Question 1
On a map drawn at a scale of 1:50,000, two schools are 4 centimeters apart. How far apart are they on the ground?
Human geography calculator: density, growth, rank-size and gravity
The formulas the course uses, worked for your numbers: rate of natural increase and doubling time, three kinds of density, the rank-size rule and the gravity model. The working is shown so you can do it by hand on exam day.
Natural increase and doubling time
Rate of natural increase: (28 − 8) ÷ 10 = 2% a year. Doubling time: 70 ÷ 2 ≈ 35 years.
Three kinds of density
- Arithmetic density: 50,000,000 ÷ 500,000 = 100 people per km²
- Physiological density: 50,000,000 ÷ 50,000 = 1,000 people per km² of arable land
- Agricultural density: 10,000,000 ÷ 50,000 = 200 farmers per km² of arable land
The rank-size rule
- City of rank 1: 6,000,000 ÷ 1 = 6,000,000
- City of rank 2: 6,000,000 ÷ 2 = 3,000,000
- City of rank 3: 6,000,000 ÷ 3 = 2,000,000
- City of rank 4: 6,000,000 ÷ 4 = 1,500,000
- City of rank 5: 6,000,000 ÷ 5 = 1,200,000
The gravity model
Interaction index: 400,000 × 900,000 ÷ 150² = 16,000,000. Doubling the distance cuts it to a quarter; doubling either population doubles it.
| Doubling time | 70 ÷ growth rate (%) |
|---|---|
| Physiological density | People ÷ arable land |
| Rank-size rule | City n = largest city ÷ n |
| Gravity model | Population A × population B ÷ distance² |
When the exam uses them
- Density questions ask which measure shows pressure on farmland: physiological density (people per unit of arable land), not arithmetic density (people per unit of all land).
- Rank-size questions compare a country's cities with the rule; a largest city far more than twice the second is a primate city.
- Gravity model questions ask which pair of places interacts most: big populations close together.
- Calculators are not allowed on this exam, so practice the arithmetic with round numbers.
Try 2 questions
Question 2
| Urban area | Population (millions) |
|---|---|
| Urban area 1 | 24.0 |
| Urban area 2 | 14.5 |
| Urban area 3 | 8.2 |
| Urban area 4 | 21.3 |
| Urban area 5 | 11.0 |
Using thresholds of 10 million people for a megacity and 20 million for a metacity, how many of the urban areas in the table are megacities but not metacities?
Next step
College Board's AP Human Geography course page, with the unit weights
Questions people ask
What is the difference between arithmetic and physiological density?
Arithmetic density divides the population by all the land; physiological density divides it by arable land only, so it shows the pressure people put on land that can grow food.
How does the rank-size rule work?
The second-largest city has about half the population of the largest, the third about a third, and so on: the city of rank n has 1/n of the largest.
Can I use a calculator on the AP Human Geography exam?
No. College Board's calculator policy allows calculators only on the exams it lists, and AP Human Geography is not one of them (a four-function calculator is allowed only with an approved accommodation). Our practice questions never need one.