Download Algebra 1 A 3 Tri Final Exam Review

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Algebra 1 A Final Exam Review: Fractions and Chapter 1
1. What is the greatest common factor of 120 and 72?
3. Write two fractions that are equivalent to
5. Write
2. What is the greatest common factor of 51 and 39?
28
.
36
4. Write the fraction
25
as a decimal.
75
6. Write 4
7. Write 0.875 as a fraction in simplest form.
60
in simplest form.
100
3
as a decimal.
25
8. Write 0.4545 as a fraction in simplest form.
9. Find each sum or difference (Write each answer in lowest terms—simplest form)
a.
2 1

4 3
b.
2 6

5 8
d.
5 2

10 3
e. 4
2
1
2
7
3
c.
4w 2w

9
3
f. 3
1
1
5
4
2
10. Find each product or quotient (Write each answer in lowest terms—simplest form)
a.
6 3

5 4
b.
7 8

9 10
c. 3  2
d.
2 4

7 12
e.
3
1
2
6
4
f. 4
2
3
1
2
2
1
2
3
2
11. Write
7
as a percent.
8
13. Write 350% as a mixed number in simplest form.
12. Write 0.03% as a decimal.
14. Write 66% as a fraction in simplest form.
15. Define a variable and write an expression for the phrase: “the quotient of 13 and a number.”
16. Define a variable and write an equation to model the situation: “What is the number of pieces of pie left from an 8piece pie after you have eaten some pieces?”
17. Define variables and write an equation to model the relationship in the table.
Number of Videos
Cost
1
$7.00
2
$10.00
3
$13.00
4
$16.00
18. Write a phrase for the expression: 2m – 5 .
21. Evaluate (mp 2 )  q for m  3 , p  7 , and q  4 .
19. Simplify 14[52  (42  32 )  2] .
20. Simplify 43  8  1  5  8 .
22. The equation s  p  0.15 p represents the sale price s of an item with an original price p, after a 15% discount. Make
a table to find the discount prices for items with original prices of $12, $16, $20, and $25.
23. Name the set(s) of numbers to which each number belongs:
a. -1
e.
b. 7
5
f.
c. 0.3
17
25
g. 
d. 0
20
4
24. Use <, =, or > to compare:
a. 
2
1
_______ 
3
6
b.
25. Order the numbers from least to greatest:
1
________ 0.333
3
7
, 0.63, 0.636 .
11
26. Find each absolute value:
a. 6  4  3
b. 3 (4)  7  2
27. a. Make a scatter plot for the set of data below. Draw a trend line on the scatter plot.
Number of Items
Total Cost
2
4
5
7
9
$3.50
$7.30
$9.00
$12.00
$16.00
b. Is there is a positive correlation, negative correlation, or no correlation between these two sets of data?
d. Predict the total cost for 13 items.
28. Would you expect a positive correlation, negative correlation, or no correlation between the two data sets below?
the sales of bathing suits and the amount of snowfall
29. Use the data set: 12, 15, 10, 7, 15, 12, 6, 11, 13, 9, 2
a. Find the mean for the data set above.
b. Find the median for the data set above.
c. Find the mode for the data set above.
d. Find the range for the data set above.
e. Make a stem-and-leaf plot for the data set above.
30. You receive scores of 75, 82, and 79 on three of your history tests. What grade do you need on your next test to have
a 80 average on the four tests?
Algebra 1 A Final Exam Review: Chapter 2
31. Simplify.
a. –2.3 +7.2
5  2
9  3
b.     
c. 2
1
15
3
4
16
d.
9 
3
  2 
7  14 
32. A diver dives 47 ft. below the surface of the water and then rises 12 ft. Use addition to find the diver’s depth.
33. On two football plays, a team gains 9 yards, and then loses 12 yards. Use addition to find the result of the two plays.
34. Evaluate each expression for n  4.7 .
c. n  (5.8)
b. n 2  9.2
a. n  3.7
35. Simplify
 3 2 12  


 7   9 
   10


    2
a. 
b. 
37. Simplify each expression.
a. 6.2  9.3
c. 
b. 5.6  (7.1)
2 7

5 10
d. 11  (3)
38. Evaluate each expression for x  2 , y  3 , and z  1 .
a. x  z  y
b.  z 2  y
39. On Friday, the closing price of a JPM company share was $12.71. It had risen $2.07 from the previous day. Find the
closing price of JPM on Thursday.
40. Simplify each expression.
a. 20(3)
b. 8(4.3)
c. 52 (3)3
d. 2(3)2
41. Evaluate each expression for m  
a. 7 p 
2m
n
1
, n  2 , and p  1 .
2
b. m  p  (n)
c. p (m  n)
d. 3p3  m
42. Simplify each expression.
12  32
a.
5
b. 22  (3  5)
44. Complete the table.
43. Evaluate
s
2r
1
3
for r   and s  .
3s
8
4
3
s 5
4
–3
–1
2
–4
45. Simplify using the Distributive Property.
a. 4(999)
b. 23(1003)
46. The school librarian got money to buy additional books for the library. To find the cost c of n books, she used the
function c  32.99n . Use the Distributive Property to find how much she spent on 3 books.
47. Simplify each expression.
a. 0.25(6q  12)
2
3
b.  (6n  9)
c. 19t 2  30.7t 2  2t  5
48. Identify the terms, coefficients, and constant of 17m2  12m2  3m  9  4 .
8
 15
b 
9
 16
d. 144 
49. Write an expression for each phrase.
a. –4 times the quantity 3 plus t
b. the product of 2.5 and the quantity b minus –7
50. Complete the table.
52. Simplify the expression: 6
k
1
1 1 2
 4 1  .
2
3 2 3
2(k  4)
–10
–5
3.5
0
51. Name the property that each equation illustrates.
a. 5  0  5
b. 8 17  17 8
c. (5  4)  3  5  (4  3)
d. 2(5  6)  2(5)  2(6)
53. You buy 3 grapefruits for $2.10, a pound of apples for $1.19, some grapes for $3.90, and some bananas for $0.81.
Use the commutative and associate properties to find the total cost of the fruit.
54. Use the spinner above. Find the theoretical probability of landing on the given section(s) of the spinner.
a. P(black)
b. P(2)
c. P(1 or 5)
d. P(greater than 5)
55. Use the spinner above. Find each odds.
a. odds in favor of a multiple of 3
b. odds against a prime
e. P(not prime)
56. A forest contains about 500 trees. You randomly pick 67 trees and find that 27 of them are oaks.
a. What is the experimental probability that a tree in the forest is an oak?
b. Predict how many oak trees there are in the forest.
57. Suppose you roll a number cube. Find P(3 or 4).
58. You roll a blue number cube and a green number cube. Find each probability.
a. P(blue 1 and green 1 or 2)
b. P(blue and green both less than 6)
59. Suppose you choose a marble at random from a bag containing 3 green marbles, 4 blue marbles, and 5 red marbles.
You replace the first marble in the bag and then choose again. Find each probability.
a. P(red and red)
b. P(blue and green)
c. P(red and blue)
60. Suppose you choose a tile at random from a bag containing 2 A’s, 3 B’s, and 4 C’s. You choose a second tile without
replacing the first one. Find each probability.
a. P(A then B)
b. P(two B’s)
c. P(C then A)
d. P(two C’s)
61. Four girls and three boys volunteer to represent their class at a school assembly. The teacher selects one name and
then another from a bag containing the seven students’ names. What is the probability that both representatives will be
girls?
62. A refrigerator contains 12 drinks: 4 lemon, 5 apple, and 3 orange. Julie grabs a drink on her way to school. Then
Jenny grabs a drink on her way to school. What is the probability that Julie will get an apple drink and Jenny will get an
orange drink, if they grab drinks at random?
Algebra 1 A Final Exam Review: Chapter 3
63. Solve each equation. Check your answer.
a. 6 
a
2
4
b. −15 = −4m + 5
c. 1 
m
 2
9
d.
1
v38
3
64. Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
65. Alex spends ½ of his allowance each week on school lunches. Each lunch costs $1.25. How much is his weekly
allowance?
66. Miles has already saved $40. He wants to buy a CD player for $160 in sixteen weeks. How much should he save
each week?f
67. Solve each equation. Check your answer.
a. 4x + 6 + 3 = 17
b. −2 + a + 3 = −4
c. r + 11 + 8r = 29
d. 7m – 3m – 11 = 9
68. A gardener is planning a rectangular garden area in a community garden. His garden will be next to an existing 12-ft
fence. The gardener has a total of 42 ft of fencing to build the other three sides of his garden. How long will the garden
be if the width is 12 ft?
69. Two friends are renting an apartment. They pay the landlord the first month’s rent. The landlord also requires them
to pay an additional half of a month’s rent for a security deposit. The total amount they pay the landlord before moving in
is $975. What is the monthy rent?
70. Solve each equation. Check your answer.
a. 4(−x + 4) = 12
b. −2 = −(n−8)
c. 18 = 3(3x – 6)
d. –5(n + 5) = −30
71. Solve each equation. Check your answer.
a.
m
3
4
8
4
b.
a 1
 8
5 5
c.

7y y
 3
8 2

d.
1 5w 2


5 15 3

72. Solve each equation. Check your answer.
a. 0.4x + 3.9 = 5.78
b. 9.2r + 5.51 = 158.23
c. –5.6 –8x = –78.4
d. 3.64 + 12.3v = 146.32
73. Solve each equation. Check your answer.
a. 4a + 3 = 2a + 17
b. 4m + 2 = 2m + 9
c. 5b + 13 = –8 – 2b
d. 13 – 2x = 4x – 5
74. One health club charges a $45 sign-up fee and $25 per month. Another health club charges a $100 sign-up fee and
$20 per month. For what number of months is the cost the same?
75.Solve each equation. If the equation is an identity, write identity. If it has no solution, write no solution.
a. 4(3x + 5) = 2(6x + 10)
b. 16 – 4b = –2(3 + 2b) c. –4(t + 3) = 2(4 – 4t )
d. 13 – 2x = 4x – 5
76. Find each unit rate.
a. $13 for 5 gallons
b. $8/ 3lb
c. 700 calories for 1.75 hours
d. $0.88 for 16 ounces
77. In 2000, Lance Armstrong completed the 3630-km Tour de France course in 92.5 hours. Traveling at his average
speed, how long would it take Lance Armstrong to ride 295 km?
78. Express each rate in miles per hour.
a. 1 mile in 3 min
b. 270 ft in 10.8 min
c. 10560 ft in 60 min
d.
2640 feet in 4 min
d.
9 n

4 7
79. Solve each proportion.
a.
7 x

5 3

b.
7 8

n 7
c.

3 5

n 8


79. Molly bought two heads of cabbage for $1.80. How many heads of cabbage can Willie buy if he has $28.80?
80. Gabriella bought three cantaloupes for $7. How many cantaloupes can Shayna buy if she has $42?
81. Solve each proportion.
a.
6
9

b 1 7

b.
4 r3

9
6

c.
x3 9

x
10

82. The figures in each pair are similar. Find the missing length.
X
5 ft
8 ft
5 ft
d.

7
4

n2 n
83. The figures in each pair are similar. Find the missing length
40 ft
8 ft
X
5 ft
84. A tree casts a shadow 9 ft long. A woman 5.5 ft tall casts a shadow 3 ft long. The triangle created by the tree and its
shadow is similar to the triangle created by the woman and her shadow. How tall is the tree?
85. A certain model airplane is
long is the airplane’s wing?
1
3
of the airplane’s actual size. The length of the model airplane’s wing is
ft. How
45
4


86. The scale of a map is 1 in. :16.5 mi. Find the actual distance corresponding to each map distance.
a. 5 in.
b. 8.3 in.
c. 18.6 in.
d. 20 in.
87. The length of a garden is 2 yd more than twice its width. The perimeter of the garden is 40 yd. What are the length
and width of the garden?
88. The length of a rectangle is 6 in. more than the width. The perimeter of the rectangle is 32 in. What are the length
and width of the rectangle?
89. The sum of three consecutive even numbers is 48. What are these numbers?
90. The sum of three consecutive numbers is 72. What are these numbers?
91. Ryan left the science museum and drove South at a speed of 28 mph. Gabriella left one hour later driving 35 mph in
an effort to catch up to him. In how many hours will Gabriella catch up with Ryan?
92. A cattle train left Miami and traveled toward New York at a speed of 10 km/h. 14 hours later a diesel train left
traveling at 45 km/h in an effort to catch up to the cattle train. In how many hours will the diesel train finally catch up
with the cattle train?
93. An aircraft carrier made a trip to Guam and back. The carrier travels at 8 km/h on the trip there and 6 km/h on the
return trip. If the total travel time is 7 hours, how long did the trip to Gaum take?
94. A passenger plane made a trip to Las Vegas and back. On the trip there it flew 432 mph and on the return trip it went
480 mph. If the total travel time is 19 hours, how long did the return trip take?
95. A submarine left Hawaii at the same time as an aircraft carrier but in the opposite direction. The aircraft carrier
travels 16 mph faster than the submarine. After nine hours, the vessels are 288 miles apart. Find the speed of the aircraft
carrier and the submarine.
96. Kali and Matt left home and traveled in opposite directions on a straight. Kali drives 10 mph faster than Matt. After
4 hours they are 380 miles apart. Find Kali’s and Matt’s rate.
97. Find each percent of change. Describe the percent of change as an increase or decrease. If necessary, round
to the nearest tenth.
a. 33 ft to 47 ft
b. $109 to $98
c. 55 grams to 70 grams
d. 43 minutes to 28 minutes
98. You have been working out and have increased your endurance. You used to be able to only run 1.5 miles
before stopping. Now you can run 2.1 miles before stopping. Find the percent of increase to the nearest
percent.
99. Find the greatest possible error for each measurement.
a. 4.1 cm
b. 56.35 grams
c. 152 lbs
d. 10.5 in.
100. Find the minimun and maximum possible areas for rectangles with the following measured areas.
a. 5 cm x 8 cm
b. 3 mi x 10 mi
c. 14 in. x 9 in.
d. 4 cm x 6 cm
101. Find the percent error of each measurement.
a. 5 miles
b. 9.02 in.
c 6.3 ft
d. 13 in.
c.  .09
d.  64
102. Simplify each expression.
a.
b. 
121

4
49



102. Tell whether each expression is rational or irrational.
a.

b. 
40

16
52
c.  .16

d.  64

103. Between what two consecutive integers each square root.
a.
b. 
54

25
5
c.


d.  199
174

104. Find the value of each expression. If necessary, round to the nearest hundredth.
a.
b. 
484


81
25
c.
d.  2.5
150


105. The elasticity coefficient e of a ball relates the height h from which it is dropped to the height r of its rebound. You
can use the function e 
r
to find the elasticity coefficient. What is the elasticity coefficient of a basketball that when
h
dropped from a height of 6 ft rebounds 3.6 ft. Round to the nearest hundredth.

106. For the values given, a and b are legs of a right triangle, and c is the hypotenuse. Find the length of the missing side
of each triangle. If necessary, round to the nearest tenth.
a. a = 16, b = 30
b. a = ¾, b = 1
c. a = 5, c = 9
d. b = 45, c = 51
107. A 20 ft ladder is placed 5ft from the base of a building. How high on the building will the ladder reach?
108. Determine whether the given lengths can be sides of a right triangle.
a. 6.4ft, 12ft, 12.2ft
b. 5 cm, 12cm, 13cm
c. 2.1m, 7.2m, 7.5m
d. 6ft, 8ft, 9ft
Algebra 1 A Final Exam Review: Chapter 4
109. Is each number a solution of x ≤ 5?
a. 3
b. −4
c. 8
d. −9
110. Is each number a solution of 3x  7  1?
a. 3
b. −4
c. 8
d. −9
110. Is each number a solution of 6 
a. 3
b. −4
b. −4
d. −9
c. 8
111. Is each number a solution of 10 
a. 3
m
 4?
2
c. 8
p
7?
2
d. −9
112. Graph each inequality.
a. x ≥ 3
b. −2 < r
c. k ≤ −4
d. 4 > b
113. Write an inequality for each graph.
a.
b.
c.
d.
114. Define a variable and write an inequality to model each situation.
a. The acceptable speed on the highway is at most 70 mph.
b. Maple Field can hold at most 2,500 people.
c. There are more than 150 students in the marching band.
115. Solve each inequality. Graph and check your solution.
a. −5 + x ≤ 2
c.
1
 b  2
2
b. k − 2 < −3
d. k + 1.4 < −2.1
116. The school club is selling popcorn to raise money for a field trip that costs $1200. In the first week they made
$350. In the second week they made $475. Write and solve an inequality to show how much money they still need to
make so they can go on the field trip.
117. You have saved $17. You are going to dinner and the movies with a friend. You spent $5 at McDonald’s on dinner
and the movie costs at least $8.50. Write and solve an inequality to find how much money you have to spend on movie
concessions.
118. Solve each inequality. Graph and check your solution.
a. 1.5 
c. 2  
n
2
1
n
2
b.
2
x4
3
3
2
d.  a  6
119. Solve each inequality. Graph and check your solution.
a. 4b ≤ 16
b. −15 > −3x
c. 8 < 3.2x
d. −0.8m ≥
120. Suppose you earn $8.25 per hour working part-time as a cashier. Write and solve an inequality to find how many
full hours you must work to earn at least $300.
121. Students in the school band are selling calendars. They earn $0.45 on each calendar they sell. Their goal is to earn
more than $399. Write and solve an inequality to find the fewest number of calendars they can sell and still reach their
goal.
122. On a trip out west, Julie wants to cover at least 550 miles in the first 8 hours. What must her average rate of speed
be?
123. Solve each inequality.
a. 11  29  3x
b. 4(r  5)  1  3
c. 3(0.3  5s)  2(4  2.3s)
d.
3
1 5
x2 x  x
4
8 2
124. The freshmen class is planning a talent show. The cost for the use of a stage is $600. To pay for the stage, there is a
fee of $2.00 for each student and $3.00 for each guest that is not a student. There are 230 students that plan to attend.
Write and solve an inequality to find how many guests must attend for the freshmen to pay for the cost of the stage.
125. Write a compound inequality that represents each situation. Graph your solution.
a. all real numbers x that are between -2 and 7
b. all the real numbers x that are at least 5 or less than 2
126. Solve each compound inequality. Graph your solution.
a. 1.3  x  2.6  5.4
b. 15  2t  3  5
c. 3  2m  2 or 5m  2  3
d.
2x 1
1  x
 2  3 or
4
3
2
127. Solve each equation.
a. 17  5 p  3
b. r  5  3
c. 2 x  10
d. 1.3 5d  3.9
128. Solve each inequality. Graph your solution.
a. 4 x  3  19
b. 3 m  4  9
c. 5  6 p  3  13
129. A box of cereal should weigh 568 g. The quality control inspector randomly selects boxes to weigh. The inspector
sends back any box that is not within 6 g of the ideal weight. Write an absolute value inequality for this situation. What
is the range of allowable weights for a box of cereal?