AP Human Geography — Cheatsheet
Formulas, exam-day tips, and key terms on one page.
Formulas & relationships
Reading map scale
large-scale map = small area, more detail | small-scale map = large area, less detail
The scale ratio (1:1,000 vs 1:1,000,000) works like a fraction: 1/1,000 is larger than 1/1,000,000, so 1:1,000 is the “large-scale” map even though it covers less ground.
Three measures of population density
arithmetic = people / total area | physiological = people / arable land | agricultural = farmers / arable land
A high physiological density with a low agricultural density (developed) vs. a high agricultural density (developing) tells you about pressure on farmland and the level of agricultural technology.
Natural increase & doubling time
NIR (%) = (CBR − CDR) / 10 doubling time ≈ 70 / NIR(%)
Crude birth/death rates are per 1,000 people, so dividing their difference by 10 converts to a percent. The Rule of 70 then estimates years to double. NIR ignores migration.
Von Thünen’s core relationship (bid rent)
land rent a farmer can pay ↓ as distance to market ↑, offset by lower transport cost for durable goods
Perishable, heavy, low-value-per-weight goods (milk, vegetables) locate near the market; durable, light, high-value goods (grain, livestock) locate farther out. Each land use outbids the others in the ring where it is most profitable.
On the exam
- On the exam, never call a projection “wrong.” Frame every map choice as a **trade-off**: name the property preserved (shape, area, distance, or direction) and the property sacrificed, then tie it to the map’s purpose. That reasoning earns the point.
- When a prompt gives arable land, expect **physiological** or **agricultural** density, not arithmetic. Label your units (“people per km² of arable land”) and interpret the number — high physiological density = pressure on farmland; low agricultural density = developed, mechanized farming.
- On the exam, first decide **relocation vs. expansion**: did people *move* and carry the trait (relocation), or did it spread while staying strong at the source (expansion)? Only then choose the expansion sub-type — contagious, hierarchical, or stimulus.
- Keep the vocabulary exact: **state = country** (sovereign political unit), **nation = a people** (shared identity). A **nation-state** matches them; a **stateless nation** is a people with no country; a **multinational state** is one country with many nations. Sloppy use of these words costs FRQ points.
- Von Thünen’s rings turn on two variables: **perishability** and **transport cost** (relative to product value and weight). Innermost ring = perishable/heavy/low-value-per-weight; outermost = durable/light/high-value-per-weight. Cite these, not climate or soil, since the model assumes uniform physical conditions.
- Keep the three North American models distinct by their shape: **Burgess = rings** (concentric zones), **Hoyt = wedges** (sectors along transport lines), **Harris–Ullman = multiple nodes** (no single center). One word each — rings, wedges, nodes — anchors the answer.
- Weber in one rule: **bulk-reducing → locate near raw materials** (inputs are heavy); **bulk-gaining or perishable → locate near the market** (the product is heavy or spoils). Identify which weighs more — inputs or output — and the location answers itself.
How to get a 5
- Vocabulary is paramount in APHG. Do not just memorize definitions; be able to apply them to real-world examples (e.g., identify an actual primate city, not just the definition).
- Always consider scale. A phenomenon might look different at the local, national, and global scales. The exam frequently asks how scale changes an analysis.
- When discussing models (Von Thünen, DTM, Central Place), know the assumptions they are based on and the reasons why they might not perfectly fit the modern world.
- In FRQs, pay close attention to the verb. 'Identify' requires only a short answer. 'Describe' requires traits/characteristics. 'Explain' requires cause and effect (the 'how' or 'why').
- Every free-response part begins with a command word, and the reader scores exactly that verb. "Identify" needs a name only, "describe" needs specific characteristics, and "explain" needs a causal because clause. Writing a beautiful explanation where the prompt says identify wastes time and earns one point at most; failing to explain when asked earns zero.
- Attach a real place to every model. Von Thünen with the Dutch flower trade, Weber with Pittsburgh steel versus soft drink bottling, primate cities with Bangkok, superimposed boundaries with the Berlin Conference, smart growth with Portland. Free-response prompts increasingly require a specific example, and generic answers cap your score.
- Drill the four calculations until they are automatic: natural increase = (CBR − CDR)/10, doubling time = 70 divided by the percent growth rate, the three densities (total land, arable land, farmers over arable land), and the gravity model with distance squared. These are the only arithmetic on the exam and they are free points.
- Learn each model together with its main criticism, because part G of a free-response question is almost always "explain one limitation." Von Thünen assumes an isolated state and no refrigeration, the demographic transition model generalizes from Western Europe and ignores migration, Rostow understates colonial legacies, and North American urban models do not travel to the Global South.
- Do not write introductions or conclusions. Label each response A through G in order and answer only what is asked, one tight paragraph per part. Readers find the point in the part it belongs to, so an idea buried in the wrong section frequently goes uncredited.
Key terms
Demographic Transition Model (DTM) — Stages 1-5 showing population change over time. High birth/death rates (1) transition to low birth/death rates (4) as a country industrializes.
Thomas Malthus' Theory — Predicted population grows exponentially while food production grows linearly, leading to mass starvation. (Mostly avoided due to the Green Revolution).
Relocation vs. Expansion Diffusion — Relocation: trait moves with migrating people (e.g., Spanish in Latin America). Expansion: trait spreads outward from a hearth (includes hierarchical, contagious, stimulus).
Von Thünen Model — Agricultural model. Rings outward from market: 1) Dairy/Market Gardening (perishable/expensive transport), 2) Forest, 3) Extensive Crops (wheat), 4) Ranching (livestock).
Green Revolution — Mid-20th century. Introduction of high-yield seeds (wheat/rice), chemical fertilizers, and pesticides. Massively increased food production but caused environmental damage.
Centripetal vs. Centrifugal Forces — Centripetal forces UNIFY a state (e.g., shared language, nationalism). Centrifugal forces DIVIDE a state (e.g., ethnic conflict, geographic barriers).
Gerrymandering — Redrawing political voting districts to favor one political party. Types include 'packing' (concentrating opposition) and 'cracking' (diluting opposition).
Christaller's Central Place Theory — Explains the spatial distribution of human settlements using hexagons. Larger settlements are fewer and farther apart, providing higher-order goods/services.
Concentric Zone vs. Sector Model — Burgess Concentric: city grows in rings outward from CBD. Hoyt Sector: city grows in wedges/corridors following transportation routes.
Rank-size rule vs. primate city — Rank-size rule: the nth largest city is about 1/n the population of the largest, indicating a balanced urban hierarchy (United States, Germany). Primate city: the largest is more than twice the second and dominates politics, economy, and culture (Bangkok, Mexico City, Buenos Aires), often a colonial legacy.
Rostow's Stages of Economic Growth — Modernization model (5 stages): Traditional society → Pre-conditions for take-off → Take-off (industrialization) → Drive to maturity → High mass consumption.
Core-Periphery Model (Wallerstein) — World Systems Theory. Core countries (rich/industrialized) exploit Periphery countries (poor/raw materials). Semi-periphery are developing (e.g., BRICS).
The three density measures — Arithmetic density = total population / total land area. Physiological density = total population / arable land. Agricultural density = number of farmers / arable land. Egypt shows why they differ: low arithmetic density but very high physiological density because habitable land is confined to the Nile valley and delta.
Rate of natural increase and doubling time — NIR = (CBR − CDR) / 10, expressed as a percent and excluding migration. Doubling time ≈ 70 / NIR in percent. At 2 percent growth a population doubles in 35 years; at 1 percent, 70 years.
Total fertility rate and replacement level — TFR is the average number of children a woman would bear over her lifetime at current age-specific rates. Replacement level is about 2.1 — slightly above 2 to account for childhood mortality and the sex ratio at birth. Below 2.1 sustained means eventual natural decrease.
Demographic transition model — the five stages — Stage 1: high birth and death rates, low growth. Stage 2: death rate plummets, birth rate stays high, fastest growth (Niger). Stage 3: birth rate falls as urbanization and female education spread (Mexico, India). Stage 4: both low, growth near zero (United States). Stage 5: births below deaths, natural decrease (Japan, Italy).
Demographic momentum and the epidemiological transition — Momentum: population keeps growing after TFR reaches 2.1 because a large youth cohort is still entering childbearing years. Epidemiological transition: the shift in leading causes of death from infectious and parasitic disease (Stage 2) to degenerative and chronic disease such as heart disease and cancer (Stages 4 and 5).
Reading a population pyramid — Wide base and narrow apex means high fertility and high youth dependency (Stage 2). Rectangular shape means low fertility and an aging population (Stage 4 to 5). A bulge in working ages with a male skew indicates labor in-migration (Qatar, UAE). Notches reveal wars, famines, or baby booms.
Von Thünen model — rings and the logic — From the market outward: market gardening and dairying, forest (historically for fuel and timber), field crops and grain, then livestock ranching. The driver is bid rent — perishability and transport cost per kilometer determine how steeply each activity’s willingness to pay declines with distance. Refrigeration and cheap transport have globalized the gradient.
Weber’s least cost theory — Firms minimize transport, labor, and agglomeration costs. Bulk-reducing (weight-losing) industries such as copper smelting and steel locate near raw materials; bulk-gaining industries such as soft-drink bottling and auto assembly locate near markets. Single-market and perishable products also pull toward consumers.
Christaller’s central place theory — threshold and range — Threshold is the minimum population needed to support a service; range is the maximum distance people will travel for it. High-order services (specialty hospitals, opera houses) have large thresholds and ranges and are few; low-order services (convenience stores) have small ones and are numerous. Hinterlands are modeled as nesting hexagons.
The three North American urban models — Burgess concentric zone (1925): rings outward from a single CBD, driven by invasion and succession. Hoyt sector (1939): wedges radiating along transport corridors, so high-status housing forms a sector rather than a ring. Harris and Ullman multiple nuclei (1945): several specialized nodes, matching polycentric automobile-era metros.
Griffin-Ford (Latin American) and McGee (Southeast Asian) city models — Griffin-Ford: CBD plus an elite commercial spine, then zones of maturity, in situ accretion, and peripheral squatter settlements, with disamenity zones — the poor are at the edge. McGee: no formal CBD; the old colonial port dominates, with commercial, government, alien commercial (often Chinese), and mixed-use zones radiating from it.
Rostow vs. Wallerstein — Rostow’s stages of growth (traditional, preconditions for takeoff, takeoff, drive to maturity, mass consumption) treats development as a linear internal path. Wallerstein’s world-systems theory treats the world as one system with core, semi-periphery, and periphery in structurally unequal roles. Rostow is criticized for ignoring colonial legacies and global constraints.