AP® Human Geography

Formulas you must know

The exam gives you no formula sheet and no calculator. These are the rates, densities and ratios it asks you to work out by hand or read from a table, a pyramid or a map, in our own words: what each means, when to use it, and the trap that costs points.

Three habits that save points

Interpret, do not define. "Physiological density is people per farmland" earns little; "Egypt's physiological density is far above its arithmetic density, so its farmland along the Nile is under heavy pressure" earns the point.
Name the place and the scale. Say where a value is high or low, and at what scale the data are.
Say what the number means. A doubling time of 35 years means the population needs twice the schools and jobs in a generation.

Births, deaths and growth

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$\text{CBR}$ $= \frac{\text{births in a year}}{\text{population}} \times 1{,}000$ Worked: $\frac{30{,}000}{1{,}000{,}000} \times 1{,}000$ $= 30\,\text{ per }1{,}000$	The crude birth rate: births per 1,000 people a year. Comparing how fast places add people by birth.	It is per 1,000 people, not a percent, and not per woman (that is the total fertility rate).	Unit 2 Population DynamicsPractice it: Population lab
$\text{RNI} = \frac{\text{CBR} - \text{CDR}}{10}$ Worked: $\frac{30 - 10}{10} = 2\,\%$	The rate of natural increase: the percent a population grows each year from births minus deaths. Reading growth from the two crude rates.	Migration is not in it, and the order is births minus deaths. Divide by 10 to turn "per 1,000" into a percent.	Unit 2 Population DynamicsPractice it: Population lab
$\text{doubling time}$ $\approx \frac{70}{\text{RNI}\ (\%)}$ Worked: $\frac{70}{2} = 35\,\text{ years}$	Doubling time by the rule of 70: about how many years a population takes to double at its current rate of natural increase. Turning a growth rate into a time.	Use the RNI as a percent (2, not 0.02). A population that is not growing has no doubling time.	Unit 2 Population DynamicsPractice it: Population lab
$\text{NMR}$ $= \frac{\text{immigrants} - \text{emigrants}}{\text{population}} \times 1{,}000$ Worked: $\frac{6{,}000 - 2{,}000}{1{,}000{,}000} \times 1{,}000$ $= 4\,\text{ per }1{,}000$	The net migration rate: people gained or lost by migration, per 1,000 people a year. Adding migration to natural increase to see total growth.	More people leaving than arriving gives a negative rate.	Unit 2 Causes of MigrationPractice it: Population lab

Age and sex

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$\text{dependency ratio}$ $= \frac{\text{under }15 + 65\text{ and over}}{15\text{ to }64} \times 100$ Worked: $\frac{30 + 20}{100} \times 100 = 50$	The dependency ratio: people of the ages that usually depend on others, per 100 people of working age. Reading the strain a population pyramid shows: many children, many older people, or both.	The working-age group (15 to 64) goes on the bottom. Youth and elderly ratios use one group each.	Unit 2 Aging PopulationsPractice it: Population lab
$\text{sex ratio}$ $= \frac{\text{males}}{\text{females}} \times 100$ Worked: $\frac{105}{100} \times 100 = 105$	The sex ratio: males per 100 females. Reading the two sides of a population pyramid.	Above 100 means more males. It changes with age: women live longer on average.	Unit 2 Population CompositionPractice it: Population lab

Density

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$\text{arithmetic density}$ $= \frac{\text{population}}{\text{total land area}}$ Worked: $\frac{1{,}000{,}000}{50{,}000\ \text{km}^2}$ $= 20\,\text{ per km}^2$	Arithmetic density: people per unit of all the land. A first comparison of crowding between places.	It hides where people live: deserts and mountains count as land.	Unit 2 Consequences of Population DistributionPractice it: Population lab
$\text{physiological density}$ $= \frac{\text{population}}{\text{arable land}}$ Worked: $\frac{1{,}000{,}000}{5{,}000\ \text{km}^2}$ $= 200\,\text{ per km}^2$	Physiological density: people per unit of farmland, the pressure on the land that grows food. Judging how hard a country's farmland must work.	The bottom is arable land only. Do not confuse it with carrying capacity, which is how many people land can support.	Unit 2 Consequences of Population DistributionPractice it: Population lab
$\text{agricultural density}$ $= \frac{\text{farmers}}{\text{arable land}}$ Worked: $\frac{100{,}000}{5{,}000\ \text{km}^2}$ $= 20\,\text{ per km}^2$	Agricultural density: farmers per unit of farmland. A clue to how mechanized farming is: fewer farmers per unit usually means more machines.	The top is farmers, not everyone.	Unit 2 Consequences of Population DistributionPractice it: Population lab

Cities and interaction

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$P_n = \frac{P_1}{n}$ Worked: $\frac{12{,}000{,}000}{3}$ $= 4{,}000{,}000$	The rank-size rule: the city of rank n has about 1/n the population of the largest city. Checking whether a country's cities follow the rule or have a primate city.	A primate city is far larger than the rule predicts for rank 1 against rank 2.	Unit 6 The Size and Distribution of CitiesPractice it: City lab
$\text{interaction}$ $= k \times \frac{P_1 \times P_2}{d^2}$ Worked: $\frac{4 \times 3}{2^2} = 3$	The gravity model: interaction between two places rises with their populations and falls with the square of the distance between them. Comparing which pair of cities will have more trips, calls or trade.	Square the distance. Twice as far means a quarter of the interaction, not half.	Unit 6 The Size and Distribution of CitiesPractice it: City lab
$\%\ \text{change}$ $= \frac{\text{new} - \text{old}}{\text{old}} \times 100$ Worked: $\frac{150 - 120}{120} \times 100$ $= 25\,\%$	Percent change: how much a value grew or shrank, as a share of where it started. Reading a table of populations or outputs over time.	Divide by the old value, not the new one.	Skills you need Reading Maps and DataPractice it: Map reader

Map scale

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$\text{ground distance}$ $= \text{map distance} \times \text{scale denominator}$ Worked: $4\ \text{cm} \times 50{,}000 = 2\,\text{ km}$	A ratio scale (1:50,000) turns a map length into a ground distance: 1 cm on the map is 50,000 cm on the ground. Measuring on a reference map.	A large-scale map (1:10,000) shows a small area in detail; a small-scale map (1:10,000,000) shows a large area. Map scale is not the scale of analysis.	Skills you need Scale of Analysis and Map ScalePractice it: Scale lab

Ideas to read off a source

Scale of analysis. The scale of the data shown (global, regional, national, local), not the size of the area on the map. Provinces of one country are local (subnational) data. Scale of Analysis and Map Scale
Pyramid shapes. A wide base (expansive) means many children and fast growth; straight sides (stationary) slow growth; a narrow base (constrictive) an aging, shrinking population. Population Composition
Demographic transition stages. A pair of rates is consistent with a stage of the model; a country is never in a stage as a fact. Negative natural increase fits stage 5. The Demographic Transition Model
Say what a source cannot show. A national map hides differences inside the country; one year of data shows no trend. Reading Maps and Data

On exam day

No calculator. The AP® Human Geography exam allows no calculator. Every number it asks for (a rate, a density, a ratio, a doubling time) can be worked out by hand.
No formula sheet. Nothing on this page is printed in Bluebook: know what each measure means and how to read it from a table, a pyramid or a map.

Practice with it

Free unit practice tests · Formulas flashcards · Skills terms flashcards · Models you must know · Free notes for every topic · Full practice exams