📚 Year 11 WJEC Geography: Formula & Theorem Quick Reference Guide | WJEC 11年级地理公式定理速查手册
The WJEC GCSE Geography specification expects you to handle quantitative data with confidence. This quick reference guide assembles every essential formula, definition and theorem you need to analyse river systems, population change, urbanisation and development. Use it to speed up your revision and to secure those calculation marks on exam day.
WJEC GCSE 地理大纲要求你能够自信地处理定量数据。这本速查手册汇集了分析河流系统、人口变化、城市化和发展所需的所有基本公式、定义和定理。用它来加快复习进度，稳稳拿下考试中的计算分。
1. River Discharge | 河流流量
Discharge is the volume of water passing through a river channel cross‑section in one second. It is the most important measure of a river’s capacity to transport sediment.
流量是指一秒钟内通过河道横截面的水量，是衡量河流输沙能力的最重要指标。
Q = A × V
Q = discharge (m³/s), A = cross‑sectional area of the channel (m²), V = mean water velocity (m/s).
Q = 流量（m³/s），A = 河道横截面积（m²），V = 平均流速（m/s）。
To find A, measure the width and several depths across the channel, then sum the areas of trapezoidal sections. Velocity is usually measured with a flowmeter or by timing a float over a known distance and correcting for surface speed (multiply by 0.85).
计算 A 时需测量河宽和多个深度，然后把若干梯形面积相加。流速通常用流速仪测量，或利用浮标经过已知距离的时间并加以表面流速修正（乘以 0.85）。
Always check your units – mixing centimetres and metres will throw the result out by orders of magnitude. Practise converting widths and depths into metres before calculating area.
务必核对单位——把厘米与米混用会使结果差出几个数量级。在计算面积前，先练习将宽度和深度统一转换为米。
2. River Gradient | 河流坡度
Gradient describes the steepness of a river channel or valley floor. It influences flow velocity and the river’s erosive power.
坡度描述河道或谷底的陡峭程度，它影响流速和河流的侵蚀力。
Gradient = Vertical rise ÷ Horizontal distance
Express the gradient as a ratio, e.g. 1:25, or as a fraction. A rise of 2 m over a distance of 50 m gives a gradient of 2/50 = 1:25.
坡度用比例表示，如 1:25，或写成分数。若在 50 米距离内高差为 2 米，则坡度为 2/50 = 1:25。
On Ordnance Survey maps you calculate it by counting contour intervals between two points and measuring the straight‑line distance. Remember to use the same units for both rise and run.
在 Ordnance Survey 地图上，通过数两点间的等高线间隔并测量直线距离来计算。高差和水平距离须使用相同单位。
A steeper gradient (smaller ratio denominator) means faster flow and greater energy for vertical erosion, while a gentle gradient encourages deposition and meandering.
坡度越陡（比例分母越小），流速越快，下切侵蚀的能量越强；平缓的坡度则促进沉积与曲流发育。
3. Stream Velocity | 水流流速
Velocity is the speed of water flowing in a channel. It determines whether the river can erode, transport or deposit material.
流速是河道中水体流动的速度，决定了河流是侵蚀、搬运还是沉积物质。
v = d / t
v = velocity (m/s), d = distance travelled by a float or dye (m), t = time taken (s). For more accurate fieldwork, use a flowmeter that reads directly in m/s.
v = 流速（m/s），d = 浮标或示踪剂移动的距离（m），t = 所用时间（s）。实地测量时建议使用直接读取米/秒的流速仪以获得更准确的结果。
Surface velocity is faster than the mean velocity of the whole column of water. Multiply surface float velocity by 0.85 to estimate the mean velocity for discharge calculations.
表层流速快于整层水体的平均流速。进行流量计算时，将浮标表层流速乘以 0.85 以估算平均流速。
Velocity varies across the channel – it is slowest near the bed and banks due to friction, and fastest near the centre and just below the surface in a straight reach.
流速在河道断面上是变化的——由于摩擦，靠近河床和河岸处最慢，在顺直河段中心偏下的位置最快。
4. Population Density | 人口密度
Population density shows how crowded a place is and helps explain pressure on resources, services and infrastructure.
人口密度反映一个地方的拥挤程度，有助于解释资源、服务和基础设施所承受的压力。
Population Density = Total population ÷ Area
Units are usually people per km². For example, 500 000 people living in an area of 200 km² gives a density of 2500 people/km².
单位通常为人/km²。例如，50 万人居住在 200 km² 的地区，人口密度为 2500 人/km²。
Do not confuse population density with distribution – density is a number; distribution describes the pattern of where people live. A high density can mask uneven distribution within the area.
勿将人口密度与人口分布混淆——密度是一个数值，分布则描述人们的居住格局。高密度可能掩盖区域内分布不均的情况。
5. Birth Rate & Death Rate | 出生率与死亡率
Crude birth rate (CBR) and crude death rate (CDR) are fundamental indicators used to understand natural population change.
粗出生率（CBR）和粗死亡率（CDR）是理解人口自然变动的基本指标。
CBR = (Number of live births / Total population) × 1000
Calculate per 1000 people to avoid tiny decimals. A CBR of 12 indicates 12 live births per 1000 population in a given year.
按每千人计算以避免极小的小数。CBR 为 12，表示某年内每千人有 12 个活产婴儿。
CDR = (Number of deaths / Total population) × 1000
CR rates are labelled ‘crude’ because they do not account for the age structure of the population. Always use mid‑year population estimates for accuracy.
这些比率之所以称“粗”，是因为它们未考虑人口的年龄结构。为确保准确，始终使用年中人口估计数。
6. Natural Increase Rate | 自然增长率
Natural increase shows how fast a population is growing (or shrinking) purely from the balance of births and deaths, ignoring migration.
自然增长率反映仅由出生与死亡平衡决定的人口增长（或减少）速度，不包括迁移。
Natural Increase Rate = CBR – CDR
The result is expressed per 1000 population per year. If CBR = 18 and CDR = 6, natural increase is 12 per 1000, or 1.2% when divided by 10.
结果以每年每千人为单位。若 CBR = 18，CDR = 6，自然增长率为 12‰，除以 10 后为 1.2%。
A negative natural increase occurs when death rate exceeds birth rate, a pattern seen in many stage 5 countries of the demographic transition model.
当死亡率超过出生率时出现自然负增长，这在人口转变模型第五阶段的许多国家中可见。
7. Net Migration Rate | 净迁移率
Net migration rate captures the difference between the number of people entering (immigration) and leaving (emigration) a region.
净迁移率表示迁入（移民）与迁出（外迁）某地区人数的差额。
NMR = (Immigration – Emigration) / Total population × 1000
Use the same mid‑year population and express the result per 1000. A positive NMR means net in‑migration; a negative value indicates net out‑migration.
使用相同的中期人口估算，结果以每千人为单位。正值表示净迁入，负值表示净迁出。
Net migration is crucial for understanding population change in urban centres and regions experiencing counter‑urbanisation or refugee flows.
净迁移对于理解城市中心以及经历逆城市化或难民流地区的人口变化至关重要。
8. Population Growth Rate | 人口增长率
The overall population growth rate combines natural increase and net migration to show the real annual change in total population.
总体人口增长率结合自然增长和净迁移，展示总人口的实际年度变化。
Population Growth Rate (%) = (CBR – CDR + NMR) ÷ 10
Since CBR, CDR and NMR are per 1000, dividing by 10 converts the total change into a percentage. A rate of 2.5% implies the population could double in about 28 years.
因为 CBR、CDR 和 NMR 都以千分比为单位，除以 10 即将总变动转化为百分比。2.5% 的增长率意味着人口约在 28 年内翻一番。
This rate is used to project future population size and to plan for housing, schools and healthcare. Always show your working in exam questions that ask for percentage growth.
该增长率用于预测未来人口规模并规划住房、学校和医疗。回答要求计算百分比增长的考题时，务必展示运算过程。
9. Urbanisation Level | 城市化水平
Urbanisation level measures the proportion of a country’s population that lives in towns and cities. It is a key indicator of economic development.
城市化水平衡量一国人口中居住在城镇的比例，是经济发展的关键指标。
Urbanisation Level (%) = (Urban population / Total population) × 100
For example, if 60 million out of a country’s 80 million people are urban, the urbanisation level is 75%.
例如，若一国 8000 万人口中有 6000 万为城市人口，城市化水平为 75%。
The pace of urbanisation – the rate at which this percentage increases – is often fastest in emerging economies experiencing rural‑to‑urban migration and natural increase.
城市化速度（该比例的增长速率）在经历乡城迁移和自然增长的新兴经济体中往往最快。
10. GDP per Capita | 人均国内生产总值
GDP per capita is the average economic output per person. It gives a rough measure of wealth and living standards, though it hides inequality.
人均 GDP 是每人平均经济产出，可粗略衡量财富和生活水平，但掩盖了不平等。
GDP per Capita = Total GDP / Total population
It is typically quoted in US dollars ($). Make sure the units match – GDP in millions of dollars and population in millions for a quick per‑capita figure.
通常以美元（$）表示。确保单位一致——若 GDP 单位为百万美元，人口以百万计，直接相除即可得到人均数值。
To compare purchasing power between countries, geographers often use GDP per capita at purchasing power parity (PPP) rather than nominal exchange rates.
为比较不同国家的购买力，地理学者常使用按购买力平价（PPP）计算的人均 GDP，而非名义汇率。
11. Dependency Ratio | 抚养比率
The dependency ratio compares the economically dependent population (young and elderly) with the working‑age population. It highlights potential pressure on social services.
抚养比率将受抚养人口（幼年和老年）与劳动年龄人口进行比较，突显社会服务的潜在压力。
Dependency Ratio = (Population aged 0‑14 + Population aged 65+ ) / Population aged 15‑64 × 100
A ratio of 60 means there are 60 dependants for every 100 people of working age. The higher the number, the greater the economic burden carried by the working population.
抚养比率为 60，意味着每 100 名劳动年龄人口负担 60 名受抚养者。数值越高，劳动人口承担的 经济负担越重。
Youth dependency and old‑age dependency can be calculated separately. Many ageing countries face rising old‑age dependency, increasing demand for pensions and healthcare.
少儿抚养比和老年抚养比可分别计算。许多老龄化国家面临不断上升的老年抚养比，加剧了对养老金和医疗的需求。
12. Mean Daily Temperature & Temperature Range | 日均温与温度较差
Temperature data is essential for understanding climate graphs, ecosystems and microclimate investigations. Daily mean temperature is the simplest temperature statistic.
气温数据对于理解气候图、生态系统和小气候调查不可或缺。日均温是最简单的气温统计量。
Mean Daily Temperature = (Tmax + Tmin) / 2
Tmax is the day’s highest thermometer reading, usually recorded in a Stevenson screen; Tmin is the lowest, often just before dawn.
Tmax 为当日的最高温度读数，通常在百叶箱中记录；Tmin 为最低温度，常出现在拂晓前。
Diurnal Temperature Range = Tmax – Tmin
Annual Temperature Range = Warmest month mean – Coldest month mean
Temperatures must be in the same units (°C). A large diurnal range suggests clear skies and dry air, while a small annual range is typical of equatorial climates.
温度单位需一致（℃）。日较差大说明晴空干燥，年较差小则是赤道气候的典型特征。
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