Year 11 Cambridge Geography: Formula & Theorem Quick Reference Handbook | 剑桥十一年级地理：公式定理速查手册

📚 Year 11 Cambridge Geography: Formula & Theorem Quick Reference Handbook | 剑桥十一年级地理：公式定理速查手册

This quick reference guide brings together the essential calculations, key formulas, and fundamental quantitative concepts required for the Year 11 Cambridge Geography syllabus. Use it to revise map skills, population indicators, climate statistics, river discharge, and the Human Development Index – all presented with clear step-by-step explanations in both English and Chinese.

本速查手册汇集了剑桥十一年级地理课程中必须掌握的核心计算、关键公式以及重要定量概念。内容涵盖地图技能、人口指标、气候统计、河流流量和人类发展指数等，全部配以清晰的中英双语逐步讲解，方便快速复习。

1. Birth Rate & Total Fertility Rate | 出生率与总和生育率

The crude birth rate (CBR) measures the number of live births per 1000 people in a given year. It is a fundamental demographic indicator used to compare fertility across populations.

粗出生率衡量的是某一年内每1000人中的活产婴儿数。它是比较不同人口生育水平的基本人口指标。

Birth Rate = (Number of live births / Total population) × 1000

出生率 = (活产婴儿数 / 总人口) × 1000

While the birth rate gives a general picture, the Total Fertility Rate (TFR) provides a more refined measure: the average number of children a woman would have during her reproductive years, assuming current age-specific fertility rates remain constant. A TFR of about 2.1 is considered replacement level in developed countries.

出生率提供的是总体情况，而总和生育率则更为精确：它表示在现行各年龄别生育率保持不变的情况下，一名妇女在育龄期间预期生育的平均子女数。在发达国家，总和生育率约2.1被视为更替水平。

2. Rate of Natural Increase | 人口自然增长率

The Rate of Natural Increase (RNI) shows how fast a population is growing (or shrinking) purely from births and deaths, excluding migration. It is often expressed as a percentage.

人口自然增长率反映的是仅由出生和死亡（不含迁移）导致的人口增长或减少速度，通常以百分比表示。

RNI (%) = [(Births − Deaths) / Total population] × 100

自然增长率 (%) = [(出生人数 − 死亡人数) / 总人口] × 100

Alternatively, you can calculate it directly from birth and death rates: RNI (per 1000) = Birth rate − Death rate. Then divide by 10 to convert to a percentage. A positive RNI indicates natural increase, while a negative RNI signals natural decrease.

你也可以直接用出生率和死亡率计算：自然增长率（每千人）= 出生率 − 死亡率。再除以10即可转换为百分比。正自然增长率表示自然增长，负值则表示自然减少。

3. Population Density | 人口密度

Population density describes how crowded an area is. It is a simple but essential concept for understanding settlement patterns, resource pressure, and service provision.

人口密度描述一个地区的拥挤程度。这个简单概念对于理解聚落分布、资源压力和服务供给至关重要。

Population Density = Total population / Land area (km²)

人口密度 = 总人口 / 土地面积（平方公里）

Be careful with units: land area should be in square kilometres (km²). For very small areas, you might see persons per hectare; 1 km² = 100 hectares. Always check which unit the exam question expects.

注意单位：土地面积应用平方公里。在小范围地区，有时会用到“人/公顷”；1 平方公里 = 100 公顷。答题时务必看清题目要求的单位。

4. Dependency Ratio | 抚养比

The dependency ratio compares the economically dependent population (young and old) with the working-age population. It is a useful indicator of the pressure on the productive segment of society.

抚养比将需要经济供养的人口（幼年与老年）与劳动年龄人口进行比较，是反映社会生产性群体负担程度的有用指标。

Dependency Ratio (%) = [(Population aged 0−14 + Population aged 65+) / Population aged 15−64] × 100

抚养比 (%) = [(0−14岁人口 + 65岁及以上人口) / 15−64岁人口] × 100

A high dependency ratio, common in many developing countries with youthful populations, can strain education and healthcare systems. An ageing population in developed countries creates a different type of dependency pressure.

许多发展中国家因年轻人口多而抚养比较高，这会给教育和医疗系统带来压力。发达国家人口老龄化则带来另一种抚养压力。

5. Sex Ratio | 性别比

The sex ratio measures the number of males per 100 females in a population. It helps reveal patterns of gender imbalance, often influenced by migration, birth preferences, or conflict.

性别比衡量的是每100名女性对应的男性人数，有助于揭示由于迁移、生育偏好或冲突等因素造成的性别失衡模式。

Sex Ratio = (Number of males / Number of females) × 100

性别比 = (男性人口 / 女性人口) × 100

A ratio above 100 means there are more males than females; below 100 indicates more females. The global average is roughly 101–102 males per 100 females at birth, but this varies regionally.

数值高于100表示男性多于女性，低于100则表示女性多于男性。全球出生性别比大约为每100名女性对应101–102名男性，但地区差异显著。

6. Level of Urbanisation | 城市化水平

Urbanisation level is the percentage of a country’s total population living in urban areas. It is a key measure of development and internal migration trends.

城市化水平是指一国总人口中居住在城市地区的人口所占百分比，是衡量发展水平和国内迁移趋势的关键指标。

Urbanisation Level (%) = (Urban population / Total population) × 100

城市化水平 (%) = (城市人口 / 总人口) × 100

The rate of urbanisation – how fast this percentage is growing over time – is just as important as the level itself. Rapid urbanisation in emerging economies often brings challenges such as housing shortages and infrastructure strain.

城市化速度——即这个百分比随时间的增长速度——与城市化水平本身同样重要。新兴经济体的快速城市化往往带来住房短缺和基础设施紧张等挑战。

7. Map Scale and Distance | 地图比例尺与距离

Map scales allow you to convert a measurement on a map to the actual distance on the ground. For Cambridge Geography, you must be able to use both linear (graphic) scales and ratio (representative) scales.

地图比例尺能够将图上测量的距离换算为实地真实距离。在剑桥地理考试中，你需要同时掌握直线比例尺和数字比例尺的使用。

Actual distance = Map distance × Scale factor

实地距离 = 图上距离 × 比例尺倍数

For a 1:50 000 map, 1 cm on the map represents 50 000 cm (or 0.5 km) on the ground. When using a linear scale, simply mark the map distance on the edge of a piece of paper and read off the ground distance. Always express your answer in km or metres, and show the unit.

对于1:50 000地形图, 图上1厘米代表实地50 000厘米 (0.5公里)。使用直线比例尺时，只需在纸条边缘标出图上的距离，然后对应读取实地距离。答案务必以公里或米为单位，并注明单位。

8. Area Calculation on Maps | 地图面积测算

Estimating area from a map is a core practical skill. Common methods include counting grid squares (each small square on a 1:50 000 map is typically 1 km² after scale conversion) or applying geometric formulas for regular shapes.

在地图上估算面积是一项核心操作技能。常用方法包括数格网方格（经比例转换后，1:50 000地图上每个小方格通常代表1 平方公里），或对规则图形应用几何公式。

Shape 图形	Formula 公式
Rectangle 矩形	Area = length × width 面积 = 长 × 宽
Triangle 三角形	Area = ½ × base × height 面积 = ½ × 底 × 高
Irregular area 不规则图形	Count full grid squares + ½ partial squares 数整格方格数 + ½ 不满格方格数

All map distances must be converted to ground distances before calculating the area. For irregular areas, tracing the shape onto graph paper and counting squares is a reliable technique in the exam.

所有图上距离都要先转换为实地距离才能计算面积。对于不规则图形，在考试中将轮廓描到方格纸上并数格网是一种可靠的方法。

9. Gradient Calculation | 坡度计算

Gradient measures the steepness of a slope, often used when analysing contour lines on a topographic map. It compares the vertical rise to the horizontal distance.

坡度衡量斜坡的陡峭程度, 常用于分析地形图上的等高线。它比较的是垂直高差与水平距离之间的关系。

Gradient = Vertical interval (rise) / Horizontal equivalent (run)

坡度 = 垂直高差 / 水平距离

Both measurements must be in the same units. A gradient is typically expressed as a ratio, e.g. 1:12, meaning a 1 m rise for every 12 m horizontally. You may also see it as a fraction or percentage. On a 1:50 000 map, use contour lines to find the height difference, and the scale to find the horizontal distance.

两个数值必须使用相同单位。坡度通常表示为一个比例，例如1:12，意味着每水平移动12米，高度上升1米。也可能看到分数或百分比形式。在1:50 000地形图上，利用等高线求高差，利用比例尺求水平距离。

10. River Discharge | 河流流量

River discharge is the volume of water flowing past a cross‑section of a river channel per unit of time. It is fundamental to understanding flood risk, erosion, and water resource management.

河流流量是指单位时间内通过河槽某一横截面的水量，是理解洪水风险、河流侵蚀和水资源管理的基础。

Q = A × v

流量 (Q) = 横截面积 (A) × 流速 (v)

Q is discharge in cubic metres per second (m³/s), A is the cross‑sectional area of the river (m²), and v is the average flow velocity (m/s). To find A, multiply the average channel width by the average depth. In fieldwork, you may measure velocity with a float and distance with a tape measure.

Q代表流量（立方米/秒），A代表河流横截面积（平方米），v 代表平均流速（米/秒）。计算A时，将河道的平均宽度乘以平均水深。在实地考察中，你可能会用浮标测流速，用卷尺量距离。

11. Temperature and Precipitation Calculations | 气温与降水计算

Climate statistics help geographers describe and compare weather patterns. Two of the most common calculations are temperature range and mean precipitation.

气候统计数据有助于地理学者描述和比较天气模式。最常见的两种计算是气温范围和平均降水量。

Temperature Range = Tₘₐₓ − Tₘᵢₙ

气温较差 = 最高温 (Tₘₐₓ) − 最低温 (Tₘᵢₙ)

The annual temperature range is the difference between the highest and lowest mean monthly temperatures. Mean annual precipitation is simply the total rainfall for the year divided by 12. When analysing climate graphs, always state the units (°C for temperature, mm for precipitation) and identify the months of maximum and minimum values.

年较差即为最高月均温与最低月均温之差。年均降水量即全年总降雨量除以12。分析气候图表时，务必说明单位（气温用℃，降水用毫米），并指出最高值和最低值出现的月份。

12. Human Development Index (HDI) | 人类发展指数

The Human Development Index (HDI) is a composite indicator created by the United Nations. It combines health, education, and standard of living into a single value between 0 and 1, making cross‑country comparisons more holistic than income alone.

人类发展指数是由联合国创建的综合指标。它将健康、教育和生活水平综合为一个介于0和1之间的值，使跨国比较比单纯收入数据更加全面。

HDI = ∛(I_health × I_education × I_income)

HDI = ∛(健康指数 × 教育指数 × 收入指数)

I_health uses life expectancy at birth. 健康指数使用预期寿命。
I_education combines mean years of schooling and expected years of schooling. 教育指数综合了平均受教育年限和预期受教育年限。
I_income uses Gross National Income (GNI) per capita, adjusted to reflect diminishing marginal utility. It is expressed as a logarithm to ensure that income increases above a certain threshold have less impact on HDI. 收入指数使用人均国民总收入，并经调整反映边际效用递减。它采用对数形式，确保收入超过一定阈值后再进一步增长对HDI的影响减弱。

Each sub-index is normalised on a 0–1 scale before the geometric mean is calculated. A higher HDI indicates higher human development. In the Cambridge syllabus, you need to understand how HDI is calculated, interpret it, and discuss its advantages and limitations compared with single measures such as GDP.

每个分项指数都先归一化为0–1之间的值，再计算几何平均数。HDI越高，人类发展水平越高。在剑桥大纲中，你需要理解HDI的计算方法，解读其含义，并讨论它与GDP等单一指标相比的优势和局限性。

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Year 11 Cambridge Geography: Formula & Theorem Quick Reference Handbook | 剑桥十一年级地理：公式定理速查手册