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Algebra 1A Exam Review (chapters 1-5)
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Name:______________________________Hr.____
Chapter 1:
Write an algebraic expression for each phrase.
1. a number p minus 19
1._______________
2. 12 more than 5 times c
2._______________
3. 1 less than the quotient of a number n and 6
3._______________
4. 9 times the sum of a number t and 3
4._______________
5. x cookies split equally among 5 kids
5._______________
Simplify each expression.
6._______________
6. 22 + (32 – 42)
7.
625
8. (33 – 9)2
7._______________
8._______________
9. –10 – (–2) • (–43)
 1
10.   
 4
3
11. 52 ÷ 2
9._______________
10.______________
11.______________
Evaluate each expression for the given values of the variables.
12. 5x + 2y2 ; x = 2 and y = 4
13. (3c + 2)3 +
d
; c = –2 and d = 8
2
12.______________
13.______________
14. Name the subset(s) of real numbers to which each number belongs.
(Real, Irrational, Rational, Integers, Whole, Natural)
3 ___________________________________________
-8
___________________________________________
7
___________________________________________
5
15. Which property is illustrated by –8 + 0 = –8?
15.______________
16. Which property is illustrated by –8 + 2 = 2 + –8?
16.______________
17. Given and example of the distributive property.
18. Is x = 6 a solution to the equation 2x – 7 = -5? Show your work.
18._______(Yes/No)
19. Is the ordered pair (–8, –7) a solution to the equation 3x + 10 = 2y? Show your work.
19._______(Yes/No)
3
3 5
1
, 1 ,  , and 
4 4
4 from least to greatest.
20. Order the numbers 4
20.______________
Evaluate each expression for a = –2 and b = 5.
21.______________
21.
6a
b3
22. –2b – 3a
23. (ab)2
22.____________
23.____________
Simplify each expression.
24. 2x (3x – 7 ) + 5x – 8
25. 15 – (–3) – 22
26. –2( x – 7) - 2x
24.____________
25.____________
26.____________
27. Use a Table, an Equation, and a Graph to represent each relationship.
Jessica is selling candy bars for $1.50 each. Write and equation relating the # of candy bars b to the
amount of money m she will bring in. Fill in the table a use it to graph your results.
Equation:________________
Candy Bars
(b)
Money (m)
0
10
20
30
40
Solve and reduce. Keep your answer as a fraction and show all work.
28.____________
3
29. 7
6
5
29.____________
28. 6 
7

5
30.
2 3

7 4
30.____________
Chapter 2:
31. x – 10 = -5
32. –3n = 27
33.
3
x  18
8
31.________
32.________
33.________
34.
x
4

6
3
35. –7x + 18 = - 17
36.
x
 2  10
4
34.________
35.________
36.________
3
5
38.  (10x + 15 ) = 48
37. 5x + 3(x + 4) = 28
37.________
38.________
39. Company Clogged Up will pay you $200 up front and $18 per hour to clean outhouses. Define your variable,
then write and solve an equation for how many hours you must work to earn $686.
Defined Variable:_______________
39.____________
40. 4x – 7 = 7x - 34
41. 3(x – 2) +7 = 4(x + 1)
40._________
41._________
42. You currently have $42 and you save $2.50 per week. Your brother has $110 dollars and will spend
6 dollars per week. When will you and your brother have the same amount of money?
a. Define your variable:
42a.________
b. Write and solve an algebraic equation:
42b.________
For 43 – 44, solve each formula for w.
43. P = 2l + 2w
44. N 
( w  8)
3
43._________
44._________
Rewrite the following equations by getting y by itself. Then find the values of y if x = -2, 0, 3
45. 4x + 2y = 10
x
y
45. y = __________
-2
0
3
Convert the following, show your work:
46. 648 in. to yards
47.
100 ft
to mi/hr.
min
46.____________
47.____________
Solve the proportions for x, show your work!:
48.
1.25 x 10

9
16
49.
x5 5

9
7
48.____________
49.____________
50. Solve for x by setting up a proportion.
50.____________
51. An architect created a scale model of what a building will look like once construction is
51.____________
finished. The scale for the model is 3 in.: 25 ft. The tallest building in the model is 8.5 in.
tall. How tall is the actual building?
52. 9 is what percent of 21?
52.____________
53. 18 is 40% of what number?
53.____________
54. A pair of pants originally marked $68 is now 30% off. What is the new price?
54.____________
55. A pair of pants was $92 and now sells for $118? What is the % increase?
55.____________
Chapter 3:
Is each number a solution of the given inequality?
56. 5x - 1 ≤ –3
a. –3
b. 0
56a. (yes /no)____
56b. (yes /no)____
Graph the following inequalities
57. -8  x < 5
58. 3  x
Write and graph an inequality that represents the statement.
59. x is less than 4 and greater than 1
59. Inequality:________________
Graph:
60. x is less than or equal to –2 or greater then 5
60. Inequality:________________
Graph:
Solve the inequality for x and graph the results.
61. 2x - 4 ≤ 1
62.
x
+1 ≥ 8
2
63.
3
8 4
x 
5
3 3
61.____________
62.____________
63.____________
65. 4  2x  6  15
64. 5x – 4 > -2x – 12
64.____________
65.____________
Write each interval as an inequality. Then graph the solutions.
66.
1,5
66. Inequality:_______________
67. [-2, )
Graph:
67. Inequality:______________
Graph:
Write a compound inequality and interval that each graph could represent.
68.
68. Inequality:_______________
Interval:_________________
69. Bananas costs $0.15 per pound. Write & solve an inequality to show how
many pounds of bananas b that Miles can afford if he has $20.
Write each set in roster form and in set-builder notation.
70. M is the set of integers that are less than 1.
69.____________
70. Roster:______________________________
Set Builder:___________________________
71. A long distance phone company offers a plan such that each month you pay a
$20 service fee and $0.12 per minute. How many minutes can you spend talking
if you have a $55 budget for your phone bill? Set up an inequality and solve.
71.____________
For 72 – 73 solve and graph the equation/inequality. (hint: and / or answer?)
72.
73. 2 x  4 + 7 = 21
5x  1 = 11
72.____________
73.____________
74.
Solve and Graph:
x
-6 <5
4
74.____________
Graph:
75. Suppose U = {1, 3, 5, 7…} is the universal set and A = {1, 3}. What is A' ?
76. Suppose U = {all the days of the week} is the universal set and
A = {school days}and B = {days that end in the letter y}. Find A' and B'
75.____________
76. A'=________________
B'=________________
77. Find the subsets of the following set.: ham(h), turkey(t ), salami(s) :_______________________________
78. Find each union or intersection. Let A = {0, 2, 4, 6, 8, 10},
B ={x | x is a positive even integer less than 16}, C = {1, 2, 4, 7}, and D = {–3, 2}.
a. A  B
b. A ∩ C
c. B ∩ D
d. D  C  B
78a.____________
78b.____________
78c.____________
78d.____________
79. There are 84 students in choir. There are 92 students in band. There are 18 students
that participate in both choir and band.
a. Draw a Venn Diagram to illustrate the following:
b. How many total students are in either choir or band?
79b.____________
c. If there are 450 total students, how many are not in choir or band?
79c.____________
Chapter 4:
Sketch a graph to represent the situation. Label each section.
80. The temperature of the water in a bottle from the time you fill it up with tap water,
put it in the freezer, then take it out of the freezer and set it outside on a warm day.
For each table, determine whether the relationship is a function and tell why or why
not.
81.
82.
81. _________________________
__________________________
82. _________________________
_________________________
Each set of ordered pairs represents a function. Write a rule that represents the function.
83. (1, -2), (2, -1), (3, 0), (4, 1)
84. (3, 8), (2, 6), (1, 4), (0, 2)
83.____________
84.____________
Write a function rule that represents each sentence.
85. 20 more than one half of x is y.
85.____________
86. 9 less than the product of a number q and 5 is r.
86.____________
Identify the domain and range of each relation.
87. {(−1, 5), (0, 4), (1, -7), (2, 8)}
87. D:_________
R:_________
Find the range of each function for the given domain.
88. f(x) = 3x - 4; {−1, 1, 3, 5}
88.____________
89. Describe how you know a sequence of numbers is an arithmetic sequence.
90. You go to the store to buy some oranges. Each orange costs $0.15. If you graphed
the relationship between the # of oranges and the cost, your graph would look like
which of the following?
a. Discrete/Continuous b. Discrete/Linear
c. Continuous/Linear
d. Continuous/Non-Linear
90._____________
e. Discrete/Non-Linear
91. Write a function rule for the area of a rectangle whose base is 4 ft more than twice its height. 91.___________
Drawing:
Function Rule:
92. The cost c of a gym membership is $24 per month m plus a one-time fee of $50.
a. Write an equation relating c and m.
a. ___________________
b. What is the Dependent Variable ?
b. ___________________
c. How much would it cost for an 8 month membership?
c. ___________________
d. Graph the results for the delivering up to 24 months.
months
6
12
18
24
cost
Graph the following functions.
93. y = -3x + 4
Choose
x
Substitute x into equation to
find y
x
y=
(x, y)
-2
-1
0
1
2
Graph the following functions.
94. y = x  1  1
Choose
x
Substitute x into equation to
find y
x
y=
-3
-2
-1
0
1
(x, y)
Graph the following functions.
95. y = x 2  2
Choose
x
Substitute x into equation to
find y
x
y=
(x, y)
-2
-1
0
1
2
For 96 – 97, use the recursive formula / explicit formula to write the first 4 terms of the sequence.
96. A(1) = 3, A(n) = A(n - 1) - 3
97. A(n) = 3n – 5
96._____________
97.___________
98. Write a Recursive Formula and an Explicit Formula for the following sequences of #’s.
-4, -1, 2, 5, …
98. R:_______________________
E:_______________________
Chapter 5:
99. Find the slope of the line that passes through the following points.
(6, -5) (4, 3)
99. m = _________
100. A helium balloon ascends into the air at a constant rate. At 2 seconds the height of
the balloon is 8 ft. At 8 seconds the height of the balloon is 24 ft. What is that rate
of change in the height of the balloon over time?
101. Graph y = -2x + 4
102. Graph 2x + 4y = 8
103. y  4 
100._____________
2
 x  2
3
For #104, write the following as an algebraic equation.
104. The temperature t in the oven starts at 70 degrees and increases at a rate of
25 degrees per minute m.
104.___________
105. Write an equation in slope intercept form of the line that passes through the given
points.
(8, 6) and (6, -2)
105.___________
106. Write an equation in point slope form to a line that
106._________
107. What is the equation to the
following line:
107.________
2
passes through (-4, 3) and has a slope of
. Graph.
5
Graph by finding the x- and y-intercepts.
108. -9x + 6y = 18
x
y
109. A bag of popcorn costs $2 and a coke costs $1.50. Write and graph
an equation that describes the number of each item you can buy with $18.
x
y
110. Describe a situation that has a positive correlation between two sets of data.
111. If a graph has a correlation coefficient of r = -0.34, what does this tell you about the relationship between
the two sets of data?
112a. Find the equation for the line of best fit for the data shown below. The data represents
the amount of lead emissions from fuel combustion for the years 1988 (x = 0) to
1997 (x = 9).
112a.__________
112b. Using your equation for the line of best fit, what would the emissions be for the
year 2013?
112b.__________
113b. Put the following equation into slope-intercept form. 2x -3y = 19
113b.__________
114a. Graph y = x  2
x
0
-1
-2
-3
-4
a. Vertex:_____________
b. Symmetric
about the line:__________
y
114b. How did + 2 to the x-value effect the graph of y = x ? _____________________________________
115a. Graph y = x  1 + 2
x
-2
-1
0
1
2
a. Vertex:_____________
b. Symmetric
about the line:__________
y
c. Slope of right side:________
d. Reflect over line of symmetry.
115b. a. How did – 1 from the x-value effect the graph y = x ?
___________________________
b. How did + 2 outside of the absolute value effect the graph of y = x ?
116. Write an equation to the graph:
_____________________
_____________________
Exam Review Grading:
Day #
1
2
3
Assignment
# Correct
Productive Use
Work Shown
of Time Points
Points (10, 5, 0)
(10, 5, 0)
Total Points
Corrected By: