APES - Fall Final FRQ and Math
Problems All Solved Correct 2025-
2026 Updated.
Chapter 1 Math Connection:
If a made-up population has a crude birth rate of 39 and a crude death rate of 14, calculate the
percent annual natural increase.
Calculate the doubling time using the rule of 70. - Answer 2.5%
39 births - 14 deaths/100 x 100% = 2.5%
28 years
DT = 70/2.5% = 28 years
Chapter 1 Math Connection:
Imagine that within a population of humans, there were 28 births per 1000 people (crude birth
rate) and 10 deaths per 1000 people (crude death rate).
Calculate the annual natural increase for this population.
Calculate the doubling time using the rule of 70. - Answer 1.8%
28 births - 10 deaths/1000 x 100% = 1.8%
39 years
70/1.8% = 39 years
Chapter 2 Math Connection:
A watt is a measurement of power that expresses the rate at which a device uses electricity. For
example, a 60-watt lightbulb draws a constant 60 watts of electricity while it is turned on.
Electricity is measured in kilowatt hours. One kWh represents the amount of energy needed by
a 1000-watt device to operate for one hour. Leaving a 100-watt lightbulb on for 10 hours
consumes 1 kWh of energy. Coal burning powerplants generate a constant output of electricity.
Calculate the amount of power in kWh produced from burning one ton of coal. Use the
following:
1 ton = 2000 lbs
12,500 BTU = 1 lb
1 kWh = 3412 BTU - Answer 7327 kWh electricity
1 ton coal x 2000lbs/1 ton x 12,500BTU/1lb x 1kWh/3412BTU
,1 ton = 2000 lbs
12,5000 BTU = 1 lb
1 kWh = 3412 BTU - Answer 1.45 tons of coal
10,619 kWh x 3412BTU/1 kWh x 1lb/12,500BTU x 1 ton/2000lbs = 36,232,028/25,000,000 =
1.45 tons
Chapter 3 Math Connection:
In a laboratory Petri dish with on area of 58 cm?,a population of E. coli bacteria colonies is
estimated at 2320 colonies. How many colonies are there per cm²? - Answer 2320
colonies/58 cm² = 40 colonies per cm²
Chapter 3 Math Connection:
What is the percent change in E. coli colonies?
(52 colonies and 40 colonies) - Answer 30% increase
(52 colonies - 40 colonies)/40 colonies x 100 = 12 colonies/40 colonies x 100 = 30% increase
Chapter 3 Math Connection:
What is the percent difference in colonies of E. coli?
(52 colonies and 40 colonies) - Answer 26.1% difference
(52 colonies - 40 colonies)/(52 colonies + 40 colonies)/2 x 100 = 12 colonies/46 colonies x 100 =
26.1% difference
Chapter 3 Math Connection:
If the population density of White-Toiled Deer in 2015 is 329 per mile? and 632? per mile² in
2022, calculate the percent change and percent difference:
PC: - Answer 92%
1 original - new 1 / original x 100%
329 deer/mi² - 632 deer/mi² /329 deer/mi² x 100% = 92%
Chapter 3 Math Connection:
If the population density of White-Toiled Deer in 2015 is 329 per mile? and 63? per mile² in
2022, calculate the percent change and percent difference:
PD: - Answer 63.1%
, Consider the following data table indicating a total of 11 possible species of bottom dwelling
invertebrates found.
Mayflies - 1 - ?
Stoneflies - 3 - ?
Caddisflies - 5 - ?
Dobson flies - 0 - ?
Midges - 6 - ?
Craneflies - 1 - ?
Dragonflies - 3 - ?
Scuds - 6 - ?
Pouch snails - 6 - ?
Tubiflex worms - 8 - ?
Leeches - 5 - ?
N=?
Sum n(n-1) = ? - Answer Invertebrates - # of orgs - n(n-1)
Mayflies - 1 - 0
Stoneflies - 3 - 6
Caddisflies - 5 - 20
Dobson flies - 0 - 0
Midges - 6 - 30
Craneflies - 1 - 0
Dragonflies - 3 - 6
Scuds - 6 - 30
Pouch snails - 6 - 30
Tubiflex worms - 8 - 56
Leeches - 5 - 20
N = 44
Sum n(n-1) = 198
Chapter 4 Math Connection:
Plug in the total for "N" and the total for "n(n-1)":
Problems All Solved Correct 2025-
2026 Updated.
Chapter 1 Math Connection:
If a made-up population has a crude birth rate of 39 and a crude death rate of 14, calculate the
percent annual natural increase.
Calculate the doubling time using the rule of 70. - Answer 2.5%
39 births - 14 deaths/100 x 100% = 2.5%
28 years
DT = 70/2.5% = 28 years
Chapter 1 Math Connection:
Imagine that within a population of humans, there were 28 births per 1000 people (crude birth
rate) and 10 deaths per 1000 people (crude death rate).
Calculate the annual natural increase for this population.
Calculate the doubling time using the rule of 70. - Answer 1.8%
28 births - 10 deaths/1000 x 100% = 1.8%
39 years
70/1.8% = 39 years
Chapter 2 Math Connection:
A watt is a measurement of power that expresses the rate at which a device uses electricity. For
example, a 60-watt lightbulb draws a constant 60 watts of electricity while it is turned on.
Electricity is measured in kilowatt hours. One kWh represents the amount of energy needed by
a 1000-watt device to operate for one hour. Leaving a 100-watt lightbulb on for 10 hours
consumes 1 kWh of energy. Coal burning powerplants generate a constant output of electricity.
Calculate the amount of power in kWh produced from burning one ton of coal. Use the
following:
1 ton = 2000 lbs
12,500 BTU = 1 lb
1 kWh = 3412 BTU - Answer 7327 kWh electricity
1 ton coal x 2000lbs/1 ton x 12,500BTU/1lb x 1kWh/3412BTU
,1 ton = 2000 lbs
12,5000 BTU = 1 lb
1 kWh = 3412 BTU - Answer 1.45 tons of coal
10,619 kWh x 3412BTU/1 kWh x 1lb/12,500BTU x 1 ton/2000lbs = 36,232,028/25,000,000 =
1.45 tons
Chapter 3 Math Connection:
In a laboratory Petri dish with on area of 58 cm?,a population of E. coli bacteria colonies is
estimated at 2320 colonies. How many colonies are there per cm²? - Answer 2320
colonies/58 cm² = 40 colonies per cm²
Chapter 3 Math Connection:
What is the percent change in E. coli colonies?
(52 colonies and 40 colonies) - Answer 30% increase
(52 colonies - 40 colonies)/40 colonies x 100 = 12 colonies/40 colonies x 100 = 30% increase
Chapter 3 Math Connection:
What is the percent difference in colonies of E. coli?
(52 colonies and 40 colonies) - Answer 26.1% difference
(52 colonies - 40 colonies)/(52 colonies + 40 colonies)/2 x 100 = 12 colonies/46 colonies x 100 =
26.1% difference
Chapter 3 Math Connection:
If the population density of White-Toiled Deer in 2015 is 329 per mile? and 632? per mile² in
2022, calculate the percent change and percent difference:
PC: - Answer 92%
1 original - new 1 / original x 100%
329 deer/mi² - 632 deer/mi² /329 deer/mi² x 100% = 92%
Chapter 3 Math Connection:
If the population density of White-Toiled Deer in 2015 is 329 per mile? and 63? per mile² in
2022, calculate the percent change and percent difference:
PD: - Answer 63.1%
, Consider the following data table indicating a total of 11 possible species of bottom dwelling
invertebrates found.
Mayflies - 1 - ?
Stoneflies - 3 - ?
Caddisflies - 5 - ?
Dobson flies - 0 - ?
Midges - 6 - ?
Craneflies - 1 - ?
Dragonflies - 3 - ?
Scuds - 6 - ?
Pouch snails - 6 - ?
Tubiflex worms - 8 - ?
Leeches - 5 - ?
N=?
Sum n(n-1) = ? - Answer Invertebrates - # of orgs - n(n-1)
Mayflies - 1 - 0
Stoneflies - 3 - 6
Caddisflies - 5 - 20
Dobson flies - 0 - 0
Midges - 6 - 30
Craneflies - 1 - 0
Dragonflies - 3 - 6
Scuds - 6 - 30
Pouch snails - 6 - 30
Tubiflex worms - 8 - 56
Leeches - 5 - 20
N = 44
Sum n(n-1) = 198
Chapter 4 Math Connection:
Plug in the total for "N" and the total for "n(n-1)":
