Pre-Calculus Final ExamName _________________________ Score.docx

Pre-Calculus Final Exam
Name: _________________________
Score: ______ / ______
Multiple Choice: Type your answer choice in the blank next to
each question number.
_____1.
Find the indicated sum.
A. 2
B. 54
C. 46
D. -54

_____2.
Graph the ellipse and locate the foci.
A.
foci at (0, 6) and (0, -6)
C.
foci at (, 0) and (-, 0)
B.
foci at ( 5, 0) and (-5, 0)
D.
foci at (0, 5) and (0, -5)
_____3.
Solve the system by the substitution method.
2y - x = 5
x2 + y2 - 25 = 0
A.

B.
C. {( 5, 0), ( -5, 0), ( 3, 4)}
D. {( -5, 0), ( 3, 4)}
_____4.
Graph the function. Then use your graph to find the indicated
limit.
f(x) = 5x - 3, f(x)
A. 5
B. 25
C. 2
D. 22
_____5.
Use Gaussian elimination to find the complete solution to the
system of equations, or state that none exists.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
A. {(8, -7, -2)}
B. {(-8, -7, 9)}

C. ∅
D. {(2, -7, -1)}
_____6.
Solve the system of equations using matrices. Use Gaussian
elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
A. {( 1, -4, -2)}
B. {( -2, 1, -4)}
C. {( 1, -2, -4)}
D. {( -2, -4, 1)}
_____7.
A woman works out by running and swimming. When she runs,
she burns 7 calories per minute. When she swims, she burns 8
calories per minute. She wants to burn at least 336 calories in
her workout. Graph an inequality that describes the situation.
Let x represent the number of minutes running and y the number
of minutes swimming. Because x and y must be positive, limit
the graph to quadrant I only.

A.
C.
B.
D.
Short Answer Questions: Type your answer below each
question. Show your work.
8
A statement Sn about the positive integers is given. Write
statements S1, S2, and S3, and show that each of these
statements is true.
Sn: 12 + 42 + 72 + . . . + (3n - 2)2 =

9
statements Sk and Sk+1, simplifying Sk+1 completely.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10
Joely's Tea Shop, a store that specializes in tea blends, has
available 45 pounds of A grade tea and 70 pounds of B grade
tea. These will be blended into 1 pound packages as follows: A
breakfast blend that contains one third of a pound of A grade
tea and two thirds of a pound of B grade tea and an afternoon
tea that contains one half pound of A grade tea and one half
pound of B grade tea. If Joely makes a profit of $1.50 on each
pound of the breakfast blend and $2.00 profit on each pound of
the afternoon blend, how many pounds of each blend should she
make to maximize profits? What is the maximum profit?

11
Your computer supply store sells two types of laser printers.
The first type, A, has a cost of $86 and you make a $45 profit
on each one. The second type, B, has a cost of $130 and you
make a $35 profit on each one. You expect to sell at least 100
laser printers this month and you need to make at least $3850
profit on them. How many of what type of printer should you
order if you want to minimize your cost?
12
statements is true.
Sn: 2 + 5 + 8 + . . . + ( 3n - 1) = n(1 + 3n)/2

13
Use mathematical induction to prove that the statement is true
for every positive integer n.
2 is a factor of n2 - n + 2
14
statements is true.
Sn: 2 is a factor of n2 + 7n
15
(i.) f(x)
(ii.) f(x)
(iii.) What can you conclude about f(x)? How is this shown by
the graph?

(iv.) What aspect of costs of renting a car causes the graph to
jump vertically by the same amount at its discontinuities?
16
Use mathematical induction to prove that the statement is true
for every positive integer n.
8 + 16 + 24 + . . . + 8n = 4n(n + 1)
17
The following piecewise function gives the tax owed, T(x), by a
single taxpayer on a taxable income of x dollars.
T(x) =
(i) Determine whether T is continuous at 6061.
(ii) Determine whether T is continuous at 32,473.
(iii) If T had discontinuities, use one of these discontinuities to
describe a situation where it might be advantageous to earn less
money in taxable income.

18
statements Sk and Sk+1, simplifying Sk+1 completely.
Sn: 1 + 4 + 7 + . . . + (3n - 2) = n(3n - 1)/2
19
An artist is creating a mosaic that cannot be larger than the
space allotted which is 4 feet tall and 6 feet wide. The mosaic
must be at least 3 feet tall and 5 feet wide. The tiles in the
mosaic have words written on them and the artist wants the
words to all be horizontal in the final mosaic. The word tiles
come in two sizes: The smaller tiles are 4 inches tall and 4
inches wide, while the large tiles are 6 inches tall and 12 inches
wide. If the small tiles cost $3.50 each and the larger tiles cost

$4.50 each, how many of each should be used to minimize the
cost? What is the minimum cost?
20
The Fiedler family has up to $130,000 to invest. They decide
that they want to have at least $40,000 invested in stable bonds
yielding 5.5% and that no more than $60,000 should be invested
in more volatile bonds yielding 11%. How much should they
invest in each type of bond to maximize income if the amount in
the stable bond should not exceed the amount in the more
volatile bond? What is the maximum income?
2
Running Head: Water Quality and Contamination
1
Water Quality and Contamination
6
Melonie Lindsey
SCI 207: Dependence of man on the environment

Michelle Kozlowski
May 19, 2014
Introduction
Body Paragraph #1 - Background: The outline of the
introduction should describe the background of water quality
and related issues using cited examples. You should include
scholarly sources in this section to help explain why water
quality research is important to society. When outlining this
section, make sure to at least list relevant resources in APA
format that will be used in the final paper to develop the
background for your experiment.
Body Paragraph # 2 - Objective: As we know our planet is made
up of 70% water and only a small amount of this water is usable
freshwater which is only 1%, so 99% of water is saltwater. We
survive off the 1% of freshwater because it cost so much for us
to transform salt water into freshwater. There is only a few
ways to get freshwater which is either surface water or ground
water. We have to have some type of water treatment in place
in order for us not to consume contaminated water. Now that
we know a little bit about the water that we drink, this
experiment is basically to understand the effects of pollutants
on groundwater and how soil can remove the pollutants before it
reached groundwater.
Body Paragraph # 3 - Hypotheses: Experiment 1: If oil is
dumped on the ground, then the groundwater below will contain
traces of oil. Oil can leak past the soil and contaminate the
water that we drink. If vinegar were to be dumped on the
ground for whatever reason, then the groundwater below will
not have traces of the vinegar in it. If laundry detergent were to
be dumped on the ground then the groundwater below would not
have traces of the detergent in it. Experiment 2, if water mixed
with soil is passed through the filtration system, then it will
emerge free of soil. Experiment 3: If the three water sources

are tested for chemical contaminants, then tap water will have
the highest concentration and Dasani water the lowest
concentration of contaminants.
Materials and Methods
Body Paragraph # 1: For experiment 1 what you will need are
(8) 250 mL beakers, permanent marker, 3 wooden stir sticks,
100 mL graduated cylinder, 10 mL vegetable oil, 10 mL
vinegar, 10 mL liquid laundry detergent, 100 mL beaker, 240
mL soil, funnel, cheesecloth, scissors, and water. First thing
you will need to do is form a hypothesis based on it water was
mixed with items such as oil, vinegar and laundry detergent will
soil be able to stop them from reaching groundwater. Next take
all 8 beakers and write one number on each beaker 1 to 8. After
that is complete set beakers 5-8 to the side and take beakers 1-4
with 100 mL of water using the 100 ML graduated cylinder. In
the table record your observations of the water in beaker 1 in
table 1. Add 10 mL oil to beaker 2, mix with wooden stir stick
and record observations for beaker 2 in table 1. Add 10 mL
vinegar to beaker 3, mix with wooden stir stick, and record
observations of the water in beaker 4 table 1. Cut your
cheesecloth into 5 different pieces make sure to set aside 1
piece for the next experiment. Fold all 4 pieces into 4 layers
thick and big enough to line the funnel, place the cloth in the
funnel. Measure 60 mL of soil using the 100 mL beaker and
place it into the cheesecloth-lined funnel, place the funnel
inside beaker 5, pour the water from beaker 1 into beaker 5
through the funnel so it filters into beaker 5 for 1 minute,
record observations for beaker 5 in table 1. Discard the
cheesecloth and soil from funnel. Repeat the steps 9-13 for
beakers 2, 3, and 4 report observations on table 1. Experiment
2: Water treatment, you will ned 100 mL potting soil, (2) 250
mL beakers (2) 100 mL beakers, 100 mL graduated cylinder, 40
mL sand, 20 mL activated charcoal, 60 mL gravel,1 wooden stir
stick, alum, funnel, cheesecloth, bleach , stopwatch and water.
There are many pollutants, this experiment focuses on if a
filtering method works to purify contaminated water. First

record your hypothesis, then add 100 mL of soil to the 250 mL
beaker, fill to the 200 mL mark with water. Pour the solution
between the two 250 mL beakers 15 times. After the solution is
done our 10mL of the contaminated water into a clean 100 mL
beaker. Add 10 grams of alum to the 250 mL beaker containing
the contaminated water, stir with wooden stick slowly for 1-2
minutes, and let the solution sit for 15 minutes. While waiting
rinse the empty 250 mL beaker, place the funnel into the clean
250 mL beaker, fold a piece of cheesecloth so that its 4 layers
thick and big enough to line the funnel. Place in funnel. Begin
layering the funnel, pouring 40 mL of sand into the cheesecloth
lined funnel, then 20 mL activated charcoal, then 40 mL gravel.
Use a 100 mL beaker to measure the amounts. I poured clean
tap water through the filter and repeated 4 more times. Filled
the funnel back up and let sit for 5 minutes. I poured about ¾
of the contaminated water into the funnel. I removed the filter
and added some bleach to the filtered water then stirred.
Results
Tables: The outline of the results section should include all
tables used in your experiment. All values within the tables
should be in numerical form and contain units. For instance, if
measuring the amount of chloride in water you should report as
2 mg/L or 0 mg/L not as two or none.
Table 1: Water Observations (Smell, Color, Etc.)
Beaker
Observations
1
Water is a little cloudy white color, no smell
2
Lots of bubbles, the oil seems to stay together, not really much
of a smell, yellow tint
3
Bubbly, has a strong smell, the bubbles are separated unlike the
oil.
4
Green in color, smells good, a few bubbles, the bubbles seem to

stick to the walls of the beaker
5
Water is brown, doesn’t have a smell
6
The oil went through the soil not all of it but a lot of it, it is not
as brown as the plain water, the bubbles are separated
7
The vinegar came through, the bubbles are much smaller, the
bubbles seem to be on the top more than anything
8
The color is a dirty green and there are a lot more bubbles then
just with water, the bubbles are just on top
Table 2: Ammonia Test Results
Water Sample
Test Results
Tap Water
0 mg/L
Dasani® Bottled Water
0 mg/L
Fiji® Bottled Water
0 mg/L
Table 3: Chloride Test Results
Water Sample
Test Results
Tap Water
0 mg/L
0 mg/L
0 mg/L
Table 4: 4 in 1 Test Results
Water Sample
pH
Total Alkalinity
Total Chlorine
Total Hardness

Tap Water
7 mg/L
1.0 mg/L
80 mg/L
120 mg/L
5 mg/L
0.2 mg/L
40 mg/L
50 mg/L
7 mg/L
1.0 mg/L
40 mg/L
120 mg/L
Table 5: Phosphate Test Results
Water Sample
Test Results
Tap Water
50 ppm
0 ppm
10 ppm
Table 6: Iron Test Results
Water Sample
Test Results
Tap Water
0.15 ppm
0 ppm
0 ppm
Body Paragraph # 1: Tables 2 and 3 shows the 3 different waters
have 0mg/L of ammonia and chloride .Tap water and Fiji
showed 7 mg/L in table 4.4. 0 ppm of iron was found in both

the Fiji and Dasani water as shown on table 6.
Discussion
Body Paragraph #1 - Hypotheses: The outline of the discussion
section should interpret your data and provide conclusions. Start
by discussing if each hypothesis was confirmed or denied and
how you know this.
Body Paragraph # 2 - Context: The outline of your discussion
should also relate your results to the bigger water concerns and
challenges. For example, based on your experiments you might
discuss how various bottled water companies use different
filtrations systems. Or, you could discuss the billion dollar
bottled water industry. For example, do you think it is worth it
to buy bottled water? Why or why not? Your outline should at
least list some of the resources that you plan to utilize in your
final paper to put your results into context.
Body Paragraph #3 – Variables and Future Experiments:
Finally, the outline of your results section should also address
any possible factors that affected your results, such as possible
contamination in the experiments or any outside factors (i.e.,
temperature, contaminants, time of day) that affected your
results? If so, how could you control for these in the future?
You should also propose some new questions that have arisen
from your results and what kind of experiment might be
proposed to answer these questions.
Conclusions
Body Paragraph #1: This section of your outline should briefly
summarize the key points of your experiments. What main
message would you like people to have from this report?
References
Include at least 4 scholarly sources and your lab manual here in
APA format.
Lab 2 – Water Quality and Contamination
Experiment 1: Effects of Groundwater Contamination

Table 1: Water Observations (Smell, Color, Etc.)
Beaker
Observations
1
Water is a little cloudy white color, no smell
2
Lots of bubbles, the oil seems to stay together, not really much
of a smell, yellow tint
3
Bubbly, has a strong smell, the bubbles are separated unlike the
oil.
4
Green in color, smells good, a few bubbles, the bubbles seem to
stick to the walls of the beaker
5
Water is brown, doesn’t have a smell
6
The oil went through the soil not all of it but a lot of it, it is not
as brown as the plain water, the bubbles are separated
7
The vinegar came through, the bubbles are much smaller, the
bubbles seem to be on the top more than anything
8
The color is a dirty green and there are a lot more bubbles then
just with water, the bubbles are just on top
POST LAB QUESTIONS
1. Develop hypotheses on the ability of oil, vinegar, and laundry
detergent to contaminate groundwater.
a. Oil hypothesis = My hypothesis is that the soil will not be
able to stop the oil from reaching our groundwater.
b. Vinegar hypothesis = My hypothesis is that the soil will stop
the vinegar from reaching groundwater.
c. Laundry detergent hypothesis = My hypothesis is that the soil

will stop the vinegar from reaching groundwater.
2. Based on the results of your experiment, would you reject or
accept each hypothesis that you produced in question 1?
Explain how you determined this.
a. Oil hypothesis accept/reject = I accept because the oil went
through the soil like I expected.
b. Vinegar hypothesis accept/reject = I reject because I thought
the soil would have stopped the vinegar from getting to the
water
c. Laundry detergent hypothesis accept/reject = I reject because
like with the vinegar I thought the soil would have stopped the
detergent.
3. What affects did each of the contaminants have on the water
in the experiment? Which contaminant seemed to have the most
potent effect on the water?
Answer = All of the contaminants had bubbles in them weather
it was just a few or if it was a lot.
4. Using at least one scholarly source, discuss what type of
affects these contaminants (oil, vinegar, detergent) might have
on a town’s water source and the people who drank the water?
Answer =
5. Describe what type of human activity would cause
contaminants like oil, acid and detergents to flow into the water
supply? Additionally, what other items within your house do
you believe could contaminate the water supply if you were to

dump them onto the ground?
Answer = I think maybe after cooking throwing the oil outside
in the grass instead of disposing of it correctly. I think gas,
cleaning products, and insect killers.
Experiment 2: Water Treatment
POST LAB QUESTIONS
1. Develop a hypothesis on the ability of your filtration
technique to remove contaminants.
Hypothesis = My hypothesis is that filtration techniques can get
rid of a lot of contaminants but I don’t think it does all.
accept the hypothesis that you produced in question 1? Explain
how you determined this.
Accept/Reject = I would reject my hypothesis because the filter
system did work to clean the water.
3. What are the differences in color, smell, visibility, etc.
between the “contaminated” water and the “treated” water?
Answer = The differences are the color of the contaminated
water is much darker then the filtered water, the smell of the
soil is a lot stronger in the contaminated water. The treated
water is still a little brown but not bad.

4. From the introduction to this lab, you know that there are
typically five steps involved in the water treatment process.
Identify the processes (e.g., coagulation) that were used in this
lab and describe how they were performed.
Answer = Take the soil and mix with water make sure it’s all
mixed up then make the filter system with the sand charcoal,
and rocks, next filter water through the filtration system to
clean the charcoal, next filter the contaminated water, last
compare the contaminated and treated water.
Experiment 3: Drinking Water Quality
Table 2: Ammonia Test Results
Water Sample
Test Results
Tap Water
0
0
0
Table 3: Chloride Test Results
Water Sample
Test Results
Tap Water
0
0
0
Table 4: 4 in 1 Test Results
Water Sample
pH
Total Alkalinity

Total Chlorine
Total Hardness
Tap Water
7
1.0
80
120
5
0.2
40
50
7
1.0
40
120
Table 5: Phosphate Test Results
Water Sample
Test Results
Tap Water
50
0
10
Table 6: Iron Test Results
Water Sample
Test Results
Tap Water
0.15
0

0
POST LAB QUESTIONS
1. Develop a hypothesis on which water source you believe will
contain the most and least contaminants.
Hypothesis = My hypothesis is that Fiji water will have more
contaminants then the tap water and Dasani water and I think
the tap water will have the least amount.
accept the hypothesis that you produced in question 1? Explain
how you determined this.
Accept/reject = I would reject because Fiji water had the most
contaminants but dasani had the lease.
3. Based on the results of your experiment, what major
differences, if any, do you notice between the Dasani, Fiji, and
tap water?
Answer = For the most part everything was pretty much the
same except for the 4 in 1 test. There were a lot of differences
between the waters but the most comparable would be the Fiji
water and tap water.
4. Based on your results, do you believe that bottled water is
worth the price? Why or why not?
Answer = If you are getting Fiji water I will say no but Dasani I
will say yes. I would like to have checked out the different
waters drink like nestle or anything of that sort to see the

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