APES
st
1
Semester Math
Review
2015
APES mastering the math part 1 video
APES mastering the math part 2 video
Comparing the value of two washing
machines.
An average family washes 5 loads of laundry per week. How many
loads does the family wash in a year?
Comparing the value of two washing
machines.
An average family washes 5 loads of laundry per week. How many
loads does the family wash in a year?
5 loads
Week
x 52 weeks
Year
= 260 load
Year
A traditional machine uses 150 L of water per load
of laundry and the efficient machine uses 75 L.
How many liters would the efficient washing
machine save per year?
A traditional machine uses 150 L of water per load
of laundry and the efficient machine uses 75 L.
How many liters would the efficient washing
machine save per year?
(150 L – 75L)/load x 260 loads/year = 19,500 L/year
The average cost of water in the Unites States is
$0.40 for every 1,000 L. How much money would
you save each year by using the more efficient
washing machine?
The average cost of water in the Unites States is
$0.40 for every 1,000 L. How much money would
you save each year by using the more efficient
washing machine?
$0.40/1000 L x 19,500 L /year = $7.80 /year
How many years would you have to own the more
efficient machine that cost $800 before you save
money compared to the traditional machine that
cost $400?
How many years would you have to own the more
efficient machine that cost $800 before you save
money compared to the traditional machine that
cost $400?
$800 - $400 = 51.3 years
$7.80/year
Is this a big enough economic incentive to save water for most people?
What are the ecological benefits for saving water?
An older showerhead uses 150L for a 10 minute
shower, whereas a reduced flow showerhead uses
only 95L. If you take one shower per day, how
many liters of water would you save in 1 year if you
replaced your older showerhead?
An older showerhead uses 150L for a 10 minute
shower, whereas a reduced flow showerhead uses
only 95L. If you take one shower per day, how
many liters of water would you save in 1 year if you
replaced your older showerhead?
Old shower – New shower = 150L per
day– 95L per day = 55L per day
55L/day x 365 days per year = 20,075
liters
Tropical Rainforests are being cleared at
32,500 hectares per day. A hectare is an area
that is 10,000 square meters. A soccer field is
6,500 square meters. How many soccer fields
of rainforest are being cleared a day?
Tropical Rainforests are being cleared at
32,500 hectares per day. A hectare is an area
that is 10,000 square meters. A soccer field is
6,500 square meters. How many soccer fields
of rainforest are being cleared a day?
32,500 hectares x 10,000 m2 = 325,000,000 m2
hectare
325,000,000 m2 x 1 soccer field = 50,000 soccer fields
6,500 m2
Describe 3 negative environmental effects
associated with the removal of so much
rainforest per day.
1. Removal of trees removes habitat for animals like insects, birds and
small mammals. These organisms are prey for larger animals. If the
trees are taken away these small organisms cannot survive and will
impact the size of the populations of larger organisms because
larger organisms will have less to eat.
2. Trees take in carbon dioxide and release oxygen. If the trees are
removed, there will be less oxygen in the air and more carbon
dioxide in the air. People and animals need oxygen to survive. Less
oxygen means that fewer animals and people can survive. More
carbon dioxide in the air is linked to increased temperatures on
earth which can cause animals that are intolerant of temperature
increases to either migrate towards higher elevation or the poles
where it is cooler or go extinct. More carbon dioxide raises
temperatures because carbon dioxide is a greenhouse gas, meaning
it traps heat that is reradiated from the ground.
3. The removal of trees can cause erosion. Tree roots stabilize the soil.
It the trees are removed, the frequent rains of the equator will
wash away the soil. This soil will end up in bodies of water and can
cause eutrophication because the runoff carries soil with nutrients
which can cause algae to grow quickly and die. The fast growth of
the algae can block sunlight and cause plants in the water body to
die. Bacteria break down the dead organisms removing oxygen
from the system thus causing other aquatic organisms to die
because of hypoxic conditions.
4. Soil in the aquatic environment can also cover up riparian habitat
that riparian organisms depend on for foraging or nesting.
Sediments in the water can also clog fish and invertebrate gills and
block light from photosynthesizing plants.
5. You can also discuss the loss of tourism and aesthetic beauty that
the trees provide for people, or the economics of mudslides and the
loss of private property, infrastructure or agricultural lands.
A radioactive material has a half life of 5 days.
The sample mass was originally 100,000
grams. The mass of the sample is currently
3,125 grams. How old is the sample?
A radioactive material has a half life of 5 days. The sample
mass was originally 100,000 grams. The mass of the sample is
currently 3,125 grams. How old is the sample?
3,125 grams / 100,000 grams = 1/32
1/32 is 5 half lives.
5 half lives x 5 days = 25 days
Half Life
Parent fraction (radioactive isotope)
0
1
1
1/2
2
1/4
3
1/8
4
1/16
5
1/32
The sun gives out approximately 1,000 joules
per second per square meter at the equator.
How much energy will be captured by 4 square
meters of rainforest plants in 5 seconds?
The sun gives out approximately 1,000 joules
per second per square meter at the equator.
How much energy will be captured by 4 square
meters of rainforest plants in 5 seconds?
1,000 joules /meter2/second x 4
meter2 x 5 seconds = 20,000 joules.
Primary producers absorb 1% of the
energy from the sun
.01 x 20,000 joules = 200 joules.
Of that 200 joules absorbed by the plants, how
much energy can be transferred to a secondary
consumer like a jaguar?
Of that 200 joules absorbed by the plants, how
much energy can be transferred to a secondary
consumer like a jaguar?
10 % of energy gets to
primary consumers and 10%
of that energy gets to
secondary consumers.
200 joules x 0.1 = 20 joules
20 joules x .01 = 2 joules.
A population of desert tortoise has a growth rate
of 3 percent. How many years will it take that
population to double?
A population of desert tortoise has a growth rate
of 3 percent. How many years will it take that
population to double?
Use the rule of 70.
70/3 = 23.3 years.