Elementary Algebra
Review for Exam 2
Solve the problem.
1) In a survey of 650 students, the
students showed these preferences
for instructional materials. Answer
the questions.
FALL 2004
Find the coordinates of the y-intercept and the
coordinates of all x-intercepts.
7)
10 y
5
-10
-5
5
x
-5
-10
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.
2) y = 4x + 3
Solve by graphing.
8) During the month of January 1997,
the depth, d, of snow in inches at the
base of one ski resort could be
approximated by d = -2t + 70, where
t is the number of days since
December 31st. Use a graph to
estimate the depth of snow on
January 30th.
3) 3y + 18x = -12
4) y = 1 x
4
5) 9x = -63
6) 45 + 5y = 0
Find the intercepts, then graph the equation.
9) -2x + 5y = 10
10) y = -4x+ 8
Write the equation of the line represented by
the graph and state the slope.
11)
10 y
5
-10
-5
5
Draw a linear graph to represent the given
information.
14) In 1996 there were approximately 12
million computers sold in a
particular region of the world and
the figure was increasing at a rate of
about 2.2 million per year.
x
-5
-10
Write the equation of the line represented by
the graph and state the slope.
12)
10 y
5
-10
-5
5
x
-5
-10
Solve the problem.
13) 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?
Solve the problem.
15) The following graph shows data for
a recent train ride from New York to
Toronto. What was the average
speed of the train?
400
300
200
100
1
2
3
4
Time of Day (PM)
5
Use the graph to solve the problem.
16) 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.
40
30
Solve the problem.
20) 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?
21) 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.
22) Slope - 1 ; y-intercept (0, 6)
2
20
10
00
90
80
Find the slope and the y-intercept of the line.
23) y = 15 x - 4
4
Income (in $1000's)
24) -6x + 8y = 8
Find the slope of the line, or state that the slope
is undefined if appropriate.
17)
5 y
4
3
25) 5x + 7y = 29
Find the slope-intercept equation for the line
with the indicated slope and y-intercept.
26) Slope - 4 ; y-intercept (0, 5)
7
2
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5x
-2
-3
-4
-5
Find the slope of the line containing the given
pair of points. If the slope is undefined, state
so.
18) (-6, -5) and (5, -9)
19) (4, 3) and (7, -4)
27) Slope 3 ; y-intercept (0, 1)
2
Graph the linear equation.
28) -4x - 20y = -4
29) y = - 1 x - 4
4
Solve the problem.
30) 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.
Determine whether the pair of equations
represents parallel lines.
31) 12x + 4y = 16
21x + 7y = 29
c)
y
5
32) y = 4x - 4
12x + 3y = 7
-5
Write a point-slope equation for the line with
the given slope that contains the given point.
33) m = -5; (5, -2)
5
x
5
x
-5
d)
y
Write the slope-intercept equation for the line
containing the given pair of points.
34) (-2, 3) and (2, 5)
Graph the line.
5
-5
-5
35) y - 3 = - 1 (x - 3)
4
36) y + 2 = 2(x + 3)
Provide the proper response.
37) Identify whether the slope is
positive, negative, zero or undefined.
a)
y
Provide an appropriate response.
38) Explain how you would find the x
intercept of a line with an equation
of the form
Ax + By = C.
39) What can you say about the graph of
Ax + By = C if B is equal to zero?
5
-5
5
x
40) What can you say about a line if
every point on the line has the same
x coordinate?
-5
41) Is it possible for the x-intercept and
the y-intercept of a straight line to be
at the same point? Explain your
answer.
b)
y
5
-5
5
-5
x
42) What is the y-intercept of the line
y = b?
43) Does every straight line have an
x-intercept? If not, give an example
of an equation whose graph does not
have an x-intercept.
Simplify. Assume that no denominator is zero
and that 00 is not considered.
44) (y + 2)8(y + 2)9
45) (pq6)(pq)5
Determine the leading term, leading
coefficient, and the degree of the polynomial.
60) x - 2x2 - 6x3 - 4x5 + 5
Evaluate the polynomial.
61) 3x2 + 9x - 9 for x = 2
46) (5x3)(6x3)
q)8
47) (p - 2
(p - q)
9 5
48) g 2h
gh
7
49) 32x
-8x3
Simplify the expression.
50) 3z0 when z = 14
51)
(-4)0 -
(-4)1
Simplify.
52) (5r7)3
53) (-4a5)4
54) (w8z)4(w4z2)
Simplify. Assume that no denominator is zero
and that 00 is not considered.
3
55) 5
3a
5 5
56) x 2y
z
3 4 2
57) 2x y6
7z
Identify the terms in the polynomial.
58) -2t7 + 5t4 - 2t2 + 3
Determine the coefficient and the degree of
each term in the polynomial.
59) 3w7 - 4w3 - w
62) -2x2 + 6x - 3 for x = -2
Solve the problem.
63) The position of an object moving in a
straight line is given by s = 5t2 - 2t,
where s is in meters and t is the time
in seconds the object has been in
motion. How far will an object move
in 3 seconds?
Add.
64) (6a5 + 8a2) + (8a5 - 6a2)
65) (-7 + 4n7 - 6n5) + (9n7 + 4n5 - 8)
66) (-9 + 4x2 + 9x4 - 9x3) + (3x3 - 7x2 - 5
+ 3x4)
Subtract.
67) (17a4 - 9a2) - (-6a4 - 17a2)
68) (8n5 - 16n3 + 16) - (4n3 + 2n5 + 14)
69) (4x5 + 7x7 - 5 - 5x6) - (-7 - 2x6 + 2x7
+ 6x5)
Solve the problem.
70) Midtown Antiques collects 3% sales
tax on all sales. If total sales
including tax are $1201.48, find the
portion that is the tax. Round to the
nearest cent if necessary.
71) A tax-exempt school group received
a bill of $242.74 for educational
software. The bill incorrectly
included sales tax of 6%. How much
should the school group pay?
Answer Key
Testname: EA EXAM 2 REVIEW F04
1) a) 18%
b) 234 students
c) 52 students
5)
y
10
y
5
10
5
-10
-10
-5
5
10
-5
10
x
5
10
x
-5
x
-10
-5
6)
-10
2)
3)
5
y
10
y
5
10
5
-10
-10
-5
5
10
-5
-5
x
-10
-5
7)
8)
9)
10)
-10
y
10
(0, 2), (-5, 0)
10 inches
(-5, 0), (0, 2)
(0, 8), (2, 0)
10 y
5
-10
-5
5
10
5
x
-5
-10
4)
-5
5
-10
-5
-10
11) x = -4, Slope is undefined
12) y = 6, Slope is 0
13) 18.3 miles/gallon
10 x
Answer Key
Testname: EA EXAM 2 REVIEW F04
14)
26) y = - 4 x + 5
7
27) y = 3 x + 1
2
28)
30
24
y
18
10
12
5
6
-10
-5
1990 1992 1994 1996 1998 2000 2002
15)
16)
17)
18)
19)
20)
21)
22)
Year
50 miles per hour
4 points per thousand dollars
3
-1
2
- 4
11
-7
3
0.73
12.5%
y
10
5
-10
-5
5
10
x
10
x
5
10
x
5
10
x
-5
-10
y
10
5
-10
-5
-5
-10
29)
30)
31)
32)
33)
y = 25x + 30
Yes
No
y + 2 = -5(x - 5)
34) y = 1 x + 4
2
35)
y
-5
10
-10
23) 15 ; (0, -4)
4
24) 3 ; (0, 1)
4
25) - 5 ; (0, 29 )
7
7
5
5
-10
-5
-5
-10
Answer Key
Testname: EA EXAM 2 REVIEW F04
25 5
56) x 10y
z
36)
y
10
6 8
57) 4x y12
49z
5
-10
-5
5
10
x
-5
-10
37) a) Positive
b) Undefined
c) Negative
d) Zero
38) Let y = 0 and solve for x.
39) The graph is a vertical line.
40) The line is vertical.
41) Yes. If the line passes through the origin,
then both the x-intercept and the
y-intercept are at (0, 0).
42) (0, b)
43) 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.
44) (y + 2)17
45) p6q11
46) 30x6
47) (p-q)6
48) g7h4
49) -4x4
50) 3
51) 5
52) 125r21
53) (-4)4a20
54) w36z6
55) 1253
27a
58) -2t7, 5t4, -2t2, 3
59) Coefficients: 3, -4, -1;
degrees: 7, 3, 1
60) -4x5, -4, 5
61) 21
62) -23
63) 39 meters
64) 14a5 + 2a2
65) 13n7 - 2n5 - 15
66) 12x4 - 6x3 - 3x2 - 14
67) 23a4 + 8a2
68) 6n5 - 20n3 + 2
69) 5x7 - 3x6 - 2x5 + 2
70) $34.99
71) $229.00