ALGEBRA 2
Third Nine Weeks Test Review
1
Name_________________________
The chart below indicates the relationship between x and y.
x
y
2
4
240 120
6
80
8
10
60 48
How would you describe the relationship between x and y?
A
B
C
D
x is directly related to y.
y is directly related to x.
x and y are inversely related.
no relationship exists between x and y.
2 Hooke‘s law states that the force required to stretch a spring varies
directly with the distance the spring is stretched. If an 18-pound force
stretches a spring 13.5 inches, what force is required to stretch the spring
15 inches?
A
B
3
15 pounds
20 pounds
C
D
25 pounds
30 pounds
g ( x)  3x  5
h( x)  2 x 2  2
What is the equivalent of h(g (6)) ?
A 74
B 140
C 52
D 79
4
f ( x)  3x  4
g ( x)  x 2  2
Which of the following expressions represents g ( f ( x)) ?
A
B
C
D
3x 2  14
9 x 2  24 x  14
9 x 2  14
3x 2  3x  2
1
ALGEBRA 2
Third Nine Weeks Test Review
Name_________________________
5
Which of the following expressions is the inverse of f ( x) 
4 x  10
5
10
x
5
f 1 ( x) 
4
10
x
5
f 1 ( x) 
4
4 x  10
f 1 ( x) 
5
4x  5
10
f 1 ( x) 
A
B
C
D
6 Which is equivalent to
5
8
 2 ?
4a 6a b
A
13
10
C
B
30a 2 b  32a
12a 2 b
D
8 Which is equivalent to
13
10a 3 b
15ab  16b
12a 2 b
2x  1
8

?
x 1 x 1
A
2x  9
x 1
C
2x  9
x  1x  1
B
2 x 2  5x  1
D
16 x  8
x 1
9 Which expression is equivalent to
A
x9
x9
B
1
3x  9
?
3x  9
C
D
x9
x9
x3
x3
2
ALGEBRA 2
Third Nine Weeks Test Review
10
11
Name_________________________
x 2 - 8x + 16
Which is equivalent to
?
x-4
A
x+4
x-4
C
B
x+4
D
What is
x-4
x-4
x-4
2x 4
(y + 2)(y   )
simplified?
•
6(y + 2)
6x 2
A
x 2 (y - 4)
18
C
2x 2 (y  4 )
36x 2
B
x (y  4)
18
D

xy
6
12 What is a correct simplification of the expression below?
2x  16
8x 2
÷
(x  8 )(x + 6) (X + 6)(x  6)
A
B
x6
4x 2
16 2
x  6x  62
C
x6
8x 2
D
16x 2
x  6x  6
3
ALGEBRA 2
Third Nine Weeks Test Review
13
What value of y is the solution to the equation
2x - 2 4 x  3

= 12?
4
3
A
y=
28
5
C
y=
5
5
B
y=
69
11
J
y=
23
24
14 Which is the solution to
A
B
15
18
Name_________________________
1
1

?
a  6 4a
–1
0
C
D
1
2
C
y=
D
x2  5
3x  6
Which function is undefined at x = 2?
x +2
x- 4
A
y=
B
x9
x2
3
x+4
Which of the following is the equation of a rational function?
A
y
2
x
3
C
y
2
5x  3
B
y  x 2  2x
D
y  8x
4
ALGEBRA 2
Third Nine Weeks Test Review
19
Name_________________________
Which is the graph of a quadratic function?
A
C
B
D
5
ALGEBRA 2
Third Nine Weeks Test Review
20
What is the equation(s) of the vertical asymptote(s) of the function?
x4
f (x) 
( x  3)( x  2)
A
x = –2
C
x = 3, x = –2
B
x=4
D
x= 2, x = –3
21 Which is the graph of f ( x ) 
A
B
Name_________________________
1
?
x 1
C
D
6
ALGEBRA 2
Third Nine Weeks Test Review
3
8x 3 ?
22
Simplify
23
Which is equivalent to ( 5x ) 3 ?
A
B
_
Name_________________________
5x
C
D
5x
5x 5x
x
3
2
24 Simplify 25 ?
25
Which sets of numbers does 1.005 belong in?
A integer, rational, real
B irrational, real
C rational, real
D integer, whole, rational, real
26 Solve x 2 – 4x = 9?
27
Solve – 2x² + 5x + 4 = 0 by graphing. If exact roots cannot be
found, state the consecutive integers between which the roots
are located.
28 A certain third-degree polynomial function has zeros at –8, –2, and 3.
Which could not be a factor of the expression that defines the function?
A
B
x+8
x+2
C
D
x+3
x–3
7
ALGEBRA 2
Third Nine Weeks Test Review
Name_________________________
29 This is a portion of the graph of a polynomial function.
If written in order of descending powers, which could be the first term of
the polynomial?
A2.3a
30 What is equivalent to 405 ?
A
9 5
C
5i 9
B
9i 5
D
9 5
31 What are the factors of a polynomial function if its graph has xintercepts at 0, – 6, and 12?
A
B
(x + 6)(x – 12)
(x –6)(x + 12)
C
D
x(x – 6)(x + 12)
x(x + 6)(x – 12)
C
D
20x
20x 2
A2.3d
32 Which is equivalent to 5 2x • 2 2x ?
A
B
20 2x
20 x
8
ALGEBRA 2
Third Nine Weeks Test Review
Name_________________________
A2.6b
35
Which is the solution set for 24x2 – 14x = 6?
36
A
14 ± 772

48




B
14 ± 2i 95 


48


C
14 ± 380

48




D
 14 ± 380

48




Write the equation of a circle that satisfies the given conditions:
Center (7, -4) and radius is 6 units.
37 Find the center and radius of a circle with the given equation and then
graph the circle.
(x + 3)2 + (y + 5)2 = 64
A
B
D
C
9
ALGEBRA 2
Third Nine Weeks Test Review
38
Name_________________________
Which is the equation of the ellipse that satisfies the given set of
conditions? Major axis 8 units long and parallel to the x-axis, minor
axis 4 units long, and center at (5, 2).
39
A
( x  5) 2 ( y  2) 2

1
64
16
C
( x  5) 2 ( y  2) 2

1
4
2
B
( x  5) 2 ( y  2) 2

1
16
4
D
x2 y2

1
64 16
Which conic section is represented by the equation
x
 6
y2

1?
49
7
2
40 Find the exact solution(s) of the given system of equations graphically.
y=x+6
y = 5x2
Which is equivalent to i 24?
41
A
B
i
–1
C
D
–i
1
42 What is the range of f(x) = 2x2 – 8x + 10?
A
B
y > 10
y>2
C
D
set of all real numbers
set of all integers
10
ALGEBRA 2
Third Nine Weeks Test Review
43
Name_________________________
What is the solution set to the system of equations below?
y = x2 – x – 6
y = x2 + 14x + 24
44
What are the equations of the vertical asymptotes, and the values of x
for any holes(discontinuities) in the graph of the following rational
function?
x2
f(x) = 2
x  3 x  10
A asymptotes: x = 2, hole: x = – 5
B asymptotes: x = – 5, hole: x = 2
C asymptotes: x = 5, hole: x = – 2
D asymptotes: x = – 2, hole: x = 5
11