📚 Eduqas GCSE Geography Formula & Theorem Quick Reference | Eduqas GCSE 地理公式定理速查手册
This quick-reference handbook brings together all the essential formulae, calculations and theoretical models you need to master for the Eduqas GCSE Geography specification. From river discharge and map‑work gradients to population metrics and development indicators, the guide explains each item with clarity, followed by a worked example or contextual notes to reinforce understanding.
本速查手册汇集了 Eduqas GCSE 地理课程要求掌握的所有核心公式、计算方法和理论模型。从河流流量和地图坡度量测，到人口指标与发展指数，本指南对每个条目都做出清晰说明，并配以实例或背景注解，帮助巩固理解。
1. River Hydraulics: Discharge | 河流水文学：流量
Discharge (Q) is the volume of water passing a point in a river per unit time. It is the product of the cross‑sectional area (A) and the average velocity (V) of the water. River discharge is usually measured in cubic metres per second (m³ s⁻¹). Understanding discharge is critical for flood hazard analysis and for comparing river regimes between different drainage basins.
流量（Q）是单位时间内通过河流某一点的水体积，由过水断面面积（A）与平均流速（V）相乘得到。河流流量通常以立方米每秒（m³ s⁻¹）计。理解流量对洪水灾害分析以及比较不同流域的河流情势至关重要。
Q = A × V
To calculate cross‑sectional area, you typically divide the river channel into a series of vertical sections (segments), measure the depth at each boundary and multiply the average depth of a segment by its width. Velocity is measured with a flowmeter at 0.6 of depth from the surface, or taken as an average of readings at 0.2 and 0.8 of depth in deeper water. For GCSE, you will usually be given pre‑calculated values but must be able to apply the formula in reverse if needed.
计算过水断面面积时，通常将河道划分成若干垂直分段，测量各边界处的水深，再将分段平均深度乘以宽度。流速测量通常在距水面 0.6 倍水深的位置进行，在水深较大时则取 0.2 和 0.8 倍水深读数的平均值。在 GCSE 阶段，通常会给定现成的数据，但需要能够逆向运用公式。
2. Hydraulic Radius and Wetted Perimeter | 水力半径与湿周
The hydraulic radius (R) describes the efficiency of a river channel in conveying water. It is calculated by dividing the cross‑sectional area (A) by the wetted perimeter (P), the total length of the bed and banks in contact with water. A higher hydraulic radius means less friction per unit of water volume, so the river can flow faster and transport more sediment.
水力半径（R）用于描述河槽输水效率，由过水断面面积（A）除以湿周（P）得到，后者是河底与河岸与水接触的总长度。水力半径越大，单位体积水体所受摩擦越小，因此流速更快，输沙能力更强。
R = A ÷ P
Wetted perimeter can be estimated by measuring the length of the river bed along the same cross‑sectional line. In a smooth, semi‑circular channel, the hydraulic radius is high; in a wide, shallow, rough bed channel, it is low. This concept helps explain why deep, narrow channels (e.g. in the lower course) are more efficient than wider, shallower ones during normal flows.
湿周可通过丈量同一断面线上的河底长度进行估算。在光滑的半圆形河槽中，水力半径较大；而在宽浅且粗糙的河床上水力半径较小。这一概念有助于解释为何深而窄的河道（如下游河段）在正常水流下比宽而浅的河道更高效。
3. River Gradient and Long Profile | 河流坡度与纵剖面
Gradient is the steepness of a river’s long profile, usually expressed as a dimensionless ratio (e.g. 1:50) or as a fall in metres per kilometre (m km⁻¹). It strongly influences velocity and the type of erosion, as well as the size of sediment the river can carry. The gradient is measured between two points along the river’s course.
坡度是指河流纵剖面的陡峭程度，通常用无量纲比（如 1:50）或以每公里下降米数（m km⁻¹）表示。坡度对流速、侵蚀类型及河流能够搬运的沉积物大小影响重大。坡度是在河流沿程两点之间量测的。
Gradient = Vertical difference in height (m) ÷ Horizontal distance (m)
For a map study, you will use contour lines to obtain the change in height and measure horizontal distance with a ruler, then apply the map scale. The river’s long profile changes from a steep upper course to a gentle lower course. Steep gradients result in high kinetic energy, promoting vertical erosion, while low gradients lead to lateral erosion and deposition. The Bradshaw Model describes these systematic downstream changes in gradient and other channel characteristics.
在地图学习中，通过等高线获取高差，用直尺测量水平距离，再应用地图比例尺。河流纵剖面从陡峭的上游逐渐变为平坦的下游。陡坡提供高动能，促进下蚀作用；缓坡则导致侧蚀与沉积。Bradshaw 模型描述了坡度及其他河道特征沿程发生的系统变化。
4. Map Skills: Scale, Distance and Area | 地图技能：比例尺、距离与面积
Map work accounts for a significant portion of the GCSE examination. You must be able to use linear scale (line scale) and representative fraction (RF) to convert map distances to real‑world measurements. Calculating area, both regular and irregular, is equally important for land‑use studies and comparing field sites.
地图技能在 GCSE 考试中占很大比重。要能利用直线比例尺（线段比例尺）和数字比例尺（RF）将图上距离换算为实地距离。计算规则与不规则面积同样重要，用于土地利用研究和野外场地比较。
Distance:Measure the straight‑ ed distances, use the edge of a piece of paper or a piece of string, marking off segments, then read against the scale bar.
距离：量测地图上的直线长度（厘米），乘以比例尺系数。例如 1:25 000 地图上，1 厘米 = 25 000 厘米 = 250 米。弯曲距离可用纸条边缘或细绳沿路径分段标记，再对照比例尺读取。
Area:c formulae. For irregular shapes, overlay a grid (e.g. 1 cm × 1 cm squares) or use the dot‑rid method. Count full and partial squares, remembering that each square represents a real‑world area based on the map scale.
面积：规则图形量测尺寸后代入标准几何公式。不规则图形可叠加方格网（如每格 1 cm × 1 cm）或使用点格法，统计完整和不完整方格，每个方格代表的实地面积由比例尺决定。
5. Cross‑Sections and Vertical Exaggeration | 剖面图与垂直夸大
A cross‑section (profile) drawn from a contour map reveals the shape of the land along a chosen line. When the horizontal and vertical scales differ, vertical exaggeration (VE) describes how much the height dimension has been stretched to make relief features stand out. Knowing how to calculate VE is essential for interpreting landform profiles in the exam.
根据等高线地图绘制的剖面图能展现所选线段的地表起伏形态。当水平比例尺和垂直比例尺不同时，垂直夸大（VE）表示将高度维度放大了多少倍，以突出地势变化。掌握 VE 的计算对考试中解读地貌剖面非常重要。
VE = Vertical scale ÷ Horizontal scale
convert each to a representative fraction (e.g. 1 cm : 100 m = 1:10 000), then divide. A VE of 5 means the height is shown five times larger than the horizontal distance, making slopes appear steeper than they really are.
两个比例尺必须用相同单位表达（如垂直轴：1 cm 代表 100 m；水平轴：1 cm 代表 500 m）。先将各比例尺转化为数字比例尺（如 1 cm : 100 m = 1:10 000），然后相除。VE 为 5 意味着高度被放大了 5 倍，使坡度看起来比实际更陡。
6. Population Metrics: Density, Natural Increase and Dependency | 人口指标：密度、自然增长与抚养比
GCSE Geography requires you to be comfortable with a core set of population calculations. Population density describes the degree of crowding in an area. Natural increase (or natural decrease) summarises the difference between births and deaths, excluding migration. The dependency ratio shows the economic pressure on the working‑age population from the young and old dependents.
GCSE 地理要求熟练使用一组核心人口计算。人口密度描述区域内的拥挤程度。自然增长（或自然减少）概括了出生与死亡之间的差值，不含迁移。抚养比体现了劳动年龄人口承受的来自少儿和老年被抚养人口的经济压力。
Population Density = Total population ÷ Land area (km² or mi²)
Crude Birth/Death Rate (‰) = (Number of births/deaths ÷ Total population) × 1000
Natural Increase Rate (%) = (Births − Deaths) ÷ Total population × 100
Dependency Ratio (%) = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
Some exam questions may ask you to describe trends from a graph of Crude Birth Rate and Crude Death Rate over time, linking the convergence or divergence of the lines to stages of the Demographic Transition Model (DTM). A falling dependency ratio can create a ‘demographic dividend’ that boosts economic growth.
部分试题可能要求根据粗出生率和粗死亡率的历时曲线描述变化趋势，并将两线的汇合或分离与人口转变模型（DTM）阶段联系起来。抚养比下降可带来促进经济增长的“人口红利”。
7. Urbanisation and Settlement Patterns | 城市化与聚落格局
Urbanisation is measured in two main ways: the rate of urban growth (annual percentage increase of the urban population) and the level of urbanisation (the proportion of a total population living in urban areas). Urban primacy indicates the dominance of a single city, measured by the extent to which its population exceeds that of the next largest city.
城市化的度量主要有两种：城市人口增长率（城市人口的年均百分比增速）和城市化水平（城市人口占总人口的比例）。城市首位度反映单一城市的支配性，用该城市人口超出第二大城市人口的程度来衡量。
Level of Urbanisation (%) = (Urban population ÷ Total population) × 100
Primacy Ratio = Population of largest city ÷ Population of second largest city
You may also use a Chi‑squared test to analyse whether the distribution of services or settlements deviates from an expected pattern (e.g. threshold populations), but Eduqas tends to focus on descriptive statistics and simple indices rather than formal statistical tests.
有时也可能使用卡方检验分析服务设施或聚落分布是否偏离预期格局（如门槛人口），但 Eduqas 更侧重描述性统计和简单指数，而非正式的统计检验。
8. Development Indicators: GDP, GNI and HDI | 发展指标：GDP, GNI 与 HDI
Economic wealth is commonly expressed as Gross Domestic Product (GDP) or Gross National Income (GNI) per capita. The Human Development Index (HDI) combines income, health (life expectancy) and education (mean years of schooling and expected years) into a single score between 0 and 1. Understanding how HDI is constructed helps you evaluate the limitations of purely economic measures.
经济财富通常用人均国内生产总值（GDP）或人均国民总收入（GNI）表示。人类发展指数（HDI）将收入、健康（预期寿命）和教育（平均受教育年限与预期受教育年限）结合成一个 0 到 1 之间的综合得分。了解 HDI 的组成有助于评价纯经济指标的局限性。
GDP per capita = Total GDP ÷ Mid‑year population
The Gini coefficient measures income inequality within a country on a scale from 0 (perfect equality) to 1 (perfect inequality). While you will not be asked to compute it, you should be able to interpret Lorenz curves and recognise that a more curved line indicates greater inequality. Other important indices include the Happy Planet Index (HPI) and the Gender Inequality Index (GII).
基尼系数衡量一国内部的收入不平等程度，范围从 0（绝对平等）到 1（绝对不平等）。虽然考试不要求计算，但应能解读洛伦兹曲线，并知道曲线越弯表示越不平等。其他重要指数包括幸福星球指数（HPI）和性别不平等指数（GII）。
9. Weather and Climate Statistics | 天气与气候统计
Weather data analysis relies on a range of descriptive statistics. Mean daily temperature is the average of maximum and minimum readings over 24 hours; diurnal range is the difference between them. Annual precipitation totals and temperature ranges are common in climate graph interpretation.
天气数据分析依赖一系列描述性统计。日平均气温是 24 小时内最高温度与最低温度的平均值；日较差则是两者之差。年降水总量和年温差常用于气候图解读。
Mean Daily Temperature = (Max temp + Min temp) ÷ 2
Diurnal Range = Max temp − Min temp
Annual Temperature Range = Mean temp of warmest month − Mean temp of coldest month
When dealing with synoptic charts, you will not use formulae but must apply conceptual knowledge of fronts, isobars and wind direction. However, some questions require percentage frequency calculations, e.g. ‘What percentage of days did the wind come from the south‑west?’
处理天气图时虽不涉及公式，但要运用锋面、等压线和风向等概念知识。不过部分题目要求进行百分比频率计算，如“西南风日数所占百分比是多少？”。
Percentage frequency (%) = (Number of observations in category ÷ Total observations) × 100
10. Coastal Geography: Wave Energy and Longshore Drift | 海岸地理：波浪能及沿岸漂移
Although there is no single universal formula for longshore drift, you are expected to understand the relationship between wave approach angle, swash and backwash, and sediment transport. Wave energy can be estimated by a simplified relationship involving wave height and period, but at GCSE level this is conceptual.
尽管沿岸漂移没有统一的公式，但需要理解波浪入射角、冲流和回流与沉积物搬运之间的关系。波浪能可通过波高和周期的简化关系估算，但在 GCSE 阶段更多是概念性了解。
Eduqas fieldwork may require you to measure sediment size using callipers or a ruler and construct percentage frequency histograms, or calculate the mean clast size for a beach transect. These are descriptive statistics rather than coastal‑specific formulae.
在 Eduqas 的野外调查中，可能需要用卡尺或直尺测量沉积物粒径，并绘制百分比频率直方图，或计算海滩剖面上砾石的平均粒径。这些属于描述性统计，而非海岸专属公式。
Mean sediment size = Σ (length × frequency) ÷ Σ frequency
When studying wave refraction, you should recall that wave energy is concentrated on headlands and dissipated in bays, but no direct calculation is required. Beach gradient can be quantified as the rise ÷ horizontal distance, essentially the same formula as a river gradient.
学习波浪折射时，要记住波能集中于岬角而在海湾消散，但不需直接计算。海滩坡度可通过垂直升高 ÷ 水平距离量化，基本公式与河流坡度相同。
11. Key Geographical Theorems and Models | 关键地理定理与模型
Geographical models are simplified representations of reality that help explain patterns and processes. For Eduqas GCSE, you must be able to describe and apply several well‑known models: the Bradshaw Model for river characteristics; the Demographic Transition Model (DTM) for population change; the Burgess and Hoyt models for urban land use; and the Clark‑Fisher model for employment structure change over time.
地理模型是对现实的简化表述，有助于解释格局和过程。在 Eduqas GCSE 中，必须能够描述并应用若干著名模型：关于河道特征的 Bradshaw 模型，关于人口变化的人口转变模型（DTM），关于城市土地利用的 Burgess 和 Hoyt 模型，以及关于就业结构随时间演变的 Clark‑Fisher 模型。
The Bradshaw Model predicts that downstream, discharge, hydraulic radius, velocity, channel depth and width all increase, while bedload particle size and gradient decrease. Though not a formula, you may be asked to plot scatter graphs of gradient against distance from source to test the model.
Bradshaw 模型预测，沿河流向下游，流量、水力半径、流速、河槽深度和宽度均增加，而河床质粒径和坡度减小。虽并非公式，但可能被要求绘制坡度与距源头距离的散点图以检验该模型。
For the DTM, the formula‑like component is the natural increase rate mentioned earlier. The Rostow model of development outlines five stages from traditional society to high mass consumption; it is often contrasted with dependency theory. Although not computational, you should be prepared to draw labelled diagrams of these models and explain the connections between their stages and real‑world examples.
在 DTM 中，类似公式的部分是前述的自然增长率。Rostow 发展模型描述了从传统社会到高度大众消费的五个阶段，常与依附理论对比。尽管这些不是计算性的，但要准备好绘制这些模型的标注示意图，并解释其阶段与实际案例间的联系。
12. Simple Statistical Measures for Fieldwork | 野外调查的简单统计方法
Fieldwork is an essential component of the Eduqas GCSE and requires you to present and analyse data. The most commonly used statistical measures are measures of central tendency (mean, median, mode) and measures of dispersion (range, interquartile range). Knowing how to compute and compare these for two or more data sets is vital.
野外调查是 Eduqas GCSE 的重要组成部分，要求进行数据展示和分析。最常用的统计量包括集中趋势量数（平均值、中位数、众数）和离散程度量数（极差、四分位距）。掌握如何计算和比较两个或以上数据集的这些指标至关重要。
Mean (x̄) = Σ values ÷ number of values
Range = Maximum value − Minimum value
Interquartile Range (IQR) = Upper quartile (Q₃) − Lower quartile (Q₁)
The percentage change formula is particularly useful when comparing before‑and‑after data, such as river velocity before and after a meander restoration project. Likewise, the chi‑squared test formula is sometimes introduced for categorical data, but Eduqas typically provides the necessary critical value table and asks you to state whether a relationship is significant.
百分比变化公式在比较前后数据时尤其有用，如河道裁弯恢复工程前后的流速对比。同样，有时会引入用于类别数据的卡方检验公式，但 Eduqas 通常提供所需的临界值表，要求你说明某关系是否显著。
Percentage change (%) = (New value − Old value) ÷ |Old value| × 100
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