📚 Year 10 OCR Geography: Formula & Theorem Quick Reference Guide | 公式定理速查手册
This quick reference handbook brings together all the essential formulae, key equations, and model ‘theorems’ you need to master for the Year 10 OCR Geography course. Whether you are analysing population change, calculating river gradients, or interpreting urban land‑use models, having these tools at your fingertips will sharpen your exam technique and deepen your geographical understanding. Use it alongside your class notes and case studies to turn numerical data into meaningful geographical stories.
这本速查手册汇集了 Year 10 OCR 地理课程中所有重要的公式、关键方程和模型“定理”。无论你是在分析人口变化、计算河流比降，还是解读城市土地利用模型，把这些工具牢记于心都能提升你的应试技巧，加深对地理学的理解。请结合课堂笔记和案例研究使用，将数字数据转化为有意义的地理故事。
1. Population Density | 人口密度
Population density measures how crowded an area is, expressed as the number of people per square kilometre. It helps geographers compare the distribution of people across different regions and identify patterns of sparse or dense settlement.
人口密度衡量一个区域的拥挤程度，以每平方千米的人口数表示。它帮助地理学家比较不同地区的人口分布，并识别人口稀疏或密集定居的模式。
Population Density = Total Population ÷ Area (km²)
When calculating, make sure both population and area data refer to the same year and administrative unit to avoid misleading conclusions. A high density does not automatically mean overcrowding; it may indicate high‑rise urban living, while low density often reflects rural or mountainous terrain.
计算时确保人口和面积数据属于同一年和同一行政单元，以免得出误导性结论。高密度未必意味着过度拥挤，可能反映高层城市居住模式，而低密度通常反映农村或山区地形。
2. Crude Birth Rate (CBR) | 粗出生率
The crude birth rate is the number of live births per 1,000 people in a population over one year. It is a simple indicator of fertility that does not consider the age structure of the population.
粗出生率是某一年内每千人口中的活产婴儿数。它是一个简单的生育率指标，未考虑人口的年龄结构。
CBR = (Number of Live Births ÷ Total Population) × 1,000
Crude rates are called ‘crude’ because they treat the whole population as denominator, including men, children, and elderly people who are not capable of giving birth. For deeper analysis, geographers often compare CBR with the total fertility rate, but CBR remains useful for quick regional comparisons.
之所以称为“粗”率，是因为它们将总人口作为分母，包括男性、儿童和老年人等无法生育的人群。在深入分析中，地理学家常将粗出生率与总和生育率进行比较，但 CBR 对于快速进行区域比较仍然很有用。
3. Crude Death Rate (CDR) | 粗死亡率
The crude death rate is the number of deaths per 1,000 people in a population per year. Alongside the birth rate, it drives natural population change and reflects the health, sanitation, and age profile of a country.
粗死亡率是每年每千人口中的死亡人数。与出生率一起，它驱动着人口的自然变动，并反映一个国家的健康、卫生和年龄结构状况。
CDR = (Number of Deaths ÷ Total Population) × 1,000
A high CDR is often associated with an ageing population, poor healthcare, or epidemic outbreaks. When combined with the CBR, the natural change of a population can be observed, which is fundamental to the Demographic Transition Model (DTM).
高粗死亡率通常与人口老龄化、医疗水平低或流行病暴发相关。将粗死亡率与粗出生率结合，可以观察到人口的自然变动，这对人口转变模型（DTM）至关重要。
4. Rate of Natural Increase (RNI) | 自然增长率
The rate of natural increase expresses the difference between births and deaths as a percentage or per 1,000, showing whether a population is growing or declining in the absence of migration. It is the engine of population change in many low‑ and middle‑income countries.
自然增长率用百分比或千分比表示出生与死亡之间的差额，显示在没有迁移的情况下人口是在增长还是减少。它是许多中低收入国家人口变化的主要动力。
RNI (per 1,000) = CBR – CDR
RNI (%) = (CBR – CDR) ÷ 10
When working with exam data, check whether the question asks for the RNI in crude rate form or as a percentage. A negative RNI indicates a natural decrease and is increasingly common in parts of Europe and East Asia.
在考试数据题中，要看清问题是要求用粗率形式还是百分比形式表示自然增长率。自然增长率为负值表明自然减少，这在欧洲和东亚部分地区日益普遍。
5. Net Migration Rate | 净迁移率
The net migration rate captures the balance between immigration and emigration per 1,000 population. It is a key component of total population change, especially in gateway cities and regions with strong economic pull factors.
净迁移率反映每千人口中迁入与迁出的差额。它是总人口变动的一个关键组成部分，特别是在门户城市和有强大经济拉力因素的地区。
Net Migration Rate = (Immigrants – Emigrants) ÷ Total Population × 1,000
Positive net migration adds to population growth and often brings a younger workforce, whereas negative net migration can accelerate ageing and depopulation in rural areas. Combining RNI and net migration gives the total population growth rate.
净迁移为正会增加人口增长，并常常带来更年轻的劳动力，而净迁移为负则可能加速农村地区的老龄化和人口减少。将自然增长率与净迁移率相加，即得到总人口增长率。
6. Dependency Ratio | 抚养比
The dependency ratio compares the economically dependent part of the population (young and old) to the working‑age population. It is a crucial measure of the pressure on a country’s productive workforce and social services.
抚养比将经济上依赖他人的人口（幼年与老年）与劳动年龄人口进行比较。它是衡量一个国家生产性劳动力和社会服务压力的关键指标。
Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
A high youth dependency ratio is typical of many low‑income countries, whereas a high old‑age dependency ratio characterises ageing wealthy nations. Both situations present distinct challenges for health care, education, and pension systems.
高少儿抚养比是许多低收入国家的典型特征，而高老年抚养比则代表老龄化的富裕国家。这两种情况都对医疗保健、教育和退休金体系提出了不同的挑战。
7. Urbanisation Level and Rate | 城市化水平与速度
The urbanisation level is the percentage of a country’s population living in urban areas. The urbanisation rate tells us how quickly this share is changing over time, an important insight into the pace of rural‑to‑urban migration and city expansion.
城市化水平是一个国家居住在城市地区的人口百分比。城市化速度告诉我们这个比例随时间变化有多快，这是了解农村向城市迁移速度和城市扩张的重要视角。
Urbanisation Level (%) = (Urban Population ÷ Total Population) × 100
Urbanisation Rate = Change in Urban Population % over a given period
In OCR exam questions, you may be given census data for two different years and asked to calculate the absolute change and the percentage change in the urban population. Always label your units and show your working clearly.
在 OCR 考试题中，可能给出两个不同年份的人口普查数据，要求计算城市人口的绝对变化和百分比变化。务必标明单位，并清晰地展示计算过程。
8. Gradient of a River or Slope | 河流或坡度比降
Gradient expresses the steepness of a landform, often applied to river long profiles or hillslopes. Understanding gradient helps geographers explain flow velocity, erosion power, and flood risk along a river’s course.
比降表示地貌的陡峭程度，常用于河流纵剖面或山坡。了解比降有助于地理学家解释河流的流速、侵蚀力和沿途的洪水风险。
Gradient = Vertical Rise (height difference) ÷ Horizontal Distance
Gradient is usually written as a ratio, e.g. 1:50, meaning the land rises 1 metre for every 50 metres horizontally. In practical fieldwork, you might measure the angle of a slope with a clinometer and convert it to a gradient ratio for mapping.
比降通常写为比值形式，例如 1:50，表示水平距离每 50 米，高度上升 1 米。在实地考察中，你可能会用测斜仪测量坡度角，并将其转换为比降比值以便绘制地图。
9. Discharge of a River | 河流流量
River discharge is the volume of water passing a given point in the channel per unit of time. It is the fundamental output of a drainage basin system and directly influences the shape of a hydrograph and the risk of flooding.
河流流量是单位时间内通过河道某一断面的水量。它是流域系统的基本输出，直接影响着流量过程线的形态和洪水风险。
Discharge (Q) = Cross‑sectional Area (A) × Mean Velocity (V)
Where cross‑sectional area is measured in square metres (m²) and velocity in metres per second (m/s), giving discharge in cubic metres per second (cumecs). In field investigations, velocity is often found using a flowmeter or float method at several points across the channel.
其中横截面积以平方米（m²）为单位，流速以米每秒（m/s）为单位，流量单位为立方米每秒（cumecs）。在实地调查中，流速通常用流速仪或浮标法在河道不同点位测量。
10. Percentage Change | 百分比变化
Percentage change is one of the most frequently used calculations in geography, applied to population growth, economic data, urban expansion, and environmental change. It shows the relative magnitude of change between two values.
百分比变化是地理学中最常用的计算之一，适用于人口增长、经济数据、城市扩张和环境变化。它反映两个数值之间变化的相对幅度。
Percentage Change = [(New Value – Original Value) ÷ Original Value] × 100
Always state whether the result is an increase or a decrease. When the original value is very small, even a modest absolute change can produce a dramatic percentage change, so always interpret the result in context.
始终说明结果是增长还是减少。当原始值很小时，即使是适度的绝对变化也可能产生巨大的百分比变化，因此务必结合背景来解释结果。
11. Map Scale Conversion | 地图比例尺转换
Using map scales correctly is a core geographical skill. The scale links a distance on the map to the real distance on the ground, allowing you to measure straight‑line distances, calculate areas, and interpret the level of detail shown.
正确使用地图比例尺是一项核心地理技能。比例尺将地图上的距离与实际地面距离联系起来，帮助你测量直线距离、计算面积，并解读所展示的详细程度。
Real Distance = Map Distance × Scale Factor
For a 1:25,000 OS map, 1 cm on the map represents 25,000 cm (250 m) on the ground. Always convert map distances to real‑world units such as kilometres to keep your answers clear and logical.
对于 1:25 000 的英国陆地测量局地图，地图上 1 厘米代表地面 25 000 厘米（250 米）。始终将地图距离转换为公里等现实单位，以保持答案清晰、符合逻辑。
12. The Demographic Transition Model as a Geographical Theorem | 作为地理定理的人口转变模型
While not a numerical formula, the Demographic Transition Model (DTM) functions as a geographical theorem that predicts how birth rates, death rates, and total population change as a country develops. You must know how to label its five stages and explain the changes in population momentum.
虽然不是一个数值公式，但人口转变模型（DTM）作为一个地理定理，能够预测一个国家在发展过程中出生率、死亡率和总人口如何变化。你必须要会标注它的五个阶段，并解释人口动能的变化。
DTM theorem: As a country moves from pre‑industrial to post‑industrial, death rate falls first, followed by birth rate, generating rapid population growth in the central stages.
In an OCR exam, you may be asked to use the DTM to interpret population pyramids or to justify why a country has a particular rate of natural increase. Refer back to the Crude Birth Rate and Crude Death Rate formulas when describing stage‑specific trends.
在 OCR 考试中，你可能会被要求利用人口转变模型来解读人口金字塔，或论证为什么某个国家具有特定的自然增长率。在描述各阶段趋势时，要回顾粗出生率和粗死亡率的公式。
13. Burgess and Hoyt Urban Land‑Use Models | 伯吉斯与霍伊特城市土地利用模型
The Burgess concentric zone model and the Hoyt sector model are spatial theorems that explain how urban land use is organised. They predict the location of the central business district, industrial zones, and residential areas based on accessibility and land value.
伯吉斯同心圆模型和霍伊特扇形模型是解释城市土地利用如何组织的空间定理。它们根据可达性和土地价值预测了中央商务区、工业区和住宅区的位置。
Burgess theorem: Cities grow outward in concentric rings from the CBD, with socio‑economic status increasing with distance.
Hoyt theorem: Urban land use develops in sectors along transport routes, integrating industry and high‑status residential wedges.
When answering extended‑response questions, link these models to real city examples and explain why modern cities often deviate from the classic patterns due to regeneration, planning policies, and edge cities.
在回答长篇问题时，将这些模型与真实城市案例联系起来，并解释为什么现代城市由于城市更新、规划政策和边缘城市的存在而常常偏离经典模式。
14. The Bradshaw Model for River Characteristics | 布拉德肖河流特征模型
The Bradshaw model is a conceptual theorem describing how river channel characteristics change from source to mouth. It predicts downstream trends in discharge, velocity, channel depth, and bedload size, helping you interpret fieldwork data along a river’s long profile.
布拉德肖模型是一个描述河流河道特征从源头到河口如何变化的概念定理。它预测了流量、流速、河道深度和推移质粒径沿下游的变化趋势，帮助你解读沿河纵剖面的实地考察数据。
Bradshaw theorem: Discharge, velocity, and channel depth increase downstream, while bedload particle size and channel gradient decrease.
In your controlled assessment or fieldtrip report, you would plot measured values against distance downstream and compare the patterns with the Bradshaw model. Any anomalies can open a discussion about geology, tributary inputs, or human interference.
在控制性评估或野外考察报告中，你要将实测值沿下游距离绘图，并与布拉德肖模型进行对比。任何异常都可以引发关于地质、支流输入或人为干预的讨论。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply