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

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

This handbook compiles the essential formulas, calculations, and key concepts needed for KS3 Cambridge Geography. It includes map skills, population statistics, climate measurements, fieldwork techniques, and development indicators. Each section explains the method and gives a clear worked example so you can apply these tools confidently in classwork, homework, and assessments.

本手册汇集了 KS3 剑桥地理所需的基本公式、计算方法和关键概念，涵盖地图技能、人口统计、气候测量、实地考察技术以及发展指标。每个部分都解释了方法并给出了清晰的示例，便于你在课堂练习、作业和测验中自信地应用这些工具。

1. Map Scales: Converting Map Distance to Real Distance | 地图比例尺：图上距离与实际距离换算

Map scale tells you how much smaller the map is compared to the real world. The most common scale on KS3 Ordnance Survey maps is 1:25 000, meaning 1 cm on the map equals 25 000 cm in reality. To find the real straight-line distance in metres or kilometres, measure the distance on the map in centimetres and multiply by the scale denominator, then convert to the desired unit.

地图比例尺表示地图比实际世界缩小了多少。KS3 常用的测量局地图比例尺为 1:25 000，即图上 1 cm 代表实地 25 000 cm。计算实际直线距离（单位米或千米）时，先量出图上的厘米数，再乘以比例尺分母，最后换算成所需单位。

Actual distance (cm) = Map distance (cm) × Scale denominator

实际距离 (cm) = 图上距离 (cm) × 比例尺分母

Example: On a 1:50 000 map, a footpath measures 4.2 cm. Actual distance = 4.2 × 50 000 = 210 000 cm = 2 100 m = 2.1 km.

示例：在一张 1:50 000 的地图上，一条步道长度为 4.2 cm。实际距离 = 4.2 × 50 000 = 210 000 cm = 2 100 m = 2.1 km。

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2. Compass Directions and Bearings | 罗盘方向与方位角

Direction can be given as a 16-point compass direction (e.g. NW, ESE) or as a three-figure bearing measured clockwise from north. Bearings are always written with three digits, from 000° to 360°.

方向可以用 16 方位罗盘描述（如西北、东南偏东），也可以用从正北顺时针量取的三位方位角表示。方位角必须用三位数字书写，范围从 000° 到 360°。

Bearing = angle measured clockwise from North, written as 3 digits

方位角 = 从正北顺时针测量的角度，写成三位数

Example: A hilltop is exactly east of your position. Its bearing is 090°. If it lies exactly southwest, the bearing is 225°.

示例：山顶在你的正东方向，其方位角为 090°。若正好在西南方向，则方位角为 225°。

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3. Contour Lines and Gradient | 等高线与坡度

Contour lines connect points of equal height above sea level. The vertical interval (contour interval) is the difference in height between two successive contours. Gradient tells you how steep a slope is and is calculated as the vertical rise divided by the horizontal distance (run). A steeper slope has a larger gradient ratio.

等高线连接海平面上高度相等的点。相邻两条等高线之间的高度差称为等高距。坡度表示斜坡的陡峭程度，等于垂直升高除以水平距离。坡度比越大，斜坡越陡。

Gradient = Vertical rise (m) ÷ Horizontal distance (m)

坡度 = 垂直升高 (m) ÷ 水平距离 (m)

The result is often simplified to a ratio, e.g. 1:5 meaning for every 5 m horizontally you go up 1 m. To compare slopes easily, always keep the vertical part as 1.

结果常简化为比，如 1:5 表示每水平移动 5 m 上升 1 m。为便于比较，通常将比值的前项化为 1。

Example: The contour lines show a rise of 100 m over a horizontal map distance of 800 m. Gradient = 100 ÷ 800 = 0.125 = 1:8.

示例：等高线显示在水平距离 800 m 内上升了 100 m。坡度 = 100 ÷ 800 = 0.125 = 1:8。

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4. Grid References: 4-Figure and 6-Figure | 网格坐标：四位坐标与六位坐标

Ordnance Survey maps have a grid of blue lines called eastings (vertical lines, read first) and northings (horizontal lines, read second). A 4-figure grid reference locates a 1 km × 1 km square, while a 6-figure grid reference pinpoints a location within 100 m × 100 m. Remember the rule: ‘along the corridor and up the stairs’ – eastings first, then northings.

测量局地图上有蓝色网格线，竖线称为东距线（先读），横线称为北距线（后读）。四位坐标可定位一个 1 km × 1 km 的方格，六位坐标则能精确到 100 m × 100 m 的位置。记住口诀：‘先横后纵’——即先读东距，再读北距。

6-figure reference = easting 3-digit + northing 3-digit (based on tenths inside square)

六位坐标 = 3 位东距数字 + 3 位北距数字（根据方格的十分数估算）

Example: A church lies 4 tenths across from easting 62 and 7 tenths up from northing 34 inside square 6234. Its 6-figure reference is 624347.

示例：一座教堂位于方格 6234 内，从 62 号东距线向右 4/10，从 34 号北距线向上 7/10。其六位坐标为 624347。

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5. Climate Graphs: Temperature Range and Total Precipitation | 气候图表：气温范围和总降水量

A climate graph shows average monthly temperature (usually as a red line with dots) and precipitation (blue bars). The annual temperature range is the difference between the hottest and coldest month’s average temperatures. Total annual precipitation is the sum of all 12 months’ rainfall.

气候图表用红色带点的折线表示月平均气温，用蓝色条形表示降水量。气温年较差是最热月与最冷月平均气温之差。年总降水量为 12 个月的降水总和。

Temperature range (°C) = Hottest month temp. – Coldest month temp.

气温年较差 (°C) = 最热月气温 – 最冷月气温

Total precipitation (mm) = Sum of all monthly precipitation values

总降水量 (mm) = 各月降水量之和

Example: A place has January 2°C, July 22°C. Range = 22 – 2 = 20°C. If monthly rainfall figures are 50, 45, 40 … mm, add them all to find the yearly total.

示例：某地 1 月 2°C，7 月 22°C。年较差 = 22 – 2 = 20°C。若各月降水量为 50, 45, 40 … mm，全部相加得到年总量。

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6. Population Density | 人口密度

Population density tells you how crowded an area is on average. It is measured as the number of people per square kilometre. This formula helps compare urban and rural settlements or different countries.

人口密度表示一个地区平均拥挤程度，以每平方千米的人数来衡量。这个公式有助于比较城市与乡村聚落或不同国家。

Population density (people/km²) = Total population ÷ Area (km²)

人口密度 (人/km²) = 总人口 ÷ 面积 (km²)

Example: A country has 5 million people and an area of 200 000 km². Density = 5 000 000 ÷ 200 000 = 25 people per km².

示例：某国有 500 万人口，面积 20 万平方千米。人口密度 = 5 000 000 ÷ 200 000 = 25 人/km²。

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7. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率和自然增长率

These vital rates are given per 1000 people per year. The birth rate is the number of live births per 1000 people, death rate the number of deaths per 1000. Natural increase (or decrease) shows whether population is growing excluding migration. Natural increase rate is often expressed as a percentage.

这些生命统计率以每年每千人中的发生次数表示。出生率是每千人中的活产婴儿数，死亡率是每千人中的死亡人数。自然增长（或减少）显示不含迁移的人口变动情况，自然增长率常以百分比表示。

Crude Birth Rate (per 1000) = (Number of births ÷ Total population) × 1000

粗出生率 (‰) = (出生人数 ÷ 总人口) × 1000

Natural increase (per 1000) = Birth rate – Death rate

自然增长率 (‰) = 出生率 – 死亡率

To turn per 1000 into a percentage, divide by 10. Example: Birth rate 20/1000, death rate 8/1000. Natural increase = 12 per 1000, or 1.2%.

要将千分率转为百分比，除以 10。示例：出生率 20‰，死亡率 8‰。自然增长率 = 12‰，即 1.2%。

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8. River Velocity and Discharge (Fieldwork) | 河流流速和流量（实地考察）

River fieldwork often involves measuring velocity using a float and stopwatch. The velocity is distance travelled by the float divided by the time taken. Discharge is the volume of water flowing past a point per second, calculated from the cross-sectional area and velocity.

河流实地考察常用浮标和秒表测量流速。流速等于浮标漂流的距离除以所用时间。流量是每秒流过某断面的水量，由横截面积和流速计算得出。

Velocity (m/s) = Distance (m) ÷ Time (s)

流速 (m/s) = 距离 (m) ÷ 时间 (s)

Discharge (m³/s) = Cross-sectional area (m²) × Average velocity (m/s)

流量 (m³/s) = 横截面积 (m²) × 平均流速 (m/s)

For a rectangular channel, cross-sectional area = width × average depth. Example: A float travels 10 m in 25 s. Velocity = 10 ÷ 25 = 0.4 m/s. If the stream is 2 m wide and average depth 0.3 m, area = 0.6 m². Discharge = 0.6 × 0.4 = 0.24 m³/s.

对于矩形河道，横截面积 = 宽度 × 平均深度。示例：浮标 25 秒漂流 10 m。流速 = 10 ÷ 25 = 0.4 m/s。若溪流宽 2 m，平均深度 0.3 m，则面积 = 0.6 m²。流量 = 0.6 × 0.4 = 0.24 m³/s。

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9. Latitude and Longitude: Locating Places on the Globe | 经度和纬度：在地球上定位地点

Latitude lines run horizontally, measuring degrees north or south of the Equator (0°). Lines of longitude run vertically, measuring degrees east or west of the Prime Meridian (0°). Always give latitude first, then longitude. Each degree can be subdivided into 60 minutes (′), though for KS3 whole degrees are enough.

纬度线水平环绕，测量赤道（0°）以北或以南的度数。经度线纵向分布，测量本初子午线（0°）以东或以西的度数。书写时总是先写纬度，再写经度。每一度可细分为 60 分（′），不过 KS3 阶段掌握整度数即可。

Coordinates: (Latitude °N/S, Longitude °E/W)

坐标： (纬度 °N/S, 经度 °E/W)

Example: London is approximately 51°N, 0°W. Rio de Janeiro is 23°S, 43°W. Note the compass direction letters are essential.

示例：伦敦大致位于 51°N, 0°W。里约热内卢位于 23°S, 43°W。注意必须标明南北、东西方向字母。

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10. Time Zones and Longitude | 时区与经度

The Earth rotates 360° in 24 hours, so it moves 15° of longitude per hour. Time zones are roughly 15° wide. To find the time difference between two places, divide the difference in longitude by 15. Places to the east are later (add time), to the west are earlier (subtract).

地球每 24 小时自转 360°，因此每小时转动 15° 经度。时区大致宽 15°。要计算两地时差，用经度差除以 15。东边的地方时间更晚（加时间），西边的地方时间更早（减时间）。

Time difference (hours) = Longitude difference (°) ÷ 15

时差 (小时) = 经度差 (°) ÷ 15

Example: City A is at 30°E, City B at 15°W. Total difference = 30 + 15 = 45°. Time difference = 45 ÷ 15 = 3 hours. City A is ahead of City B by 3 hours.

示例：A 城位于 30°E，B 城位于 15°W。经度差 = 30 + 15 = 45°。时差 = 45 ÷ 15 = 3 小时。A 城比 B 城快 3 小时。

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11. Development Indicators: GNI per Capita and Literacy Rate | 发展指标：人均国民总收入和识字率

Development is measured using economic, social and environmental indicators. Two common ones are GNI per capita (Gross National Income divided by population, usually in US$) and literacy rate (percentage of adults who can read and write). These help classify countries as HICs, MICs or LICs.

发展程度通过经济、社会和环境指标来衡量。常用的有人均国民总收入（国民总收入除以人口，通常以美元计）和识字率（能读写的成年人百分比）。这些指标有助于将国家划分为高收入、中等收入或低收入国家。

GNI per capita (US$) = Total GNI ÷ Total population

人均国民总收入 (美元) = 国民总收入 ÷ 总人口

Literacy rate (%) = (Number of literate adults ÷ Total adult population) × 100

识字率 (%) = (识字成年人数量 ÷ 成年人总数) × 100

Example: A country has a GNI of 800 billion dollars and 40 million people. GNI per capita = 800 000 000 000 ÷ 40 000 000 = 20 000 US$. If 38 million out of 42 million adults can read, literacy rate = (38 ÷ 42) × 100 ≈ 90.5%.

示例：某国国民总收入 8000 亿美元，人口 4000 万。人均 GNI = 800 000 000 000 ÷ 40 000 000 = 20 000 美元。若 4200 万成年人中有 3800 万识字，识字率 = (38 ÷ 42) × 100 ≈ 90.5%。

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12. Population Pyramids and Dependency Ratio | 人口金字塔与抚养比

A population pyramid shows the age and sex structure of a population. The dependency ratio tells us how many dependents (aged 0–14 and 65+) there are for every 100 working-age people (15–64). A high ratio means greater pressure on the working population.

人口金字塔显示人口的年龄和性别结构。抚养比表示每 100 名劳动年龄人口（15–64 岁）需要抚养多少非劳动年龄人口（0–14 岁和 65 岁以上）。比率越高，劳动人口的压力越大。

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

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

Example: A town has 2 000 children, 5 000 working-age adults and 1 000 elderly. Dependents = 2 000 + 1 000 = 3 000. Dependency ratio = (3 000 ÷ 5 000) × 100 = 60. This means 60 dependents for every 100 workers.

示例：某镇有 2000 名儿童，5000 名劳动年龄成人，1000 名老人。受抚养人口 = 2000 + 1000 = 3000。抚养比 = (3000 ÷ 5000) × 100 = 60，即每 100 名劳动者需抚养 60 人。

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