Algebra 2
Review 3
1.
Simplify completely:
8 6  2 24
a.
b.
c.
d.
e.
2.
3.
4.
120
10 30
10 6
12 6
16 6
Simplify completely:
5 7 y  4 14 y
What is the least positive value of
x that makes 7  x rational?
a.
b.
c.
d.
5.
7
3
2
91
Simplify completely:
3 125x 5 y10
a. 20y 98
a. 5xy 3 x 2 y
b. 20 98y 2
b. 5x 2 y 5 5x
c. 20y 21
d. 140y 2
e. 140 2y
c. 5x 3 y 9 3 x 2 y
Simplify completely:
5
3
a.
b.
c.
d.
e.
25
3
5 3
3
15
5
5 3
5
d. 5xy 3 5x 2 y
e. 5xy 3 3 x 2 y
6.
Simplify completely:
1
81 4 .
a.
1
3
b. 
1
3
c. 3
d. 9
81
e.
4
7.
Factor: 64x3 + 27
a.
b.
c.
d.
e.
8.
(4x - 3)(16x2 + 12x +9)
(4x + 3)3
(4x + 3)(16x2  12x + 9)
(4x  3)(16x2 + 24x + 9)
4x  3)(16x2  24x + 9)
Simplify:
x 2  25
5x 3  10x 2
a.
9.

b
Divide and simplify:
3x 2  4 x  2
x 2
6
x 2
22
b. 3x  10 
x 2
2
c. 3x  2 
x 2
18
d. 3x  10 
x 2
a. 3x  2 
5x 3
x 2  x  20
g
x x 5
2
( x  2)( x  4)
x x 5
b.
( x  2)( x  4)
5
c.
2
10x  x  4
5x 3 x  5
d.
(5x 3  10x 2 )( x  4)
b
g
b
g
10.
Simplify:
4
3x  1

x  2 x2  4
x9
( x  2)( x  2)
x 7
b.
( x  2)( x  2)
x 1
c.
( x  2)( x  2)
7x  9
d.
( x  2)( x  2)
a.
11.
Which of the following represents the
graph of 4x - 5y = 10?
12.
Which of the following represents the
graph of 3x + 2y > 4?
a.
a.
b.
b.
c.
c.
d.
d.
e.
13.
Write an equation for the line
containing (-1,-3) and (4,-5).
2x 6
 , or
5 5
2x  5y  6
2x 33
b. y  
, or

5
5
2x  5y  33
5x
c. y  
 5 , or
2
5x  2y  10
2x 17
d. y  
, or

5
5
2x  5y  17
15.
a.
b.
c.
d.
a. y  
14.
Write the equation of the line that has
3
a slope of  and a
4
2
y-intercept of
3
2x 3
 , or
3 4
-8x + 12y = -12
4 2
y
 , or
3x 3
4x + 3y = 2
3x 2
y
 , or
4 3
-9x + 12y = 8
3x 2
y
 , or
4 3
9x + 12y = -8
3x 2
y
 , or
4 3
9x + 12y = 8
16.
17.
c.
d.
e.
y
x
x
y
-8
-4
-8
-4
x
x
y
y
=
=
=
=
-6
2
-6
2
Find the slope of the line parallel to
3x 8y = 10.
a.
8
3
b. 
c.
3
8
3
8
d. 
18.
=
=
=
=
Write the equation of the vertical line
through (-6,2) .
a.
b.
c.
d.
a. y 
b.
Write the equation of the horizontal line
through (-8, -4).
8
3
Find the slope of the line perpendicular
to 4x + 3y = 8.
a. 
4
3
3
4
4
c.
3
b.
d. 
3
4
19.
Which of the following best represent
the graph of the ellipse:
20.
bx  1g2  by  1g2 =1.
16
by  2g2  bx  1g2  1
25
4
a.
a.
b.
Which of the following best represents
the graph of the hyperbola:
b.
c.
c.
d.
d.
9
21.
Which of the following represents the
graph of the parabola:
22.
x  2(y  2)2  1
or
1
2
x 1  y  2
2
b
g b
Which of the following represent the
graph of the ellipse with center at
(-3,4)
g
a.
b.
a.
bx  4g 2  by  3g 2  1
b.
bx  3g 2  by  4g 2  1
c.
bx  3g  by  4g 2  1
d.
bx  3g 2  by  4g 2  1
e.
bx  3g  by  4g 2  1
9
4
9
4
2
9
4
3
2
2
c.
d.
e.
2
3
23.
Which of the following represent the
graph of the hyperbola with center at
(-1,2).
a.
by  2g  bx  1g
b.
by  2g 2  bx  1g 2  1
c.
2
y  2g
x  1g
b
b


1
d.
by  1g  bx  2g 2  1
2
16
4
16
24.
Which of the following represent the
graph of the parabola with vertex at
(2,-1).
1
a.  ( y  1)2  2 or -3(x2)=(y+1)2
3
2
1
b.
4
2
16
1
c.  ( y  2)2  1
3
4
2
16
1
( y  1)2  2
3
d.
4
25.
1
( y  2)2  1
3
or 3(x  2)=(y + 1)2
or -3(x +1)=(y 2)2
or 3(x + 1)=(y  2)2
Solve for x: x2 - 2x - 6 = 0
a.
2 7
b.
c.
d.
e.
12 7
1 7
1  7
2  7
26.
Solve for x: 4x2 + x + 5 = 0
a.
29.
1  i 79
8
e
b. 1, 5
4
Solve for x: 5x2+ 8x +3  0
a.
j
b.
Solve for x: x3 -4x2 = -3x
c.
0, -3, -1
-1, -3
0, 3, 1
3, 1
d.
28.
3
,)
5
1
x < 5 or x >
3
or
1
(  ,5] U [ ,  )
3
1
x   or x  5
3
or
1
(  , ] U [5 ,  )
3
(  ,1] U [ 
1  i 79
8
1  79
d.
8
a.
b.
c.
d.
1  x  
Solve for x: x4 + 5x2 - 36 = 0
a.
b.
c.
d.
e.
3i, 2i
2i, 3
-9, 4
3, 2
3i, 2
3
5
or
c.
27.
x  1 or x  
3
5
or
3
5
[1,  ]
30.
4 x  3  11
Solve:
7
2
a.
x=
b.
x=
c.
d.
7
,2
2
x = 2
7
x = , 2
2
31.
Solve: 25 = 125
a.
b.
c.
d.
32.
Solve:
a.
b.
c.
d.
33.
Solve:
a.
3x  1
2
3
4
x=
9
5
x=
9
1
x=
3
x=
4x
3

4
x  2 x 1
35.
10  209
8
7
x=
4
x = 2  15
2
x= 
11
x=
3x  1  2x
x = 1, x =
1
4
1
is extraneous
4
b.
x = 1, 
c.
x = -1
d.
x  1, x  
e.
34.
1
,
24
or
no solution
1
x   , 1 is extraneous
4
36.
3
4x

2
x  2 x  3x  4
Solve:
a.
x = 1, 2
b.
x = 5  41
c.
x = 3, 4
d.
x=
e.
x = 1, 4
4  i 14
3
5 3x  1  25 x  2
Solve:
9
5
a.
x
b.
x9
c.
x
3
5
d.
x
33
275
1
Solve: x 4 
a.
x
b.
x
c.
x
d.
x
2
3
4 54
3
16
3
42
81
16
81
37.
For which equation is x = 5 a
solution?
a.
b.
38.
5x  5
2x 7
d.
x 2  25
 10
x 5
Solve:
RS5x  2y  4
Ty  4 x  5
a.
(-3, -17)
b.
(2, 3)
c.
FG 2 , 7 IJ
H 3 3K
d.
(3, 2)
FG  7 , 2 IJ
H 3 3K
Solve:
a.
2x  32
c.
e.
39.
40.
RS3x  7y  6
T2x  9y  4
FG 6 , 10 IJ
H 13 13 K
b.
(2, 0)
c.
FG 10 , 6 IJ
H 13 13 K
d.
(0, 2)
e.
FG  1 ,1IJ
H 3 K
A skate shop rents roller-skates for $4
and in-line skates for $5. A total of 110
pairs of skates are rented today, and
sales are $500. How many pairs of each
type of skates did the shop rent?
a.
55 pairs of in-line skates, and
55 pairs of roller-skates.
b.
50 pairs of in-line skates, and
60 pairs of roller-skates.
c.
22 pairs of in-line skates, and
88 pairs of roller-skates.
d.
88 pairs of in-line skates, and
22 pairs of roller-skates.
e.
60 pairs of in-line skates, and
50 pairs of roller-skates.
41.
Which of the following systems of
inequalities represents the graph?
44.
a.
a.
b.
c.
d.
e.
42.
Let f(x) = -6x2 + 5.
Find f(-2).
a.
b.
c.
d.
43.
RS2x  3y  9
T3x  2y  2
RS2x  3y  9
T3x  2y  2
RS2x  3y  9
T3x  2y  2
RS2x  3y  9
T3x  2y  2
RS2x  3y  9
T3x  2y  2
29
-19
149
-139
Let f(x) = x + 7 and g(x) = x2.
Find f g 4 .
c b gh
a.
b.
c.
d.
-9
16
23
9
b.
c.
d.
Which of the following is a function?
45.
Given:
46.
Find the inverse of the function
y = 2  7x.
1
2  7x
a.
y
b.
y  2  7 x
Choose the graph of the inverse.
c.
y
a.
d.
y  2  7x
e.
y
47.
b.
1
2
x
7
7
1
2
x
7
7
Choose the example of direct variation.
a.
Relationship between the
softness of a stuffed animal and
the freshness of bed sheets.
b.
Relationship between color of
eyes and ethnic background.
c.
c.
Relationship between the amount
of time it takes to clean a house
and the number of people
cleaning.
d.
Relationship between hair color
and I.Q.
d.
e.
Relationship between computer
ownership and computer usage.
48.
Choose the example of inverse
50.
variation.
The number of accidents in the student
parking ot at lunch varies directly with
the number of students going to lunch
a.
b.
c.
d.
e.
49.
Relationship between the
and inversely with the number of
softness of a stuffed animal and
minutes in the lunch.
the freshness of bed sheets.
average of 8 accidents per day with 200
Relationship between color of
students and 40 minutes for lunch.
eyes and ethnic background.
How many accidents would occur in an
Relationship between the
average day if 500 students went to
amount of time it takes to clean
lunch in a 60 minute lunch period.
a house and the number of
Round the number of accidents to the
people cleaning.
nearest whole number.
Relationship between hair color
and I.Q.
a.
5 accidents
Relationship between computer
b.
64 accidents
ownership and computer
c.
13 accidents
knowledge.
d.
2 accidents
Y varies jointly as x and z and inversely
as
There is an
51.
Given:
w . If x = 2, w = 9, and z = 6,
9
then y = 12. Find y when x = 5, w =
25, and z = 7.

a.
y = 21
b.
245
y=
3
c.
y=
d.
y=
48
7
84
25
8
Find  in degrees to the nearest 10th.
a.
41.6˚
b.
62.7˚
c.
27.3˚
d.
48.4˚
52.
A ladder 30 feet long is propped
against the side of a building, forming
an 80˚ angle with the ground.
54.
Find the sine, cosine, and tangent of a
30˚ angle.
How
high is the top of the ladder from the
ground?
53.
a.
5.2 feet
b.
29.5 feet
c.
170.1 feet
d.
30.5 feet
cos 30˚
tan 30˚
a.
3
2
1
2
3
b.
1
2
3
2
1
3
c.
3
2
1
2
3
3
d.
2
2
2
2
1
e.
3
2
1
2
Use the Law of Sines to find the length
of side AB, correct to the nearest 10th.
A
140˚
B
sin 30˚
10˚
15
30˚
a.
55.5
b.
43.2
c.
12.5
d.
19.3
C

1
3
Answers for CRT Review 3
1.
D
29.
A
2.
D
30.
D
3.
B
31.
C
4.
C
32.
D
5.
E
33.
B
6.
C
34.
C
7.
C
35.
A
8.
B
36.
D
9.
C
37.
C
10.
B
38.
B
11.
D
39.
B
12.
B
40.
E
13.
D
41.
C
14.
E
42.
B
15.
D
43.
C
16.
A
44.
B
17.
C
45.
A
18.
B
46.
C
19.
B
47.
E
20.
D
48.
C
21.
C
49.
A
22.
C
50.
C
23.
B
51.
C
24.
A
52.
B
25.
C
53.
B
26.
A
54.
B
27.
C
28.
E