MWM-Int. Alg. 2 – Final Exam Review Key
CHAPTER 1
21.
Distance depends on the time driven.
22.
The range is 0 to 15 miles.
23.
$9.50 per person
24.
9 weeks
25.
y  55x  67 where x = the number of hours and y = total cost
26.
8.53 cm
27.
2.4, undefined, -0.4
28.
20.6 inches
29.
No. y  75000  2000x where x = 10 year interval and y = population
x = 12.5 so in 125 years the population reaches 50,000 which is not within my lifetime

30.
31.
Inverse variation since the gallons of gasoline remaining is decreasing as the number of miles traveled
increases
Thad is wrong. It is linear but goes through y = 0.
Erin is wrong. Direct variation is linear.
32.
1
6
33.
y  0.25x  2.50 where x = the number of miles and y = the cost.

y = 0.25(15) + 2.50 so y = 6.25. Yes, he has enough money.
34.
y = 4x where x = length of side and y = perimeter.
Justification: 0 = 4(0), 0 = 0
18 = 4(4.5), 18 = 18
28 = 4(7), 28 = 28
44 = 4(11), 44 = 44
The situation is direct variation. The graph is continuous through the origin with a constant of proportionality of
4.
MWM-Int. Alg. 2 – Final Exam Review Key
Page 1 of 8
CHAPTER 2
17. In the 12th year – 2006
18. The trend line should go through (0, 0) since working 0 hours would earn 0 dollars. One
possible solution is:
(0 ,0) and (25, 125)
125
m 
 5
25
y  5x, where x  number of hours and y  amount paid
Since m = 5, the average hourly rate is $5.
Using the above model,

19.
210  5x
so 42 hours of work earns $210.
42  x
mean = $2.48; median = $2.42; mode = $2.09
Since there aren’t any outliers, the mean would be the best number to use for the constant of proportionality.
y = 2.48x, y = 2.48(25) = $62

y = 1715 + 0.43x
18 months = 6 three month time period so y = 1715 + 0.43(6) = $1717.58
mean = $2.13; median = $2.13; mode = $2.15
20.
21.
The mean is most affected by the higher price. The new values are mean = $2.20; median = $2.14 and
mode = $2.15.
According to Logan’s equation, it costs $3.50 for each movie that is rented. According to Steven’s
equation, it costs $1.50 to rent each movie and $5 is the original fee or membership fee.
22.
23.
24.
25.
26.
0.23 is the slope of the line and it represents the charge for each mile the car is driven.
If x = 0 then y = 1.15 + 0.01(0) = 1.15 so 1.15 is the weight of the jar with 0 pennies in it.
2.25 hours
Since Larry is paying his parents $125 every week and the amount of money he owes them is decreasing, the
slope of the equation should be –125, not +125. Therefore, Ken is incorrect.
27.
y = 4.75x is an example of a direct variation function since it goes through the point
(0, 0). y = 4.75x + 12 has the same slope as the other equation but it is not a direct variation equation since it goes
through the point (0, 12).
28.
The dependent variable is always graphed on the horizontal axis. In this situation the
weight of the children
depends on their age so the weight is the dependent variable. Therefore the weight of the children is graphed on the
horizontal axis.
29.
Scatterplot
y = 6050x – 38500 where x = number of years of school and y = annual median salary
y = 6050(10) – 38500 = $22,000
30.
If the slope is positive there is a positive correlation between the data. If the slope is negative there is a negative
correlation between the data.
MWM-Int. Alg. 2 – Final Exam Review Key
Page 2 of 8
CHAPTER 3
17
18.
They bought 13, $15 tickets and 11, $45 tickets
y = 10 + 0.10x and y = 0.15x where x = the number of text messages and y = the cost
graph
(200, 30)
For 200 text messages the cost is $30 with both providers
19.
2(2)  3(2)  6
4  6  6
10  6
and  2   3
Since (-2, -2) makes a true statement when substituted in each inequality, (-2, -2) is a solution of the system.
20.

21.
22.
23.
24.

25.
x  0; y  0; x  y  25; 72x  48y  1440
graph
(0, 0), (10, 15), (0, 30) and (20, 0)
0 pencils and 30 erasers yields the most profit.
Profit
Vertex
(0, 0)
(10, 15)
(0, 30)
(20, 0)
$0
$21.25
$22.50
$20
x + y = 550 and 1.50x + y = 750 where x = number of milk chocolate bars and y = number of white chocolate bars
2 sweaters can be purchased for $60 from both catalogs.
$2.63

$1.84
7
 
6

 8 

Fresh
$1.31
$2.63
$0.79 

$0.89
Soph Jr Srs
26.
12
8
5
5


9 22 8
 7
Substitution would be the most efficient since the first equation is already solved for one variable.
27.
$2500 in sales for $600 in earnings.

28.
29.

1.25
 0.75


1.25
1.75
x  y  125
x  0
y  0
15x  12y  360 where x  number of pine trees and y  number of oak trees
MWM-Int. Alg. 2 – Final Exam Review Key

Page 3 of 8
30.
9.9 or $9.90
CHAPTER 4
17
Answer:
Front View
Side View
Removing the back right 3 cubes will
not change the front or side views since
the column of 5 cubes will be what you
see when looking at the front or the side
of the figure.
18.
The basic element is one star. The pattern is made by rotating the star 45˚.
19.
On possible answer is below.
20.
The picture has reflection symmetry.
21.
One possible answer is below.
22.
23.
24.
48 feet tall
25.
6 feet
26.
2
27.
250
8

x
0.5
A
B
x = 15.625 inches

x
8

8.4
0.5
x = 134.4 feet

28.
x'  x  5
y'  y  3
Sally is sliding the pattern left and up. She is not changing the size, shape or orientation. Therefore
Sally is translating the pattern.
These equations are moving the pattern left 5 spaces, up 3 spaces and reflecting it over the x-axis.
MWM-Int. Alg. 2 – Final Exam Review Key
Page 4 of 8
x'   x
y'  y
29.
The y-coordinate will not change because each point will be the same number of units up. The x-coordinate
needs to be the same number of units from the y-axis but on the opposite side. Therefore the sign of the xcoordinate must change.
30.
11.25 miles
ABE and ACD are similar.
The scale factor is 1.6 which means the bigger triangle is 1.6 times the smaller triangle.
CHAPTER 5
17
Victor’s football goes 5.64 feet higher.
12
x
5
6
y   x  18
5
y 
18.
At 5 seconds the student stopped walking away from the motion detector and started walking toward the
motion detector. I know this because the slope changed from positive to negative and the distance went
from increasing to decreasing.
19.
The graph is nonlinear because linear equations have x as their highest degree.
y   2x 2  6x  5
20.
y   2(x 2  3x  2.25)  5  4.5
y   2(x  1.5)2  9.5
vertex  (1.5, 9.5)
21.
22.

23.
y   3x2  6x  9

y   (x  3)2  4
domain: x   5; range: y  0

0  2(3x 2  x  4)
24. 0 
 2(3x  4)(x 
 1)
4
, 1  x
3

MWM-Int. Alg. 2 – Final Exam Review Key
Page 5 of 8
4(x 2  x 
1
)  3 1
4
1 2
)  4
2
1
(x  )2  1
2
3
1
x  , 
2
2
4(x 
25.
26.

No, this is not correct. If x = 0 is substituted into the equation, y = 20. This represents the height of the coin as it
is dropped. Therefore the range is 0  y  20.
27.
[0,  ) because the domain of the inverse of a graph is the range of the original graph.
28.
Check graphs.


4
, 1
3
29.
x=
30.
10.25 feet, 0.625 seconds, about 1.425 seconds, When the ball hits the grounds its height is 0. The solution to

16t 2  20t  4  0 is 1.425.
31.
When t = 0, y = 5 feet

The maximum height of the water is 6.5625 feet so it will not reach the hanging pot.
CHAPTER 6
18.
19.
The data is exponential. y  4(3) x where x is the year and y is the population. I know the data is exponential
because there is a common quotient of 3. It is were linear the population would increase by the same amount
every time.

y  55(2)x where x is the number of hours and y is the number of bacteria; 1 day is 24 hours so
y  55(2)24  922,746,880 ; using the table of the graph there will be 7040 bacteria in 7 hours
20.
f (x)  3x has an initial value or y-intercept of 1 while f (x)  2  3x has an initial value or y-intercept of

2.
21.
exponential, y  1500( ) x where x is the year
 and y is the population
1
5
22.
2007
23.
I disagree. The form of the equation is y  ab x and 0  b  1 for the equation to be exponential decay.
The value of a does not determine growth or decay.
24.
y  a5x  3 where a > 1

MWM-Int. Alg. 2 – Final Exam Review Key


Page 6 of 8
25.
f (x)  10(0.93)x
26.
log (9) + log (5)

1
4
27.
log( )
28.
log5125  3

29.
x=2
30.
31.
x = 2.404
f (x)  584000(0.95)20  20,935;
14600  58400(0.95) x

0.25  0.95x
log 0.25  log 0.95
x  27 years
CHAPTER 7
18.
linear because there is a constant increase every year, the original amount or her principal, y = 1200 +

36x
19.
y = 850(0.75)(2) = 127.50
127.50 + 850 = $977.50
20.
$21,320
21.
59.60 + 0.15(2500 – 817) = 59.60 +252.45 = $312.05
22.
y = 1.05x where x is the price of the item and y is the total cost including tax, yes because it has a constant slope
and goes through (0, 0), $94.45
23.
1750(0.09)(5) = $2537.50
1750(1.05)5  $2233.49
24.
22,500(1.015)4  $23,880.68

25.

500(1  0.005)(
(1  0.005)36  1)
 $19766.39
0.005
25000(0.85) x  10000
26. 0.85x  0.4
x  5.6
about 6 years

MWM-Int. Alg. 2 – Final Exam Review Key
Page 7 of 8
27.
444.65 x 60 = 26,679
26,679 – 23,000 = $3,679
28.
$307.36
29.
$88,949.60
CHAPTER 8
Jim should take his boat out approximately 94 feet from the bank. At that
point the treasure chest is approximately 66 feet deep.
17
18.
BC
19.
1
x

0.819
500

x = 610 yards

20.
The triangles are no longer similar so the same proportion cannot be used.
x
0.5
cos 22û 
x = 0.46 mile

21.
tan A 
25
50
 A = 26.565˚
22.
1.26 minutes
22.
Sine of
150˚
23.
Check to make sure student graph meets criteria.
24.
These equations are of the form f (t)  Asin(B(t  C))  D. A is the amplitude or loudness of the note.
Note 1 has an amplitude of 0.001 and note 2 has an amplitude of 0.005. Since 0.005 > 0.001, note 2 is louder.
25.
Check scatterplots, 1.5 feet, 10 steps
26.
sin 7û 
3
, x = 24.6 feet
x
27.
sin x 
30
, x = 36.87˚
50


28.
MWM-Int. Alg. 2 – Final Exam Review Key


BC
AC
Page 8 of 8