📚 Year 8 Edexcel Geography: Formula & Theorem Quick Reference Handbook | Year 8 Edexcel 地理：公式定理速查手册
This quick reference handbook compiles the essential formulas, theorems, and models you will meet in Year 8 Edexcel Geography. Use it as a go‑to revision aid to master map skills, population calculations, river models, weather data, and development indicators. Each entry presents the key idea in a concise English explanation, immediately followed by a matching Chinese version so you can reinforce your understanding in both languages.
这本速查手册汇集了 Year 8 Edexcel 地理课程中的核心公式、定理和模型。把它当作随身复习工具，帮你掌握地图技能、人口计算、河流模型、气象数据和发展指标。每个条目先用简明的英文解释，紧接着是配对的中文版本，让你在双语环境中巩固理解。
1. Map Scale and Distance | 地图比例尺与距离
On any Ordnance Survey or atlas map, the scale tells you the ratio between a distance on the map and the real distance on the ground. The most common scale types are the linear (graphical) scale, the statement scale, and the representative fraction (RF). To calculate real‑world straight‑line distance from a paper map, measure the map distance with a ruler and apply the scale.
在任何地形测量图或地图册中，比例尺告诉你图上距离与实地距离的比率。最常见的比例尺类型是直线比例尺、文字比例尺和数字比例尺（分数式）。要根据纸本地图计算实地直线距离，先用直尺量出图上距离，再套用比例尺。
Real Distance = Map Distance × Scale Factor
实地距离 = 图上距离 × 比例尺倍数
0 cm, which is 2.5 km. For curved roads or rivers, use a piece of string to trace the path, then measure the string length against the scale.
例如，在 1:50 000 的地图上量得 5 厘米，代表实地 5 × 50 000 = 250 000 厘米，即 2.5 公里。对于弯曲的道路或河流，可用细绳沿路径描摹，然后把绳长与比例尺比对。
2. Gradient and Contours | 坡度与等高线
Gradient describes the steepness of a slope. It is calculated as the vertical rise (the difference in height between two contour lines) divided by the horizontal distance between those two points on the map. The result is usually expressed as a ratio like 1:5, meaning for every 5 metres travelled horizontally, the land rises by 1 metre.
坡度描述斜坡的陡峭程度。计算时，用垂直高差（两条等高线之间的高度差）除以图上两点间的水平距离。结果通常用比率表示，如 1:5，意味着每水平前进 5 米，地面升高 1 米。
Gradient = Vertical Interval ÷ Horizontal Equivalent
坡度 = 垂直间距 ÷ 水平距离
Remember to convert both measurements to the same unit, typically metres. Closely spaced contour lines indicate a steep slope; widely spaced contours show a gentle slope or flat land.
记得把两个测量值换成相同单位，通常是米。等高线密集表示陡坡；等高线稀疏表示缓坡或平地。
3. Population Density | 人口密度
Population density measures how crowded an area is. It is a fundamental concept in human geography, linking the number of people to the space they occupy. The formula is simply the total population divided by the total land area. The result is expressed in persons per square kilometre (people/km²).
人口密度衡量一个地区的拥挤程度。它是人文地理学的基本概念，将人口数量与其所占空间联系起来。公式很简单：总人口除以总土地面积，结果以每平方公里人数（人/平方公里）表示。
Population Density = Total Population ÷ Total Land Area (km²)
人口密度 = 总人口 ÷ 土地总面积（平方公里）
For example, a region with 20,000 people living in an area of 500 km² has a density of 40 people/km². Areas with high population density often have flat land, fertile soil, or economic opportunities; low‑density areas may be mountainous, desert, or extremely cold.
例如，一个地区有 20 000 人，面积为 500 平方公里，人口密度是 40 人/平方公里。人口密度高的地区通常地势平坦、土壤肥沃或有经济机会；低密度地区可能是山区、沙漠或极寒区域。
4. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率和自然增长
These vital rates help us understand whether a population is growing, stable, or declining without considering migration. The crude birth rate is the number of live births per 1,000 people per year. The crude death rate is the number of deaths per 1,000 people per year. Natural increase is simply the birth rate minus the death rate.
这些基本人口率帮助我们在不考虑迁移的情况下，了解人口是在增长、稳定还是下降。粗出生率是每年每千人中的活产婴儿数。粗死亡率是每年每千人中的死亡人数。自然增长率就是出生率减去死亡率。
Crude Birth Rate = (Total Live Births ÷ Total Population) × 1000
粗出生率 = （活产婴儿总数 ÷ 总人口）× 1000
Crude Death Rate = (Total Deaths ÷ Total Population) × 1000
粗死亡率 = （死亡总数 ÷ 总人口）× 1000
Natural Increase = Crude Birth Rate − Crude Death Rate
自然增长 = 粗出生率 − 粗死亡率
The natural increase is usually expressed as a percentage. A positive value means the population is expanding naturally; a negative value signals a natural decrease. Remember that the total population growth rate also includes net migration.
自然增长率通常用百分比表示。正值表示人口自然增长；负值表示人口自然减少。请记住，总人口增长率还需加上净迁移量。
5. The Demographic Transition Model (DTM) | 人口转变模型
The DTM is a theoretical model that explains how a country's population changes over time as it develops economically. It is divided into five stages, each with characteristic birth rates, death rates, and total population changes. In Year 8, you mainly focus on stages 1 to 4.
人口转变模型是一个理论模型，解释一个国家随着经济发展，其人口如何随时间变化。它分为五个阶段，每个阶段都有特定的出生率、死亡率和总人口变化特征。在 Year 8，你主要学习第一至第四阶段。
Stage 1 – High Stationary: Both birth and death rates are high and fluctuate. Population is low and stable. Linked to pre‑industrial societies.
第一阶段 高位静止：出生率和死亡率都很高且波动。人口数量少且稳定。与前工业社会相关。
Stage 2 – Early Expanding: Death rate drops sharply due to improved medicine and sanitation, while birth rate remains high. Rapid population growth occurs.
第二阶段 初期扩张：由于医疗和卫生改善，死亡率急剧下降，而出生率仍高。人口迅速增长。
Stage 3 – Late Expanding: Birth rate begins to fall as family size decreases and women's status improves. Population growth slows.
第三阶段 后期扩张：出生率开始下降，家庭规模缩小，妇女地位提高。人口增长放缓。
Stage 4 – Low Stationary: Both birth and death rates are low and balanced. Total population is high but stable. Typical of developed countries.
第四阶段 低位静止：出生率和死亡率都很低且平衡。总人口高但稳定。典型发达国家。
The DTM is a theorem that helps geographers predict future population trends and compare countries at different stages of development.
DTM 是一个定理，帮助地理学家预测未来人口趋势，并比较处于不同发展阶段的国家。
6. The Bradshaw Model and River Discharge | 布拉德肖模型与河流流量
The Bradshaw model describes how a river's characteristics change from its source in the uplands to its mouth at the sea. It is an idealised model that summarises the downstream variations in discharge, velocity, channel width, depth, load size, and roughness.
布拉德肖模型描述河流从上游高地源头到入海口的过程中，其特征如何变化。这是一个理想化模型，总结了流量、流速、河道宽度、深度、搬运物粒径和粗糙度的下游方向变化。
According to the model, as the river flows downstream, discharge (the volume of water passing a point per second) increases, velocity generally increases, channel width and depth grow, and bedload becomes smaller and more rounded. These patterns are directly linked to the processes of erosion, transportation, and deposition.
根据该模型，随着河流向下游流动，流量（每秒通过某点的水量）增加，流速总体加快，河道宽度和深度增大，河床搬运物变得更小、更圆滑。这些规律直接与侵蚀、搬运和沉积过程相关。
Discharge (Q) = Cross‑Sectional Area (A) × Velocity (V)
流量（Q）= 横截面积（A）× 流速（V）
Discharge is measured in cubic metres per second (cumecs). To estimate the cross‑sectional area of a stream, you multiply the average width by the average depth. This formula is crucial for understanding flood risk and river management.
流量以每秒立方米（立方米/秒）为单位。要估算河道的横截面积，可以用平均宽度乘以平均深度。这一公式对理解洪水风险和河道管理至关重要。
7. Water Balance in a Drainage Basin | 流域水量平衡
A drainage basin is an open system with inputs, outputs, and stores. The water balance equation expresses the long‑term relationship between precipitation, evapotranspiration, runoff, and storage changes. It helps geographers understand how water is cycled within a river basin.
流域是一个包括输入、输出和储存的开放系统。水量平衡方程表达了降水、蒸散发、径流和储蓄变化之间的长期关系。它帮助地理学家理解水在流域内如何循环。
Precipitation (P) = Runoff (Q) + Evapotranspiration (E) ± Change in Storage (ΔS)
降水（P）= 径流（Q）+ 蒸散发（E）± 储蓄变化量（ΔS）
In this equation, runoff includes both surface runoff and baseflow. Evapotranspiration combines evaporation from surfaces and transpiration from plants. In a typical wet season, precipitation exceeds the sum of runoff and evapotranspiration, so storage increases; in a dry season, storage decreases. This principle is a foundation for studying floods and droughts.
在这个方程中，径流包括地表径流和基流。蒸散发结合了表面蒸发和植物蒸腾。在典型湿季，降水超过径流和蒸散发之和，储蓄增加；干季储蓄减少。这一原理是研究洪水与干旱的基础。
8. Weather Measurements and Climate Summaries | 气象测量与气候汇总
Meteorologists use standard instruments to record weather elements. When you are asked to construct or interpret a climate graph, you need to handle temperature and rainfall data correctly. Key summary statistics include mean, range, and total.
气象学家使用标准仪器记录天气要素。当你需要绘制或解读气候图时，必须正确处理气温和降水数据。关键的汇总统计包括平均值、较差和总量。
Mean Monthly Temperature = Sum of Daily Temperatures ÷ Number of Days in Month
月平均气温 = 每日气温总和 ÷ 该月天数
Annual Temperature Range = Highest Monthly Mean − Lowest Monthly Mean
年气温较差 = 最高月平均温度 − 最低月平均温度
Total Annual Rainfall = Sum of All Monthly Rainfall Totals
年总降水量 = 各月降水量总和
On a climate graph, temperature is shown as a red line and rainfall as blue bars. Always label the axes and include units (°C and mm). A wet season with high temperatures often indicates a tropical climate; a dry, cool pattern suggests a Mediterranean or temperate climate.
在气候图上，气温用红色折线表示，降水用蓝色柱状表示。务必标注坐标轴和单位（摄氏度和毫米）。高温多雨的季节通常指示热带气候；干凉的模式则暗示地中海或温带气候。
9. Measuring Development: GNI per Capita and HDI | 衡量发展：人均国民总收入和人类发展指数
Development is about wealth, health, and education. To quantify it, geographers use single indicators like GNI (Gross National Income) per capita, and composite indicators like the Human Development Index (HDI). GNI per capita is the total income of a country divided by its population; HDI combines life expectancy, education, and income into a single score between 0 and 1.
发展涉及财富、健康和教育。为了量化发展，地理学家使用单一指标（如人均国民总收入 GNI）和综合指标（如人类发展指数 HDI）。人均 GNI 是一个国家的总收入除以其人口；HDI 将预期寿命、教育和收入综合成一个 0 到 1 之间的分数。
GNI per capita = Total GNI ÷ Total Population
人均 GNI = 国民总收入 ÷ 总人口
The HDI is not calculated through a simple arithmetic formula but is constructed by normalising each dimension index. The theorem behind it is that money alone cannot measure development; health and knowledge are equally important. In Year 8, you learn to compare HDI values: a score close to 1 indicates very high development, while a score below 0.55 suggests low development.
HDI 不是通过简单算术公式计算，而是通过标准化每个维度指数来构建的。其背后的定理是：单凭金钱无法衡量发展；健康与知识同等重要。在 Year 8，你学习比较 HDI 值：接近 1 的分数表示非常高的发展水平，低于 0.55 的分数表示低发展水平。
10. Settlement Hierarchy and Sphere of Influence | 聚落等级体系与影响范围
Settlements can be organised into a hierarchy based on their size, services, and sphere of influence. A higher‑order settlement (e.g., a city) offers more specialised services and attracts people from a much wider area than a lower‑order settlement (e.g., a hamlet). The relationship between the number of settlements and their size follows an inverse pattern: there are many small settlements and very few large ones.
聚落可根据其规模、服务功能和影响范围划分为等级体系。高阶聚落（如城市）提供更专门的服务，其影响范围远大于低阶聚落（如小村）。聚落数量和规模之间呈反比关系：小型聚落很多，大型聚落很少。
While there is no single mathematical formula for the hierarchy, the Rank‑Size Rule states that the nth largest settlement in a country has a population approximately equal to the population of the largest settlement divided by n. However, in Year 8, the focus is on the conceptual model: higher‑order settlements are fewer, more widely spaced, and provide a wider range of services.
虽然没有单一的数学公式来定义等级，但等级规模法则指出：一个国家第 n 大的聚落，其人口约等于最大聚落人口除以 n。不过在 Year 8，重点是概念模型：高阶聚落数量更少，间距更大，提供的服务范围更广。
11. Longshore Drift Theory and Coastal Transport | 沿岸漂移理论与海岸搬运
Longshore drift is the process by which sediment is moved along a coastline by wave action. Waves rarely approach the shore exactly parallel to the beach; the prevailing wind pushes them in at an oblique angle. The swash carries sediment up the beach at that angle, while the backwash, under gravity, pulls it straight back down. Over time, this zigzag motion shifts sand and pebbles parallel to the shore.
沿岸漂移是指波浪作用将沉积物沿海岸线搬运的过程。波浪很少完全平行于海岸推进；盛行风吹动它们以斜角冲向海滩。冲流以该角度将沉积物推上海滩，而回冲流在重力作用下将其垂直带回。久而久之，这种之字形运动使泥沙和卵石沿海岸平行移动。
This is a key theorem in coastal geography. The volume of longshore drift depends on the wave energy, the angle of wave approach, and the size of the sediment. Human structures like groynes are built to trap this moving sediment and protect beaches from erosion.
这是海岸地理学的一个关键定理。沿岸漂移量取决于波浪能量、波浪入射角和沉积物粒径。丁坝等人工建筑物被修建来拦截这些移动的沉积物，保护海滩免遭侵蚀。
12. The Nutrient Cycle in an Ecosystem | 生态系统中的养分循环
The nutrient cycle model describes how nutrients move between three stores in an ecosystem: biomass (living organisms), litter (dead organic matter on the ground), and soil (decomposed organic matter). The size of the arrows indicates the rate of transfer. In a healthy deciduous forest, the transfer from litter to soil is fast, allowing rich vegetation to thrive.
养分循环模型描述养分如何在生态系统的三个储存库之间移动：生物量（活着的有机物）、枯枝落叶层（地面上的死亡有机质）和土壤（已分解的有机质）。箭头的粗细表示转移速率。在健康的落叶林中，从枯枝落叶层到土壤的转移很快，使丰富的植被得以繁茂生长。
s through Leaching + Accumulation in Soil. Understanding this model helps explain why deforestation or climate change can break the nutrient cycle and degrade the ecosystem.
储存和流动可以在概念上表达，但你也可以用基本平衡方程来思考：枯枝落叶输入 = 植物吸收 + 淋溶损失 + 土壤积累。理解这一模型有助于解释为什么森林砍伐或气候变化会破坏养分循环，导致生态系统退化。
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