Elementary Algebra ~ Review for Exam 2
Sections 2.5 - 3.7
Solve the problem.
1) The sum of three consecutive even integers is
198. Find the integers.
2) The second angle of a triangle is 3 times as
large as the first. The third angle is 35° more
than the first. Find the measure of all three
angles of the triangle.
3) 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?
11)
2
(2x - 1) < 6
3
12) -5(6y - 8) < -35y + 20
13) 3(2y - 3) > 21
Solve the problem.
14) In a survey of 650 students, the students
showed these preferences for instructional
materials. Answer the questions.
4) In New York City, taxis charge $3 .50 plus
$2 .25 per mile. How far can Ralph travel for
$44.00?
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
b)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Solve using the addition and multiplication principles.
Graph and write set-builder notation for the answer.
7) a) -7n + 5 > -8n + 16
b) -5 +12a - 12 ≥ 13a
8)
x
>4
5
9) 9 + 2x ≤ 35
Solve using the addition and multiplication principles.
Write your answer using set builder notation.
10) -6 - 10z + 3 ≥ -11z - 10
a) What percent of students prefer lecture?
b) How many students prefer computers?
c) How many more student prefer film than
TV?
Plot the ordered pairs on a rectangular coordinate system.
15) A(6, 2), B(-4, 4), C(0, -7), D(3, -4), E(-6, -4)
Decide whether or not the ordered pair is a solution to the
equation.
16) a) 5x + y = 23; (4, 3)
b) 2x - 5y = 20; (5, 2)
2
c) y = - x + 7; (6, 3)
3
Graph the equation.
17) y = 4x + 3
18) -4x - 20y = -4
Review for Exam 2 - Fall 2012
Page 2
19) 3y + 18x = -12
20) y =
28) To the nearest dollar, the average tuition at a
public four-year college was $3076 in 1998 and
$3496 in 2001. Find, to the nearest dollar per
year, the rate at which tuition was increasing.
1
x
4
Write the equation of the line represented by the graph
and state the slope.
29) a)
21) 9x = -63
22) 45 + 5y = 0
10
Solve by graphing.
23) The value, v, in hundreds of dollars, of Juan's
1
computer is approximated by v = - t + 9,
2
where t is the number of years since he first
bought the computer. Graph the line, then use
the graph to estimate the value of the
computer 6 years after it was purchased.
y
5
-10
-5
5
10 x
5
10 x
-5
-10
b)
Find the coordinates of the x- and y-intercepts for the
given line.
24)
10
y
5
10 y
-10
5
-5
-5
-10
-5
5
10 x
-10
-5
-10
Find the x- and y-intercepts, then graph the equation.
25) -2x + 5y = 10
26) y = -4x+ 8
Use the graph to solve the problem.
30) The graph depicts a relationship between
scores achieved on a standardized test and
family income. Find the rate of change of test
scores with respect to family income.
540
530
520
Score
Solve the problem.
27) At 10:00 AM, Gavin rented a mountain bike.
He biked for 32.5 miles and returned the bike
at 3:00 PM. He paid $26.00 for the rental. Find
the following rates:
a) Gavin's average speed, in miles per hour;
b) the rental rate, in dollars per hour;
c) the rental rate, in dollars per mile.
510
500
490
480
470
Income (in $1000s)
20 30 40 50 60 70 80
Review for Exam 2 - Fall 2012
Page 3
Find the slope of the line.
31)
Determine whether the pair of equations represents
parallel lines.
40) 12x + 4y = 16
21x + 7y = 29
6 y
5
4
3
2
1
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
1 2 3 4 5 6x
Find the slope of the line containing the given pair of
points.
32) a) (-6, -5) and (5, -9)
b) (4, -4) and (7, 3)
Solve the problem.
33) 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?
34) 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.
1
35) Slope - ; y-intercept (0, 6)
2
Find the slope and the y-intercept of the line.
15
36) y =
x-4
4
37) -6x + 8y = 8
38) 5x + 7y = 28
Graph the linear equation.
2
39) y = - x - 2
5
Write the slope-intercept equation of the line with the
given slope that contains the given point.
3
41) Slope ; y-intercept (0, 2)
4
Write a point-slope equation for the line with the given
slope that contains the given point.
42) m = -2; (5, -3)
Write the equation for the line in the indicated form with
the given slope that contains the given point.
43) a) m = -8; (3, -7) in point-slope form
4
b) m = ; (0, -2) in slope-intercept form
5
44) m = -2; (4, -3)
a) in point-slope form
b) in slope-intercept form
Write the slope-intercept equation for the line containing
the given pair of points.
45) (-2, 3) and (2, 5)
46) (8, 4) and (-3, 1)
Graph the line.
47) y - 3 = -
1
(x - 3)
4
48) y + 2 = 2(x + 3)
Provide an appropriate response.
49) What can you say about a line if every point on
the line has the same x coordinate?
Combine like terms.
50) a) 8a - 6a + 2
b) -7 + (-6x) + 9x + 2
c) 6x - (-8x) + 2 - (-9x) + 6
Review for Exam 2 - Fall 2012
Simplify.
51) a) -5 2
b) (-5)2
52) 4(-3) + 12(-8)
Evaluate.
53) -21 ÷ x(x + 13)2 , for x = -3
Use the distributive law to factor the given expression.
54) 42a + 7b
55) 5s + 55 + 10t
Solve the equation.
56) 20y - 6 = 17y
57) -5x + 5(-3x - 7) = -50 - 5x
58) 9x - (4x - 1) = 2
59) -4.6q + 1.4 = -12.6 - 1.8q
60)
2
1
x- x=4
5
3
61)
1
1
1
x- x=3x
4
8
16
Solve the problem.
62) 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?
63) 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?
Page 4
Answer Key
Testname: EAREVIEW2_SP2013
1)
2)
3)
4)
64, 66, 68
29°, 87°, 64°
48 in., 78 in.
18 miles
17)
y
10
5
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
5) a)
-10
-5
5
10 x
5
10 x
5
10 x
5
10 x
-5
b)
-7 -6 -5 -4 -3 -2 -1 0
6) a) {x∣x ≤ 4}
7) a) {n n > 11}
8
9
1
2
3
4
5
6
7
b) {x∣x > -3}
-10
18)
10
11
12
13
y
14
10
b) {a -17 ≥ a}
-20
-19
5
-18
-17
-16
-15
-14
-10
-5
8) {x x > 20}
18
-5
19
20
21
22
23
24
9) {x x ≤ 13}
9
-10
19)
10
11
12
13
14
y
15
10
10) {z z ≥ -7}
11) {x x < 5}
12) {y y < -4}
13) {y y > 5}
14) a) 18%
b) 234 students
c) 52 students
15)
5
-10
-5
-5
-10
8
y
20)
y
10
B
A
5
8 x
-8
E
D
C
-8
16) a) Yes, b) No c) Yes
-10
-5
-5
-10
Answer Key
Testname: EAREVIEW2_SP2013
21)
26) (0, 8), (2, 0)
y
10 y
10
5
5
-5
-10
-5
5
-5
-5
-10
27) a) 6.5 miles per hour
b) $5.20 per hour
c) $0.80 per mile
28) $140 per year
29) a) x = -4, Slope is undefined
b) y = 6, Slope is 0
4
30) points per thousand dollars
3
-10
22)
y
10
5
-10
-5
5
10 x
-5
31) -
1
2
32) a) -
-10
4
11
b)
7
3
33) 0.73
34) 12.5%
35)
23)
10
x
5
10 x
v
y
10
5
5
5
10
15
20 t
-10
value after 6 years = $600
24) (0, 2), (-5, 0)
25) (-5, 0), (0, 2)
-5
-5
-10
y
5
-5
5
-5
5
x
36)
15
; (0, -4)
4
37)
3
; (0, 1)
4
38) -
5
29
; (0,
)
7
7
10 x
Answer Key
Testname: EAREVIEW2_SP2013
39)
y
10
5
-10
-5
5
10 x
-5
-10
40) Yes
41) y =
3
x+2
4
59) 5
60) 60
61) 16
62) $312
63) 22,350 people
42) y + 3 = -2(x - 5)
43) a) y + 7 = -8(x - 3)
4
b) y = x - 2
5
44) a) y + 3 = -2(x - 4)
b) y = -2x + 5
45) y
= 1x + 4
2
46) y =
3
20
x+
11
11
47)
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
48)
y
10
5
-10
-5
-5
-10
49) The line is vertical.
50) a) 2a + 2
b) 3x - 5 or -5 + 3x
c) 23x + 8
51) a) -25 b) 25
52) 84
53) 700
54) 7(6a + b)
55) 5(s + 11 + 2t)
56) 2
57) 1
1
58)
5