📚 Year 9 Edexcel Geography Formula & Theorem Quick Reference Handbook | 九年级爱德思地理公式定理速查手册
This handbook brings together the essential formulas, theorems and models you will encounter in Year 9 Edexcel Geography. It covers map skills, population dynamics, urban models, river and coastal processes, and development indicators — all with clear definitions and worked examples. Use it as a quick revision tool to check your understanding before tests and exams.
本手册汇总了九年级爱德思地理课程中必备的公式、定理和模型。涵盖地图技能、人口动态、城市模型、河流与海岸过程以及发展指标——全部配有清晰的定义和示例。可用作考前快速复习工具，帮助你查漏补缺。
1. Map Scale and Distance Calculations | 地图比例尺与距离计算
A map scale expresses the ratio between distance on the map and the actual distance on the ground. For a scale of 1:25 000, 1 cm on the map represents 25 000 cm (250 m) in reality.
地图比例尺表示图上距离与实际地面距离的比值。以 1:25 000 比例尺为例，图上 1 厘米代表实地 25 000 厘米（250 米）。
Actual distance (m) = Map distance (cm) × Scale denominator ÷ 100
实地距离 (米) = 图上距离 (厘米) × 比例尺分母 ÷ 100
When measuring a straight line, simply multiply. For curved lines, use a piece of string to follow the route, then measure the string length against the linear scale.
测量直线距离时直接相乘即可。测量曲线时，用细绳沿路线放置，再将绳长对比直线比例尺读数。
2. Gradient and Relief on Contour Maps | 等高线地形图的坡度与起伏
Gradient compares the vertical drop to the horizontal distance between two points on a slope. It can be expressed as a ratio, fraction or percentage.
坡度比较的是斜坡上两点之间的垂直高差与水平距离。可用比例、分数或百分比表示。
Gradient = Vertical interval (m) ÷ Horizontal distance (m)
坡度 = 垂直高差 (米) ÷ 水平距离 (米)
To find relief, subtract the lowest contour value from the highest contour value within a grid square or area. Cross‑sections can be drawn to visualise the shape of the land.
求地形起伏时，用区域网格内的最高等高线数值减去最低等高线数值。绘制剖面图可直观显示地形形态。
3. Population Density and Distribution | 人口密度与分布
Population density measures how crowded an area is, expressed as the number of people per square kilometre.
人口密度衡量一个地区的拥挤程度，以每平方千米人口数表示。
Population density (people/km²) = Total population ÷ Total land area (km²)
人口密度 (人/平方千米) = 总人口 ÷ 土地总面积 (平方千米)
Distribution describes the pattern of where people live — clustered, linear or dispersed. A dot map or choropleth map is often used to display both density and distribution.
人口分布描述的是人们居住的空间模式——聚集、线状或分散。点值图或分级统计图常用于同时展示密度与分布特征。
4. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率和自然增长率
The crude birth rate (CBR) is the number of live births per 1,000 people in a given year. The crude death rate (CDR) is the number of deaths per 1,000 people per year.
粗出生率 (CBR) 指某年每千人口中的活产婴儿数。粗死亡率 (CDR) 指某年每千人口中的死亡人数。
CBR = (Number of live births ÷ Total population) × 1 000
CBR = (活产婴儿数 ÷ 总人口) × 1 000
CDR = (Number of deaths ÷ Total population) × 1 000
CDR = (死亡人数 ÷ 总人口) × 1 000
The rate of natural increase (RNI) is the difference between the birth rate and death rate, excluding migration. It is usually expressed as a percentage.
自然增长率 (RNI) 是出生率与死亡率之差，不含迁移因素，通常以百分比表示。
RNI (%) = (CBR − CDR) ÷ 10
自然增长率 (%) = (CBR − CDR) ÷ 10
5. Migration and Net Migration Rate | 迁移与净迁移率
Net migration is the difference between the number of immigrants (people moving into a country) and emigrants (people leaving).
净迁移是指迁入人口（移民入境）与迁出人口（移民出境）之差。
Net migration = Immigrants − Emigrants
净迁移 = 迁入人口 − 迁出人口
The net migration rate shows this balance per 1,000 inhabitants, giving a clearer picture of population change independent of natural factors.
净迁移率表示每千名居民中的迁移差额，能够更清晰地显示除去自然变动后的人口变化。
Net migration rate (per 1 000) = (Net migration ÷ Total population) × 1 000
净迁移率 (每千人) = (净迁移 ÷ 总人口) × 1 000
6. Urbanisation and Settlement Models | 城市化与聚落模型定理
The level of urbanisation measures the proportion of a country's population living in towns and cities. It increases as people migrate from rural to urban areas.
城市化水平衡量的是一个国家城镇人口占总人口的比例。当人口从农村迁往城市时，该比例上升。
Urbanisation level (%) = (Urban population ÷ Total population) × 100
城市化水平 (%) = (城镇人口 ÷ 总人口) × 100
Two classic models describe urban land use. The Burgess concentric zone model (1925) states that a city grows outward in rings: CBD, transition zone, low‑class housing, medium‑class housing and commuter zone. The Hoyt sector model (1939) argues that land uses develop in wedges or sectors along transport routes, not perfect rings.
有两个经典模型描述城市土地利用。伯吉斯同心圆模型 (1925) 认为城市向外呈环状扩展：中央商务区、过渡带、低阶层住宅、中阶层住宅和通勤区。霍伊特扇形模型 (1939) 则主张土地利用沿交通线呈扇形或楔形发展，而非完美的圆环。
Both models are theorems of urban structure, helping explain why certain zones emerge where they do. In reality, modern cities often combine elements of both patterns.
这两个模型都是城市结构的定理，帮助解释各功能区为何出现在特定位置。现实中，现代城市常常结合了两种模式的元素。
7. River Channel Measurements and Discharge | 河道测量与流量
River discharge is the volume of water flowing through a channel cross‑section in one second, measured in cubic metres per second (cumecs).
河流流量是指每秒流过河道某一横断面的水体体积，单位为立方米/秒。
Discharge (Q) = Cross‑sectional area (A) × Mean velocity (V)
流量 (Q) = 横截面积 (A) × 平均流速 (V)
Cross‑sectional area is calculated by multiplying the average width by the average depth at a site. Velocity is often found by timing a float over a known distance and applying a correction factor (typically 0.8 for surface floats).
横截面积通过平均宽度乘以平均深度计算。流速通常用浮标漂过已知距离的时间求得，并乘以修正系数（表面浮标一般为 0.8）。
A (m²) = Average width (m) × Average depth (m)
截面积 (平方米) = 平均宽度 (米) × 平均深度 (米)
8. Hjulström Curve – Erosion, Transport and Deposition | 赫斯特罗姆曲线——侵蚀、搬运与沉积定理
The Hjulström curve is a fundamental theorem in fluvial geomorphology. It describes the critical velocities required to erode, transport and deposit sediment particles of different sizes.
赫斯特罗姆曲线是河流地貌学中的基础定理。它描述了侵蚀、搬运和沉积不同粒径沉积物所需的临界流速。
Larger particles (e.g. coarse sand and gravel) need higher velocities to be picked up but settle quickly once velocity drops.
较大颗粒（如粗砂和砾石）需要较高的流速才能起动，但一旦流速下降就迅速沉积。
Silt and clay particles require relatively high velocities for erosion because they are cohesive, yet they can stay in suspension at very low velocities.
粉砂和粘土颗粒因具有粘聚力，需要相对较高的流速才能被侵蚀，却能在极低流速下保持悬浮。
Sand‑sized particles are the easiest to erode and transport; they illustrate the principle of entrainment thresholds.
砂粒大小的颗粒最易被侵蚀和搬运，体现了起动临界值的原理。
The table below summarises approximate threshold velocities for different grain sizes, based on the Hjulström diagram.
下表根据赫斯特罗姆图解总结了不同粒径的大致临界流速。
| Grain size / 粒径 | Erosion threshold / 侵蚀临界速 (cm/s) | Deposition threshold / 沉积临界速 (cm/s) |
|---|---|---|
| Clay / 粘土 (<0.002 mm) | >200 | <0.1 |
| Silt / 粉砂 (0.002–0.06 mm) | ~100–200 | <0.1 |
| Sand / 砂 (0.06–2 mm) | ~20–30 | ~10–20 |
| Pebbles / 砾石 (>2 mm) | >100–600 | ~50–100 |
Data illustrate typical values for clear‑water flow; values shift slightly with sediment supply and turbidity.
数据为清水水流的典型值，实际值随泥沙补给和浊度略有变化。
9. Longshore Drift and Coastal Processes | 沿岸漂移与海岸过程
Longshore drift is the movement of sediment along a coast by wave action. The prevailing wind drives waves to hit the shore at an oblique angle, creating a zigzag pattern of swash and backwash. The theorem of longshore drift explains why beaches often show net sediment movement in one direction.
沿岸漂移是波浪作用下沉积物沿海岸移动的过程。盛行风使波浪以斜角冲击海岸，形成冲刷和回流的锯齿状路径。沿岸漂移定理解释了为何海滩沉积物常沿某一方向净移动。
Although no single formula is used in Year 9, you can relate the rate of longshore drift to wave energy and sediment size. The amount of material transported depends on the angle of wave approach, wave height and grain size.
虽然九年级不要求单一公式，但可将沿岸漂移速率与波浪能量和颗粒大小相联系。搬运物质的数量取决于波浪入射角、波高和粒径。
Destructive waves have a stronger backwash, removing material from the beach, while constructive waves build up the beach with stronger swash — a key concept in coastal management.
破坏性波浪回流较强，带走海滩物质；建设性波浪冲流较强，堆积海滩——这是海岸管理中的关键概念。
10. Development Indicators and Composite Indices | 发展指标与综合指数
Development is measured using single indicators such as GNI per capita, life expectancy, literacy rate and infant mortality, as well as composite indices that combine several measures.
衡量发展可用单一指标，如人均国民总收入、预期寿命、识字率和婴儿死亡率，也可使用综合多项指标的综合指数。
ortality rate (per 1 000) = (Number of deaths under age 1 ÷ Number of live births) × 1 000
婴儿死亡率 (每千) = (一岁以下死亡人数 ÷ 活产婴儿数) × 1 000
The Human Development Index (HDI) combines life expectancy, education (mean and expected years of schooling) and GNI per capita into a single score between 0 and 1. It is the most widely used theorem for comparing levels of development.
人类发展指数 (HDI) 将预期寿命、教育（平均受教育年限和预期受教育年限）以及人均国民总收入合并为一个 0 到 1 之间的指数。这是最广泛用于比较发展水平的定理。
The Gini coefficient measures income inequality on a scale from 0 (perfect equality) to 1 (perfect inequality). Its calculation is beyond Year 9, but the concept is essential for understanding uneven development.
基尼系数衡量收入不平等，范围从 0（绝对平等）到 1（绝对不平等）。其计算方法超出九年级范围，但准确把握该概念对理解发展不均衡至关重要。
11. Population Pyramids and Dependency Ratios | 人口金字塔与抚养比
A population pyramid visualises the age–sex structure of a country. The shape reveals the stage of the Demographic Transition Model (DTM) a country is in and allows calculation of dependency burdens.
人口金字塔直观展示了一个国家的年龄—性别结构。其形状可揭示该国处于人口转变模型 (DTM) 的哪一阶段，并可计算抚养负担。
Youth dependency ratio = (Population aged 0–14 ÷ Working‑age population 15–64) × 100
少年抚养比 = (0–14 岁人口 ÷ 15–64 岁劳动年龄人口) × 100
Elderly dependency ratio = (Population aged 65+ ÷ Working‑age population 15–64) × 100
老年抚养比 = (65 岁以上人口 ÷ 15–64 岁劳动年龄人口) × 100
Total dependency ratio (youth + elderly) indicates the economic pressure on the productive segment of society. A wide base on the pyramid signals high youth dependency, typical of Stage 2 or early Stage 3 countries.
总抚养比（少年 + 老年）反映了社会生产性人口承担的经济压力。底部宽阔的金字塔表明少年抚养比高，常见于 DTM 第二阶段或第三阶段早期的国家。
12. Climate Graphs and Aridity Index | 气候图表与干旱指数
Climate graphs combine monthly average temperature (line graph) and precipitation (bar chart) for a location. They are used to identify climate types and seasonal patterns.
气候图表将某地各月平均气温（折线图）和降水量（柱状图）结合，用来识别气候类型和季节特征。
An aridity index can be estimated to classify a climate as humid or dry. A simplified formula, derived from the UNEP aridity index, is:
可估算干旱指数以划分湿润或干燥气候。由 UNEP 干旱指数衍生的简化公式为：
Annual precipitation (mm) ÷ Potential evapotranspiration (mm)
年降水量 (毫米) ÷ 潜在蒸散发量 (毫米)
Values below 0.2 indicate hyper‑arid conditions, while values above 0.65 suggest humid climates. This formula helps explain the distribution of biomes and agricultural potential.
比值低于 0.2 表明极端干旱，高于 0.65 则属湿润气候。该公式有助于解释生物群系的分布和农业潜力。
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