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.

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