CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
Name: ___________________________________________
Algebra CT: Final Exam Dates: Thurs 12/17 and Fri 12/18
Unit 1 Review
Simplify:
1. Name the coordinates of each point:
2. Name the coordinate of each point.
a.) _______
A_______
b.) _______
B_______
c .) _______
C_______
d.) _______
D_______
e.) _______
E________
3. Evaluate the expression:
4  ( 5 2 + 2)
4. Evaluate the expression:
8 + 4(9 - 2)
a.) 42
b.) 36
c.) 84
d.) 28
5. Simplify:
-7(2x – 4) – 8x
6. Simplify:
9x – 3(2x + 6)
a.) 3x + 6
b.) 3x – 6
c.) 3x + 18
d.) 3x – 18
Solve:
7. Solve: 3x – 9 = 30
8. Solve: 2x – 11 = 41
a.) 26
b.) 15
c.) 30
d.) 52
10. 8x 17  3x  18
a.)
7
b.)
1
11
c.) 18
d.) -7
Page1
9. 4  2 x  3  10  8 x
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
Solve:
11.
5(3x – 1) = 17 + 4x
12.
– (10 – x) = 3(x + 4)
a.) x = -7
b.) x 
11
2
c.) x = -11
d.)
13.
x – 2(3x – 9) = -7
14.
x = 11
3x – 2(4 – x) = -23
a.) x  15
b.) x  3
c.) x  3
d.) x  31
15.
2
( x  9)  4  20
3
16.
3
4
 ( x  8)  11  23
32
3
80
b.) x 
3
c.) x  24
d.) x  8
a.) x 
6 r

7 15
18.
m 87

16 232
1
a.)
m=
b.)
m=
c.)
m=6
d.)
m=8
6
1
8
Page2
17.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
Solve:
19.
3x  4 3

x5 2
20.
x  3 2x  5

3
7
a.) x = -36
b.) x = -8
c.) x = 6
d.) x = -27
21.

2
3
x
4
5

a.)
x=
b.)
23.
Solve for t: I = Prt
3
22.
4
x=
d.)
x=
a.)
b.)
c.)
d.)
13
2
8
39
6
x=
52
c.)
24.
x
39
8
26
3
Solve for h: V =
h
1
 r²h
3
3V
 r2
V 2
h
r
3
2
V r
h
h
3
 r2
3V
Unit 2 Review
Solve:
-x + 1 ≤ 3x + 21
26.
-2x + 9 ≤ 5x - 12
a.) x < -3
b.) x ≥ 3
c.) x ≤ -3
Page3
25.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
d.) x > -3
Solve:
27. 4  2x < 12
28.
a.)
b.)
c.)
d.)
29.
-2x + 6 > -8
30.
-5 < -x – 3 ≤ 7
-10 ≤ x < -2
-10 ≥ x ≥ 2
-10 ≥ x > 2
-10 ≤ x < 2
2
x  3  11
3
a.) x ≥ 16/3
b.) x ≤ 12
c.) x ≥ 12
d.) x ≥ 11
Graph:
31.
-2(x – 4) ≤ 3x – 12
32.
5x + 15 > 7(x + 3)
33. An amusement park charges $12 for admission and 1.50 for each ride. You go the park with $36. Write an
inequality that represents the possible number of rides you can go on. What is the maximum number of rides you can go
on?
Page4
34. Tony works at a bike store and earns $200 every week plus $15 for every bike that he sells. Write an inequality that
can be used to determine the number possible number of bikes Tony must sell in one week if he wants to earn a minimum
of $500 for that week. What is the minimum number of bikes Tony must sell in one week to earn a weekly salary of
$500?
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
Unit 3 Review
Find the slope:
35. Find the slope for the
relationship shown in the table.
Y
-4
-25
-3
-21
a) -2
-1
b) − 2
11
c) 2
31
1
d)
2
2
5
10
37. (-1, 4), (3, -2)
36. Find the slope for the relationship shown in the table.
X
Y
X
1
-5
-7
-2
-13
3
-23
7
-31
11
-39
38. (7, 2), (-8, -3)
a.) 1
b.) 3
c.) -3
d.)
39. (-5, 2), (-5, 4)
1
3
40. (4, 6), (-2, 6)
a.) 1
b.) 0
c.) undefined
Find the slope:
41.
42.
43.
44.

1
4
Page5
d.)
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
45. Find the slope of the line represented by the equation
1
x – 5.
4
a.) 2
b.) -3
c.) -2
d.) 2x
47. Find the slope of the line represented by the equation
x + 3y = 12.
48. Find the slope of the line represented by the equation
6x – 2y = 9.
a.) 
b.)
c.)
d.)
9
2
6
3
-3
49. Find the x-intercept and the y-intercept for the
equation:
3x – 6y = -12
50. Find the x-intercept and y-intercept for the equation:
-x + 2y = 10
x-intercept: ______________________
x-intercept: ______________________
y-intercept: ______________________
y-intercept: ______________________
Which ordered pair is a solution to the given equation.
51. -3x – y = -9
a.)
b.)
c.)
d.)
(0, 3)
(-6, 9)
(4, -3)
(-2, -3)
Graph:
53. 2 x  3 y  12
52.
a.)
b.)
c.)
d.)
54.
y
3
4
x
1
x  2 y  5
3
(-3, -2)
(3, 2)
(9, -1)
(-6, 1)
55.
y  4
Page6
y=
46. Find the slope of the line represented by the equation
y = -3 + 2(x – 4).
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
58.
59.
60.
61.
Page7
Unit 4 Review
Write each equation in slope-intercept form using the information given:
56.
57.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
62. What is the equation of the horizontal line that
passes through the point (7, -3)?
63. What is the equation of the vertical line that passes
through the point (7, -3)?
a.) y = -3
b.) x = 7
c.) y = x
d.) y = 7x – 3
2
of ?
3
66. What is the slope-intercept form of a line that passes
through (1, 7) and (3, -5)?
65. What is the equation of the line in slope-intercept form
that passes through the point (-5, -1) and has a slope of
a.)
y
b.)
y
c.)
y
d.)
y
3
4
3
4
3
4
3
4
3
?
4
x4
x
x
x
19
4
17
4
11
4
67. What is the slope-intercept form of a line that passes
through (-3, -5) and (6, -2)?
a.)
b.)
c.)
1
x
3
1
y  x2
3
1
y  x4
3
y
Page8
64. What is the equation of the line in slope-intercept
form that passes through the point (1, -7) and has a slope
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
Write the equation in slope-intercept form.
68. y – 4 = – 3(x + 5)
y
69.
4x – 3y = 6
a.)
-3y = -4x + 6
b.)
c.)
d.)
70. A sales person for the local bike shop earns a
weekly pay of $220 plus $23 per sale. Write an equation in
slope-intercept form that gives the total weekly pay y in
terms of the number of sales x.
1
x 8
3
d.)
4
x–2
3
4
y=  x+2
3
4
y= x+6
3
y=
71. A sales person for the local computer shop earns a
weekly pay of $275 plus $35 per sale. Write an equation in
slope-intercept form that gives the total weekly pay y in
terms of the number of sales x.
a.) y  275x  35
b.) 35x  y  275
c.) y  35x  275
d.) y  35x  275
72. Write an equation in slope-intercept form represented
by the given table.
x
-4
-2
0
-6
2
10
2
4
18
26
1
y   x 1
3
b.) y  3x  3
c.) y  3x  1
1
d.) y   x  3
3
a.)
x
y
3
2
1
-6
-3
0
0
-1
3
6
Write the equation of the two parallel lines given in the graph below.
Page9
74.
y
73. Write an equation in slope-intercept form represented
by the given table.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
75. Which set of equations represent the parallel lines.
2
x3
3
a.)
3
y  x4
2
y
y  3x 
c.)
2
x3
3
b.)
2
y   x4
3
2
3
2
y  4 x 
3
y
2
x3
3
2
y  x4
3
y
d.)
76. A bathtub that is filled with water is being drained. After 5 minutes, the bathtub has a volume of water of 46
gallons. After 10 minutes, the bathtub’s volume is down to 21 gallons.
Use this information to complete problems a-e.
a) What is the slope in gallons per minute?
b)
Write a linear equation, in point slope form.
Page10
c) Write a linear equation, in slope-intercept form.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
d) How many gallons of water are left in the tub after 13 minutes?
e)
If the water continues to drain, after how many minutes will the bathtub have 8 gallons of water remaining?
f) What is the real-world meaning of the
1. Slope?
2.
Y-intercept?
77. Tad’s brother gave Tad his collection of baseball cards when he left for college. After 5 years, the value of the
collection was $870. After 18 years, the collections value is up to $1260.
Use this information to complete problems a-e.
a) What is the slope in dollars per year?
b)
Write a linear equation, in point slope form.
Page11
c) Write a linear equation, in slope-intercept form.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
d) How much will the collection be worth after 37 years?
e)
If Tad continues to save, after how many years will the collection be worth $1500?
f) What is the real-world meaning of the
3. Slope?
4.
Y-intercept?
Unit 5 Review
78.
Solve by graphing:
79. Use the graph to determine the solution to the system
of equations.
Page12
x+y=3
2x + y = 2
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
Identify each system as having one solution, no solution, or infinitely many solutions.
80.
81.
82.
Solve the system of linear equations:
83.
15x – 5y = –20
–3x + y = 4
84.
y = –2x + 10
y = 5x – 18
a.) (2, 3)
b.) (4, 3)
c.) (2, 4)
d.) (4, 2)
5x – 4y = 23
7x + 8y = 5
86.
-2x + 3y = -8
5x – 2y = -2
a.) (-2, -4)
b.) (-4, -2)
Page13
85.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
c.) (2, -1)
d.) (-1, 2)
87. At what point do the lines 3x - 5y = -30 and
x - 5y = –20 intersect?
88. At what point do the lines -7x + y = -3 and
3x - 8y = 24 intersect?
a)
b)
c)
d)
(0, –3)
(4, –1)
(3, -4)
(2, 0)
Write the system of equations for each scenario.
89. Mrs. Gonzales bought centerpieces to put on each table at a graduation party. She spent $31.50. There are 8 tables
each requiring either a candle or a vase. Candles cost $3 and vases cost $4.25.
System ___________________
___________________
Write the system of equations for each scenario.
90. For a community bake sale, you purchased 12 pounds of sugar and 15 pounds of flour. Your total cost was $9.30.
The next day, at the same prices, you purchased 4 pounds of sugar and 10 pounds of flour. Your total cost the second day
was $4.60.
a.)
12s  4s  9.30
15 f  10 f  4.60
b.)
c.)
12s  15 f  9.30
4s  10 f  4.60
c.)
12s  15 f  4.60
4s  10 f  9.30
12s  15 f  9.30
10s  4 f  4.60
System ___________________
Page14
91. Stephanie is deciding between two cell-phone plans. The first plan has a $60 sign-up fee and costs $15 per month.
The second plan has a $20 sign-up fee and costs $35 per month.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
___________________
Solve:
92.
Hannah is 17 years younger than Claire. The sum of their ages in years is 109. What are both of their ages?
93. Juanita has a jar containing 80 coins, all of which are either quarters of nickels. The total value of the coins is
$14.60. How many of each type of coin do they have?
94. 2x – y ≥ 4
95. y < -x + 3
96. Write the inequality of the graph.
97. Which of the following ordered pairs is a solution to the
system of inequalities?
Page15
Graph:
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
a.)
b.)
c.)
d.)
98. Graph the system of inequalities and indicate the
solution
(1, 3)
(-7, -7)
(1, 5)
(-5, -4)
99. Write a system of inequalities to describe the shaded
area of the graphs
y  3  2x
y  2
Unit 6 Review
Simplify:
9x 7
5
ab
103.
101.
3
4ab
 3x 
5 3
4y
104.
5
4
102.
 x3 
 7
y 
105.
 3x    x    x 
3
2
3
20 y
Page16
100.
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6
106.
 4 x y 5x y 
3
c.)
20x6 y12
20x6 y12
20x5 y8
d.)
20x5 y8
a.)
b.)
6
2
2
107.
12 x 4 y 2 5 x 4 y 0

15 y
3x3
4 x5 y
a.)
3
4 x13
b.)
3y
17 x 5 y
18
4 xy 5
d.)
3
c.)
108.
 x3 y 1 
 1 3 
 3x y 
3
109.
110. Anna makes an initial deposit of 800 in her savings
account. The account pays a 4% annual interest.
Let x represent the number of years the money has been in
the account and let y represent the balance in the account.
a) Write an exponential equation to model the account
balance for any given number of years.
b) What is the account balance after 6 years?
24 xy 2 2 x3 y 3

x 3 y 5
8 x
111. You buy a used truck for $10,500. Each year the truck
depreciates by 10%. Which equation below represents this
situation?
a.)
y  10,500(1  .1) x
b.)
y  .10 x  10,500
c.)
y  10,500(1  10) x
d.)
y  10,500(1  .1) x
Answer: ___________________
Answer: ___________________
Answer: ___________________
Page17
For Problems 112 – 114, classify each graph as linear, exponential, or neither:
112.
113.
114.
Page18
CT Algebra 1-1
Final Exam Review 2015
Units 1 - 6