📚 Year 8 Edexcel Geography: Formula & Theorem Quick Reference Handbook | 八年级爱德思地理：公式定理速查手册
Mastering the key formulas and simple 'theorems' in Geography gives you the confidence to tackle map skills calculations, population analysis, and fieldwork data with ease. This quick reference handbook pulls together every essential equation you will encounter in Year 8 Edexcel Geography, from map scale conversions to gradient, population density, vital rates, percentage change and even the Rule of 70. Each section explains what the formula measures, how to use it step by step, and provides a practical example so you can revise quickly and accurately.
掌握地理学科中的关键公式和简单的“定理”，能让你轻松应对地图技能计算、人口分析和实地考察数据。这本速查手册汇集了八年级爱德思地理课程中你会遇到的所有重要公式，从比例尺换算到坡度、人口密度、人口自然变动率、百分比变化，乃至 70 规则。每个小节都解释了公式的测量对象、使用方法与步骤，并给出了实例，以便你能高效、精确地进行复习。
1. Map Scale & Real Distance | 地图比例尺与实际距离
A map scale expresses the relationship between a distance on the map and the corresponding distance on the ground. The most common scale on OS maps and Edexcel map extracts is 1:25 000 or 1:50 000. The basic formula is:
地图比例尺表示图上距离与对应实地距离之间的关系。在 OS 地图和爱德思地图摘录中最常见的比例尺是 1:25 000 或 1:50 000。基本公式为：
Real Distance = Map Distance × Scale Factor
5 000, the scale factor is 25 000. If you measure 4 cm on the map, the real-world straight‑ m. Convert centimetres to metres by dividing by 100, giving 1 000 m (1 km). Always check the unit requested; Edexcel questions often ask for the answer in metres or kilometres.
对于 1:25 000 的比例尺，比例因子为 25 000。如果你在图上量得 4 厘米，实地直线距离就是 4 cm × 25 000 = 100 000 cm。将厘米转换为米需除以 100，得到 1 000 米（1 千米）。务必确认题目要求的单位；爱德思考题常常要求答案以米或千米表示。
2. Measuring Curved Distances on a Map | 地图上曲线距离的测量
Rivers, winding roads and paths cannot be measured accurately with a ruler. Instead, use the string method:
河流、蜿蜒的道路和小径无法用直尺准确测量。此时需使用细线法：
Curved Distance = Length of String laid on the route × Scale Factor
e its length against the map’s linear scale or with a ruler. Multiply the length by the scale factor to obtain the real distance. For example, if the string measures 7.2 cm on a 1:25 000 map, the real distance is 7.2 × 25 000 = 180 000 cm = 1 800 m.
将一根细线精确地沿着地图上的弯曲地物放置，在线上的起点和终点处做标记。把线拉直，对照地图的直线比例尺或用尺子量出其长度。将长度乘以比例因子即可得到实际距离。例如，在 1:25 000 地图上线长 7.2 cm，则实际距离为 7.2 × 25 000 = 180 000 cm = 1 800 m。
3. Calculating Area on a Map | 地图上的面积计算
Edexcel mapwork tasks sometimes ask you to estimate the area of a feature such as a forest, lake or settlement. The grid‑square method is the most reliable:
爱德思地图作业有时会要求你估算某个地物的面积，比如森林、湖泊或聚落。方格法是最可靠的方法：
Area on the ground = Number of grid squares occupied × Area each square represents
On a 1:25 000 map, each 1‑ f is inside and treat them as half a square. Multiply the total squares by the area per square. For a feature covering 14 full squares and 6 partial squares treated as 3, total squares = 17. Area = 17 × 0.25 km² = 4.25 km².
在 1:25 000 地图上，每个 1 厘米见方的网格代表 0.25 平方千米（250 000 平方米）。先数出边界内完整的方格数，再观察不完整的方格：若超过半格在边界内则计为半格。将总方格数乘以每格代表的面积。若某地物覆盖 14 个完整方格和 6 个按半格计算的不完整方格，总格数为 17。面积 = 17 × 0.25 km² = 4.25 km²。
4. Gradient (Slope) Calculation | 坡度（梯度）计算
Gradient describes the steepness of a slope and is essential when drawing cross‑sections or assessing land use. The formula compares vertical height difference to horizontal distance:
坡度描述的是斜坡的陡峭程度，在绘制横截面或评价土地利用时很关键。公式将对垂直高差与水平距离进行比较：
Gradient = Vertical Height Difference ÷ Horizontal Distance
ce in Both measurements must be in the same unit. Find the difference in contour values between two points to get the height difference. Measure the straight‑ for every 10 units horizontally. For a 100 m height difference over a 2 000 m horizontal stretch, gradient = 100 ÷ 2 000 = 1 / 20, so the ratio is 1:20.
两项测量值必须使用相同的单位。找出两点之间的等高线差值作为高差。量出地图上的直线水平距离并将其转换为相同单位（通常为米）。将坡度写成一个比率，如 1:10，表示水平方向每前进 10 个单位，垂直高度上升 1 个单位。若高差为 100 m，水平距离为 2 000 m，则坡度 = 100 ÷ 2 000 = 1/20，比率为 1:20。
5. Drawing & Interpreting Contour Cross‑Sections | 绘制与解读等高线横截面
A cross‑section is a side‑view diagram that shows the shape of the land along a line between two points. The essential measurements and steps are:
横截面是一个展示两点之间地表形态的侧视图。关键的测量数据与步骤如下：
Vertical Scale = Vertical Height ÷ Length of the chosen vertical axis
t these heights on a graph where the horizontal axis represents distance along the line and the vertical axis represents elevation. Choose a vertical scale that exaggerates the relief just enough to show details – oints with a smooth curve. The gradient between adjacent points can be checked using the gradient formula. Always label peaks, valleys and any major features.
沿剖面线标记每条穿过等高线的高程。将这些高程绘制在图纸上，横轴表示沿线距离，纵轴表示高度。选择的垂直比例尺应能略微夸大起伏以显示细节——常见的垂直夸大倍数为水平比例尺的 2 到 5 倍。将各点用平滑曲线连接。相邻点之间的坡度可用梯度公式进行检验。务必标注山峰、谷地以及所有重要地物。
6. Population Density | 人口密度
Population density describes how crowded a place is and helps compare different regions. The formula is simple but fundamental:
人口密度描述了一个地方的拥挤程度，有助于比较不同区域。公式简单但至关重要：
Population Density = Total Population ÷ Total Area
y is 67 000 000 ÷ 242 500 ≈ 276 people/km². In Edexcel exams, you may also be asked to calculate the area or population when given the density and one other variable.
结果通常用每平方千米人数（人/km²）表示。若某国人口为 6 700 万，面积为 242 500 km²，则人口密度为 67 000 000 ÷ 242 500 ≈ 276 人/km²。在爱德思考试中，也可能已知密度和另一个变量，要求计算面积或人口总数。
7. Vital Rates & Natural Increase | 人口自然变动率与自然增长
Birth rate, death rate and natural increase show how a population changes without migration. All rates are normally expressed per 1 000 people per year.
出生率、死亡率和自然增长率反映了不考虑迁移时的人口变化。所有比率通常表示为每年每 1 000 人中的数量。
Crude Birth Rate (CBR) = (Number of births ÷ Total population) × 1 000
Crude Death Rate (CDR) = (Number of deaths ÷ Total population) × 1 000
Natural Increase Rate (NIR) = CBR − CDR
tage, divide by 10. For example, if CBR = 28/1 000 and CDR = 8/1 000, NIR = 20/1 000 = 2.0% r. Remember that NIR can be negative if deaths exceed births, indicating natural decrease.
自然增长率常写成百分比形式。将每千人的比率转换为百分比只需除以 10。例如，若出生率 CBR = 28‰，死亡率 CDR = 8‰，则自然增长率 NIR = 20‰ = 2.0% 每年。请注意，如果死亡人数超过出生人数，NIR 可能为负值，这表示自然减少。
8. Rule of 70 (Doubling Time) | 70 规则（人口翻倍时间）
The Rule of 70 is a simple 'theorem' used to estimate how many years it takes for a population to double given a constant annual growth rate:
70 规则是一个简单的“定理”，用于估算在年增长率固定不变的情况下人口翻倍所需的年数：
Doubling Time (years) ≈ 70 ÷ Annual Growth Rate (%)
If a country’s population is growing at 3.5% doubling time ≈ 70 ÷ 3.5 = 20 years. This rule works well for growth rates below about 10% ent growth rates. The same rule can be applied to resource consumption or economic growth.
如果一个国家的人口年增长率为 3.5%，则翻倍时间 ≈ 70 ÷ 3.5 = 20 年。该规则对低于约 10% 的增长率效果很好。它在发展地理学中极为有用，可预测未来的人口压力，并比较增长率不同的国家。同一规则也适用于资源消耗或经济增长。
9. Percentage Change | 百分比变化
Percentage change is widely used to compare differences in population, employment, farmland area or climatic variables over time:
百分比变化广泛用于比较人口、就业、耕地面积或气候变量随时间的变化：
Percentage Change = [(New Value − Original Value) ÷ Original Value] × 100
opulation grew from 15 000 to 17 250, the change is (17 250 − 15 000) ÷ 15 000 × 100 = +15% erpreting data in fieldwork, always state whether the change is an increase or a decrease.
正值表示增加，负值表示减少。例如，某城镇的人口从 15 000 增长到 17 250，则变化为 (17 250 − 15 000) ÷ 15 000 × 100 = +15%。在解读实地考察数据时，务必说明变化是增加还是减少。
10. River Discharge | 河流流量
River discharge is the volume of water flowing past a point in a river channel per unit time. It is a core measurement in river studies and fieldwork:
河流流量是指单位时间内流过河道某个断面的水体体积。它是河流研究与实地考察中的核心测量值：
Discharge (Q) = Cross‑sectional Area (A) × Mean Velocity (V)
Cross‑ r or by timing a float over a known distance. If a stream is 3 m wide, has an average depth of 0.5 m, and water flows at 0.8 m/s, the area is 1.5 m², and discharge Q = 1.5 m² × 0.8 m/s = 1.2 cubic metres per second (m³/s). Discharge increases downstream as tributaries join and as surface runoff enters the channel.
横截面积由河宽乘以平均水深得出（面积 = 宽度 × 平均深度）。流速通常使用流速仪测量，或通过计时浮标通过已知距离来估算。若一条溪流宽 3 m，平均水深 0.5 m，流速为 0.8 m/s，则面积为 1.5 m²，流量 Q = 1.5 m² × 0.8 m/s = 1.2 立方米/秒（m³/s）。流量会随着支流汇入和地表径流汇入而向下游增大。
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