Download Algebra 1 A Semester Exam Review Answers 2015-2016

ALGEBRA 1 A
Semester Exam Review ANSWERS
Algebra 1 A
Semester Exam Review Answers
2015-2016
MCPS © 2015–2016
ALGEBRA 1 A
Semester Exam Review ANSWERS
Unit 1, Topic 1
P  2L
1
P
1
or  P  2 L  or
 L or P  L
2
2
2
2
1.
W
2.
A.
C
3.
B.
The equation is always true, because both sides are identical.
4.
A.
There is one solution, and it is x  30 .
5.
C.
The equation is never true, because solving gives the statement 27  15 .
6.
a.
H  400
b.
The total amount of money earned by selling sodas in a day was at least $1,000.
c.
H SF
d.
S
C
e.
H  PH  F  PF  2000
5 F  160
9
1500  F  3F  700
f.
7.
200 orders of fries were sold.
800  4 F
200  F
Distributive Property
Addition Property of Equality
Multiplication Property of Equality
8.
Subtraction Property of Equality (Addition Property is ok)
Multiplication Property of Equality
Distributive Property
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ALGEBRA 1 A
9.
a.
Semester Exam Review ANSWERS
His score was 69.
S  2  36 
b.
12
 69.
4
She got 20 questions wrong.
53  2  29 
53  58 
W
4
W
4
W
4
20  W
5  
c.
He got 41 questions correct.
8
4
80  2C  2
80  2C 
C  41
Unit 1, Topic 2
10.
B.
20.00  3.75b  41.25
11.
Statement
True or
False?
Justification (Note: It is ok to pick two numbers for a and b and show
that the statements are true or false based on those numbers)
a 8  b8
True
Adding the same number to both sides of an inequality does not
change the direction of the inequality.
a7  b7
True
Subtracting the same number to both sides of an inequality does not
change the direction of the inequality.
7 a  7b
False
Multiplying the same side of the inequality by a negative number
means that the direction of the inequality must be changed.
a
b

10 10
True
Dividing both sides of an inequality by a negative number means that
the direction of the inequality must be changed.
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ALGEBRA 1 A
12.
Semester Exam Review ANSWERS
a.
$320
b.
50  100h  600
c.
h  5.5
d.
0
1
2
3
4
5
6
7
e.
In order for Mr. Flood to pay at most $600, the plumber can spend at most
5.5 hours fixing the leak.
13.
B.
4 x  9  17
14.
a.
88  5  3.75  $69.25
b.
88  3.75w  25
3.75w  63
w  16.8
Kendall can buy Young Teen magazine for 16 weeks.
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ALGEBRA 1 A
Semester Exam Review ANSWERS
Unit 1, Topic 3
15.
A.
25x
16.
C.
164 x  16 x 7
17.
a.
Month
0
1
2
3
4
5
6
7
8
9
10
Number of Comic Books that
Jared has
1
3
9
27
81
243
729
2187
6561
19683
59049
Number of Comic Books that
Sally has
1
9
81
b.
12 months after Jared started collecting, or 4 months after Sally started collecting
c.
3m
d.
9m8
e.
16 months (solution below)
3m  9m8
2 m8 
3m  3 
3m  32 m16
m  2m  16
m  16
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ALGEBRA 1 A
18.
a.
84  4096
b.
322  1024
c.
The number of Cranicus bacteria h hours after on cell of Cranicus bacteria was put in
the dish.
d.
The number of Bevus bacteria h hours after one cell of Cranicus bacteria was put
in its dish. The exponent is h  4 because the first Bevus bacteria was put in its
dish 4 hours after the first Cranicus bacteria was put in.
e.
8  2 3, 32  2 5
f.
10 hours (solution below)
8h  32h4
5 h4
23h  2  
3h  5h  20
2h  20
h  10
19.
a.
3x  2  37
x27
x5
19.
Semester Exam Review ANSWERS
b.
25 x 1  5 x 3
2 x 1
5    5 x 3
2x  2  x  3
x  5
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ALGEBRA 1 A
19.
Semester Exam Review ANSWERS
c.
9 x  2  27 x
2 x2
3    33 x
2 x  4  3x
x4
19.
d.
1x
 8 x 3
4
3 x 3
22 x  2  
2 x  3 x  9
9  5x
9
x
5
Unit 2, Topic 1
20.
21.
a.
The price of a pizza is a function of the number of toppings.
b.
P  2   12.50
c.
0,1, 2,3, 4
d.
No, there is not a constant increase in the price for each additional topping.
e.
10.75,11.75,12.50,13.00,13.25
a.
b.
w
T  w
0
2
4
50
66
82
Independent Variable: number of games won (w)
Dependent Variable: number of prize tokens ( T  w  )
c.
The number of prize tokens is a function of the number of games won.
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ALGEBRA 1 A
Semester Exam Review ANSWERS
d.
The variables are discrete. The number of games won and the number of prize
tokens can be whole numbers only.
e.
The number of prize tokens after winning 3 games is 74.
f.
{ 0, 1, 2, 3, 4, 5, 6, 7}
g.
w5
22.
C.
 3, 2 
23.
A.
The point  5,12  is on the graph of the function f.
24.
B.
13
y
25.
Points can be connected by
straight or curved lines.
1
O
26.
1
x
a.
0  t  7 or  0, 7 
b.
3  F  3 or  3,3
c.
The temperature when t  0 or the temperature at midnight.
d.
t 6
e.
3  t  6 or 3, 6
f.
Five hours after midnight, the temperature of the freezer is –2o F.
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ALGEBRA 1 A
27.
28.
29.
Semester Exam Review ANSWERS
a.
The relation is a function. For every element of the domain, there is exactly one
range element.
b.
The relation is NOT a function. Several elements of the domain (for example
x  1 ) has multiple range elements paired with it.
c.
The relation is NOT a function. The domain element 2 is paired with two
different range elements (7 and 12).
d.
The relation is a function. For every element of the domain, there is exactly one
range element.
e.
The relation is NOT a function. The domain element 5 is paired with two range
elements (4 and 8).
f.
The relation is a function. For every element of the domain, there is exactly one
range element.
a.
=
b.
<
c.
>
a.
Column A
b.
Column A
c.
Column B
d.
equal
e.
Column A
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ALGEBRA 1 A
Semester Exam Review ANSWERS
Unit 2, Topic 2
30.
a.
Option A
Option B
t
A t 
t
B t 
0
1
2
3
$60,000
$63,000
$66,000
$69,000
0
1
2
3
$60,000
$61,800
$63,654
$65,563.62
b.
Option A
Option B
A  0   60, 000
B  0   60, 000
A  t   A  t  1  3, 000
B  t   1.03  B  t  1
c.
Option A
Option B
A  t   60, 000  3, 000t
d.
B  t   60, 000 1.03t 
Option A
Option B
t
31.
D.
Sequences 1, 2, and 3
32.
a.
100 coupons after 1 week, 170 coupons after 2 weeks
b.
60 coupons after 1 week, 120 coupons after 2 weeks
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t
ALGEBRA 1 A
33.
Semester Exam Review ANSWERS
a.
3, 6, 12, 24, 48
b.
I would use the explicit formula. Using the recursive formula, I would start with
f 1 , then find f  2  , f  3 , f  4  , and so on until I got to f  30  . Using the
explicit formula, I just need to substitute into the rule.
34.
A  0   8192
a.
3
A  n    A  n  1 or A  n   0.75  A  n  1
4
b.
$4,608
c.
d.
B  0   8192
B  n   B  n  1  1024
$6,144
e.
n
A n
B  n
0
1
2
3
4
5
6
7
8
8,192
6,144
4,608
3,456
2,592
1,944
1,458
1,093.50
820.13
8,192
7,168
6,144
5,120
4,096
3,072
2,048
1,024
0
After the 7th year, the value of the computer using Option A will be greater.
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ALGEBRA 1 A
35.
Semester Exam Review ANSWERS
a.
An explicit rule for an arithmetic sequence would be a linear function.
b.
The recursive formula f  0   20, f  n   30  f  n  1 represents a geometric
sequence; its explicit rule would be an exponential function.
36.
c.
The sequence 10, 12, 14, 16, 18, 20 has a constant difference of 2.
d.
The sequence 10, 20, 40, 80, 160 has a constant ratio of 2.
a.
b.
n
R  n
1
2
3
4
5
6
700
780
860
940
1020
1100
Day 12:
1580  700  80  n  1
n  12
c.
R 1  700
R  n   R  n  1  80
d.
R  n   700  80  n  1 or R  n   80n  620
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ALGEBRA 1 A
37.
Semester Exam Review ANSWERS
a.
or
b.
c.
t
N t 
1
2
3
4
5
6
7
1
2
4
8
16
32
64
130
120
110
100
Number of Squares
90
80
70
60
50
40
30
20
10
0
0
d.
1
2
3
Figure Number
4
5
6
7
N 1  1
N  t   2  N  t  1
e.
N  t   2t 1
f.
It is a geometric sequence; there is a constant ratio of 2.
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ALGEBRA 1 A
38.
a.
Joe will charge a total of 25  50x dollars
b.
Kathy will charge a total of 70  40 x dollars
Semester Exam Review ANSWERS
c.
25  50 x  70  40 x
10 x  45
x  4.5
If a brake job takes 4.5 hours, the total charge will be the same.
39.
Let p represent the number of people they will invite.
The total charge for Over the Top Party Palace will be 100  15 p dollars.
The total charge for Make ‘Em Envious Emporium will be 300  10 p dollars.
100  15 p  300  10 p
5 p  200
p  40
If they invite 40 people, then it doesn’t matter which location they choose; the cost will
be the same.
If they invite fewer than 40 people, then Over the Top Party Palace will be cheaper.
If they invite more than 40 people, then Make ‘Em Envious Emporium will be cheaper.
40.
A.
All of the statements below are true.
41.
B.
exactly 1 solution (the lines have different slope, so they intersect in one point.)
42.
B.
y 3
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ALGEBRA 1 A
Semester Exam Review ANSWERS
43.
a.
b.
12c  g  106
50c  2 g  420
Multiply the first equation by 2, then subtract.
24c  2 g  212
50c  2 g  420
26c  208
c 8
g  10
Old MacDonald has 8 cows and 10 goats.
44.
D.
45.
D.
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ALGEBRA 1 A
Semester Exam Review ANSWERS
46.
a.
s  k  14
25s  10k  200
b.
20
18
Hours Worked at the Bike Shop
16
14
12
10
8
6
4
2
0
0
2
4
6
8
10
12
14 16
18 20
Hours Worked at the Supermarket
c.
Example: Lance works 8 hours at the Supermarket and 4 hours at the Bike Shop.
8  4  12  14
25  8  4 10  300  200
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ALGEBRA 1 A
Semester Exam Review ANSWERS
47.
a.
40 x  30 y  1200
2 x  3 y  90
b.
y
Number of Middle School Students
50
45
40
35
30
25
20
15
10
5
0
0
5
10
15
20
25
30
35
40
45
50
x
Number of High School Students
c.
Choose any point in the viable region and show that its coordinates make each
inequality true.
For example: 25 high school students and 10 middle school students:
40  25  30 10  1300  1200
2  25  3 10  80  90
d.
The lines intersect at the point 15, 20  .
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