Cambridge IGCSE Geography Year 10: Formula & Theorem Quick Reference | 剑桥IGCSE地理十年级：公式定理速查手册

📚 Cambridge IGCSE Geography Year 10: Formula & Theorem Quick Reference | 剑桥IGCSE地理十年级：公式定理速查手册

This quick reference handbook compiles the essential formulas, key definitions, and calculation methods required for the Cambridge IGCSE Geography Year 10 syllabus. It covers population dynamics, urbanisation, economic development indicators, map skills, fieldwork measurements in river environments, and climate statistics. Each entry is presented with a concise explanation and the central formula, enabling rapid revision and exam preparation.

本速查手册汇编了剑桥 IGCSE 地理十年级教学大纲所必需的关键公式、重要定义和计算方法。内容涵盖人口动态、城市化、经济发展指标、地图技能、河流环境的实地测量以及气候统计。每个条目都配有简明解释和核心公式，以便快速复习和备考。

1. Population Change Formulas | 人口变化公式

The crude birth rate (CBR) measures the number of live births per 1000 people in a given year. It is defined as:

CBR = (Number of live births ÷ Total population) × 1000

粗出生率（CBR）衡量某一年内每千人中的活产婴儿数，定义如下：

CBR =（活产婴儿数 ÷ 总人口）× 1000

The crude death rate (CDR) indicates the number of deaths per 1000 people per year. It is calculated as:

CDR = (Number of deaths ÷ Total population) × 1000

粗死亡率（CDR）表示每年每千人中的死亡人数。计算公式为：

CDR =（死亡人数 ÷ 总人口）× 1000

Natural increase per 1000 population is the simple difference between CBR and CDR:

Natural Increase (per 1000) = CBR − CDR

每千人的自然增长为粗出生率与粗死亡率之差：

自然增长（每千人）= CBR − CDR

To express natural increase as a percentage, divide the per-thousand figure by 10:

Natural Increase (%) = (CBR − CDR) ÷ 10

将每千人的自然增长转换为百分比时，需除以 10：

自然增长率（%）=（CBR − CDR）÷ 10

The net migration rate (NMR) accounts for the balance between immigrants and emigrants per 1000 population:

= [(Number of immigrants − Number of emigrants) ÷ Total population] × 1000

净迁移率（NMR）表示每千人中迁入与迁出人数的平衡状态：

NMR = [（迁入人数 − 迁出人数）÷ 总人口] × 1000

The overall population growth rate, combining natural change and net migration, can be expressed as a percentage:

Population Growth Rate (%) = [(CBR − CDR) + NMR] ÷ 10

综合自然变动与净迁移的总人口增长率百分比公式如下：

人口增长率（%）= [（CBR − CDR）+ NMR] ÷ 10

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2. Population Density and Distribution | 人口密度与分布

Population density describes the average number of people living per unit area, usually square kilometres. Arithmetic density is the most common measure:

Population Density = Total population ÷ Land area (km²)

人口密度指单位土地面积（通常为平方公里）上居住的平均人数。最常用的衡量指标是算术人口密度：

人口密度 = 总人口 ÷ 土地面积（km²）

When interpreting population distribution, areas can be described as densely or sparsely populated. Density alone does not explain distribution patterns; factors such as relief, climate, and economic opportunities must be considered.

在解释人口分布时，可描述为“人口密集”或“人口稀少”。密度本身并不能解释分布规律，还需考虑地形、气候和就业机会等因素。

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3. Dependency Ratio | 抚养比

The dependency ratio is an age-population measure that compares the economically dependent groups (young and old) to the working-age population. It indicates the pressure on the productive population to support dependents:

tion aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100

抚养比是按年龄分组衡量受抚养人口（幼年和老年）与劳动年龄人口的比例，用以显示劳动人口所承受的抚养压力：

抚养比 = [（0–14 岁人口 + 65 岁以上人口）÷ 15–64 岁人口] × 100

A high dependency ratio can signal greater demand for schools, healthcare, and pensions, while a lower ratio often indicates a larger workforce relative to dependents.

抚养比高可能意味着对教育、医疗和养老金的更大需求，而较低的抚养比通常表明劳动力人口相对较多。

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4. Urbanisation Rate | 城市化率

The level of urbanisation expresses the share of a country's population living in urban settlements. It is a key indicator of spatial development:

Urbanisation Rate (%) = (Urban population ÷ Total population) × 100

城市化率反映一国居住在城镇地区的人口比重，是衡量空间发展的重要指标：

城市化率（%）=（城镇人口 ÷ 总人口）× 100

The rate of urbanisation tells how quickly the urban share is growing over time. It differs from urbanisation level, which is a snapshot of the proportion at one point in time.

城市化速率表示城镇人口比重随时间的增长速度，与仅仅反映某一时点比重的城市化率有所不同。

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5. Economic Indicators | 经济指标

Gross Domestic Product (GDP) per capita divides the total value of all goods and services produced in a country by its population, offering a rough measure of average economic output:

GDP per capita = Total GDP ÷ Population

人均国内生产总值（人均 GDP）将一个国家生产的全部商品和服务的总价值除以人口数，粗略衡量平均经济产出：

人均 GDP = 总 GDP ÷ 人口

Gross National Income (GNI) per capita includes income earned by residents from abroad and excludes income sent abroad by non-residents. It is often used alongside GDP per capita for a more complete picture.

人均国民总收入（GNI per capita）包含本国居民从国外获得的收入，并扣除支付给国外人士的部分。常与人均 GDP 并用，以更全面地反映收入状况。

GNI per capita = Total GNI ÷ Population

人均 GNI = 总 GNI ÷ 人口

The Human Development Index (HDI) is a composite statistic combining life expectancy at birth, education indicators (mean years of schooling and expected years of schooling), and gross national income per capita. Although its calculation is beyond the scope of this level, HDI values range from 0 to 1, with higher scores reflecting greater human development.

人类发展指数（HDI）是一个综合指标，融合了预期寿命、教育指标（平均受教育年限和预期受教育年限）以及人均国民总收入。尽管详细计算超出本阶段要求，HDI 取值介于 0 到 1 之间，数值越高代表人类发展水平越高。

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6. Map Scale and Distance | 地图比例尺与距离

Map scale expresses the ratio between a distance on the map and the corresponding distance on the ground. For a ratio scale 1 : X, the actual ground distance is obtained by multiplying the map distance by the scale denominator X:

Ground Distance = Map Distance × X

地图比例尺表示图上距离与对应实地距离之比。对于比例尺 1 : X，实际地面距离可通过将图上距离乘以分母 X 得到：

实地距离 = 图上距离 × X

ample, on a 1 : 50 000 map, a measured length of 4 cm corresponds to 4 cm × 50 000 =

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