📚 Year 12 WJEC Geography: Formula & Theorem Quick Reference Guide | Year 12 WJEC 地理：公式定理速查手册
This quick-reference guide brings together the key formulas, equations and models you need for Year 12 WJEC Geography. Mastering these will help you analyse physical landscapes, population dynamics and urban patterns with confidence.
这份速查手册汇总了 Year 12 WJEC 地理所需的关键公式、方程和模型。掌握它们将帮助你自信地分析自然景观、人口动态和城市格局。
1. River Discharge and Hydraulic Radius | 河流流量与水力半径
Discharge (Q) is the volume of water passing a channel cross‑section per second. It is calculated by multiplying the cross‑sectional area (A) by the mean velocity (V).
流量 (Q) 是每秒钟通过河道断面的水量。它由过水断面面积 (A) 乘以平均流速 (V) 得出。
Q = A × V
Hydraulic radius (R) shows how efficiently a channel conveys water. A larger R means less frictional resistance. It is found by dividing the cross‑sectional area (A) by the wetted perimeter (P).
水力半径 (R) 表明河道输送水流的效率。R 值越大，摩擦阻力越小。它等于过水断面面积 (A) 除以湿周 (P)。
R = A / P
2. River Gradient and Bradshaw Model | 河流梯度与布拉德肖模型
Gradient is the steepness of a river channel, expressed as the vertical drop between two points divided by the horizontal distance. It is often given as a ratio, a percentage or in metres per kilometre.
梯度是河道的陡峭程度，用两点间高差除以水平距离表示。它常用比降、百分比或每千米下降米数来表达。
Gradient = vertical drop / horizontal distance
The Bradshaw model is a conceptual theorem that predicts how channel characteristics change from source to mouth. Discharge, velocity, mean depth and hydraulic radius all increase downstream, while gradient, bedload particle size and channel roughness decrease.
布拉德肖模型是一个概念性定理，预测河道特征如何从源头到河口变化。流量、流速、平均水深和水力半径向下游增大，而梯度、河床质粒径和河道粗糙度则减小。
3. Hjulström Curve and Sediment Transport | 休斯特罗姆曲线与泥沙搬运
The Hjulström curve is a graphical theorem showing the critical mean water velocity needed to erode, transport or deposit particles of different sizes. For fine clays and silts, erosion requires higher velocities than transport because of cohesion; for sands, erosion and deposition thresholds are close.
休斯特罗姆曲线是一个图解定理，显示侵蚀、搬运或沉积不同粒径泥沙所需的临界平均流速。对于细粘土和粉砂，由于颗粒间的粘聚力，侵蚀比搬运需要更高的流速；对于砂粒，侵蚀与沉积的临界流速接近。
The relationship demonstrates that the largest particles (boulders) are only moved during floods, whereas sand‑sized sediment is moved most easily. The curve underpins understanding of river competence and capacity.
这一关系表明，最大的颗粒（漂砾）只在洪水期间被搬动，而砂粒大小的沉积物最容易被搬运。该曲线是理解河流搬运能力和容量的基础。
4. Infiltration and Soil Moisture | 渗透与土壤湿度
Infiltration rate measures how quickly water enters the soil. It is usually expressed as a volume per unit time (e.g. mm hr-1) and depends on soil texture, structure, antecedent moisture and vegetation cover.
渗透率衡量水进入土壤的快慢。它通常以单位时间的体积表示（如毫米/小时），并取决于土壤质地、结构、前期含水量和植被覆盖。
Infiltration rate = volume of water infiltrated / time
Soil moisture content is the percentage of water held in a soil sample. It is essential for understanding water availability for plants and potential surface runoff.
土壤含水量是土壤样本中水分的百分比。它对于理解植物可利用的水分和潜在的地表径流至关重要。
Soil moisture (%) = (mass of water / mass of dry soil) × 100
5. Population Metrics: CBR, CDR and Natural Increase | 人口指标：出生率、死亡率和自然增长
The crude birth rate (CBR) is the number of live births per 1,000 people in a population per year. The crude death rate (CDR) is the annual number of deaths per 1,000 people.
粗出生率 (CBR) 是某人口每年每千人的活产婴儿数。粗死亡率 (CDR) 是每年每千人的死亡人数。
= (live births / total population) × 1000 CDR = (deaths / total population) × 1000
The rate of natural increase (RNI) shows how fast a population grows (or declines) without migration. It can be expressed per 1,000 or as a percentage.
自然增长率 (RNI) 显示在没有迁移的情况下人口增长（或下降）的速度。它可以用千分数或百分比表示。
RNI = ((births – deaths) / total population) × 1000 (or × 100 for %)
The total fertility rate (TFR) is a separate measure: the average number of children a woman would have during her reproductive years. A TFR of about 2.1 is replacement level.
总和生育率 (TFR) 是另一个指标：一名妇女在育龄期预计生育的平均子女数。约 2.1 的 TFR 为更替水平。
6. Dependency Ratio | 抚养比
The dependency ratio shows the economic pressure that the non‑working‑age population places on the working‑age population. A higher ratio suggests greater social and financial demands.
抚养比显示非劳动年龄人口对劳动年龄人口造成的经济压力。比值越高，表明社会和财政负担越大。
Dependency ratio = ((pop. 0–14 + pop. 65+) / pop. 15–64) × 100
Youth dependency, old‑age dependency and overall dependency can all be calculated separately. They help interpret the shape of population pyramids and inform planning for schools, pensions and health care.
可分别计算少儿抚养比、老年抚养比和总抚养比。它们有助于解读人口金字塔的形态，并为学校、养老金和医疗保健规划提供依据。
7. Urbanisation Level and Urban Land‑Use Models | 城市化水平与城市土地利用模型
Urbanisation level is the percentage of a country's population living in areas classified as urban. It is a key indicator of development and change.
城市化水平是一个国家居住在被划为城镇地区的人口百分比。它是发展和变化的关键指标。
Urbanisation level (%) = (urban population / total population) × 100
The urbanisation pathway (theorem) describes an S‑shaped curve: low but rising urbanisation in early development, rapid urbanisation during industrialisation, and a slowing down as most people already live in towns and cities.
城市化路径（定理）描述一条 S 形曲线：早期发展中城市化水平低但开始上升，工业化期间快速城市化，当多数人口已居住在城市时城市化速度放缓。
Classic urban land‑use models are essential 'theorems' for understanding city structure. Burgess’s concentric zone model, Hoyt’s sector model and Harris–Ullman’s multiple nuclei model each explain the spatial patterns of residential, industrial and commercial land uses.
经典的城市土地利用模型是理解城市结构的必备“定理”。伯吉斯的同心圆模型、霍伊特的扇形模型以及哈里斯–乌尔曼的多核心模型分别解释了居住、工业和商业用地的空间格局。
8. Lorenz Curve and Gini Coefficient | 洛伦兹曲线与基尼系数
The Lorenz curve plots the cumulative percentage of total income (or wealth) against the cumulative percentage of the population. The 45‑degree line represents perfect equality.
洛伦兹曲线描绘了总收入（或财富）的累计百分比与人口累计百分比的关系。45 度线代表绝对平等。
The Gini coefficient measures the degree of inequality. It is derived from the area between the line of equality and the Lorenz curve (A), divided by the total area under the line of equality (A+B).
基尼系数衡量不平等程度。它由平等线与洛伦兹曲线之间的面积 (A) 除以平等线下的总面积 (A+B) 得出。
Gini coefficient = A / (A + B)
A coefficient of 0 means perfect equality; 1 means perfect inequality. In practice, values are often multiplied by 100 to give an index between 0 and 100.
系数为 0 表示绝对平等，1 表示完全不平等。实际上，数值常乘以 100，得到一个 0 到 100 之间的指数。
9. Gravity Model of Migration | 人口迁移的重力模型
The gravity model applies Newton’s law of gravitation to human migration. The flow of migrants between two places (Iij) is directly proportional to the product of their populations (Pi and Pj) and inversely proportional to the distance between them (dij), raised to a power b.
重力模型将牛顿引力定律应用于人类迁移。两地之间的迁移流量 (Iij) 与两地人口 (Pi 和 Pj) 的乘积成正比，与它们之间的距离 (dij) 的 b 次方成反比。
Iij = k × (Pi × Pj) / dijb
The constant k and the exponent b must be calibrated from real data. The model helps explain why large cities attract more long‑distance migrants and why shorter distances generate larger flows.
常数 k 和指数 b 需根据实际数据校准。该模型有助于解释为何大城市吸引更多长距离移民，以及为何较短距离会产生较大的迁移流。
10. Demographic Transition Model (DTM) | 人口转变模型
The Demographic Transition Model (DTM) is a fundamental theorem linking population change to economic development. It describes five stages based on trends in birth rates, death rates and natural increase.
人口转变模型 (DTM) 是将人口变化与经济发展联系起来的核心定理。它根据出生率、死亡率和自然增长的变动趋势描述了五个阶段。
- Stage 1 High fluctuating birth and death rates – low growth. 阶段一 高出生率与高死亡率波动 – 低增长。
- Stage 2 Death rates fall, birth rates stay high – rapid growth. 阶段二 死亡率下降，出生率居高 – 快速增长。
- Stage 3 Birth rates begin to fall – growth slows. 阶段三 出生率开始下降 – 增长放缓。
- Stage 4 Low birth and death rates – low/stable growth. 阶段四 低出生率与低死亡率 – 低稳定增长。
- Stage 5 Birth rates fall below death rates – natural decrease. 阶段五 出生率低于死亡率 – 自然减少。
The model helps explain past changes in the UK and is used to compare countries at different stages of development today.
该模型有助于解释英国过去的变化，并用于比较当今处于不同发展阶段的国家。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图