Year 9 Cambridge Geography: Formula & Theorem Quick Reference | Year 9剑桥地理：公式定理速查手册

📚 Year 9 Cambridge Geography: Formula & Theorem Quick Reference | Year 9剑桥地理：公式定理速查手册

This concise handbook brings together the key formulas, equations, and calculation-based skills required for Year 9 Cambridge Geography. It covers map work, population studies, river measurements, and data analysis. Keep this reference close during revision to boost your confidence with numerical questions.

本简明手册汇集了 Year 9 剑桥地理所需的核心公式、方程和计算类技能。内容涵盖地图工作、人口研究、河流测量和数据分析。在复习期间反复查阅，可增强处理数值类问题的信心。

1. Map Scale and Distance Conversion | 地图比例尺与距离转换

Map scale expresses how much the real world has been reduced to fit on a map. It may appear as a statement, a representative fraction (RF), or a linear scale. The fundamental relationship is:

地图比例尺表示真实世界缩小了多少以适合地图。它可以文字说明、数字比例尺 (RF) 或直线比例尺出现。基本关系为：

Actual distance = Map distance × Scale denominator

y without multiplication. Always convert units carefully: 100 cm = 1 m, and 1000 m = 1 km.

使用直线比例尺时，可借助比例尺条直接换算，无需乘法。每次都要仔细转换单位：100 厘米 = 1 米，1000 米 = 1 公里。

5 cm on a 1:50,000 map represents 5 × 50,000 = 250,000 cm, which is 2.5 km on the ground.

例如，在 1:50 000 地图上量得 5 厘米，实际距离为 5 × 50,000 = 250,000 厘米，即实地 2.5 公里。

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2. Gradient Calculation | 坡度计算

Gradient describes the steepness of a slope. It is the ratio of vertical rise to horizontal run, both measured in the same units. The formula is:

坡度描述斜坡的陡峭程度。它是垂直上升高度与水平延伸距离的比值，两者须使用相同单位。计算公式为：

Gradient = Vertical interval (VI) / Horizontal equivalent (HE)

Gradients can be written as a ratio (e.g., 1:20), a fraction (1/20), or a percentage (5%). A 1:20 gradient means the land rises 1 unit for every 20 units travelled horizontally.

坡度可以用比值（如 1:20）、分数 (1/20) 或百分比 (5%) 表示。坡度 1:20 指每水平移动 20 个单位，地面上升 1 个单位。

To obtain gradient from a contour map, subtract the lower elevation from the higher to get VI, then measure the straight-line distance between the points for HE (converted to the same units).

在等高线图上求坡度时，将较高点减去较低点得到垂直高差 (VI)，再量取两点间的直线距离作为水平距离 (HE)，并转换为相同单位。

For instance, VI = 50 m and HE = 1000 m, so gradient = 50/1000 = 1/20 or 1:20.

例如，VI = 50 米，HE = 1000 米，坡度 = 50/1000 = 1/20 或 1:20。

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3. Population Density | 人口密度

Population density measures how many people live in a given unit of area. It is usually expressed as people per square kilometre. The formula is:

人口密度衡量单位面积上居住的人数，通常以每平方公里人数表示。公式为：

Population density = Total population / Total land area

This measure helps geographers compare settlement pressure, resource demand, and levels of urbanisation. High densities are typical of city centres, while mountains and deserts have low densities.

该指标有助于地理学家比较居住压力、资源需求和城市化水平。市中心人口密度高，山区和沙漠则密度低。

ple and 250,000 km² of land area has a density of 5,000,000 / 250,000 = 20 people per km².

示例：一国有 500 万人口，面积 25 万平方公里，密度 = 5,000,000 / 250,000 = 20 人/平方公里。

Keep in mind that an average density can hide uneven distribution within a country.

请注意，平均密度可能掩盖地区间的差异。

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4. Natural Increase and Population Change | 自然增长与人口变化

Natural increase (NI) is the difference between births and deaths in a population, excluding migration. It is calculated as:

自然增长 (NI) 指出生与死亡人数之差，不含迁移。计算公式：

Natural increase = Births - Deaths

It is more common to use crude rates per 1000 people:

更常用的是每千人的粗率：

Natural increase rate (per 1000) = Crude birth rate (CBR) - Crude death rate (CDR)

Total population change also includes migration:

总人口变化还需加入迁移：

Total change = (Births - Deaths) + (Immigration - Emigration)

A positive natural increase indicates a growing population; a negative value signals decline. These formulas support analysis of the Demographic Transition Model.

自然增长为正值表示人口在增长，负值表示人口在减少。这些公式对分析人口转变模型很有帮助。

le: CBR = 25 per 1000, CDR = 10 per 1000, so the natural increase rate is 15 per 1000 (1.5%).

示例：CBR = 25‰，CDR = 10‰，自然增长率为 15‰ (1.5%)。

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5. Percentage Change and Growth Rate | 百分比变化与增长率

Percentage change is widely used with population, GDP, deforestation, and other geographical data. The formula is:

百分比变化广泛用于人口、GDP、森林砍伐等地理数据。公式为：

Percentage change = ((New value - Original value) / Original value) × 100

A positive answer shows an increase; a negative answer shows a decrease. This method makes it possible to compare data sets with very different base numbers.

正数表示增加，负数表示减少。该方法能比较基数差异很大的数据系列。

For multi-year periods, you may be asked to calculate a simple percentage change; the compound annual growth rate (CAGR) is not expected at Year 9.

对于多年期数据，通常只需求简单百分比变化；Year 9 不要求计算复合年增长率。

Example: a town' se from 200,000 to 230,000. Percentage change = ((230,000 - 200,000) / 200,000) × 100 = 15% increase.

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