📚 Year 7 CAIE Geography: Quick Reference Guide of Formulas and Theorems | Year 7 CAIE 地理：公式定理速查手册
Geography is not just about memorising places on a map — it’s about measuring, calculating, and interpreting patterns in the world around us. In Year 7 CAIE Geography, you will often need to use simple formulas and rules to make sense of data, maps, and figures. This guide brings together the most essential formulas and theorems you will encounter, from map scale and distance to population density and temperature range. Keep it handy as your quick revision companion.
地理学不仅仅是记住地图上的地点，它还涉及测量、计算和解读我们周围世界的模式。在 Year 7 CAIE 地理课程中，你经常需要使用简单的公式和规则来理解数据、地图和图表。本指南汇集了你将遇到的最重要的公式和定理，从地图比例尺和距离到人口密度和气温变化范围。把它放在手边，作为你快速复习的好帮手。
1. Map Scale | 地图比例尺
Map scale tells you the relationship between a distance on the map and the actual distance on the ground. Three common types are: ratio scale, word scale, and line scale. The formula for converting between map distance and real distance is:
地图比例尺告诉你地图上的距离与地面上实际距离之间的关系。常见的三种类型是：比例尺、文字比例尺和线段比例尺。地图距离与实际距离之间的换算公式为：
Actual Distance = Map Distance × Scale Factor
实际距离 = 图上距离 × 比例尺因子
For example, with a scale of 1:50,000, 1 cm on the map equals 50,000 cm (or 0.5 km) in reality. Always ensure units are consistent before calculating.
例如，在 1:50,000 的比例尺下，图上 1 厘米等于实际 50,000 厘米（即 0.5 公里）。计算前务必确保单位一致。
2. Measuring Distance on a Map | 在地图上测量距离
Straight-line distance can be measured with a ruler and converted using the map scale. For curved distances (such as roads or rivers), use a piece of string, then straighten it against the ruler. The formula remains:
直线距离可以用直尺测量，然后利用比例尺进行换算。对于弯曲距离（如道路或河流），使用一根细绳，然后将其拉直靠在直尺上测量。公式仍然是：
Real Distance = Measured Length (cm) × Scale Factor ÷ 100,000 (to get km)
实际距离 = 测量长度（厘米） × 比例尺因子 ÷ 100,000 （得到公里）
If the scale is 1:25,000 and you measure 8 cm, then real distance = 8 × 25,000 = 200,000 cm = 2 km. Always double-check your unit conversion.
如果比例尺是 1:25,000，你测量了 8 厘米，那么实际距离 = 8 × 25,000 = 200,000 厘米 = 2 公里。始终仔细检查单位换算。
3. Calculating Area on a Map | 在地图上计算面积
To find the area of a feature (e.g., a lake or a forest) on a map, first measure the length and width if the shape is regular. For irregular shapes, use the grid square method. The basic formula for area on the ground is:
要计算地图上一个地物（如湖泊或森林）的面积，如果形状规则，首先测量其长度和宽度。对于不规则形状，使用方格法。地面面积的基本计算公式是：
Area on ground = (Map Length × Scale) × (Map Width × Scale)
地面面积 = （图上长度 × 比例尺） × （图上宽度 × 比例尺）
For example, a rectangular field on a 1:10,000 map measures 3 cm by 2 cm. Real dimensions: 300 m by 200 m, so area = 60,000 m². Remember to convert to hectares (1 ha = 10,000 m²) if needed.
例如，在一张 1:10,000 地图上，一块矩形田地尺寸为 3 厘米 × 2 厘米。实际尺寸为 300 米 × 200 米，因此面积 = 60,000 平方米。如有需要，请换算成公顷（1 公顷 = 10,000 平方米）。
4. Gradient (Slope) | 坡度（斜率）
Gradient describes the steepness of a slope. It is the ratio of vertical rise to horizontal distance. Often expressed as a fraction or ratio, the formula is:
坡度描述斜坡的陡峭程度。它是垂直爬升与水平距离的比值。通常表示为分数或比例，公式是：
Gradient = Vertical Rise ÷ Horizontal Distance
坡度 = 垂直爬升 ÷ 水平距离
If a hill rises 50 metres over a horizontal distance of 200 metres, the gradient is 50/200 = 1/4 or 1:4. A smaller denominator means a steeper slope. Use contour lines to find the vertical interval.
如果一座小山在 200 米的水平距离内升高了 50 米，则坡度为 50/200 = 1/4 或 1:4。分母越小表示坡度越陡。利用等高线来获取垂直高度差。
5. Population Density | 人口密度
Population density shows how crowded an area is. It is the number of people per unit area, usually per square kilometre. The formula is straightforward:
人口密度显示一个地区的拥挤程度。它是每单位面积上的人口数量，通常表示为每平方公里有多少人。公式很简单：
Population Density = Total Population ÷ Total Land Area (km²)
人口密度 = 总人口 ÷ 总陆地面积（平方公里）
For instance, a country with 5 million people and 100,000 km² has a density of 50 people per km². High densities often indicate urban centres; low densities may mean rural or harsh environments.
例如，一个人口 500 万、面积为 10 万平方公里的国家，人口密度为每平方公里 50 人。高密度通常表示城市中心；低密度可能意味着乡村或恶劣环境。
6. Birth Rate and Death Rate | 出生率和死亡率
These rates help geographers understand population change. They are usually given per 1,000 people per year. The formulas are:
这些比率帮助地理学家理解人口变化。它们通常表示为每年每千人的数量。公式如下：
Birth Rate = (Number of live births ÷ Total population) × 1,000
出生率 = （活产婴儿数 ÷ 总人口） × 1,000
Death Rate = (Number of deaths ÷ Total population) × 1,000
死亡率 = （死亡人数 ÷ 总人口） × 1,000
If a town of 20,000 has 200 births in a year, its birth rate is (200/20,000)×1,000 = 10 per 1,000. Natural increase can be found by subtracting death rate from birth rate.
如果一个 2 万人的小镇一年有 200 名婴儿出生，其出生率为 (200/20,000)×1,000 = 每千人 10。自然增长率可以通过出生率减去死亡率得到。
7. Temperature Range | 气温变化范围
Temperature range is the difference between the highest and lowest temperatures recorded in a period (often daily, monthly, or yearly). The formula is:
气温变化范围是指一段时间内（通常是每日、每月或每年）记录的最高气温与最低气温之间的差值。公式是：
Temperature Range = Maximum Temperature − Minimum Temperature
气温变化范围 = 最高气温 − 最低气温
For a day with a high of 28°C and a low of 14°C, the diurnal range is 14°C. Annual range compares the hottest and coldest months. A large range often suggests a continental climate.
对于一天中最高气温 28°C、最低 14°C，日较差为 14°C。年较差比较最热月与最冷月。较大的年较差通常表示大陆性气候。
8. Total Rainfall and Mean Monthly Rainfall | 总降雨量与月平均降雨量
Rainfall data is essential for describing climate. The total rainfall over a period is simply the sum of all recorded rainfall values. The mean monthly rainfall is:
降雨量数据对于描述气候至关重要。一段时期内的总降雨量就是所有记录的降雨量之和。月平均降雨量为：
Mean Monthly Rainfall = Total Rainfall in a Year ÷ 12
月平均降雨量 = 年总降雨量 ÷ 12
Always check units — rainfall is usually measured in millimetres (mm). To find the annual total, add up the 12 monthly values. This helps identify wet and dry seasons.
务必检查单位——降雨量通常以毫米（mm）为单位。要计算年总降雨量，将 12 个月的值相加。这有助于识别干湿季节。
9. Percentage Change | 百分比变化
Percentage change measures how much a quantity has grown or shrunk relative to its original value. In geography, it is used for population growth, urban expansion, deforestation rates, and more. The formula is:
百分比变化衡量一个数量相对于其原始值增长或缩小了多少。在地理学中，它用于人口增长、城市扩张、森林砍伐率等等。公式是：
Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100
百分比变化 = （（新值 − 原值） ÷ 原值） × 100
For example, if a city’s population rose from 80,000 to 92,000, the change is (12,000/80,000)×100 = +15%. Negative results indicate a decrease. Always state the original and new values clearly.
例如，如果一个城市的人口从 80,000 增加到 92,000，变化为 (12,000/80,000)×100 = +15%。负值结果表示减少。一定要清楚说明原值和新值。
10. Contour Lines and Elevation | 等高线与海拔
Contour lines on topographic maps connect points of equal elevation. The contour interval is the vertical difference between two consecutive contour lines. While there is no single formula, a useful rule for finding elevation is:
地形图上的等高线连接海拔相同的点。等高距是相邻两条等高线之间的垂直高差。虽然没有单一公式，但一个有用的规则是：
Elevation of a point = Closest labelled contour ± (Number of intervals × Contour interval)
某点海拔 = 最近的有标注的等高线高度 ± （间隔数 × 等高距）
To determine gradient using contours, identify the vertical rise between two points and measure the horizontal distance on the map, then apply the gradient formula. Closely spaced contours indicate a steep slope.
利用等高线确定坡度时，找出两点间的垂直高差，并在地图上测量水平距离，然后应用坡度公式。等高线密集表示坡度陡峭。
11. Latitude and Longitude Basics | 纬度和经度基础
Latitude and longitude are the grid system used to locate any place on Earth. Latitude lines run east-west, measuring north or south of the Equator (0°). Longitude lines run north-south, measuring east or west of the Prime Meridian (0°). A position is given as (latitude, longitude).
纬度和经度是用来定位地球上任何地点的网格系统。纬线呈东西走向，测量赤道（0°）以北或以南的位置。经线呈南北走向，测量本初子午线（0°）以东或以西的位置。一个位置表示为（纬度，经度）。
Degrees are subdivided into 60 minutes (‘) and minutes into 60 seconds (“). For example, 25°30’N, 71°15’E. This is not a formula, but a coordinate theorem essential for map work.
度可细分为 60 分（’），分可细分为 60 秒（”）。例如，25°30’N，71°15’E。这不是公式，而是地图工作不可缺少的坐标定理。
12. Interpreting Climate Graphs and Population Pyramids | 解读气候图表和人口金字塔
Climate graphs show monthly temperature (line) and precipitation (bars) together. The key rule is: if the temperature line lies above the precipitation bars, it may indicate a dry period or high evaporation. Population pyramids display age and sex distribution; the width of each bar shows the proportion of people in that age group. The dependency ratio is a useful derived formula:
气候图表同时显示月温度（折线）和降水量（柱状）。关键法则是：如果温度折线位于降水量柱状上方，可能意味着干旱期或高蒸发量。人口金字塔展示年龄和性别分布；每条柱的宽度表示该年龄组的人口比例。抚养比是一个有用的衍生公式：
Dependency Ratio = ((Population aged 0-14 + Population aged 65+) ÷ Working-age population (15-64)) × 100
抚养比 = （（0-14 岁人口 + 65 岁以上人口） ÷ 劳动年龄人口（15-64 岁）） × 100
A high dependency ratio indicates more economic burden on the working population. Use these tools to compare countries and regions.
抚养比较高表明劳动人口的经济负担较重。使用这些工具来比较各个国家和地区。
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