How are the sizes and spacing of cities within a country explained by the rank-size rule, the primate city, and central place theory?
Topic 6.4 The Size and Distribution of Cities: explain the models that describe the size and distribution of cities, including the rank-size rule, the primate city, and central place theory.
A focused answer to AP Human Geography Topic 6.4, explaining the rank-size rule, the primate city, and Christaller's central place theory, and how they describe the size, spacing, and service hierarchy of cities.
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What this topic is asking
Topic 6.4 covers the models that describe the sizes and spacing of cities within a country. The College Board wants you to explain the rank-size rule, the primate city, and central place theory (Christaller), including the ideas of range, threshold, and a nested service hierarchy. The skill is to apply and contrast these models to read a country's urban system.
The rank-size rule and the primate city
The first two models describe how city sizes are distributed.
A rank-size distribution (common in more developed, balanced economies) signals a well-integrated urban system; a primate-city distribution (common where one center concentrates power) signals an imbalanced one.
Central place theory
The third model explains spacing and the service hierarchy.
This is why a region has a few large cities far apart for specialist services and many small towns close together for everyday needs, echoing the distance-and-cost logic of the Von Thünen model (Topic 5.8).
Applying and contrasting the models
The exam often gives data and asks which pattern it fits.
- A smooth ranking where the second city is about half the first fits the rank-size rule.
- A single dominant city with a sharp drop to the rest fits a primate distribution.
- Questions about why services cluster in certain centers call for central place theory (range, threshold, hierarchy).
These models connect to globalization and world cities (6.3, which rank influence rather than size) and to the internal structure of cities (6.5).
Why this matters for the exam
Topic 6.4 is a heavily modelled topic, the urban-system counterpart to the Von Thünen and central place logic elsewhere in the course. FRQs ask you to describe a primate city, contrast it with the rank-size rule, or apply central place ideas, so practice reading a distribution and naming the model, and applying range, threshold, and hierarchy.
Try this
Q1. Identify the expected population of the third-largest city under the rank-size rule if the largest has 9 million. [Recall]
- Cue. About 3 million, since the nth city is about 1/n of the largest; the third city is about one-third of 9 million.
Q2. Explain the difference between range and threshold in central place theory. [Short explanation]
- Cue. Range is the maximum distance people will travel to obtain a good or service; threshold is the minimum market (population) needed to support it. Higher-order goods have a larger range and threshold and are found in fewer, larger centers.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2018 (style)1 marksIn a country that follows the rank-size rule, if the largest city has 8 million people, the fourth-largest city would be expected to have approximately: (A) 8 million. (B) 4 million. (C) 2 million. (D) 800,000.Show worked answer →
A stimulus-style multiple choice item. The correct answer is (C).
Under the rank-size rule, the nth largest city is about 1/n the size of the largest. The fourth-largest city is about 1/4 of 8 million, which is 2 million. Option (B) is 1/2 (the second city), and (A) is the first city itself. The rule predicts a smooth ranking, unlike a primate-city distribution where one city dominates.
The exam reward is applying the 1/n relationship to compute the expected size.
AP 2021 (style)3 marksGeographers use models to describe city systems. (A) Describe what a primate city distribution looks like. (B) Explain how the rank-size rule differs from a primate-city pattern. (C) Explain ONE idea from central place theory about why cities of different sizes are spaced as they are.Show worked answer →
A 3-point describe-explain FRQ.
(A) Describe (1 point): a primate-city distribution has one city that is far larger and more dominant than all others, with no rival of comparable size (for example, the largest city is more than twice the second).
(B) Explain (1 point): the rank-size rule predicts a smooth, graduated hierarchy where the nth city is about 1/n the size of the largest, so there are many medium cities, while a primate pattern has one dominant city and a sharp drop to the rest.
(C) Explain (1 point): central place theory holds that larger settlements offer higher-order goods and services with a larger range and threshold and are spaced farther apart, while many small centers offer low-order goods, producing a nested hierarchy.
Markers reward an accurate primate description, a clear rank-size contrast, and a valid central place idea (range, threshold, or hierarchy).
Related dot points
- Topic 6.3 Cities and Globalization: explain how globalization influences urban patterns and processes, including the role of world cities and the urban hierarchy of global influence.
A focused answer to AP Human Geography Topic 6.3, explaining how globalization shapes urban patterns, the role of world cities as centers of global economic command, and the global urban hierarchy.
- Topic 6.2 Cities Across the World: explain how the attributes and influences of urbanization vary across the world, including differences between more and less developed countries.
A focused answer to AP Human Geography Topic 6.2, explaining how the level and pace of urbanization vary across the world, the contrast between more and less developed countries, and the role of megacities and metacities.
- Topic 6.5 The Internal Structure of Cities: explain the models that describe the internal structure of cities, including the Burgess, Hoyt, multiple-nuclei, and regional urban models.
A focused answer to AP Human Geography Topic 6.5, explaining the Burgess concentric zone, Hoyt sector, multiple-nuclei, and galactic city models, and the Latin American, Southeast Asian, and African city models.
- Topic 6.1 Origin and Influences of Urbanization: explain the processes of urbanization and suburbanization, and the site and situation factors that drive the growth and decline of cities.
A focused answer to AP Human Geography Topic 6.1, explaining the processes of urbanization and suburbanization, and the site and situation factors and economic forces that drive the growth, decline, and spread of cities.
Sources & how we know this
- AP Human Geography Course and Exam Description — College Board (2020)