Algebra 2 A Semester Exam Review 2015-2016

Algebra 2 A
Semester Exam Review Answers
Algebra 2 A
Semester Exam Review
2015-2016
Answers
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Algebra 2 A
Semester Exam Review Answers
Unit 1, Topic 1
1.
2.
a.
 b, a 
b.
3
c.
yx
d.
domain
e.
range
a.
Example: Let x  4 , then f  4   16 , g 16  
1
. The original number is not
256
the result.
b.
Example: Let x  2 , then f  2   6, g  6   18 . The original number is not the
result.
3.
4.
a.
g  x 
x2
3
b.
g  x 
3
c.
g  x 
x3
5
d.
g  x   log x
e.
g  x   ex
a.
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x 9
2
b.
Algebra 2 A
5.
6.
Semester Exam Review Answers
p  18
2
a.
g
b.
25 glasses
a.
c
b.
50 items
s  200
2.5
Unit 1, Topic 2
7.
8.
9.
a.
5
b.
1
3 y
x
c.
3
z 2 or
a.

1
2
b.
4
5
c.
9
d.
3
e.
5
6
a.
1
9
b.
9
c.
10
 z
3
2
10.
Yes, x  25 is extraneous. 3 25  15  15 .
11.
x  1 is extraneous.
12.
x  8 is not extraneous.
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3
 8  2 .
Algebra 2 A
13.
14.
Semester Exam Review Answers
a.
b.
c.
d.
a.
x0
b.
f  x  7
c.
0,  
d.
 0, 7 
15.
x  200
16.
31.36 miles per hour
17.
1978
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Algebra 2 A
Semester Exam Review Answers
Unit 1, Topic 3
18.
19.
20.
21.
22.
1
or f  x    
 3
a.
f  x  3
b.
g  x   log 5 x
c.
h  x   2x
d.
m  x    log x
a.
x is between 4 and 5
b.
x is between 2 and 3
c.
x is between 1 and 2
d.
x is between 1 and 2
a.
log 4 16  2
b.
log1000  3
c.
ln1  0
a.
102 
b.
e 1 
c.
92  81
a.
2
b.
–2
c.
4
d.
1
e.
0
f.
–1
g.
3
2
h.
1
2
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x
1
100
1
e
x
Algebra 2 A
23.
24.
Semester Exam Review Answers
a.
exponential decay
b.
exponential decay
c.
exponential growth
a.
B  t   300e0.70t
b.
P  t   2000 1  0.11  2000 1.11
c.
 0.06 
F  t   500 1 

12 

d.
D  t   700 1  0.08   700  0.92 
e.
G  t   4e0.12t
a.
x  log 550  2.740
b.
t
a.
100, 000 1  0.30   100, 000 1.30 
b.
$285,610
c.
$46,402.50 per year
a.
1, 000, 000 1  0.20   1, 000, 000  0.80 
b.
$327,680
c.
– $134,464 per year
t
12 t
25.
26.
27.
t
t
$4,030.57
29.
$5,676.27
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 500 1.005 
12 t
t
ln142
 2.478
2
t
28.
t
t
t
Algebra 2 A
30.
31.
32.
Semester Exam Review Answers
a.
f, h
b.
g, p
c.
f, g
d.
f, h
e.
g, p
f.
g, p
g.
f, h
h.
h, p
i.
g, p
j.
f, h
a.
g  x   e x 1
b.
h  x   ex  4
c.
p  x   e x
d.
s  x   e x
e.
z  x   e x 3
a.
g  x   log 2  x  2 
b.
h  x   log 2  x  2 
c.
p  x    log 2 x
d.
t  x   log 2  x  3
Unit 2, Topic 1
33.
34.
a.
x  2; x  2 is extraneous
b.
The x-coordinate of the point of intersection.
c.
The bottom half of the parabola should be drawn, passing through the point
 2, 1 .
0
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Algebra 2 A
35.
36.
37.
38.
39.
Semester Exam Review Answers
a.
9  4i
b.
2  13i
c.
30  19i
d.
25
e.
24  70i
a.
x4
b.
 4, 0 
c.
always
d.
4
a.
x  3; x  7
b.
 3, 0  ;  7, 0 
c.
3 and 7
a.
sketch a parabola that intersects the x-axis in two distinct places.
b.
sketch a parabola that touches the x-axis in one place.
c.
sketch a parabola that does not intersect the x-axis.
a.
x  5i; x  5i
b.
x  3  4i; x  3  4i
c.
x
6  i 24
or x  3  i 6
2
d.
x
2  i 56
10
e.
x
1  i 75
2
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Algebra 2 A
Semester Exam Review Answers
Unit 2, Topic 2
40.
41.
42.
43.
Answers will vary.
a.
End behavior of your graph should be as x  , y   and as x  , y  
b.
End behavior of your graph should be as x  , y   and as x  , y  
c.
End behavior of your graph should be as x  , y   and as x  , y  
d.
End behavior of your graph should be as x  , y   and as x  , y  
a.
yes
b.
no
c.
no
a.
yes
b.
no
c.
yes
a.
odd
b.
neither
c.
even
44.
 3,8
45.
symmetry about the y-axis
46.
 5, 7 
47.
symmetry about the origin
48.
a.
3
b.

c.
The zeros are 0 (multiplicity 1) and –3 (multiplicity 2)
d.
 1, 4 
e.
 3, 0 
f.
 3, 1
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Algebra 2 A
49.
Semester Exam Review Answers
a.
4
b.

c.
the zeros are –1 (multiplicity 2) and 3 (multiplicity 2)
d.
1,16 
e.
 1, 0  ;  3, 0 
f.
 , 1 ; 1,3
50.
f  x   2 x  x  2 
51.
g  x 
1
2
x  x  1 x  2 
2
52.
a.
3x 2  2 x  2
b.
 x 2  2 x  16
c.
4
d.
3
e.
5 x 3  13 x 2  29 x  21
a.
no. there is a non-zero remainder (145)
53.
b.
54.
2
f  9   145
a.
0
b.
8
c.
x 8
d.
 x  8  x 2  x  7 
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Algebra 2 A
55.
Semester Exam Review Answers
Your graph may vary, but should have similar characteristics.
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