KS3 CCEA Geography: Quick Reference Handbook of Formulas and Theorems | KS3 CCEA 地理：公式定理速查手册

📚 KS3 CCEA Geography: Quick Reference Handbook of Formulas and Theorems | KS3 CCEA 地理：公式定理速查手册

This compact revision guide brings together the essential formulas, calculations and fundamental principles that underpin the KS3 CCEA Geography syllabus. From map skills and population studies to rivers and weather, having these tools at your fingertips will help you solve geographical problems with confidence.

这本精练的复习指南汇集了 KS3 CCEA 地理课程所依托的基本公式、计算方法和核心原理。从地图技能和人口研究到河流与天气，随时掌握这些工具将使你充满信心地解决地理问题。

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1. Map Scale and Distance | 地图比例尺与距离

Map scale is the relationship between a distance measured on a map and the actual distance on the Earth’s surface. It can be expressed in three ways: as a statement (e.g. ‘1 cm represents 1 km’), as a representative fraction (RF) or ratio (1:100 000), and as a linear scale (a drawn line divided into equal parts). To calculate the real-world distance, multiply the map distance by the scale factor.

地图比例尺表示图上测量的距离与地表实际距离之间的关系。它有三种表示方式：文字式（如“1 厘米代表 1 公里”）、分数式（RF）或比例式（1:100 000）以及直线比例尺（一条等分线段）。计算实际距离时，用图上距离乘以比例尺因子即可。

Real Distance (cm) = Map Distance (cm) × Scale Denominator

实际距离（厘米）= 图上距离（厘米）× 比例尺分母

Always convert the final result into more convenient units such as metres or kilometres. For example, if a map with a scale of 1:50 000 measures a distance of 4 cm, the actual distance is 4 × 50 000 = 200 000 cm = 2 km.

始终将最终结果换算成更便捷的单位，如米或千米。例如，在比例尺为 1:50 000 的地图上量得 4 厘米，实际距离就是 4 × 50 000 = 200 000 厘米 = 2 千米。

Scale Type / 比例尺类型	Example / 示例	Meaning / 含义
Statement / 文字式	1 cm to 5 km	1 cm on the map = 5 km on the ground / 图上 1 cm = 实地 5 km
Representative Fraction / 分数式	1 : 500 000	One unit on map represents 500 000 of the same units on ground / 图上 1 单位 = 实地 500 000 相同单位
Linear Scale / 直线比例尺	A drawn bar marked in km / 标有 km 的线段	Direct reading without calculation / 无需计算，直接读值

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2. Grid References and the ‘Corridor and Stairs’ Rule | 网格参考与“先走廓再上楼”法则

Ordnance Survey maps use a grid system to pinpoint locations. A four-figure grid reference identifies a whole grid square; a six-figure reference locates a point within that square to an accuracy of 100 m. The golden rule is ‘along the corridor and up the stairs’: always read the easting (horizontal coordinate) first, then the northing (vertical coordinate).

英国地形测量局地图采用网格系统来精确定位。四位数的网格参考可识别整个方格；六位数网格参考则可定位方格内的某一点，精确至 100 米。黄金法则是“先沿走廊走，再上楼”：始终先读取东距（横坐标），再读取北距（纵坐标）。

To construct a six-figure reference, you divide the square into ten tenths mentally. If a feature lies three-tenths east of easting 64 and seven-tenths north of northing 12, the reference becomes 643127. Practice is essential for speed and accuracy in the exam.

构建六位数网格参考时，需在脑海中将方格等分为十份。如果某地物落在东距 64 以东十分之三且北距 12 以北十分之七处，网格参考即为 643127。为在考试中快速准确地作答，多加练习至关重要。

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3. Gradient and Slope | 梯度与坡度

Gradient expresses how steep a slope is. It is the ratio of the vertical rise (change in height) to the horizontal run (distance). On a contour map, you identify two contour lines, note their heights, and measure the straight-line horizontal distance between them.

梯度表示一个坡有多陡。它是垂直高差（高度变化）与水平距离（水平推移）的比值。在等高线地形图上，选出两条等高线，标注其高程，并量取它们之间的直线水平距离。

Gradient = Vertical Rise (m) ÷ Horizontal Run (m)

梯度 = 垂直高差（米）÷ 水平距离（米）

The result is usually written as a ratio in the form 1 : X, where the rise is reduced to 1. For example, if a hill rises 50 m over a horizontal distance of 200 m, the gradient is 50 ÷ 200 = 0.25 = 1 : 4. A lower value for X indicates a steeper slope.

结果通常写成 1 : X 的比值形式，其中高差被约分成 1。例如，一座山丘在 200 米水平距离内升高 50 米，梯度为 50 ÷ 200 = 0.25 = 1 : 4。X 值越小，表示坡度越陡。

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

Population density measures how crowded an area is. Population distribution describes the pattern of where people live. Density is a straightforward calculation, while distribution is influenced by physical factors (relief, climate, water supply) and human factors (job opportunities, transport).

人口密度衡量一个区域的拥挤程度。人口分布则描述人们居住地点的格局。密度是一个简单的计算，而分布则受自然因素（地形、气候、水源）和人文因素（就业机会、交通）的影响。

Population Density = Total Population ÷ Land Area (km²)

人口密度 = 总人口 ÷ 土地面积（平方千米）

A high density, such as in a city, might exceed 5000 people per km², whereas a rural region could have fewer than 10 people per km². Always show the units (people/km²) in your answer.

高密度（例如城市中）可能超过 5000 人/平方千米，而农村地区可能低于 10 人/平方千米。作答时务必标明单位（人/平方千米）。

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5. Crude Birth Rate, Death Rate and Natural Increase | 粗出生率、死亡率与自然增长

These demographic indicators help geographers understand population change. The crude birth rate (CBR) and crude death rate (CDR) are expressed per 1000 people per year. The natural increase rate (NIR) can be left as a difference per 1000 or converted to a percentage.

这些人口指标帮助地理学者理解人口变化。粗出生率（CBR）和粗死亡率（CDR）以每年每千人表示。自然增长率（NIR）可用每千人之差表示，也可换算成百分比。

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

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

Natural Increase (per 1000) = CBR – CDR

NIR (%) = (CBR – CDR) ÷ 10

For example, a country with a CBR of 25 and a CDR of 9 has a natural increase of 16 per 1000, which equals a growth rate of 1.6%. A negative value indicates natural decrease.

例如，一个国家 CBR 为 25，CDR 为 9，其自然增长为每千分之十六，即 1.6% 的增长率。负值则表示自然减少。

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6. River Discharge and Velocity | 河流流量与流速

River discharge is the volume of water flowing past a point in the channel per second. It depends on the cross-sectional area of the channel and the mean velocity of the flowing water. Velocity can be measured by timing a float over a known distance, while area is found by measuring the width and average depth.

河流流量是指每秒钟流过河道某一点的体积。它取决于河道的横截面积和水流的平均流速。流速可由浮标通过已知距离的时间测得，面积则通过量取宽度和平均深度得出。

Discharge Q (m³/s) = Cross-sectional Area A (m²) × Mean Velocity v (m/s)

流量 Q（立方米/秒）= 横截面积 A（平方米）× 平均流速 v（米/秒）

For a simple rectangular channel, Area = Width (m) × Mean Depth (m). In a fieldwork investigation, taking multiple depth readings and averaging them improves accuracy. Discharge increases downstream as tributaries join the main river.

在简单的矩形河道中，面积 = 宽度（米）× 平均深度（米）。在野外调查中，多次测深并取平均值可提高精度。流量随着支流汇入主干而向下游逐渐增大。

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7. Data Analysis: Mean, Median and Range | 数据分析：平均数、中位数与极差

Geographers frequently use measures of central tendency and spread to summarise data. The mean is the arithmetic average, the median is the middle value when data are ordered, and the range shows the spread between the highest and lowest values.

地理学者常用集中趋势和离散度的度量来总结数据。平均数（均值）是算术平均值，中位数是将数据排序后居中的数值，极差则显示最大值与最小值之间的分布范围。

Mean = Sum of all values ÷ Number of values

Range = Highest value – Lowest value

The median is found by ordering the data; if there is an even number of items, take the mean of the two central numbers. Using these tools, you can compare data sets, such as annual rainfall totals for different locations or pebble sizes along a beach.

找出中位数需要先将数据排序；若项数为偶数，则取中间两个数的平均值。利用这些工具，你可以比较不同数据集，比如不同地点的年降雨总量或海滩沿岸卵石大小。

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8. The Distance Decay Principle | 距离衰减原理

Distance decay explains how the interaction between two places decreases as the distance between them increases. This principle is fundamental to understanding migration patterns, trade, and the location of services. A simplified gravity model can express this relationship.

距离衰减原理说明了两地之间的相互作用如何随着距离增加而减弱。这一原理对于理解迁移模式、贸易以及服务设施选址至关重要。一个简化的引力模型可以表达这种关系。

Interaction ∝ (Population₁ × Population₂) ÷ Distance²

相互作用 ∝ （人口₁ × 人口₂）÷ 距离²

In this model, larger populations generate more interaction, while a greater distance sharply reduces it. Although KS3 does not require numerical use of the formula, grasping the concept helps explain why a big city has a larger sphere of influence than a village.

在这个模型中，人口越多，产生的相互作用越大，而距离越远则使相互作用迅速减弱。虽然 KS3 不要求用该公式进行数值计算，但掌握这一概念有助于解释为何大城市的服务范围比村庄大。

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9. Climate and Weather Calculations | 气候与天气计算

Weather data recorded at a weather station can be processed to reveal climate patterns. The key calculations are the annual temperature range, mean annual temperature, and total annual precipitation. These are essential for constructing climate graphs.

在气象站记录的天气数据经处理后可揭示气候规律。关键的计算有年温差、年均温和年总降水量。这些对于绘制气候图表至关重要。

Annual Temperature Range = Hottest month mean temp – Coldest month mean temp

年温差 = 最热月均温 – 最冷月均温

Mean Annual Temperature = Sum of 12 monthly mean temps ÷ 12

Total Annual Precipitation = Sum of 12 monthly precipitation totals

A large temperature range often indicates a continental climate, while a small range suggests a maritime influence. Similarly, the seasonal distribution of rainfall tells you whether a place has a dry season.

年温差大通常指示大陆性气候，年温差小则表明受海洋影响。同样，降水的季节分配也能说明某地是否有旱季。

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10. Urbanisation Rate and Population Change Formula | 城市化率与人口变化公式

Urbanisation is the increasing proportion of people living in towns and cities. The rate of urbanisation is calculated as a percentage of the total population. Also, overall population change in an area takes into account both natural change and net migration.

城市化是指居住于城镇中的人口比例不断上升的过程。城市化率按占总人口的百分比计算。此外，一个地区的总体人口变化需同时考虑自然变动和净迁移。

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

Population Change = (Births – Deaths) + (Immigration – Emigration)

人口变化 =（出生 – 死亡）+（迁入 – 迁出）

These formulas allow you to compare the growth of megacities in developing countries with slower urban growth in many HICs. Net migration can be positive or negative, dramatically altering a country’s demographic profile.

利用这些公式，你可以比较发展中国家超大城市的增长与许多高收入国家较慢的城市化进程。净迁移可正可负，会显著改变一国的人口结构。

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11. Sustainable Development and Ecological Footprint | 可持续发展与生态足迹

Sustainable development is defined as meeting the needs of the present without compromising the ability of future generations to meet their own needs. While there is no single formula for sustainability, the ecological footprint measures the land and water area needed to support a person’s lifestyle. A smaller footprint implies a more sustainable way of living.

可持续发展被定义为既满足当代人的需求，又不损害后代人满足其自身需求的能力。虽然可持续发展没有单一的公式，但生态足迹衡量了支撑一个人生活方式所需的土地与水域面积。生态足迹越小，意味着生活方式越可持续。

The concept of a ‘footprint’ can be summarised by the idea that the Earth’s resources are finite. If all people lived like the average person in an HIC, we would need several planets to support us. This is a powerful theorem for evaluating resource use.

“足迹”的概念可归结为地球资源是有限的这一思想。如果所有人都像高收入国家普通人那样生活，我们将需要好几个地球来支撑。这是评估资源利用的一项有力定理。

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12. Dependency Ratio | 抚养比

The dependency ratio indicates the pressure on the productive population to support the dependents (those too young or too old to work). It is a vital statistic for planning education, healthcare and pensions.

抚养比反映的是劳动人口需要赡养非自立人口（因年龄太小或太老而不能工作的人）所承受的压力。它是规划教育、医疗和养老金的重要统计指标。

Dependency Ratio = [(Population aged 0-14 + Population aged 65+) ÷ Population aged 15-64] × 100

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

A high dependency ratio, common in some developing countries, means more resources must be directed towards schools and child healthcare. An ageing population in HICs creates a high old-age dependency ratio, putting strain on health and pension systems.

高抚养比常见于一些发展中国家，意味着必须将更多资源投向学校与儿童保健。高收入国家的人口老龄化则造成较高的老年抚养比，对医疗和养老金体系构成压力。

Published by TutorHao | Geography Revision Series | aleveler.com

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