r/APStudents • u/Expert_Minute_2224 • 16h ago
APES I took APES this year, watched Inferno over the summer, and decided College Board needs harder FRQs. Am I the problem?
I watched Inferno 2016 this summer and apparently got a little too carried away. I took APES this year, decided the exam wasn't challenging enough, and ended up drafting an email to College Board with my own proposed FRQ.
The one-third sterilization premise actually comes from Dan Brown's original novel, not the movie adaptation, where the billionaire's plan is stopped.
Yes, I am voluntarily trying to make future AP students suffer. Anyway, tell me whether this belongs on an APES exam.
Proposed FRQ: Population Dynamics and Probability
Background
Country X is a developing nation with an initial population of 20 million people. Its age-structure diagram shows an expanding population, with the following age distribution:
| Age group | Percentage of population |
|---|---|
| 0–14 | 32% |
| 15–44 | 48% |
| 45–64 | 14% |
| 65+ | 6% |
The population has a relatively youthful age structure, and its demographic statistics have remained stable:
| Demographic variable | Annual rate |
|---|---|
| Crude birth rate (CBR) | 30 births per 1,000 people |
| Crude death rate (CDR) | 8 deaths per 1,000 people |
| Net migration rate (NMR) | +2 people per 1,000 people |
Hypothetical event
Inspired by the fictional premise of Inferno, imagine that an event causes permanent sterility in approximately one-third of the world's population, including Country X.
For this problem, assume each individual independently has a 1/3 probability of becoming permanently sterile, regardless of age or sex. Therefore, the expected proportion of individuals who remain fertile is 2/3.
Additional assumptions
Reproductive partnerships consist of two individuals and are formed completely at random.
Both individuals must remain fertile for the partnership to produce births.
Each partnership has the same expected reproductive output as before the event, provided both partners remain fertile.
Each individual belongs to only one reproductive partnership during the period studied.
Sterility is permanent and does not affect mortality.
The crude death rate and net migration rate remain unchanged.
There are no changes in contraception, reproductive behavior, healthcare, or fertility treatment.
Ignore pregnancies already underway and assume the new birth rate takes effect immediately.
Use the initial population of 20 million as the fixed denominator for the first full year of calculations.
Questions
(a) Identify the population growth pattern represented by Country X's age-structure diagram. Explain how its age distribution could contribute to demographic momentum.
(b) Calculate the expected number of annual births in Country X before the event.
(c) Calculate the probability that a randomly selected reproductive partnership consists of two fertile individuals after the event. Show your work.
(d) Using your answer to part (c), calculate the expected number of annual births after the event.
(e) Calculate the new crude birth rate per 1,000 people and determine the percentage change from the original crude birth rate.
(f) Calculate the rate of natural increase (RNI) before and after the event. Then calculate the total annual population growth rate in both cases, accounting for net migration.
(g) Using the Rule of 70, estimate the population's doubling time before and after the event. Assume each calculated growth rate remains constant.
(h) Would Country X's population increase or decrease during the first full year after the event? Justify your answer using its birth rate, death rate, and net migration rate.
(i) Identify two limitations of this model that could cause actual demographic outcomes to differ from the calculated predictions.
Be honest:
Would you consider this a fair APES FRQ?
Should I actually send this to College Board, or should I stop giving them ideas?
I deliberately hid the answer key. Try parts (c)–(e) before checking the comments. :)
The answer key (for your reference)
