EA Exam 2 REVIEW F06
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Rumson Fair Haven Reg H *
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Mathematics
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Nov 24, 2024
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Elementary Algebra
FALL 2006
Review for Exam 2
Solve using the five-step problem-solving
process.
1)
The second angle of a triangle is 3
times as large as the first. The third
angle is 35
e
more than the first. Find
the measure of all three angles of the
triangle.
2)
A rectangular window has a
perimeter of 252 inches. The length of
the window is 30 inches more than
the width. What are the dimensions
of the window?
3)
A triangular lake-front lot has a
perimeter of 1,100 feet. One side is
200 feet longer than the shortest side,
while the third side is 300 feet longer
than the shortest side. Find the
lengths of all three sides.
Determine whether the given number is a
solution of the inequality.
4)
x < 11
a) -15
b) 11
c) 10.95
Graph the inequality.
5) a) x > -5
b) 0 ≤
x < 4
Describe the graph using set-builder notation.
6) a)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
b)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
Solve using the addition principle. Graph and
write set-builder notation for the answer.
7) a) -7n + 5 > -8n + 16
b) -5 + 13a - 12 ≥
12a
Solve the problem.
8)
In a survey of 650 students, the
students showed these preferences
for instructional materials. Answer
the questions.
a) What percent of students prefer
lecture?
b) How many students prefer
computers?
c) How many more student prefer
film than TV?
Graph the equation.
9)
y = 4x + 3
10)
3y + 18x = -12
11)
y = 1
4
x
12)
9x = -63
13)
45 + 5y = 0
Review for Exam 2, Fall 2006
Page 2
Find the coordinates of the y-intercept and the
coordinates of all x-intercepts.
14)
x
-10
-5
5
y
10
5
-5
-10
x
-10
-5
5
y
10
5
-5
-10
Find the intercepts, then graph the equation.
15)
-2x + 5y = 10
16)
y = -4x+ 8
Write the equation of the line represented by
the graph and state the slope.
17) a)
x
-10
-5
5
y
10
5
-5
-10
x
-10
-5
5
y
10
5
-5
-10
b)
x
-10
-5
5
y
10
5
-5
-10
x
-10
-5
5
y
10
5
-5
-10
Solve the problem.
18)
On March 10 Henry rented a van
with a full tank of gas and 12,891.0
miles on the odometer. On March 12
he returned the van with 13,074.4
miles on the odometer. The rental
agency charged Henry $76 for the
rental and needed 10 gallons to fill up
the tank. What was the van's rate of
gas consumption in miles per gallon?
19)
The following graph shows data for a
recent train ride from New York to
Toronto. What was the average
speed of the train?
1
2
3
4
5
400
300
200
100
1
2
3
4
5
400
300
200
100
Time of Day (PM)
Review for Exam 2, Fall 2006
Page 3
Use the graph to solve the problem.
20)
The graph depicts a relationship
between scores achieved on an
unspecified standardized test and
family income. Find the rate of
change of test scores with respect to
family income.
540
530
520
510
500
490
480
540
530
520
510
500
490
480
Income (in $1000's)
Find the slope of the line. If the slope is
undefined, state so.
21)
x
-5 -4 -3 -2 -1
1
2
3
4
5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1
1
2
3
4
5
y
5
4
3
2
1
-1
-2
-3
-4
-5
Find the slope of the line containing the given
pair of points. If the slope is undefined, state
so.
22) a) (-6, -5) and (5, -9)
b) (4, -4) and (7, 3)
Solve the problem.
23)
An old house has a basement
stairway that has steps with 7.25 inch
risers and 10 inch treads. What is the
slope of the stairway?
24)
Over one particular stretch of road,
the Whitepoint Highway rises 475 ft
over a horizontal distance of 3800 ft.
Find the grade of the road.
Draw a line that has the given slope and
y-intercept.
25)
Slope - 1
2
; y-intercept (0, 6)
Find the slope and the y-intercept of the line.
26)
y = 15
4
x - 4
27)
-6x + 8y = 8
28)
5x + 7y = 29
Find the slope-intercept equation for the line
with the indicated slope and y-intercept.
29)
Slope - 4
7
; y-intercept (0, 5)
Graph the linear equation.
30)
-4x - 20y = -4
31)
y = - 1
4
x - 4
Solve the problem.
32)
A moving firm charges a flat fee of $
30 plus $25 per hour. Let y be the cost
in dollars of using the moving firm
for x hours. Find the slope-intercept
form of the equation.
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Review for Exam 2, Fall 2006
Page 4
Determine whether the pair of equations
represents parallel lines.
33)
12x + 4y = 16
21x + 7y = 29
Write a point-slope equation for the line with
the given slope that contains the given point.
34)
m = -5; (5, -2)
Write the slope-intercept equation for the line
containing the given pair of points.
35)
(-2, 3) and (2, 5)
Graph the line.
36)
y - 3 = - 1
4
(x - 3)
37)
y + 2 = 2(x + 3)
Provide the proper response.
38)
Identify whether the slope is positive,
negative, zero or undefined.
a)
x
-5
5
y
5
-5
x
-5
5
y
5
-5
b)
x
-5
5
y
5
-5
x
-5
5
y
5
-5
c)
x
-5
5
y
5
-5
x
-5
5
y
5
-5
d)
x
-5
5
y
5
-5
x
-5
5
y
5
-5
Provide an appropriate response.
39)
Explain how you would find the x
intercept of a line with an equation of
the form
Ax + By = C.
40)
What can you say about the graph of
Ax + By = C if B is equal to zero?
41)
What can you say about a line if
every point on the line has the same x
coordinate?
42)
Is it possible for the x-intercept and
the y-intercept of a straight line to be
at the same point? Explain your
answer.
43)
What is the y-intercept of the line
y = b?
44)
Does every straight line have an
x-intercept? If not, give an example
of an equation whose graph does not
have an x-intercept.
Review for Exam 2, Fall 2006
Page 5
Simplify. Assume that no denominator is zero
and that 0
0
is not considered.
45) 9
7
œ
9
3
46) s
7
œ
s
4
œ
s
5
47) 2
3
œ
2
4
œ
2
6
48) (5x
3
)(6x
3
)
49)
(y + 2)
8
(y + 2)
9
50) (pq
6
)(pq)
5
51)
a
7
a
2
52)
3
8
3
2
53)
8k
3
4k
54)
(p - q)
8
(p - q)
2
55)
g
9
h
5
g
2
h
56)
32x
7
-8x
3
57)
20m
4
p
2
5m
10
p
Simplify the expression.
58) a) (8x
0
)
b) 8x
0
59) 3z
0
when z = 14
60) 11
0
+ 9
0
61) (-4)
0
- (-4)
1
Simplify.
62) (5r
7
)
3
63) (-4a
5
)
4
64) (w
8
z)
4
(w
4
z
2
)
Simplify. Assume that no denominator is zero
and that 0
0
is not considered.
65)
4
x
3
66)
a
3
b
4
2
67)
5
3a
3
68)
a
7
- 7b
4
3
69)
-3n
5
4
70)
x
5
y
z
2
5
71)
2x
3
y
4
7z
6
2
Provide an appropriate response.
72)
Identify the base and exponent in the
expression y
4
.
73)
Explain how (-4x)
2
and -4x
2
are
different.
74)
Find and explain the mistake(s); then
work the problem correctly.
-4x
4
y œ
6x
6
y
9
= -24x
24
y
10
Review for Exam 2, Fall 2006
Page 6
Solve the problem.
75)
Charlie purchased a digital camera.
The cost of the camera, including 7.5
percent sales tax was $335.40. What
was the cost of the camera before tax?
76)
In a local election, 24,138 people
voted. This was an increase of 8%
over the last election. How many
people voted in the last election?
Solve the formula for the specified variable.
77)
M = e + h + y
9
for h
Solve the equation.
78) - 2
5
+ x = - 3
4
79)
1
4
x - 1
8
x = 3 - 1
16
x
80)
9x - (4x - 1) = 2
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Answer Key
Testname: EA EXAM 2 REVIEW SP06
1) 29
e
, 87
e
, 64
e
2)
48 in., 78 in.
3)
200 ft, 400 ft, 500 ft
4)
Yes, No, Yes
5)
a) -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
-8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
b) -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
-7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
6)
a) {x
v
x ≤
4}
b) {x
v
x > -3}
7)
a) {n
n > 11}
8
9
10
11
12
13
14
8
9
10
11
12
13
14
b) {a
a ≥
6}
3
4
5
6
7
8
9
3
4
5
6
7
8
9
8) a) 18%
b) 234 students
c) 52 students
9)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
10)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
11)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
12)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
Answer Key
Testname: EA EXAM 2 REVIEW SP06
13)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
14)
(0, 2), (-5, 0)
15)
(-5, 0), (0, 2)
16)
(0, 8), (2, 0)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
17) a) x = -4, Slope is undefined
b) y = 6, Slope is 0
18)
18.3 miles/gallon
19)
50 miles per hour
20)
4
3
points per thousand dollars
21) - 1
2
22) a) - 4
11
b) 7
3
23) 0.73
24) 12.5%
25)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
26)
15
4
; (0, -4)
27)
3
4
; (0, 1)
28) - 5
7
; (0, 29
7
)
29)
y = - 4
7
x + 5
30)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
31)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
Answer Key
Testname: EA EXAM 2 REVIEW SP06
32)
y = 25x + 30
33) Yes
34)
y + 2 = -5(x - 5)
35)
y = 1
2
x + 4
36)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
37)
x
-10
-5
5
10
y
10
5
-5
-10
x
-10
-5
5
10
y
10
5
-5
-10
38) a) Positive
b) Undefined
c) Negative
d) Zero
39)
Let y = 0 and solve for x.
40)
The graph is a vertical line.
41)
The line is vertical.
42)
Yes. If the line passes through the origin,
then both the x-intercept and the
y-intercept are at (0, 0).
43)
(0, b)
44)
The x-intercept is the point where the line
crosses the x-axis. Lines parallel to the
x-axis do not intercept the x-axis. Thus the
graph of any equation of the form y = b
where b ≠
0 has no x-intercept.
45)
9
10
46)
s
16
47)
2
13
48) 30x
6
49)
(y + 2)
17
50) p
6
q
11
51)
a
5
52)
3
6
53)
2k
2
54) (p-q)
6
55) g
7
h
4
56) -4x
4
57)
4p
m
6
58)
a) 1
b) 8
59) 3
60)
2
61) 5
62) 125r
21
63) (-4)
4
a
20
64) w
36
z
6
65)
64
x
3
66)
a
6
b
8
67)
125
27a
3
68)
a
21
-343b
12
69)
81n
4
625
70)
x
25
y
5
z
10
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Answer Key
Testname: EA EXAM 2 REVIEW SP06
71)
4x
6
y
8
49z
12
72)
Base: y, exponent: 4
73)
In the first, the power applies to both. In the
second, the power only applies to the x.
74)
Error: Exponents on x were multiplied but should
have been added.
The correct answer is - 24x
10
y
10
.
75)
$312
76)
22,350 people
77)
h = 9M - e - y
78) - 7
20
79) 16
80)
1
5