📚 Year 7 CCEA Geography: Formula & Theorem Quick Reference Handbook | CCEA七年级地理：公式定理速查手册
Master the key formulas and theorems you need for Year 7 CCEA Geography. This quick reference handbook covers essential map skills, population calculations, climate data, and environmental concepts. Use it to solve problems, interpret data, and strengthen your geographical understanding.
掌握CCEA七年级地理所需的关键公式和定理。这本速查手册涵盖了基本的地图技能、人口计算、气候数据以及环境概念。用它们来解决问题、解读数据，并加深你对地理的理解。
1. Map Scale Formulas | 地图比例尺公式
A map scale shows the relationship between a distance on the map and the corresponding distance on the ground. It can be written as a ratio, a fraction, or a graphic scale. The basic formula is:
地图比例尺表示地图上的距离与地面上实际距离之间的关系。它可以用比率、分数或图示比例尺表示。基本公式为：
Scale = Map Distance ÷ Actual Ground Distance
If the scale is 1:50,000, then 1 cm on the map represents 50,000 cm (or 0.5 km) in reality. Always ensure both distances are in the same unit before calculating.
如果比例尺是1:50,000，那么地图上1厘米代表实际50,000厘米（即0.5公里）。计算前务必确保两个距离使用相同的单位。
2. Calculating Real-World Distance | 计算实际距离
To find the real distance between two points using a map, measure the map distance and multiply by the scale factor. The formula is:
要使用地图求两点间的实际距离，先测量地图距离，再乘以比例尺倍数。公式为：
Actual Distance = Map Distance × Scale Denominator
For example, with a 1:25,000 map, if two places are 4 cm apart, the actual straight‑ 4 cm × 25,000 = 100,000 cm = 1 km. Remember to convert to kilometres or metres as needed.
例如，在1:25,000的地图上，如果两地相距4厘米，实际的直线距离为：4厘米 × 25,000 = 100,000厘米 = 1公里。记得根据需要换算成公里或米。
3. Gradient Formula | 坡度公式
Gradient describes the steepness of a slope. It is the ratio of the vertical height change (rise) to the horizontal distance (run). The formula is:
坡度描述斜坡的陡峭程度。它是垂直高度变化（高差）与水平距离的比值。公式为：
Gradient = Vertical Rise ÷ Horizontal Run
On a contour map, the rise is the difference in elevation between two points. The run is the map distance converted to actual distance. Express gradient as a ratio, for instance 1:10 means for every 10 metres horizontally, the land rises 1 metre.
在等高线地图上，高差是两点之间的海拔高度差。水平距离是地图距离换算后的实际距离。坡度用比率表示，例如1:10表示水平每移动10米，地面升高1米。
4. Four-Figure and Six-Figure Grid References | 四位数与六位数网格坐标
Grid references help you locate places on a map. A four‑figure reference (e.g., 2638) identifies a 1 km by 1 km square. The rule is 'along the corridor and up the stairs' – eastings first, then northings. For a six‑figure reference, imagine the square divided into tenths to give a more precise location:
网格坐标帮助你在地图上定位。四位数坐标（如2638）标识一个1公里×1公里的方格。规则是“先横后纵”——先读东向值，再读北向值。对于六位数坐标，想象将方格分成十等份，从而获得更精确的位置：
ure reference = Eastings (first two digits + tenth) + Northings (first two digits + tenth)
Always split the easting and northing into three digits each. For example, 265387 means the point is at easting 26.5, northing 38.7 within the grid square.
始终将东向值和北向值各拆分为三位数。例如，265387表示该点位于网格方格内东向26.5、北向38.7的位置。
5. Bearing Measurement | 方位角测量
Bearings give direction measured clockwise from north. They are always given as three figures, from 000° to 360°. The formula for measuring a compass bearing on a map is:
方位角是从正北方向顺时针测量的方向。方位角始终用三位数表示，范围从000°到360°。在地图上测量罗盘方位角的公式为：
Bearing = Angle measured clockwise from Grid North to the line joining the two points
Place a protractor with its centre on the starting point and align 0° with north. Read the angle where the line to the destination intersects the protractor scale. Record as three digits, e.g., 045°.
将量角器的中心对准起点，0°对准北方。读取从起点到终点的连线在量角器刻度上的角度。以三位数记录，例如045°。
6. Population Density | 人口密度
Population density shows how crowded an area is. It is the number of people living per unit of land area. The formula is:
人口密度显示一个地区有多拥挤。它是单位土地面积上居住的人数。公式为：
Population Density = Total Population ÷ Total Land Area
If a town has 25,000 people and an area of 10 km², the population density is 2,500 people per km². High densities often indicate cities, while low densities are typical in rural areas.
如果一个城镇有25,000人，面积为10平方公里，则人口密度为每平方公里2,500人。高密度通常出现在城市，低密度则常见于乡村地区。
7. Natural Increase Rate | 自然增长率
Natural increase measures how a population grows without migration. It is the difference between the birth rate and the death rate. The formula can be expressed as a percentage:
自然增长率衡量在没有迁移的情况下人口如何增长。它是出生率与死亡率之差。该公式可以用百分比表示：
Natural Increase Rate (%) = (Birth Rate − Death Rate) ÷ 10
1,000 and the death rate is 10 per 1,000, the natural increase rate is (30 − 10) ÷ 10 = 2% per year. This means the population grows by 2% annually, excluding migration.
出生率和死亡率通常以每年每千人中的数值表示。如果出生率为千分之30，死亡率为千分之10，则自然增长率 = (30 − 10) ÷ 10 = 2% 每年。这意味着在不考虑迁移的情况下，人口每年增长2%。
8. Interpreting Climate Graphs (Temperature Range & Precipitation) | 解读气候图表（气温差与降水量）
Climate graphs display average monthly temperature and precipitation. Two useful formulas are the annual temperature range and total precipitation:
气候图表显示月平均气温和降水量。两个有用的公式是年气温差和总降水量：
Temperature Range = Highest Monthly Temperature − Lowest Monthly Temperature
Total Annual Precipitation = Sum of all monthly precipitation values
A large temperature range suggests a continental climate, while a small range indicates a maritime or equatorial climate. Precipitation patterns help identify wet and dry seasons.
年气温差大表明是大陆性气候，年气温差小则表明是海洋性或赤道气候。降水模式有助于识别雨季和旱季。
9. Latitude and Longitude Basics | 经纬度基础
Latitude lines run parallel to the Equator and measure distances north or south. Longitude lines run from pole to pole and measure distances east or west of the Prime Meridian. Key reference points are:
纬线平行于赤道，测量南北距离。经线从一极延伸至另一极，测量本初子午线以东或以西的距离。关键参考点为：
| Line | Lat/Long | Importance |
|---|---|---|
| Equator | 0° latitude | Divides Earth into Northern and Southern Hemispheres |
| Prime Meridian | 0° longitude | Divides Earth into Eastern and Western Hemispheres |
Coordinates are always written with latitude first (N or S) followed by longitude (E or W). For example, the coordinates of London are approximately 51°N, 0°W.
坐标总是先写纬度（北纬或南纬），再写经度（东经或西经）。例如，伦敦的坐标大约是北纬51°，西经0°。
10. Unit Conversions for Weather | 天气单位换算
Weather data may appear in different units. Knowing how to convert between them is a vital geographical skill. The most common conversions are:
气象数据可能以不同的单位出现。了解如何在它们之间进行换算是重要的地理技能。最常见的换算是：
| Measurement | From | To | Formula |
|---|---|---|---|
| Temperature | °C (Celsius) | °F (Fahrenheit) | (°C × 9/5) + 32 |
| Precipitation | mm (millimetres) | cm (centimetres) | mm ÷ 10 |
| Wind speed | km/h | m/s | km/h ÷ 3.6 |
Always check the required unit in an exam question. Use these conversions to compare climates across different countries.
考试时一定要看清要求使用的单位。利用这些换算来比较不同国家的气候。
11. Water Cycle Balance (Inputs = Outputs) | 水循环平衡（输入=输出）
The water cycle is a closed system at the global scale. The fundamental principle is that total inputs equal total outputs over time. The simplest water balance equation for a drainage basin is:
在全球范围内，水循环是一个封闭系统。其基本原理是，长期来看总输入量等于总输出量。流域最简单的水平衡方程是：
Precipitation (P) = Evapotranspiration (E) + Runoff (R) + Change in Storage
In Year 7, you can think of it as: water gained through precipitation must equal water lost through evaporation, transpiration, and river flow, plus any stored in lakes, soil, or groundwater.
在七年级，你可以将其理解为：通过降水获得的水量必须等于通过蒸发、蒸腾和河流流失的水量，再加上储存在湖泊、土壤或地下水中的水量。
12. The Rule of Coastal Transportation (Longshore Drift) | 沿海搬运法则（沿岸流）
Longshore drift is the process that moves sediment along a coastline. The prevailing wind approaches the coast at an angle, pushing waves in a zigzag pattern. The transport direction can be summarised as:
沿岸流是使沉积物沿海岸线移动的过程。盛行风以一定角度吹向海岸，推动波浪呈锯齿状移动。搬运方向可以总结为：
Sediment movement follows the direction of the prevailing wind along the beach
Swash carries material up the beach at an angle, and backwash drags it straight down due to gravity. The net result is sediment being shifted parallel to the shore. This principle explains the formation of spits and beaches.
冲流以一定角度将物质推上海滩，回流则在重力作用下将物质垂直带下。最终结果是沉积物平行于海岸移动。这一原理解释了沙嘴和海滩的形成。
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