FGCU STEM
High School Team
2015
Problem 1
A hot topic in the news today deals with transforming plants in order to generate transgenic crops
(GMO). Electroporation offers an alternative method for the delivery of genes directly into plant cells
without prior removal of the cell walls allowing for greater genetic manipulation potential of plant cells.
The stable or transient integration of genes into plant protoplast cells is efficiently performed with high
cell viability using a system that produces a “square wave.” It has been reported that wheat, barley leaf,
and root protoplasts have been successfully transformed.
Biology
The bread wheat genome is classified as a hexaploid genome. As such, how many complete sets of
chromosomes does the bread wheat genome contain?
Chemistry
During the fermentation and baking process, ferulic acid is set free from the bread wheat’s cell walls.
This liberation process alters the flavor and smell of bread. Ferulic acid appears to suppress a
compound called 2-Acetyl-1-pyrroline (2AP). The molecular formula for 2AP is 𝐶6 𝐻9 𝑁𝑂. What is the
molar mass of 2AP (round to the nearest tenth)?
Physics
4
1
A good approximation to the square wave can be given by the expression 𝜋 (sin 𝑥 + 3 sin 3𝑥 +
1
sin 5𝑥
5
1
1
𝜋
+ 7 sin 7𝑥 + 9 sin 9𝑥). Evaluate this expression for 𝑥 = 105 (round to the nearest hundredth).
Page 1
FGCU STEM
High School Team
2015
Mathematics
Below is a picture of the family tree of bread wheat. Assume each organism can generate with equal
probability sex cells of all possible gene combinations, what is the probability of AABB forming with DD
to make the AABBDD organism (round to 4 decimal places)?
Engineering
A process called gel electrophoresis was used for the analysis of the bread wheat DNA. A common
buffer used in this process is Tris/Acetate/EDTA (TAE). A 1X working solution of the TAE buffer will
contain a certain number of millimolars of Tris, acetic acid, and EDTA. Find the sum of the millimolars of
Tris, acetic acid, and EDTA present in a 1X working solution of the TAE buffer.
Combined Question
Using your answers from the above questions, find the sum of those answers.
Page 2
FGCU STEM
High School Team
2015
Problem 2
Human immunodeficiency virus (HIV) causes HIV infection and AIDS. The virus attacks the immune
system. As the immune system weakens, the body is at risk of getting life-threatening infections and
cancers. Once a person has the virus, it stays inside the body for life.
Biology
A healthy immune system has between 600 and 1200 CD4+ cells per cubic millimeter of blood. Below
what number of CD4+ cells per cubic millimeter is a patient considered to have AIDS?
Chemistry
There are a number of “antiretroviral drugs” that block the virus’s ability to replicate. There are four
main classes of drugs: entry inhibitors, nucleoside reverse trascriptase inhibitors, non-nucleoside
reverse transcriptase inhibitors, and protease inhibitors. Nucleoside reverse transcriptase inhibitors
stop HIV copying its genes into the cell. Nucleosides are the building block for genes. The drugs supply
faulty versions of these building blocks. One such drug is called abacavir. The molecular formula for
abacavir is 𝐶14 𝐻18 𝑁6 𝑂. In the following balance equation for a combustion (reaction with 𝑂2 ) to form
𝐶𝑂2 gas, 𝐻2 𝑂 liquid, and 𝑁2 gas, fin the sum of the coefficients that balance this equation?
𝐶14 𝐻18 𝑁6 𝑂(𝑠) + __𝑂2 (𝑔) → __𝐻2 𝑂(𝑙) + __𝐶𝑂2 (𝑔) + __𝑁2 (𝑔)
Physics
The half-life of abacavir is approximately 1.5 hours. How much of a 300 mg tablet is left in a patient’s
system 1 day (round to 4 decimal places)?
Page 3
FGCU STEM
High School Team
2015
Mathematics
In 1985 there were 15,948 diagnosed cases of AIDS in the United States. In 1990 there were 156,024.
Scientists said that if there was no research done, the disease would grow exponentially. Compute the
number of cases this model predicts for the year 2015 (write your answer in the form A.B billion).
Engineering
You are designing a molding machine for the production of abacavir. The melting point of abacavir is
165 ℃. Assume ambient temperature of a lab is 23 ℃, it takes approximately 10 minutes to cool to
60 ℃. According to Newton’s Law of Cooling, how long would it take to bring the melting point of
abacavir to 40 ℃ (round to the nearest tenth of a minute)?
Combined Question
Using your answers from the above questions, find the product of those answers (note: just use A.B
from the Mathematics section).
Page 4
FGCU STEM
High School Team
2015
Problem 3
The number of hours of daylight in Summitville, Canada varies between 9 hours and 15 hours per day.
The graph for a particular month looks like this:
Biology
Daylight is important in photosynthesis. How many water molecules are produced in the chemical
reaction of photosynthesis?
Chemistry
Smog and daylight are related. An important reaction in the formation of photochemical smog is the
photodissociation of 𝑁𝑂2 :
𝑁𝑂2 + ℎ𝑣 → 𝑁𝑂(𝑔) + 𝑂(𝑔)
The maximum wavelength of light that can cause this reaction is 420 nm. What is the maximum
strength of a bond, in kJ/mol, that can be broken by absorption of a photon of 420 nm light?
Physics
The number of hours of daylight in Summitville, Canada is due to the Earth’s tilt on its axis as the Earth
travels around the sun. Assuming an elliptical orbit, the Earth is 147 million kilometers from the Sun at
the closest point it is from the sun and it is 152 million kilometers from the Sun at the farthest point it is
from the Sun. What distance does the Earth move in a year (give you answer in million kilometers and
round to four digits)?
Page 5
FGCU STEM
High School Team
2015
Mathematics
A model for the number of daylight hours on day 𝑡 is 𝐷(𝑡) = 12 − 3 cos(0.0172(𝑡 + 11)) , 0 < 𝑡 ≤
365. (𝑡 = 1 corresponds to January 1.) How rapidly is Summitville, Canada gaining daylight 90 days after
the minimum occurs (answer in minutes per day and round to three decimal places)?
Engineering
Given an average consumption of 48 kWh of electricity per day, and the annual average of 4.0
kWh/m2/day of solar insolation, how many square meters of solar panels of efficiency 15% will I need to
install for my home to become energy independent in Summitville, Canada?
Combined Question
Find the arithmetic mean of your answers (round to the nearest tenth and only use the digits from your
Physics answer).
Page 6
FGCU STEM
High School Team
2015
Problem 4
A new homeowner wants to install a new pool filled with sea water. A cross-section of the pool is
shown below.
Biology
A concern among pool owners is the presence of algae. You were reading your biology textbook and
noticed algae can be part of the Archaeplastida. How many subgroups are there in the Archaeplastida?
Chemistry
Assume your pool contains 2.5 × 106 L of acidic water. Acidic water can be treated with basic
substances to increase the pH. Calculate the minimum mass of lime, 𝐶𝑎𝑂, needed to adjust the pH of
the pool from 5.0 to 6.5 (round to the nearest gram).
Physics
Suppose the pool is emptied of water. A pool cleaner in the shape of a box with a mass of 10 kg is
placed on the smooth (frictionless) incline of the pool that makes an angle 𝜃 with the horizontal. Find
the normal force on the box (round to the nearest Newton).
Page 7
FGCU STEM
High School Team
2015
Mathematics
𝑑𝑉
𝑑ℎ
1
We wish to find the change in volume of the pool as it fills up with water. Find 𝑑𝑡 when 𝑑𝑡 = 2 ft/s.
Engineering
The new homeowners want to add a viewing window into the pool and add a landscaping element to
allow underwater view into the pool. Calculate the force due to water pressure exerted on a 1.0 𝑚 ×
3.0 𝑚 viewing window. The window will be placed 1.0 𝑚 below the surface of the water (round to the
nearest tenth of a Newton).
Combined Question
Using your answers from above, find
Page 8
(Biology)(Chemistry)(Physics)(Mathematics)
(Engineering)
(round to the nearest tenth).
FGCU STEM
High School Team
2015
Problem 5
A bucket that weighs 70 lb when filled with water is lifted at a constant rate, by a mechanical winch,
from the bottom of a well that is 60 feet deep.
Biology
While collecting water from the well, you notice the presence of some frogs in the water. You surmise
that a recent drought is causing these frogs to go into the well in search of water. In a population of
certain frogs in which the allele for brown skin is dominant to the allele for green skin, a drought leads
to selection against green-skinned frogs. When the drought ends, 12 percent of the remaining frogs
exhibit the green-skin phenotype. If the population is now in Hardy-Weinberg equilibrium, what will be
the frequency of the green-skin allele in the next generation? Provide your answer to the nearest
hundredth.
Chemistry
Once you’ve collected the water from the well in the bucket you decide to perform an experiment. A
sample of 𝐾𝐶𝑙𝑂3 is partially decomposed (2𝐾𝐶𝑙𝑂3 (𝑠) ⟶ 2𝐾𝐶𝑙(𝑠) + 3𝑂2 (𝑔)), producing 𝑂2 gas that is
collected over water. The volume of gas collected is 0.250 L at 26 ℃ and 765 torr total pressure. How
many moles of 𝑂2 are collected (round to three digits)?
Physics
Suppose you use a pulley system instead of a mechanical winch. One end of a rope is attached to a
horizontal beam going across the well. One pulley is attached to the bucket and the other pulley is
attached back at the horizontal beam. You will use a rope looped over the two pulleys. What force
must be exerted on the rope to slowly lift the bucket’s weight (round to the nearest Newton)?
Page 9
FGCU STEM
High School Team
2015
Mathematics
The bucket has a hole in the bottom. It only weighs 35 lb when it reaches the top, due to the water
leaking out at a constant rate. Compute the work required to lift the bucket from the bottom of the well
to the top of the well. (Recall that the bucket is being lifted at a constant rate, as well.)
Engineering
The water used to fill the bucket comes from a storage tank. The surface of the water tank in that
storage tank is 30 m above the water faucet used to fill the water bucket. Calculate the water pressure
at the faucet. Assume you are using regular water at 4 ℃. (Answer in
𝑁
)
𝑚2
Combined Question
(Mathematics)+(Engineering)
Using your answers from above, find (Biology)+(Chemistry)+(Physicis) (round to the nearest hundredth).
Page 10
FGCU STEM
High School Team
2015
Problem 1
Biology: 42 chromosomes
Chemistry: 111.1
Physics: 0.19
Mathematics: 0.0010
Engineering: 40 + 20 + 1 = 61
Combined: 42 + 111.1 + .19 + .001 + 61 = 214.291
Problem 2
Biology: 200 cells per cubic millimeter
Chemistry: 18 + 9 + 14 + 3 = 44
Physics: 0.0046
Mathematics: 10106.69572 ∙ (1.577963801)26 ≈ 1.4 billion
Engineering: 40 = 23 + (165 − 23)𝑒 −.1344909145𝑡 ⇒ 𝑡 ≈ 15.7 minutes.
Combined: 200 ∙ 44 ∙ 0.0046 ∙ 1.4 ∙ 15.7 = 889.7504
Problem 3
Biology: 6𝐶𝑂2 + 12𝐻2𝑂 + light energy ⟶ 𝐶6𝐻12 𝑂6 + 6𝑂2 + 6𝐻2𝑂. Thus, 6 water molecules.
Chemistry: 285 kJ/mol
1⁄
Physics: 𝜋 [3(𝑎 + 𝑏) − ((3𝑎 + 𝑏)(𝑎 + 3𝑏)) 2] = 𝜋 [3(147 + 152) − ((3(147) + 152)(147 +
1⁄
2
3(152)))
] ≈ 939.4 million kilometers.
Mathematics: 3.095 minutes per day
Engineering: 80 square meters
Combined: 6+285+939.4+3.095+80
= 262.7
5
Page 11
FGCU STEM
High School Team
2015
Problem 4
Biology: There are 3 subgroups in the Archaeplastida: the green plants, red algae and the glaucophytes.
Chemistry: [𝐻+ ]𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 10−5.0 = 1 × 10−5𝑀 and [𝐻+ ]𝑓𝑖𝑛𝑎𝑙 = 10−6.5 = 3 × 10−7 𝑀.
(1 × 10−5 𝑀)(2.5 × 106 ) = 25 𝑚𝑜𝑙. (3 × 10−7 𝑀)(2.5 × 106 ) = 0.75 𝑚𝑜𝑙.
1 mol CaO
56.1 CaO
)(
)
2 mol 𝐻 +
1 mol CaO
24.25 (
≈ 789 grams.
25
Physics: 𝐹𝑁 = 𝑚𝑔 cos 𝜃 = 10 ∙ 9.80 ∙ √881 = 83 N
Mathematics: 𝑉 = {
𝑑𝑉
𝑑𝑡
500ℎ +
125 2
ℎ ,
8
0 < ℎ < 16
1500ℎ − 12000, 16 ≤ ℎ < 20
𝑑ℎ
⇒
𝑑𝑉
𝑑𝑡
500 𝑑𝑡 +
={
125 𝑑ℎ
ℎ 𝑑𝑡 ,
4
𝑑ℎ
1500 𝑑𝑡 ,
0 < ℎ < 16
16 ≤ ℎ < 20
⇒
1
2
= 1500 ( ) = 750.
2.0
Engineering: ∫1.0 𝜌𝑔𝑦𝜔𝑑𝑦 = 12 𝜌𝑔𝜔(𝑦22 − 𝑦12 ) = 12 (1,025)(9.8)(3.0)(2.02 − 1.02 ) = 45202.5 N
Combined: 3×789×83×750
= 3259.7
45202.5
Problem 5
Biology: √. 12 ≈ .35
Chemistry: 𝑃𝑂2 = 765 torr − 25 torr = 740 torr. 𝑛𝑂2 =
𝑃𝑂2 𝑉
𝑅𝑇
10−3 mol 𝑂2 .
=
(740)(
1
)(0.250)
760
(0.0821)(299)
31.7515 (𝑘𝑔)∙9.80
Physics: 2𝐹𝑇 − 𝑚𝑔 = 𝑚𝑎; 𝑎 = 0 ⟹ 𝐹𝑡 = 𝑚𝑔
=
≈ 156 N
2
2
60
Mathematics: ∫0 [(35 + 35
𝑥) + 0.55𝑥] 𝑑𝑥 = 4140 ft-lb
60
Engineering: ∆𝑃 = 𝜌𝑔ℎ = (1000)(9.8)(30) = 290,000
4140+290000
Combined: .35+.0092+156
= 1881.18
Page 12
𝑁
.
𝑚2
= 9.92 ×