that results in a true statement when substituted into the equation. You can graph the ordered pairs in the solution set for an equation in two variables.
| |Feedback |
|A |Are all the ordered pairs correct? |
|B |Are all the ordered pairs correct? |
|C |Correct! |
|D |Did you plot all points correctly? |
PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.2 Graph linear equations.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Graph the solution set for a given domain KEY: Domain | Graph Solutions
74. ANS: D
A solution of an equation in two variables is an ordered pair that results in a true statement when substituted into the equation. You can graph the ordered pairs in the solution set for an equation in two variables.
| |Feedback |
|A |Did you plot all points correctly? |
|B |Are all the ordered pairs correct? |
|C |Are all the ordered pairs correct? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.2 Graph linear equations.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Graph the solution set for a given domain KEY: Domain | Graph Solutions
75. ANS: B PTS: 1 DIF: Basic REF: Lesson 3-2
OBJ: 3-2.1 Solve equations. TOP: Solve linear equations by graphing.
KEY: linear function
76. ANS: D PTS: 1 DIF: Basic REF: Lesson 3-2
OBJ: 3-2.1 Solve equations. TOP: Solve linear equations by graphing.
KEY: linear function
77. ANS: B
The slope m of a nonvertical line through any two points, is the ratio of the difference of the y-coordinates to the difference of the x-coordinates. A vertical line has an undefined slope.
| |Feedback |
|A |Is that the rise over the run? |
|B |Correct! |
|C |Is that a positive number? |
|D |Is the board vertical? |
PTS: 1 DIF: Basic REF: Lesson 3-3
OBJ: 3-3.1 Use rate of change to solve problems. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3
TOP: Use rate of change to solve problems KEY: Rate of Change | Solve Problems
78. ANS: C
The slope m of a nonvertical line through any two points is the ratio of the difference of the y-coordinates to the difference of the x-coordinates. A vertical line has an undefined slope.
| |Feedback |
|A |Is the belt vertical? |
|B |Is that the run over the rise? |
|C |Correct! |
|D |Is the belt horizontal? |
PTS: 1 DIF: Basic REF: Lesson 3-3
OBJ: 3-3.1 Use rate of change to solve problems. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3
TOP: Use rate of change to solve problems KEY: Rate of Change | Solve Problems
79. ANS: A
Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity is changing over time.
| |Feedback |
|A |Correct! |
|B |What is the difference in rainfall amounts for that period? |
|C |Is that the largest rate of change? |
|D |What is the rate of change for that period? |
PTS: 1 DIF: Average REF: Lesson 3-3
OBJ: 3-3.1 Use rate of change to solve problems. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3
TOP: Use rate of change to solve problems KEY: Rate of Change | Solve Problems
80. ANS: A
Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity is changing over time. Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity is changing over time.
| |Feedback |
|A |Correct! |
|B |What is the rate of change over that period. |
|C |Is that the period with the steepest slope? |
|D |Can you determine the rate of change over that period of time? |
PTS: 1 DIF: Average REF: Lesson 3-3
OBJ: 3-3.1 Use rate of change to solve problems. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3
TOP: Use rate of change to solve problems KEY: Rate of Change | Solve Problems
81. ANS: B
Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity is changing over time. Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity is changing over time.
| |Feedback |
|A |What is the rate of change over that period? |
|B |Correct! |
|C |Is that the period with the smallest slope? |
|D |Can you determine the rate of change over that period of time? |
PTS: 1 DIF: Average REF: Lesson 3-3
OBJ: 3-3.1 Use rate of change to solve problems. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3
TOP: Use rate of change to solve problems KEY: Rate of Change | Solve Problems
82. ANS: C
A direct variation is described by an equation of the form y = kx, where k [pic] 0. We say that y varies directly with x or y varies directly as x. In the equation y = kx, k is the constant of variation.
| |Feedback |
|A |Be careful with sign rules. |
|B |Are you sure about the solution to the equation? |
|C |Correct! |
|D |Does that equation work for the given values? |
PTS: 1 DIF: Basic REF: Lesson 3-4
OBJ: 3-4.1 Write and graph direct variation equations. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3
TOP: Write and graph direct variation equations
KEY: Direct Variation | Graphs | Equations
83. ANS: C
Direct variation equations are of the form y = kx, where k [pic] 0. The graph of y = kx always passes through the origin.
| |Feedback |
|A |Does the graph match the equation? |
|B |Which variable is the independent variable? |
|C |Correct! |
|D |Do points on the graph make the equation true? |
PTS: 1 DIF: Average REF: Lesson 3-4
OBJ: 3-4.2 Solve problems involving direct variation. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Solve problems involving direct variation KEY: Direct Variation | Solve Problems
84. ANS: B
Direct variation equations are of the form y = kx, where k [pic] 0. The graph of y = kx always passes through the origin.
| |Feedback |
|A |Which variable is the independent variable? |
|B |Correct! |
|C |Do the equation and graph match? |
|D |Do points on the graph make the equation true? |
PTS: 1 DIF: Average REF: Lesson 3-4
OBJ: 3-4.2 Solve problems involving direct variation. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Solve problems involving direct variation KEY: Direct Variation | Solve Problems
85. ANS: D
Direct variation equations are of the form y = kx, where k [pic] 0. The graph of y = kx always passes through the origin.
| |Feedback |
|A |Does the graph match the equation? |
|B |Which variable is the independent variable? |
|C |Do points on the graph make the equation true? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 3-4
OBJ: 3-4.2 Solve problems involving direct variation. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Solve problems involving direct variation KEY: Direct Variation | Solve Problems
86. ANS: B
Direct variation equations are of the form y = kx, where k [pic] 0. The graph of y = kx always passes through the origin.
| |Feedback |
|A |Which variable is the independent variable? |
|B |Correct! |
|C |Do points on the graph make the equation true? |
|D |What was Luis' rate of speed? |
PTS: 1 DIF: Average REF: Lesson 3-4
OBJ: 3-4.2 Solve problems involving direct variation. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Solve problems involving direct variation KEY: Direct Variation | Solve Problems
87. ANS: A
Find the difference of the values for t and d. Use the relationship between them to write an equation.
| |Feedback |
|A |Correct! |
|B |Check the operator. |
|C |Check your answer. |
|D |Look at the hint and try again! |
PTS: 1 DIF: Basic REF: Lesson 3-6
OBJ: 3-6.1 Write an equation for a proportional or nonproportional relationship.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Write an equation for a proportional or nonproportional relationship.
KEY: Equations | Analyzing Data
88. ANS: C
The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the y-intercept.
| |Feedback |
|A |What is the slope? |
|B |What is the y-intercept? |
|C |Correct! |
|D |What is the slope of the line? |
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.1 Write and graph linear equations in slope-intercept form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Write and graph linear equations in slope-intercept form
KEY: Slope-Intercept Form | Linear Equations | Graphs
89. ANS: A
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The y-intercept represents a starting point, and the slope represents the rate of change.
| |Feedback |
|A |Correct! |
|B |What was the original length of the icicle? |
|C |What is the rate of change? |
|D |Which variable is the independent variable? |
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
90. ANS: B
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The y-intercept represents a starting point, and the slope represents the rate of change.
| |Feedback |
|A |What is the starting temperature? |
|B |Correct! |
|C |Is the temperature decreasing? |
|D |Which variable is the independent variable? |
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
91. ANS: A
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The y-intercept represents a starting point, and the slope represents the rate of change.
| |Feedback |
|A |Correct! |
|B |What is the y-intercept? |
|C |Does the number of sections standing decrease each Saturday? |
|D |What is the slope of the line? |
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
92. ANS: B
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the calculated b.
| |Feedback |
|A |What is the y-intercept? |
|B |Correct! |
|C |Is the slope positive or negative? |
|D |How did you find the y-intercept? |
PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.2 Write an equation of a line given two points on the line.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Write an equation of a line given two points on the line KEY: Slope | Lines | Equations
93. ANS: B
Solve the equation for y. Use Addition and Subtraction Properties of Equality to rewrite the equation in standard form.
| |Feedback |
|A |Did you use the correct property of equality? |
|B |Correct! |
|C |Is that standard form? |
|D |How did you determine the sign of the y-term? |
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Write linear equations in standard form. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Write linear equations in standard form KEY: Standard Form | Linear Equations
94. ANS: A
Two nonvertical lines are parallel if they have the same slope. Use the given point with the slope of the parallel line in the point-slope form. Then change to the slope-intercept form.
| |Feedback |
|A |Correct! |
|B |Be careful with signs when adding to or subtracting from both sides of the equation. |
|C |Did you add or subtract carefully? Should the slope be the same as the slope of the parallel line? |
|D |What is the slope of the parallel line? |
PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.1 Write an equation of the line that passes through a given point, parallel to a given line.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Write an equation of the line that passes through a given point, parallel to a given line
KEY: Lines | Equations | Parallel
95. ANS: C
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. There is a positive correlation when as x increases, y increases. There is a negative correlation when as x increases, y decreases. There is no correlation when x and y are not related.
| |Feedback |
|A |What is meant by negative correlation? |
|B |Does the amount of fine decrease with the number of videos rented? |
|C |Correct! |
|D |What is meant by positive correlation? |
PTS: 1 DIF: Basic REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
96. ANS: B
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. There is a positive correlation when as x increases, y increases. There is a negative correlation when as x increases, y decreases. There is no correlation when x and y are not related.
| |Feedback |
|A |What is meant by positive correlation? |
|B |Correct! |
|C |Are the variables related? |
|D |Does the number of quarts picked increase over time? |
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
97. ANS: D
Write an equation for the line of fit. Substitute to find a prediction for 2005.
| |Feedback |
|A |Do you predict that the rate will remain unchanged from 2001? |
|B |Did you write an equation for the line of fit? |
|C |Do you predict the rate will increase from 2001? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
98. ANS: D
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation of the line using the slope and one of the points.
| |Feedback |
|A |How do you read that amount? |
|B |Do you expect the amount of spending to decrease? |
|C |Did you read the graph carefully? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
99. ANS: D
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation of the line using the slope and one of the points.
| |Feedback |
|A |Is the slope of the line of fit positive? |
|B |Which variable is the independent variable? |
|C |How did you determine the slope of the line? |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
100. ANS: A
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation of the line using the slope and one of the points.
| |Feedback |
|A |Correct! |
|B |Which variable is the independent variable? |
|C |Is the slope of the line of fit positive? |
|D |How did you determine the slope of the line? |
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
101. ANS: B
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation of the line using the slope and one of the points. Use the equation to make the prediction.
| |Feedback |
|A |What is the slope in your equation? |
|B |Correct! |
|C |Do you expect the number quarts to increase? |
|D |Did you evaluate the equation carefully? |
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
102. ANS: B PTS: 1 DIF: Basic REF: Lesson 4-6
OBJ: 4-6.1 Write equations of best-fit lines using linear regression.
TOP: Regression and median fit lines. KEY: linear regression | best-fit line
103. ANS: A PTS: 1 DIF: Basic REF: Lesson 4-6
OBJ: 4-6.1 Write equations of best-fit lines using linear regression.
TOP: Regression and median fit lines. KEY: linear regression | best-fit line
104. ANS: A PTS: 1 DIF: Basic REF: Lesson 4-7
OBJ: 4-7.1 Identify and graph absolute value functions. TOP: Special functions.
KEY: absolute value function
105. ANS: C PTS: 1 DIF: Basic REF: Lesson 4-7
OBJ: 4-7.1 Identify and graph absolute value functions. TOP: Special functions.
KEY: absolute value function
106. ANS: A
Solve the inequality by adding the constant on the right to both sides of the inequality.
| |Feedback |
|A |Correct! |
|B |Add to solve this inequality. |
|C |Add to solve this inequality. |
|D |Check the inequality sign. |
PTS: 1 DIF: Average REF: Lesson 5-1
OBJ: 5-1.1 Solve linear inequalities by using addition. NAT: NA 6
TOP: Solve linear inequalities by using addition KEY: Linear Inequalities | Addition
107. ANS: C
Solve the inequality by subtracting the constant term on the left side of the inequality from both sides of the inequality.
| |Feedback |
|A |Check the inequality sign. |
|B |Use subtraction to solve this inequality. |
|C |Correct! |
|D |Use subtraction to solve this inequality. |
PTS: 1 DIF: Average REF: Lesson 5-1
OBJ: 5-1.2 Solve linear inequalities by using subtraction. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve linear inequalities by using subtraction KEY: Linear Inequalities | Subtraction
108. ANS: C
Solve the inequality by subtracting the constant term on the right side of the inequality from both sides of the inequality.
| |Feedback |
|A |Check the inequality sign. |
|B |Use subtraction to solve this inequality. |
|C |Correct! |
|D |Use subtraction to solve this inequality and check the inequality sign. |
PTS: 1 DIF: Average REF: Lesson 5-1
OBJ: 5-1.2 Solve linear inequalities by using subtraction. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve linear inequalities by using subtraction KEY: Linear Inequalities | Subtraction
109. ANS: D
Divide both sides of the inequality by the constant on the left. Remember to flip the inequality sign since you are dividing by a negative number.
| |Feedback |
|A |Use division instead of subtraction to solve this. |
|B |Use division instead of multiplication to solve this. |
|C |Remember to flip the inequality sign since you are dividing by a negative number. |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 5-2
OBJ: 5-2.2 Solve linear inequalities by using division. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve linear inequalities by using division KEY: Linear Inequalities | Division
110. ANS: C
First combine the two variable terms on the left. Secondly, combine the constants by subtracting the constant term on the left from both sides. Next, divide both sides by the coefficient of the variable. Remember to flip the inequality sign since you are dividing by a negative number.
| |Feedback |
|A |You added instead of subtracting the constant on the left from both sides. |
|B |You must combine the two variable terms before dividing. |
|C |Correct! |
|D |You forgot to flip the inequality sign since you are dividing by a negative number. |
PTS: 1 DIF: Average REF: Lesson 5-3
OBJ: 5-3.1 Solve linear inequalities with integers involving more than one operation.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve linear inequalities with integers involving more than one operation
KEY: Linear Inequalities | Integers
111. ANS: B
Using the Distributive Property, multiply to eliminate the parentheses. Combine like terms and then solve the inequality for c.
| |Feedback |
|A |Double-check your calculations. |
|B |Correct! |
|C |Is this the correct inequality sign? |
|D |Double-check your calculations. Remember to multiply every term in the parentheses by the number in front of the |
| |parentheses. |
PTS: 1 DIF: Average REF: Lesson 5-3
OBJ: 5-3.5 Solve linear inequalities with decimals involving the Distributive Property.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve linear inequalities with decimals involving the Distributive Property
KEY: Linear Inequalities | Decimals | Distributive Property
112. ANS: C
Solve each of the inequalities for g. Graph the union on the number line using the lower value of g for the endpoint of the ray.
| |Feedback |
|A |Did you use the correct inequality sign? |
|B |This is the intersection of the two inequalities instead of the union. |
|C |Correct! |
|D |Did you graph the union of the two inequalities? |
PTS: 1 DIF: Basic REF: Lesson 5-4
OBJ: 5-4.2 Solve compound inequalities containing the word or and graph their solution sets.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Solve compound inequalities containing the word 'or' and graph their solution sets
KEY: Compound Inequalities | Graphs | Solution Set
113. ANS: D
Consider two cases: that the expression inside the absolute value symbol is positive, and that the expression inside the absolute value symbol is negative.
| |Feedback |
|A |Did you consider the case that the expression inside the absolute value symbol is positive? |
|B |Did you consider the case that the expression inside the absolute value symbol is negative? |
|C |Be careful with your greater than and less than symbols. |
|D |Correct! |
PTS: 1 DIF: Basic REF: Lesson 5-5
OBJ: 5-5.1 Solve absolute value inequalities. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Solve absolute value inequalities. KEY: Absolute Value | Inequalities
114. ANS: D
The difference between 75% humidity and the actual humidity is less than or equal 5%. Let x be the actual humidity level. Write an absolute value inequality and solve.
| |Feedback |
|A |Did you consider the case that the expression inside the absolute value symbol is positive? |
|B |Did you consider the case that the expression inside the absolute value symbol is negative? |
|C |Be careful with your greater than and less than symbols. |
|D |Correct! |
PTS: 1 DIF: Basic REF: Lesson 5-5
OBJ: 5-5.2 Apply absolute value inequalities in real-world problems.
NAT: NA 2 | NA 8 TOP: Apply absolute value inequalities in real-world problems.
KEY: Absolute Value | Inequalities | Real-World Problems
115. ANS: A
The difference between the height of the record jump and the height of John’s jump is less than or equal to 6 inches. Let x be the height of John’s jump. Write an absolute value inequality and solve.
| |Feedback |
|A |Correct! |
|B |Be careful with your greater than and less than symbols. |
|C |Did you consider the case that the expression inside the absolute value symbol is positive? |
|D |Did you consider the case that the expression inside the absolute value symbol is negative? |
PTS: 1 DIF: Basic REF: Lesson 5-5
OBJ: 5-5.2 Apply absolute value inequalities in real-world problems.
NAT: NA 2 | NA 8 TOP: Apply absolute value inequalities in real-world problems.
KEY: Absolute Value | Inequalities | Real-World Problems
116. ANS: C
The difference between the average score and the actual score is less than or equal to 6 points. Let x be the actual score. Write an absolute value inequality and solve.
| |Feedback |
|A |What are the minimum and maximum scores? |
|B |Be careful with your greater than and less than symbols. What are the minimum and maximum scores? |
|C |Correct! |
|D |Be careful with your greater than and less than symbols. |
PTS: 1 DIF: Basic REF: Lesson 5-5
OBJ: 5-5.2 Apply absolute value inequalities in real-world problems.
NAT: NA 2 | NA 8 TOP: Apply absolute value inequalities in real-world problems.
KEY: Absolute Value | Inequalities | Real-World Problems
117. ANS: D
Ben needs 8 notebooks or more, and he can spend a maximum of $5.00.
| |Feedback |
|A |He must have at least 8 notebooks¸ and can spend no more than $5.00. |
|B |The price of the objects is needed in the second inequality and not in the first. |
|C |The price per notebook is not needed in the first inequality. |
|D |Correct! |
PTS: 1 DIF: Average REF: Lesson 5-6
OBJ: 5-6.2 Solve real-world problems involving systems of inequalities.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve real-world problems involving systems of inequalities
KEY: System of Inequalities | Real-World Problems
118. ANS: B
[pic]
| |Feedback |
|A |The difference in their ages is less than 35. |
|B |Correct! |
|C |Rosa's father is more than three times her age. |
|D |Rosa's father is more than three times her age. |
PTS: 1 DIF: Basic REF: Lesson 5-6
OBJ: 5-6.2 Solve real-world problems involving systems of inequalities.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve real-world problems involving systems of inequalities
KEY: System of Inequalities | Real-World Problems
SHORT ANSWER
119. ANS:
An expression that combines operations, numbers, variables, and mathematical symbols is called a mathematical expression.
For example: Four times the sum of x and y decreased by 5 can be written mathematically as [pic].
An expression written in words is called a verbal expression. An example of a mathematical expression is [pic].
PTS: 1 DIF: Basic REF: Lesson 1-1 OBJ: 1-1.3 Solve multi-step problems.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
120. ANS:
[pic]
[pic]
For example, seven times the amount saved in a single day.
Symbols used to represent unspecified numbers or values are called variables. Any letter can be used as a variable. For example: In an algebraic expression 4s, the letter s is a variable.
PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.3 Solve multi-step problems.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
121. ANS:
[pic]
[pic]
For example, twelve times the amount in a single bottle
Symbols used to represent unspecified numbers or values are called variables. Any letter can be used as a variable. For example: In an algebraic expression 4s, the letter s is a variable.
PTS: 1 DIF: Average REF: Lesson 1-1 OBJ: 1-1.3 Solve multi-step problems.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
122. ANS:
[pic]
The area of a square is equal to the product of its sides.
[pic] or A = s2
The perimeter of a square is equal to the sum of its four sides.
[pic] or P = 4s
From the problem we know that the area is equal to half the perimeter, so we can set up the problem s2 = [pic](4s) and solve for s.
[pic]
Since 0 cannot be the length of a side, s = 2.
PTS: 1 DIF: Advanced REF: Lesson 1-1 OBJ: 1-1.3 Solve multi-step problems.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
123. ANS:
[pic]; $29.26 hundred million
To calculate the total expenditure, first add the amount spent on different diseases and then multiply it with the number of years.
PTS: 1 DIF: Advanced REF: Lesson 1-3 OBJ: 1-3.4 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
124. ANS:
[pic]; $735; Substitution Property
Add the prize money won for the different points scored and multiply it by the number of people.
PTS: 1 DIF: Advanced REF: Lesson 1-3 OBJ: 1-3.4 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
125. ANS:
[pic]; $9000
To calculate the total expenditures, first add the expenses for one month and then multiply by 12.
PTS: 1 DIF: Average REF: Lesson 1-4 OBJ: 1-4.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
126. ANS:
[pic]; about 32.87 hours
[pic]
PTS: 1 DIF: Basic REF: Lesson 1-5 OBJ: 1-5.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
127. ANS:
[pic]; 57 jelly beans
[pic]
PTS: 1 DIF: Average REF: Lesson 1-5 OBJ: 1-5.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
128. ANS:
[pic]; [pic]
To find the inverse of a relation, exchange x and y in each ordered pair.
PTS: 1 DIF: Advanced REF: Lesson 1-6 OBJ: 1-6.5 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 | NA 7 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
129. ANS:
Yes
PTS: 1 DIF: Basic REF: Lesson 1-7 OBJ: 1-7.4 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3 | NA 1 | NA 6
TOP: Determine whether a relation is a function KEY: Relations | Functions
130. ANS:
Yes
PTS: 1 DIF: Basic REF: Lesson 1-7 OBJ: 1-7.4 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3 | NA 1 | NA 6
TOP: Determine whether a relation is a function KEY: Relations | Functions
131. ANS:
Yes
PTS: 1 DIF: Basic REF: Lesson 1-7 OBJ: 1-7.4 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3 | NA 1 | NA 6
TOP: Determine whether a relation is a function KEY: Relations | Functions
132. ANS:
H: It rains.
C: Mark uses an umbrella.
If it rains, then Mark uses an umbrella.
A hypothesis is a belief used as a basis for action. It follows the word if.
A conclusion is a result or outcome of an act or process. It follows the word then.
PTS: 1 DIF: Average REF: Lesson 1-8 OBJ: 1-8.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 7 | NA 1 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
133. ANS:
[pic]
Read each statement carefully and write the equation according to the given information.
PTS: 1 DIF: Average REF: Lesson 2-1 OBJ: 2-1.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
134. ANS:
[pic]; 7 miles
Read each statement carefully and write the equation according to the given information. Solve the written equation by isolating the variable on one side of the equation.
PTS: 1 DIF: Advanced REF: Lesson 2-1 OBJ: 2-1.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
135. ANS:
[pic]; $21.25
Read each statement carefully and write the equation according to the given information. Solve the written equation by isolating the variable on one side of the equation.
PTS: 1 DIF: Basic REF: Lesson 2-2 OBJ: 2-2.12 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
136. ANS:
[pic]; $11
Read each statement carefully and write the equation according to the given information. Solve the written equation by isolating the variable on one side of the equation.
PTS: 1 DIF: Advanced REF: Lesson 2-2 OBJ: 2-2.12 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
137. ANS:
[pic]; 19
First translate the verbal sentences into equations by using key words and phrases you have learned to replace words with symbols. Then to solve an equation with more than one operation, undo operations by working backward.
PTS: 1 DIF: Basic REF: Lesson 2-3 OBJ: 2-3.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
138. ANS:
[pic]; 28
First translate the verbal sentences into equations by using key words and phrases you have learned to replace words with symbols. Then to solve an equation with more than one operation, undo operations by working backward.
PTS: 1 DIF: Average REF: Lesson 2-3 OBJ: 2-3.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
139. ANS:
[pic]; 48
First translate the verbal sentences into equations by using key words and phrases you have learned to replace words with symbols. Then to solve an equation with more than one operation, undo operations by working backward.
PTS: 1 DIF: Advanced REF: Lesson 2-3 OBJ: 2-3.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
140. ANS:
0.3 days (or 7.2 hours) to 1.7 days (or 40.8 hours)
The difference between the expected time and the actual time is less than or equal to 0.7 days. Convert the actual time and the margin of error to the same units, either days or hours. To find the range, write an absolute value inequality and solve. To solve, rewrite the absolute value inequality as a compound sentence and solve each part.
(source: )
PTS: 1 DIF: Average REF: Lesson 2-5 OBJ: 2-5.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
141. ANS:
372
Read each statement carefully and write the equation according to the given information. To solve a proportion containing a variable, use cross products and other techniques to solve the equation.
PTS: 1 DIF: Advanced REF: Lesson 2-6 OBJ: 2-6.3 Solve multi-step problems.
NAT: NA 1 | NA 3 | NA 8 | NA 9 | NA 2 | NA 10 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
142. ANS:
14%
First find the amount of change. Then find the percent of change by using the original number as the base.
[pic]
PTS: 1 DIF: Advanced REF: Lesson 2-7 OBJ: 2-7.3 Solve multi-step problems.
NAT: NA 1 | NA 3 | NA 8 | NA 9 | NA 2 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
143. ANS:
93 turtles
Find the increase in sales by multiplying the rate as a decimal with the previous year’s sales. Add the amount to the previous year’s sales.
PTS: 1 DIF: Advanced REF: Lesson 2-7 OBJ: 2-7.3 Solve multi-step problems.
NAT: NA 1 | NA 3 | NA 8 | NA 9 | NA 2 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
144. ANS:
[pic]; [pic]
First translate the verbal sentences into equations by using key words and phrases you have learned to replace words with symbols. Then to solve an equation for a specific variable, use the properties of equality to isolate the specified variable on one side of the equation.
PTS: 1 DIF: Basic REF: Lesson 2-8 OBJ: 2-8.3 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 2 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
145. ANS:
44 liters of 26% vinegar solution.
| |Liters |Total Amount of Vinegar |
|49% Vinegar |136 |0.49(136) |
|26% Vinegar |n |0.26n |
|60% Vinegar |136 − n |0.60(136 − n) |
[pic]
Complete the table with expressions for liters and total amount of vinegar. Use the total amount of vinegar column in the table to write the equation for the problem.
PTS: 1 DIF: Advanced REF: Lesson 2-9 OBJ: 2-9.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
146. ANS:
12, [pic]
To find the x-intercept, set [pic] and solve for x.
To find the y-intercept, set [pic] and solve for y.
PTS: 1 DIF: Average REF: Lesson 3-1 OBJ: 3-1.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
147. ANS:
80; After speaking for 80 minutes, he will have $0 remaining on his phone card.
PTS: 1 DIF: Average REF: Lesson 3-2 OBJ: 3-2.2 Solve multi-step problems.
TOP: Solve linear equations by graphing. KEY: linear function | zeros
148. ANS:
Sample answer: 1982–1983; Look on the graph for the steepest line segment, which indicates the greatest rate of change, or calculate the biggest difference using the values given on the graph.
Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity changes over time.
PTS: 1 DIF: Average REF: Lesson 3-3 OBJ: 3-3.3 Solve multi-step problems.
NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
149. ANS:
Sample answer: Sometimes a pattern can lead to a general rule. If the equation that represents the pattern is of the form [pic], then the relationship is proportional.
In a nonproportional situation, you must add or subtract a constant to write an equation for the relationship. It is of the form [pic]. Also, nonlinear relationships are nonproportional because they do not have a constant rate of change.
The circumference of a circle and its diameter is an example of a proportional relationship.
Final velocity of a moving object which is given by [pic], where u is initial velocity, t is the time, and a is acceleration is an example of a nonproportional relationship.
PTS: 1 DIF: Advanced REF: Lesson 3-6 OBJ: 3-6.2 Solve multi-step problems.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
150. ANS:
[pic]
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the calculated b.
PTS: 1 DIF: Basic REF: Lesson 4-2 OBJ: 4-2.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
151. ANS:
[pic]
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the calculated b.
PTS: 1 DIF: Advanced REF: Lesson 4-2 OBJ: 4-2.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
152. ANS:
[pic]; [pic]; [pic]
The linear equation [pic]is written in point-slope form, where [pic] is a given point on a nonvertical line and m is the slope of the line.
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept form.
The linear equation in standard form is given as [pic], where A, B, and C are constants. Use Addition and Subtraction Properties of Equality to rewrite the equation in standard form.
PTS: 1 DIF: Basic REF: Lesson 4-3 OBJ: 4-3.4 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
153. ANS:
[pic]; [pic]; [pic]
The linear equation [pic]is written in point-slope form, where [pic] is a given point on a nonvertical line and m is the slope of the line.
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept form.
The linear equation in standard form is given as [pic], where A, B, and C are constants. Use Addition and Subtraction Properties of Equality to rewrite the equation in standard form. Remember that A, B, and C must be integers with a GCF of 1.
PTS: 1 DIF: Average REF: Lesson 4-3 OBJ: 4-3.4 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
154. ANS:
[pic]
Two nonvertical lines are parallel if they have the same slope. Use the given point with the slope of the parallel line in the point-slope form. Then change to the slope-intercept form.
PTS: 1 DIF: Average REF: Lesson 4-4 OBJ: 4-4.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
155. ANS:
No; using the equation would give –333.3 miles, which is not a reasonable estimate.
Write an equation for the line of fit. Use the equation to make the prediction.
PTS: 1 DIF: Advanced REF: Lesson 4-5 OBJ: 4-5.3 Solve multi-step problems.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
156. ANS:
[pic]
[pic]
Solve the inequality by subtracting the sum of the constant terms on the left side of the inequality from both sides of the inequality.
PTS: 1 DIF: Average REF: Lesson 5-1 OBJ: 5-1.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
157. ANS:
[pic]
[pic]
Solve the inequality by subtracting the sum of constant terms on the left side of the inequality from both sides of the inequality.
PTS: 1 DIF: Advanced REF: Lesson 5-1 OBJ: 5-1.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
158. ANS:
at least 25 hours
[pic]
Divide both sides of the inequality by the constant on the left.
PTS: 1 DIF: Basic REF: Lesson 5-2 OBJ: 5-2.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
159. ANS:
Sample answer: Let [pic], [pic]; [pic], at most 13 packets can be packed
[pic]
Divide both sides of the inequality by the constant on the left.
PTS: 1 DIF: Advanced REF: Lesson 5-2 OBJ: 5-2.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
160. ANS:
[pic]
[pic]
First add the constant terms in the numerator. Secondly, multiply both sides by the denominator. Next, subtract the constant term on the left to both sides.
PTS: 1 DIF: Basic REF: Lesson 5-3 OBJ: 5-3.6 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
161. ANS:
[pic]
Let x be the money expected at the end of the year. Calculate the 8% of the investment and add it to the original investment. The expected money must be greater than the calculated amount.
PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.6 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
162. ANS:
[pic]
Let the expression inside the absolute value symbols be less than the constant on the right and greater than the opposite of the constant. Solve each inequality. This will give two solutions.
PTS: 1 DIF: Basic REF: Lesson 5-4 OBJ: 5-4.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
163. ANS:
[pic]
The perimeter, 4s, of the kennel must lie between 14 and 48. To solve the inequality, divide each side of the inequality by the coefficient of the variable.
PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
164. ANS:
[pic]
The mean of pH values for the three days must lie between 6.8 and 7.3. To solve the inequality, first combine the constants by subtracting the constant term on the left from both sides. Next, divide both sides by the coefficient of the variable.
PTS: 1 DIF: Advanced REF: Lesson 5-4 OBJ: 5-4.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
165. ANS:
d = [pic] or d = – [pic]
[pic]
Solve by writing the equation as a compound sentence. For the first part of the compound sentence, consider the case in which [pic] is a positive number equal to 2. For the second part, consider the case in which [pic] is a negative number whose opposite is equal to 2. Solve each part of the compound sentence. Then graph the two solutions.
PTS: 1 DIF: Average REF: Lesson 5-5 OBJ: 5-5.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
166. ANS:
The solution of [pic] is [pic], and the solution to [pic] is [pic] or [pic]. Both solutions include –8 and 2, but the inequality with the less than or equal to symbol also includes all the points in between –8 and 2, and the inequality with the greater than or equal to sign also includes all points less than –8 or more than 2.
PTS: 1 DIF: Advanced REF: Lesson 5-5 OBJ: 5-5.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
167. ANS:
Sample answer: They can give away 20 of the $10 tickets and 5 of the $20 tickets or 15 of the $10 tickets and 7 of the $20 tickets.
Total number of tickets given away must be greater than equal to 20 and the total cost of the tickets must be less than or equal to $300.
PTS: 1 DIF: Advanced REF: Lesson 5-6 OBJ: 5-6.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
168. ANS:
4 cars
The number of mid-sized cars sold must be greater than or equal to twice the number of sport-utility vehicles and sum of the profit earned from car of each type must be greater than or equal to $3500.
PTS: 1 DIF: Average REF: Lesson 5-6 OBJ: 5-6.3 Solve multi-step problems.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
ESSAY
169. ANS:
a. If each side is length d, multiply 4 times d to find the perimeter. You can use the expression 4d to find the perimeter of the carrom board.
b. The perimeter of the carrom board is four times the length of one side, or the sum of the four sides. P = 4d or P = [pic]
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 1-1
OBJ: 1-1.4 Solve problems and show solutions. NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2
TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions
170. ANS:
a. The open-sentence below represents the change in points of Team B in two rounds.
[pic]
b. You can use the Identity and Equality properties to see if the data is the same.
c. For Team D, Scores in [pic], [pic], [pic].
Then by Transitive Property: [pic].
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 1-3
OBJ: 1-3.5 Solve problems and show solutions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
171. ANS:
a. The time to reach Springfield from Cleveland can be found by evaluating [pic] Likewise the time to reach Cleveland from Springfield can be found by evaluating [pic].
b. You can use the Commutative and Associative Properties to rearrange and group numbers for easier calculations.
c. Answers should include: Time [pic].
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 1-3
OBJ: 1-3.5 Solve problems and show solutions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
172. ANS:
a. [pic] where n represents the number of rides.
b. Inequalities can be used to determine how many rides can be taken with the given amount of money.
c. Real-world example should include instances such as calculating distance and shopping amount.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 1-5
OBJ: 1-5.4 Solve problems and show solutions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
173. ANS:
a. Sample answer: Expressing real-world data as relations shows how the members of a domain relate to the members of the range. For example, a table helps to organize the data or a graph may show a pattern in the data.
b. Following is the graph that shows the number of goals and shots on goal.
[pic]
c. There seems to be a positive relationship between these sets of data. The number of goals increases with the increased number of shots on goal.
Plot the points on the graph with the number of goals scored on the x-axis and the number of shots on goal on the y-axis.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 1-6
OBJ: 1-6.6 Solve problems and show solutions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 | NA 7 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
174. ANS:
Real-world data can be recorded and visualized in a graph and by expressing an event as a function of another event. A graph gives you a visual representation of the situation which is easier to analyze and evaluate. The employee’s salary doubles in five years and it almost becomes four times the original amount in ten years.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 1-7
OBJ: 1-7.5 Solve problems and show solutions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3 | NA 1 | NA 6 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
175. ANS:
a. Equations can be used to describe the relationships of average annual rainfall with the passing years.
b. To solve the equation, add 20 to each side. The solution is [pic].
c. Sample problem: “The average annual rainfall in 2001 is 40 inches more than the average annual rainfall in 1998. If the average annual rainfall in 2001 is 60 inches, what is the average annual rainfall for 1998? [pic]; 20 inches”
Read each statement carefully and write the equation according to the given information. Solve the written equation by isolating the variable on one side of the equation.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 2-2
OBJ: 2-2.13 Solve problems and show solutions. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions
176. ANS:
a.You can use the formula [pic] and voltage to find the current flow for different sized air conditioners.
b. The equation [pic] gives the current for a 20,000-watt air conditioner. The equation can be solved by dividing each side by 220. The answer is 90.9 ampere.
Read each statement carefully and write the equation according to the given information. Solve the written equation by isolating the variable on one side of the equation.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 2-2
OBJ: 2-2.13 Solve problems and show solutions. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions
177. ANS:
a. Sample answer: By using the increase in heart rate per minute, minimum heart rate, and the current heart rate, you can write and solve an equation to find the time for which the elephant seal can stay submerged in water.
b. To solve the equation, subtract 23 from each side and then divide each side by 1.25. The time for which the elephant seal can stay submerged in water is about 53 to 54 minutes.
Solve the written equation by isolating the variable on one side of the equation.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 2-3
OBJ: 2-3.4 Solve problems and show solutions.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 | NA 6 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
178. ANS:
a. Ratios are used to determine how much of each ingredient to use for a given number of servings.
b. To determine how much grenadine is needed if you use 3 scoops of ice cream, write and solve the proportion [pic], where g is the amount of grenadine. To alter the recipe to get 7 glasses of mocktail, multiply each amount by [pic].
Read each statement carefully and write the equation according to the given information. To solve a proportion containing a variable, use cross products and other techniques to solve the equation.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 2-6
OBJ: 2-6.4 Solve problems and show solutions.
NAT: NA 1 | NA 3 | NA 8 | NA 9 | NA 2 | NA 10 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
179. ANS:
a. Sample answer: Equations from physics can be used to determine the height needed to produce results.
b. (1) Use the Distributive Property to write the equation in the form [pic].
(2) Subtract 165g from each side.
(3) Divide each side by –g. The maximum height the ball can attain after being thrown from the top of the building should be 52 feet.
To solve an equation for a specific variable, use the properties of equality to isolate the specified variable on one side of the equation.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 2-8
OBJ: 2-8.4 Solve problems and show solutions.
NAT: NA 1 | NA 8 | NA 9 | NA 2 | NA 10 | NA 6 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
180. ANS:
a. Sample answer: You can graph an equation that represents how many degrees in Fahrenheit is equal to the degrees in Celsius.
b. Since for different degrees in Fahrenheit we have different degrees in Celsius, it is easier to use the graph for temperature conversions. Normal body temperature in degrees Celsius is 37°C.
The relationship between temperature in degrees Celsius and temperature in degrees Fahrenheit can be represented by a linear equation. This linear equation can be used to plot a graph between the two values. Also, the temperature conversion can be predicted from the graph.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 3-1
OBJ: 3-1.4 Solve problems and show solutions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3
TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions
181. ANS:
Sample function; [pic]. For this function [pic] is the zero. One half is the value of x for which [pic] which is the x-intercept. The line of the function intercepts the x-axis at [pic].
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 3-2
OBJ: 3-2.3 Solve problems and show solutions. TOP: Solve linear equations by graphing.
KEY: linear function | zeros
182. ANS:
Sample answer:
a. The y-intercept is the flat fee in an equation that represents a price.
b. If Mary charges $7.50 as the flat fee plus $2 per hour for babysitting, the graph representing this situation would have a y-intercept of $7.50.
The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the y-intercept. If a quantity changes at a constant rate over time, it can be modeled by a linear function. The y-intercept represents a starting point, and the slope represents the rate of change.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-1
OBJ: 4-1.4 Solve problems and show solutions.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8 TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
183. ANS:
Sample Answer
a. Plan 1: [pic]
Plan 2: [pic]
Plan 3: [pic]
b. [pic]
c. Megan should enroll in Plan 3. The graph shows that at 500 minutes, she would be paying $49.95 for Plan 3, about $60 for Plan 2, and about $55 for Plan 1.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-3
OBJ: 4-3.5 Solve problems and show solutions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Performance assessment KEY: Problem Solving | Show Solutions
184. ANS:
Sample Answer
a. and b.
| |Average Hourly Earnings (dollars) of U.S. |
| |Production Workers, 1991-2001 |
| |[pic] |
| | |
|[pic] | |
| |Year |
c. Using (1992, 10.57) and (2000, 13.76), the slope of the line is: [pic].
Find b using one of the points.
[pic]
The equation for the line of fit is [pic]
d. [pic]
Hourly earnings in 2005 should be about $15.76.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-5
OBJ: 4-5.4 Solve problems and show solutions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3 TOP: Performance assessment
KEY: Problem Solving | Show Solutions
185. ANS:
The correlation coefficient measures the how closely the best-fit line is modeling the data. The closer it is to 1 or -1, the more closely it models the data. The best-fit line is a good model for the data because -0.965 is very close to -1. The fact that it is negative means that there is a negative correlation.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-6
OBJ: 4-6.3 Solve problems and show solutions. TOP: Regression and median fit lines.
KEY: linear regression | best-fit line | correlation coefficient
186. ANS:
a. [pic]
b. If x represents Cindy’s per-hour income and her minimum earning in a day is $14, then [pic]. To solve this inequality, divide each side by 2 and do not change the direction of the inequality. The solution is [pic]. This means that her minimum wage per hour must be $7 or higher.
When each side of an inequality is multiplied by a positive number, the inequality remains true.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 5-2
OBJ: 5-2.4 Solve problems and show solutions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions
187. ANS:
a. [pic]
b. Cinema I is cheaper only if there are more than 6 children.
[pic]
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 5-3
OBJ: 5-3.7 Solve problems and show solutions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
TOP: Performance assessment KEY: Problem Solving | Show Solutions
188. ANS:
a. |x – 3.25| ≤ 1.75; {x | 1.5 ≤ x ≤ 5}
b. [pic]
c. Yes; possible explanation: This level of chlorine is below the safe range, so he should add more chlorine.
Assessment Rubric:
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 5-5
OBJ: 5-5.4 Solve problems and show solutions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4
TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions
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