Algebra I Spiral Reviews by Objectives WSFCS
(2003 NCSCOS) 3-15-10
Objective 1.01b
1. Simplify:
A.7
B.7x2
C.3 + 4x
D.3 + 4x2
2. Simplify: (9p3 – 3) – (4p2 + 4) + (5p3 + 5p2)
A.14p3 + p2 + 1
B.4p3 + p2 + 1
C.14p3 – p2 + 7
D.14p3 + p2 – 7
3. Simplify: (2x2 – 4)2
A.4x4 – 16x2 – 16
B.4x4 – 16
C.4x4 – 16x2 + 16
D.4x2 – 14x + 16
4. Simplify: (5m – 3m4 – 7) + (5m4 – 9 + 5m)
A. 2m4 + 10m+ 2
B. 10m4 – 12m– 2
C. 2m4 + 10m– 16
D. 10m4 – 12m– 16
5. Simplify: (y2 + 4y– 1)(y + 2)
A y3 + 6y2 + 8y– 2
B y2 + 3y– 2
C y3 + 4y2 – 2
D y3 + 6y2 + 7y– 2
6. Simplify:(8x + 7) (8x – 7)
A 64x2 + 49
B 64x2 – 112x + 49
C 64x2 – 49
D 64x2 – 112x – 49
Objective 1.01c
7. Factor completely: 21xy – 14y + 9x – 6
A. (3x – 2) (7y + 3)
B. (3x + 2) (7y – 3)
C. (3x + 3) (7x – 2)
D. (3x – 3) (7x + 2)
8. Factor completely: 25a2 – 64b2
A. (5a – 8b)(5a + 8b)
B. (5a – 32b)(5a + 32b)
C. (5a + 8b)2
D. (5a – 8b)(5a – 8b)
9. Factor completely: 6x2y – 8xy2
A xy(6x – 8y)
B 2xy(3x – 4y)
C 2x(3xy – 4y2)
D –2x2y2
10. Factor completely: 4x2y2 + 10xy3 – 8xy2
A xy2(4x + 10y – 8)
B 2(2x2y2 + 5xy3 – 4xy2)
C 2xy2(2x + 5y – 4)
D 4xy2(x + 2.5y – 2)
11. Which of the following binomials is a factor of 3t3 – 12t2 – 15t?
A. (t – 15)
B. (t – 5)
C. (t + 5)
D. (t – 1)
12. Which binomial is a factor of 2x2 – 3x – 5?
A.(x + 5)
B.(2x + 1)
C.(x – 1)
D.(x + 1)
Objective 1.02
13. Consider the area of a triangle A is the area, b is the base, and h is the height. Which of the following correctly expresses b in terms of the other quantities?
A.b = 2AhB.
B.D.
14. Mrs. McGee has a large outdoor thermometerin her back yard. It is marked with both Fahrenheit and Celsius scales. If the thermometer indicates that the outdoor temperature is 77°F, what is thetemperature on the Celsius scale?
[F =95C + 32]
A. 25ºCB. 60.6ºC
C. 81ºCD. 170.6ºC
Objective 4.01a
15. Solve:
A. –44
B. 44
C. 20
D. –20
Objective 4.01b
16. Jose wants his math average to be above 85 forthe year. If his averages for the first threequarters are 80, 78, and 92, what must he scorefor the fourth quarter to achieve his goal?
A. 90
B. 90 or less
C. 90 or above
D. Above 90
Objective 1.03
17. A school activity bus travels 84 miles on 11 gallons of gas. About how many gallons will it need to travel 384miles?
A. 51 gallons
B. 40 gallons
C. 30 gallons
D. 3 gallons
Objective 4.01a
18. {(− 2, − 8)(4, 0)(4, − 8)(− 2, 0)}
Describe the set of ordered pairs above.
A. a relation, but not a function.
B. a relation and a function.
C. a function, but not a relation.
D. neither a function nor a relation.
19. If the range of the function is {–8, 2, 7}, findthe domain of y = –5x + 2.
A.{2, 0, –1}
B. {–45, 0, 1}
C.{42, –8, –33}
D.{–2, 0, 1}
Objective 4.01
20. Which one of the following equations
does NOT define a function?
A. – 4x + 6y = 10
B.x2 + y = 5
C.y = 5
D.x = 4
21. What is the graph of y = 2x − 3?
A.
B.
C.
D.
Objective 4.01
22. Which graph does not define a function?
A.
B.
C.
D.
Objective 4.01a
23. Which of the relation tables represents a function?
A.
m / n1 / –4
6 / –6
9 / –1
10 / 0
1 / 1
B.
m / n0 / 2
0 / –2
2 / 4
2 / –4
7 / 6
C.
m / n2 / 10
1 / 6
0 / 0
–1 / –7
–4 / 0
D.
m / n9 / 6
3 / 8
4 / 25
7 / 7
9 / 10
Grade 8 Objectives
24. Determine the slope of the line shown.
A. m = –3B.
C. D. m = 3
25. Find the equation of the line in slope-interceptform that passes through points
(–3, 5) and (2, –5).
A. y = –2x – 3
B. y = –2x – 1
C. y = 2x – 9
D.
Objective 4.01b
26. What is true about the graph of 6x + 2y = 10?
A. Its slope is 3.
B. Its y-intercept is 5.
C. It passes through (1, –2).
D. Its x-intercept is negative.
Grade 8 Objective
27. A CD club requires a membership fee of $10. Once a member, you may purchase CDs for $6 each. Rickardo graphed this situation using the y axis for the total cost from $0 to $100 and the x axis for the number of CDs purchased from 0 to 10. The slope of the line which shows the increase in total cost for CDs purchased from 0 to 10 would be which of the following?
A. B.
C. 6 D. 10
Objective 2.02
28. Select the equation of a line perpendicular tothe line y = 2x + 3 and passing through the point (4, –1).
A. y = –2x + 7
B.
C.
D. y = 2x – 9
Objective 4.01a
29. What is ax + by = c in its slope-intercept form?
A. B.
C. D. by = −ax + c
Objective 4.01a
30. Which is the graph of y < 2x + 4?
A.
B.
C.
D.
Objective 4.01a
31. Solve : 7 < 2x – 1 ≤ 10
A. 3 x ≤ 4.5 B. 4 x ≤ 5.5
C. 5.5 x ≤ 4 D. 4.5 x ≤ 3
32. Which graph is the solution of –3 < x < 5?
A.
B.
C.
D.
33. The sum of a given number and twice thenumber is at least 45. Which of the following inequalities can beused to find the number?
A. n(2n) ≥ 45 B. n(2n) > 45
C. n + 2n > 45D. n + 2n ≥ 45
Objective 2.02
34. What is the equation of a line that is parallel toand goes through the point (6, 5)?
A. y = −2x +17 B.
C. y = 2x – 7 D.
35. Select the equation of a line perpendicular tothe line y = 2x + 3 and passing through the point (4, –1).
A. y = –2x + 7 B.
C. D. y = 2x – 9
Objective 4.03
36. Which is the graph of the solution set of the following system?
A.
B.
C.
D.
Objective 4.03
37. Which graph shows the solution of
–x + y = 4
–x – y = 2?
A.
B.
C.
D.
Objective 4.03
38. When using linear combinations (elimination) to solve
4x – 3y = –1
3x – 2y = 0,
what would be a possible first step in the
process?
A.
B.
C. 8x – 6y = –2
–9x + 6y = 0
D. 8x – 6y = 2
–9x + 6y = 0
39. In a coin bank the number of dimes exceeds thenumber of nickels by 6. If there are 24 coins inall, how many of each are there? Let d = number of dimes and n = number of nickels. The two equations representing the above situation are:
A. d = n – 6
d + n = 24
B. d = n – 6
d = 24 – n
C. n = d + 6
n – d = 24
D. d = n + 6
d + n = 24
Objective 4.03
40. Which ordered pair is in the solution set for thefollowing system of inequalities?
y 3x− 6
y + 4 ≥ x
A. (–4, –4) B. (0, 0)
C. (3, 1) D. (4, –4)
41. How many solutions are there for this pair ofequations?
3x – y = –4
6x – 2y = –8
A. 0B. 1
C. 2D. infinitely many
Objective 4.02
42. Which of the following functions is shown inthe graph below?
A. y = x2 + 1B. y = x2 – 1
C. y = –x2 + 1D. y = –x2 – 1
Objective 4.02
43. Consider the equation: x2 + 5x + 6 = 0.
How are the solutions of the above equation and the intercepts of the graph related?
A. There is only one x-intercept. Therefore thex-intercept is not the solution of theequation.
B. The solutions areor 3. Therefore the
solutions are not the x-intercepts.
C. The solutions are –3 or –2. Therefore the solutions are the x-intercepts.
D. There are no solutions for the equation.
44. Jessica is diving from a 12 meter edge. Her height h in meters above the water when she is x meters away from the edge is given by the formula h = -x2 + 2x + 10. Approximately how far away from the edge is she when she enters the water?
A. x 4.317 meters B. x -4.317 meters
C. x 10 meters D. x 12 meters
45. Solve: 64x2− 9 = 0
A. B.
C. D.
46. The distance h traveled in t seconds by an object dropped from a height is h = 16t2. If an object is dropped from a height of 45 feet, how long will it take before the object hits the ground? Round your answer to the nearest 0.01 second.
A. 2.45 seconds
B. 1.68 seconds
C. 0.75 seconds
D. 1.19 seconds
47. Find the coordinates of the vertex and determine whether the graph opens up or down for the following: y = −x2+ 5
A. (0, –5), opens down
B. (0, –5), opens up
C. (0, 5), opens down
D. (0, 5), opens up
48. Which point represents the vertex of the function y = x2 + 2x?
A. (0, 0)
B. (–1, –1)
C. (–2, 0)
D. (4, 24)
Objective 1.01a
49. The product of (5x3y)(–4x2y2) is:
A. x5y3
B. –20x5yA2
C. x5y2
D. –20x5y3
50. Simplify the following expression:
A.
B.
C.
D. 32xy2
51. Simplify the following expression:
A.
B.
C. 0
D. 1
Objective 1.01b
52. Simplify: .
A.
B.
C. 2x2– 15x + 9
D.
53. Simplify:
A. x
B. –x
C.
D. –2xy
Objective 4.01
54. A farmer has 720 acres. She will use 80 acres for alfalfa, 300 acres for corn, and 100 acres for oats. If she wants to leave between 100 and 200 acres unplanted, how many acres can she use for rye?
A. between 240 and 340 acres
B. between 140 and 240 acres
C. between 100 and 200 acres
D. between 40 and 140 acres
Objective 4.01
55. Jerome has 50 feet of fencing to build a dogpen. He wants the width of the pen to be
between 5 feet and 10 feet. Which inequality
represents the length of the dog pen?
A. 5 ≤ L ≤10B. 15 ≤ L ≤ 20
C. 5 ≥ L ≥ 10D. 15 ≥ L ≥ 20
Objective 3.03
56. Which equation matches the scatter plot?
A. y = 3 – 2x B. y = 2 – 2x
C. y = 2x + 3 D. y = 2x – 3
Grade 8 Objective 5.01
57. Which of the following is a graph of a
function?
Objective 3.03
58. Write a linear function to model the data below.
x / y0 / 8
1 / 26.1
2 / 44.2
3 / 62.3
A. y = 8 + 18.1x
B. y = 44.2 + 26.1x
C. y = 18.1 + 8x
D. y = 26.1 + 44.2x
59. The table shows the relationship between theheight and the growing times for 6 plants of thesame type. Which equation is thebestmodel for the data?
A. h= w + 3
B. h = w − 3
C. h + w = 26
D. w = h + 3
Objective 4.03
60. For the system of equations, which expression can be substituted for y in the first equation of the system
5x + 3y = 9
4x – y = 8
to solve the system by substitution?
A. 12x – 3y B.
C. 4x – 8 D. 8 – 4x
Objective 4.03
61. You want to eliminate y by addition in thissystem:
8x + 8y = 2
9x – 6y = 6
If you multiply both sides of the top equation by3, by which number would you multiply bothsides of the bottom equation?
A. –4 B. –2
C. 2 D. 4
62. Describe the graph of this system:
A. 2 parallel lines
B. 2 non-perpendicular intersecting lines
C. 1 line
D. 2 perpendicular lines
63. The treasurer of the student body reported thatthe receipts for a concert totaled $916 and that 560 people attended. If students paid $1.25 per ticket and non-students paid $2.25 per ticket, how many students attended the concert?
A. 77
B. 216
C. 344
D. 483
64. Tim's hourly wage at a grocery store is greater after 5:00 p.m. than during the day. One weekhe works 25 daytime hours and 25 eveninghours and earns $288. The next week he works20 daytime hours and 24 evening hours andearns $255. What is his evening hourly rate?
A $5.37B $5.76
C $5.80 D $6.15
Objective 1.02
65. Which expression describes the nth term of the following geometric sequence?
1, 8, 27, 64…..
A. 3n B. n3
C. n2 + n D. 3n + n
66. For the sequence of numbers 8, 9, 10, 11, the equation for the nth term, an, and the valuefor n = 10 are:
A. an= n + 8; n10= 18
B. an= n + 7, n10 = 17
C. an= 2n + 1; n10= 21
D. an= 2n – 2; n10= 18
Objective 3.03
67. The graph shows the results of a survey given to the captains of the debate team.
If the team practices four hours per day nextseason, about how many debates can you expect it to win?
A. about 10B. about 16
C. about 19D. about 21
Objective 3.03
68. This scatter plot shows the individual ages of asample audience of a TV movie and the numberof viewers at each age.
Which type of relationship most likely existsbetween age and the number of movie viewers?
A. negative correlation
B. positive correlation
C. no correlation
D. none of the above
Un-grouped Algebra I Objectives
69. Tickets to a carnival cost $5.00 each, and lunch costs $8.50 per person. Renting a bus to and from the carnival costs $47.00. Which expression can be used to represent the cost of x people going to the carnival? (Assume that thex people will fit on one bus.)
A. 5.00 + 8.50 + 47.00
B. 5.00x + 8.50 + 47.00
C. 5.00 + 8.50x + 47.00
D. 5.00x + 8.50x + 47.00
70. LaKeishia has found that her business runs most efficiently when the number of supervisors is equal to 1/5 of the number of office workers. LaKeishia presently has 200 people working for her. Given that number, which ordered pair below shows the most efficient relationship of office workers to supervisors?
A. (200, 1000)B. (200, 40)
C. (40, 200)D. (40, 8)
71. Which of the equations below represents the second step of the solution process?
Step 1: 3(5x – 2) + 27 = –24
Step 2:
Step 3: 15x + 21 = –24
Step 4: 15x = –45
Step 5: x = –3
A. 3(5x + 27) – 2 = –24
B. 3(5x + 25) = –24
C. 15x – 2 + 27 = –24
D. 15x – 6 + 27 = –24
72. A bike rental shop charges a one-time charge of$8 plus an hourly fee to rent a bike. Dan paid $24.50 to rent a bike for 5.5 hours. What is the bike shop’s hourly fee?
A. $6.00B. $4.45
C. $3.00D. $1.81
73. On March 28, 2008, Eamon Sullivan set a world record by swimming 50 meters in 21.28 seconds. A shortfin mako shark can swim at a speed of 20 km/hr. At these rates, would Sullivan or a mako shark win a 50-meter race, and by how many seconds?
A. Sullivan, by about 1 second
B. Sullivan, by about 9 seconds
C. The shark, by about 6 seconds
D. The shark, by about 12 seconds
74. Which compound inequality has no solution?
A. x > 1 OR x < –2
B. x < 1 AND x > –2
C. x < 1 OR x < –2
D. x > 1 AND x < –2
75. WylerTalkie phone company charges $18.00 for basic phone service per month and $0.15 per minute for long distance calls. AcmeCalls charges $80.00 per month with no fee for long distance calls. What is the minimum number of minutes of long distance calls for which the cost of WylerTalkie is more than the cost of AcmeCalls per month?
A. 341 B. 362
C. 414 D. 434
76. Which situation best describes a negative
correlation?
A. The speed of a runner and the time it takes to run a race
B. The number of apples in a bag and the weight of the bag of apples
C. The time it takes to repair a car and the amount of the bill
D. The number of people in a household and the amount of mail in their mailbox
77. There is a linear relationship between the wind speed at a given temperature and what that temperature “feels like.” Ahigher wind speed will make the temperature feel colder. The table below shows what an unknown temperature t “feels like” at different wind speeds.
Wind Speed (mph) / 5 / 10 / 15“Feels Like” (oF) / 36 / 34 / 32
- Write an equation in slope-intercept form relating the wind speeds to the unknown temperature.
- What does the slope mean in this situation?
- What is the unknown temperature?
- Determine what the unknown temperature feels like when the wind speed is 12 miles per hour.
78. A chemist has a bottle of a 10% acid solution and a bottle of a 30% acid solution. He mixes the solutions together to get 500 mL of a 25% acid solution. How much of the 30% solution did he use?
A. 125 mL B. 150 mL
C. 375 mL D. 450 mL
79. Joshua wants to take his friends to the drive-in movies. One drive-in charges $10 per vehicle, plus $1.25 per person. Another drive-in charges $5 per vehicle and $2.20 per person. What is the number of people for which both drive-in theatres charge the same price?
A. 4 peopleB. 7 people
C. 10 peopleD. 15 people
80. Jose and his brother Juan start saving money at the same time. Jose has $145 and will add $10 to his savings every week. Juan has $20 and will add $15 to his savings every week.
a. After how many weeks will Jose and Juan have the same amount saved?
b. What is that amount?
81. Every year, Mary Margaret knits scarves and sells them at a craft fair. This year, she used$6 worth of yarn for each scarf. She also paid $50 to rent a table at the fair. She sold each scarf for $10.
a. Write a system of linear equations to represent the amount Mary Margaret spent and the amount she collected. Tell what your variables represent. Tell what each equation in the system represents.
b. Use any method to solve the system you wrote. How many scarves did Mary Margaret need to sell to make a profit? Explain your answer.
82. Jackson is ordering game cartridges from an online retailer. The retailer’s prices, including shipping and handling, are given in the tablebelow.
Game Cartridges / Total Cost ($)1 / 54.95
2 / 104.95
3 / 154.95
4 / 204.95
Which of the following best describes why the relation given in the table is or is not a function?
A. The relation is not a function because each
number of game cartridges is assigned one price.
B. The relation is a function because the Total Cost is increasing.
C. The relation is a function because each number of game cartridges is assigned one price.
D. The relation is not a function because there are only four ordered pairs in the table.
83. The average full-time editor for a nationalnewspaper writes 2 articles per week. Eacharticle is read by an average of 3845 people. Let T represent the total number of times that all of an editor’s articles have been read w weeks into the year. Which equation below bests represents T?
A. T = 7690 B. T = 7690 + w
C. T = 7690w D. T = 7690w2
84. Referring to the previous problem (#83), which of the following is a reasonable domain toconsider for the function you choose?
A. All real numbers B.
C. D.
85. A square has sides of length x – 4. A rectangle has a length of x + 2 and width of
2x – 1. What is the total combined area of the square and the rectangle?
A. 10x – 14B. 4x – 3
C. 3x2 – 5x + 14 D. 3x2 + 3x – 18
86. In 1867, the United States purchased the Alaska Territory from Russia for about $7.2 x 106. The total area of the territory was approximately 6.5 x 105 square miles. Assuming the cost is dependent on the number of square miles, what is the constant of variation?
A. 1B. 12
C. 6 x 105D. 7.2 x 106
87. Referring to the previous problem (#86), what does the constant of variation represent?
A. The cost of the AlaskaTerritory
B. The total area of the AlaskaTerritory
C. The cost per square mile for the Alaska
Territory
D. The constant of variation has no real-life significance in this case.
88. Terron is thinking about investing $2300 at a rate of 4.5% compounded annually. After 6 years, what will be the balance to the nearest cent?
A. $2995.20B. $3033.82
C. $3072.44 D. $3111.06
89. The table below shows the cost of filling a 15-gallon tank with gas in different years.
Year / Cost per Tank ($)1982 / 45.00
1987 / 21.81
1992 / 22.50
1997 / 23.18
2002 / 24.54
2007 / 45.68
What would the slope of a trend line for this data represent?
A. The yearly change in the cost per tank
B. The price per tank of gas
C. The change in years
D. The cost of filing a 15-gallon tank with gas
90. Hinton plans to solve the system of equations below.
x + 3y = 8
5x – y = 8
Which of the following does not show an equation Hinton can use to solve the system of equations?
A. x + 3(5x – 8) = 8 B. 5(8 – 3y) – y = 8
C. x = 8 – 3y D. 5x – (x + 8) = 8
91. The function f(x) = 30,000(0.8)x gives the value of a vehicle, where x is the number of years after purchase. According to the function, what will be the value of the car 8 years after purchase? Round your answer to the nearest whole dollar.
A. $5,033B. $19,200
C. $50,300D. $192,000
92. Which is a possible situation for the graph below?
A. A car drives at a steady speed, slows down in a school zone, and then resumes its previous speed.
B. A child climbs the ladder of a slide and then slides down.
C. A person flies in an airplane for a while, parachutes out, and gets stuck in a tree.
D. The number of visitors increases in the summer, declines in the fall, and levels off in the winter.
93. A scientist was performing an experiment.Every minute, she recorded the number of bacteria. Which function models the data found in the table below?
Time (min) / Number of Bacteria0 / 12
1 / 60
2 / 300
3 / 1500
A. y = 12x B. y = 12(5)x
C. y = 5(12)x D. y = 12x2 + 5x + 15
1