📚 Year 10 CIE Geography: Formula & Theorem Quick Reference Handbook | 年10 CIE地理：公式定理速查手册
This quick reference handbook brings together all the key formulas, equations, and fundamental theorems you need for Year 10 CIE IGCSE Geography. It covers essential calculations in population, settlement, rivers, map skills, and weather – exactly the type of quantitative work that appears in Paper 1, Paper 2 and the alternative to coursework. Keep this guide handy whenever you practise geographical skills questions.
本速查手册汇集了年10 CIE IGCSE地理课程中所有关键公式、方程和基本定理。它涵盖了人口、聚落、河流、地图技能和天气等核心计算内容，完全针对试卷一、试卷二以及课程作业替代测试中常见的定量分析题。在你练习地理技能题时，请随时查阅本手册。
1. Population Density | 人口密度
Population density describes how crowded an area is. It is the average number of people living per unit of land area, usually expressed per square kilometre (km²). It helps identify whether a place is sparsely or densely populated and is a fundamental concept in population geography.
人口密度描述了一个地区的拥挤程度。它是单位土地面积上居住的平均人数，通常以每平方公里（km²）表示。它有助于判断某地是人口稀疏还是稠密，是人口地理学中的基本概念。
Population Density = Total Population ÷ Land Area (km²)
For example, if a country has 5 million people and a land area of 100 000 km², its population density is 50 persons per km². Always check the units – area must be in km² to match the standard density measure.
例如，如果一个国家有500万人口，土地面积为10万平方公里，则其人口密度为每平方公里50人。务必核对单位——面积必须使用平方公里以匹配标准密度度量。
2. Crude Birth Rate and Crude Death Rate | 出生率与死亡率
Crude birth rate (CBR) and crude death rate (CDR) are the simplest measures of fertility and mortality. They are called 'crude' because they relate to the total population without adjusting for age or sex structure. Both rates are expressed per 1000 people per year.
出生率（CBR）和死亡率（CDR）是衡量生育和死亡最简单的指标。它们之所以称为“粗”是因为它们与总人口相关，未针对年龄或性别结构进行调整。两个比率单位均为每年每千人。
CBR = (Number of live births in a year ÷ Total population) × 1000
CDR = (Number of deaths in a year ÷ Total population) × 1000
A high CBR often indicates a young population and limited access to contraception, while a high CDR may reflect an ageing population, poor healthcare or conflict. Comparing CBR and CDR gives a first idea of whether a population is growing naturally.
高出生率通常意味着人口结构年轻且避孕措施有限，而高死亡率则可能反映出人口老龄化、医疗条件差或冲突。比较出生率与死亡率可以初步判断人口是否在自然增长。
3. Natural Increase Rate | 自然增长率
Natural increase rate shows how fast a population is growing (or shrinking) purely from births and deaths, excluding migration. It can be expressed as a percentage or per 1000. The simplest formula uses the crude birth and death rates.
自然增长率表示仅由出生和死亡导致的人口增长（或减少）速度，不包括迁移。它可以表示为百分比或每千分比。最简单的公式使用粗出生率和死亡率。
Natural Increase Rate (per 1000) = CBR – CDR
Natural Increase Rate (%) = (CBR – CDR) ÷ 10
For instance, a CBR of 32 and CDR of 8 gives a natural increase of 24 per 1000, or 2.4%. Negative values indicate natural decrease, which is common in stage 5 of the demographic transition model.
例如，出生率为32，死亡率为8，自然增长率为每千人24，即2.4%。负值表示自然减少，这在人口转变模型第五阶段很常见。
4. Net Migration Rate | 净迁移率
Migration can change the size and composition of a population significantly. Net migration rate captures the difference between immigrants and emigrants in a given year, per 1000 population. Positive values show net in-migration; negative values show net out-migration.
迁移会显著改变人口的规模和结构。净迁移率反映了某一年度内迁入与迁出人口的差额，单位为每千人口。正值表示净迁入；负值表示净迁出。
Net Migration Rate = [(Immigrants – Emigrants) ÷ Total Population] × 1000
When analysing a country’s population change, always add the net migration rate to the natural increase rate. Migration can offset a declining birth rate or accelerate population growth in urban areas.
在分析一国人口变化时，务必将净迁移率与自然增长率相加。迁移可以弥补出生率下降带来的影响或加速城市地区的人口增长。
5. Population Growth Rate | 人口增长率
The total population growth rate accounts for both natural change and net migration. It is the most complete annual measure of population change, usually given as a percentage.
总人口增长率同时考虑了自然变动和净迁移。这是最全面的年度人口变化指标，通常以百分比表示。
Population Growth Rate (%) = Natural Increase Rate (%) + (Net Migration Rate ÷ 10)
If a country’s natural increase is 1.5% and the net migration rate is 5 per 1000 (i.e. 0.5%), the population growth rate is 2.0% per year. This combined rate is used to estimate future population size and resource demand.
如果某国的自然增长率为1.5%，净迁移率为5‰（即0.5%），则年人口增长率为2.0%。这一综合增长率常用于预测未来人口规模与资源需求。
6. Doubling Time (Rule of 70) | 人口倍增时间（70法则）
Doubling time estimates how many years it will take for a population to double in size if the current growth rate stays constant. The rule of 70 is a simple and widely used approximation in population geography.
倍增时间用于估算在现有增长率保持不变的情况下，人口规模翻一番所需的年数。70法则是人口地理学中一个简单且广泛使用的近似方法。
Doubling Time (years) = 70 ÷ Population Growth Rate (%)
A growth rate of 3.5% ars. This formula highlights how quickly populations can grow even with seemingly modest percentage rates.
增长率为3.5%时，倍增时间为70 ÷ 3.5 = 20年。该公式表明即使看似不太高的百分比增长率也能导致人口快速翻倍。
7. Dependency Ratio | 抚养比
The dependency ratio compares the economically dependent population (young and elderly) to the working-age population. It signals the pressure on the productive part of society to support those who are not in the labour force.
抚养比是将经济上受抚养的人口（少年儿童和老年人口）与劳动年龄人口进行比较。它反映了社会中生产性人口需供养非劳动力人口的压力。
Dependency Ratio (%) = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
A high dependency ratio, for example above 70%, is common in countries with high birth rates or ageing populations. Governments use this ratio to plan for schools, healthcare, and pensions.
高抚养比（例如超过70%）常见于高出生率或人口老龄化的国家。政府利用该比率规划学校、医疗和养老金。
8. Urbanisation Level and Rate of Urbanisation | 城市化水平与城市化速度
Urbanisation level measures the proportion of a country’s population living in urban areas. It shows the degree of urbanisation at one point in time and is distinct from the pace of urban growth.
城市化水平衡量的是一个国家居住在城市地区的人口比例。它反映的是某一时间点的城市化程度，与城市增长的速度有所不同。
Urbanisation Level (%) = (Urban Population ÷ Total Population) × 100
The rate of urbanisation, on the other hand, refers to how quickly the urban percentage is changing. It is calculated as the average annual increase in the urbanisation level over a given period.
而城市化速度是指城市化百分比变化的速度。它计算为给定时期内城市化水平的年均增长量。
Rate of Urbanisation (% per year) = (Urbanisation Levelfinal – Urbanisation Levelinitial) ÷ Number of years
While many high-income countries have a high urbanisation level, the most rapid rates of urbanisation today occur in low- and middle-income countries.
尽管许多高收入国家的城市化水平很高，但当今城市化速度最快的却是中低收入国家。
9. River Discharge and Flow Velocity | 河流流量与流速
River discharge is the volume of water flowing past a given point in a river channel per unit time. It is a fundamental measurement in hydrology and flood studies. Discharge connects channel dimensions with the speed of the water.
河流流量是单位时间内通过河道某一断面的水体体积。它是水文学和洪水研究中的基本量测数据。流量将河道断面尺寸与水流速度联系起来。
Discharge (Q) = Cross-sectional Area (A) × Average Velocity (v)
Average velocity can be measured using a flowmeter or by timing a float over a measured distance. Cross-sectional area is calculated by multiplying channel width by average depth, or more accurately by summing a series of depth measurements across the channel.
平均流速可使用流速仪测量，或通过让浮标漂过已知距离来计时。过水断面面积可通过河道宽度乘以平均水深计算，更精确的方法是将河道横断面划分成若干段深度测量后累加。
10. Gradient (Slope) from Contour Maps | 等高线图坡度
Gradient expresses the steepness of a slope and is commonly tested in map skills. It is the ratio of vertical rise to horizontal distance between two points on a contour map.
坡度表示斜坡的陡峭程度，是地图技能考查中的常见内容。它是等高线图上两点之间的垂直高差与水平距离之比。
Gradient = Vertical Interval (Rise) ÷ Horizontal Distance (Run)
metres over a horizontal distance of 2000 metres gives a gradient of 100 ÷ 2000 = 1 : 20.
两个测量值必须使用相同单位。结果通常化简为1 : X的形式。例如，垂直高差100米，水平距离2000米，则坡度为100 ÷ 2000 = 1 : 20。
11. Map Scale, Distance and Area | 地图比例尺、距离与面积
Map scale expresses the relationship between a distance on the map and the corresponding real-world distance. It is crucial for all map interpretation and fieldwork calculations.
地图比例尺表示图上距离与其对应的实地距离之间的关系。它对所有地图判读和实地考察计算都至关重要。
Real Ground Distance = Map Distance × Scale Factor
With a scale of 1 : 50 000, 1 cm on the map represents 50 000 cm (or 0.5 km) on the ground. Area is often measured by overlaying a grid of squares: count the number of full and part squares covering a feature and multiply by the real area each square represents.
在1 : 50 000的比例尺下，图上1厘米代表实地50 000厘米（即0.5公里）。面积通常通过方格网格法测量：数出覆盖某一地物的完整方格和部分方格数目，再乘以每个方格所代表的实地面积。
a on Ground = (Number of squares counted) × (Area represented by one square on the ground)
For irregular shapes, tracing the boundary onto squared paper and counting squares gives a reasonable estimate. Always check the grid resolution and map scale.
对于不规则图形，将边界描到方格纸上并数方格数可以得到合理估算。务必注意网格分辨率和地图比例尺。
12. Temperature and Precipitation Statistics | 气温与降水统计
Weather and climate studies require basic statistical calculations. These include daily temperature range, mean monthly temperature, total annual precipitation, and the reliability of rainfall.
天气和气候研究需要进行基本统计计算。这些包括每日温差、月平均气温、年总降水量以及降水的可靠性。
Diurnal Temperature Range = Maximum Daily Temp – Minimum Daily Temp (°C)
Mean Monthly Temp = Sum of daily mean temps in a month ÷ Number of days in the month
Mean Annual Temp = Sum of 12 monthly mean temps ÷ 12
Total Annual Precipitation = Sum of all monthly precipitation totals (mm)
Rainfall reliability is often shown using the interquartile range or variation from the long-term mean. A simple indicator is the coefficient of variation, but at IGCSE level you more commonly describe rainfall patterns from a climate graph rather than calculate it exactly.
降水可靠性通常通过四分位距或偏离长期平均值的变化来显示。一个简单的指标是变异系数，但在IGCSE层级，你更多是通过气候图表描述降水格局，而非精确计算。
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