📚 Year 10 CAIE Geography Formulae & Key Concepts Quick Reference | CAIE 十年级地理公式与核心概念速查手册
This quick-reference guide compiles the essential formulae, calculations, and key concepts required for Year 10 CAIE IGCSE Geography. Whether you are revising population dynamics, map skills, or river processes, having these definitions and equations at your fingertips will save time and boost exam confidence. Each entry is paired with a clear explanation to help you apply the formula correctly in data-response and case-study questions.
本速查手册汇编了 CAIE IGCSE 地理十年级所需的基本公式、计算方法和核心概念。无论是复习人口动态、地图技能还是河流过程，这些定义和方程都能帮助你快速查阅，节省时间并增强考试信心。每个条目都配有清晰的解释，帮助你在数据回答和案例分析题中正确运用公式。
1. Population Density and Distribution | 人口密度与分布
Population density is the number of people living per unit of land area, usually per square kilometre (km²). The formula is: Density = Total Population ÷ Land Area (km²). It is a simple measure of how crowded an area is, but it does not show the arrangement of people within that area, which is described by population distribution.
人口密度是指单位土地面积上居住的人口数量，通常以每平方公里（km²）计。公式为：密度 = 总人口 ÷ 土地面积（km²）。它是衡量一个地区拥挤程度的简单指标，但不能表明人口在区域内的分布格局，而人口分布则描述人口的离散或集中程度。
A high population density suggests intense pressure on resources and infrastructure, while low density may indicate a sparse population, often due to physical constraints such as mountains or deserts. When interpreting density, you should always consider the scale of the administrative unit used.
高人口密度表明资源和基础设施面临巨大压力，而低密度则可能意味着人口稀少，通常是由于山地或沙漠等自然条件限制。在解释密度时，应始终考虑所使用行政单元的尺度，因为同一个国家内密度值可能差异很大。
2. Crude Birth Rate, Death Rate and Natural Increase | 粗出生率、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 year: CBR = (Number of births ÷ Total population) × 1000. The Crude Death Rate (CDR) is calculated similarly: CDR = (Number of deaths ÷ Total population) × 1000. These are called “crude” because they do not take age structure into account.
粗出生率（CBR）是指一年内每千人口中的活产婴儿数：CBR = (出生人数 ÷ 总人口) × 1000。粗死亡率（CDR）的计算类似：CDR = (死亡人数 ÷ 总人口) × 1000。之所以称为 “粗”，是因为它们没有考虑人口的年龄结构。
The rate of natural increase (RNI) is derived from the difference between CBR and CDR, usually expressed as a percentage: RNI (%) = (CBR − CDR) ÷ 10. This shows whether a population is growing or declining from natural causes alone, excluding migration.
自然增长率（RNI）由粗出生率与粗死亡率的差值求得，通常以百分比表示：RNI (%) = (CBR − CDR) ÷ 10。它反映仅由出生和死亡引起的人口增长或下降，不包括迁移。
When a country’s death rate falls while the birth rate remains high, the RNI surges, leading to rapid population growth typical of Stage 2 of the Demographic Transition Model. Remember to divide by 10 to convert the per-thousand difference into a percentage.
当一个国家的死亡率下降而出生率保持高位时，自然增长率会飙升，导致人口快速增长，这是人口转变模型第2阶段的典型特征。记住要除以10，将千分比差值转化为百分比。
3. Dependency Ratio and Age Structure | 抚养比与年龄结构
The dependency ratio measures the proportion of the population that is economically dependent on the working-age group. It is calculated as: Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100. The result is the number of dependants per 100 people of working age.
抚养比衡量的是经济上依赖于劳动适龄人口的人口比例。计算公式为：抚养比 = [(0-14岁人口 + 65岁及以上人口) ÷ 15-64岁人口] × 100。结果表示每100名劳动适龄人口所对应的受抚养人数。
A high dependency ratio, common in developing countries with youthful populations, puts strain on education and healthcare services. An ageing population, as seen in many high-income countries, raises the old-age dependency ratio and increases demand for pensions and elderly care. Analysing population pyramids helps explain these pressures.
高抚养比常见于人口年轻的发展中国家，给教育和医疗保健服务带来压力。而许多高收入国家出现的人口老龄化则提高了老年抚养比，并增加了对养老金和老年护理的需求。分析人口金字塔有助于解释这些压力。
4. Net Migration Rate and Migration Types | 净迁移率与迁移类型
Net migration rate accounts for the balance between immigration and emigration, expressed per 1,000 population: Net Migration Rate = [(Number of immigrants − Number of emigrants) ÷ Total population] × 1000. A positive value indicates net in-migration; a negative value shows net out-migration.
净迁移率反映入境移民与出境移民的差额，通常以每千人表示：净迁移率 = [(移民入境人数 − 移民出境人数) ÷ 总人口] × 1000。正值表示净迁入，负值表示净迁出。
Migration can be classified as internal (within a country) or international, and as voluntary or forced. Push factors (e.g., unemployment, natural disasters) drive people away, while pull factors (e.g., job opportunities, safety) attract them. The total population growth rate of an area is the sum of natural increase and net migration.
迁移可分为国内迁移和国际迁移，也可分为自愿迁移和被迫迁移。推力因素（如失业、自然灾害）将人推离原居地，拉力因素（如就业机会、安全）吸引人们迁入。一个地区的总人口增长率是自然增长率与净迁移率之和。
5. Map Skills: Scale, Distance and Area | 地图技能：比例尺、距离与面积
Maps use scale to represent real-world distances. As a representative fraction (RF), 1:50,000 means 1 cm on the map equals 50,000 cm (0.5 km) on the ground. To find ground distance: Ground Distance = Map Distance (cm) × Scale Factor. Convert cm to km by dividing by 100,000.
地图用比例尺来表示真实距离。以数字比例尺（RF）为例，1:50,000表示图上1厘米等于实地50,000厘米（0.5公里）。计算实地距离的公式为：实地距离 = 图上距离 (cm) × 比例尺分母。将厘米转换为公里需除以100,000。
Measuring straight-line distance with a ruler is straightforward, but curved distances (e.g., roads, rivers) require a piece of string or a map measurer. Area of a regular shape on a map can be calculated using length × width on the ground, while irregular areas are estimated by grid squares.
用直尺测量直线距离很简单，但测量弯曲距离（如道路、河流）则需要用细线或地图测量器。地图上规则形状的面积可以用实地长乘以宽计算，而不规则面积则通过网格方格估算。
Always check the scale carefully, and remember to give the answer in the required units (e.g., metres or kilometres). Common exam tasks include comparing distances or describing the locational relationship between two features.
务必仔细检查比例尺，并注意用要求的单位（如米或公里）给出答案。常见的考题任务包括比较距离或描述两个地物之间的位置关系。
6. Gradient and Slope Calculations | 坡度与斜率计算
Gradient expresses the steepness of a slope, typically shown as a ratio or a percentage. The formula is: Gradient = Vertical Interval (Rise) ÷ Horizontal Distance (Run). For example, a rise of 100 metres over a horizontal distance of 2 km yields a gradient of 1:20 (or 5%). Use consistent units.
坡度表示斜坡的陡峭程度，通常用比率或百分比表示。公式为：坡度 = 垂直高差 (上升) ÷ 水平距离 (延伸)。例如，水平距离2公里内上升100米，得出的坡度为1:20（或5%）。务必使用一致的单位。
On a topographic map, to find gradient between two points, you read the contour lines to obtain the rise and measure the horizontal distance using the scale. Gradient is essential for river valley profiles, transport route planning, and understanding mass movement hazards. A steeper gradient (>1:10) often correlates with faster runoff and greater erosion potential.
在地形图上，要找出两点之间的坡度，需要读取等高线来获得高差，并利用比例尺测量水平距离。坡度对于河谷剖面、交通路线规划以及理解重力移动灾害至关重要。较陡的坡度（大于1:10）通常与较快的径流和更大的侵蚀潜力相关。
7. Drainage Basin Metrics: River Discharge and Drainage Density | 流域指标：河流流量与河网密度
River discharge is the volume of water flowing past a given point per unit time, usually in cubic metres per second (m³/s or cumecs). It is calculated by: Discharge (Q) = Cross-sectional Area (A) × Velocity (V). Area is measured in m² and velocity in m/s.
河流流量是指单位时间内通过某一断面的水量，通常以立方米/秒（m³/s 或 cumecs）为单位。计算公式为：流量 (Q) = 横截面积 (A) × 流速 (V)。面积以平方米计，流速以米/秒计。
Drainage density indicates how well a basin is drained by its stream network: Drainage Density = Total length of streams (km) ÷ Area of drainage basin (km²). A high drainage density (many channels per unit area) suggests impermeable rock and rapid storm runoff, leading to a flashy hydrograph
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