📚 Year 10 Cambridge Geography: Formula & Theorem Quick Reference Handbook | Year 10 剑桥地理：公式定理速查手册
This handbook compiles the essential formulas and theorems covered in Year 10 Cambridge Geography. Mastering these calculations will help you interpret maps, analyse population data, understand river processes and succeed in fieldwork examinations. Use it as a quick revision tool before your tests.
本手册汇编了 Year 10 剑桥地理课程中的关键公式和定理。掌握这些计算将帮助你解读地图、分析人口数据、理解河流过程并在野外考察考试中取得优异成绩。可作为考前快速复习工具。
1. Map Scale & Distance Conversion | 比例尺与距离换算
A map scale expresses the relationship between a distance on the map and the corresponding distance on the ground. The most common type is a representative fraction (RF), such as 1:25,000, meaning 1 cm on the map stands for 25,000 cm on the Earth's surface. You will also encounter linear scales marked as a bar.
地图比例尺表示图上距离与对应实地距离的关系。最常见的类型是数字比例尺 (RF)，如 1:25,000，表示图上 1 厘米代表地面 25,000 厘米。你也会遇到用线段表示的直线比例尺。
Actual distance (cm) = Map distance (cm) × Scale denominator
To obtain the real-world distance, measure the straight-line or curved distance on the map in centimetres, and multiply by the scale denominator. Then convert the result into metres (divide by 100) or kilometres (divide by 100,000).
要获得实地距离，先用厘米量算图上的直线或曲线距离，然后乘以比例尺分母。最后将结果换算为米（除以 100）或公里（除以 100,000）。
When you need to calculate a true area from a map, the scale factor must be squared. For a rectangular patch, compute actual length and width first, then multiply. Alternatively, use the area formula below.
当需要从地图计算实际面积时，比例因子必须取平方。对于矩形地块，可先算出实际长和宽再相乘，或者直接使用下面的面积公式。
True area (cm²) = Map area (cm²) × (Scale denominator)²
cm². Always adjust the unit of your final answer to be sensible for the feature being measured.
请注意 1 m² = 10,000 cm²;，1 km² = 10,000,000,000 cm²;。最终答案的单位应根据所测地物的实际大小进行调整。
2. Gradient & Vertical Exaggeration | 梯度与垂直夸大
Gradient describes the steepness of a slope. It is the ratio of the vertical interval (VI) to the horizontal equivalent (HE). Both must be measured in the same units, usually metres. A steep slope has a large VI relative to HE, giving a ratio closer to 1.
梯度描述斜坡的陡峭程度，是垂直高差 (VI) 与水平距离 (HE) 的比值。两者必须使用相同单位，通常为米。陡坡的 VI 相对 HE 较大，比值更接近 1。
Gradient = VI ÷ HE or expressed as 1 in X, where X = HE ÷ VI
radient is 20÷500 = 0.04. You can write this as 1 in 25 (since 500÷20 = 25).
例如，一座小山在水平 500 米内上升 20 米，梯度为 20÷500 = 0.04，可写成 1:25（因为 500÷20 = 25）。
Vertical exaggeration (VE) is used when drawing cross-sections to make relief more visible. It is the ratio of the vertical scale to the horizontal scale, both expressed as representative fractions or as units per centimetre.
垂直夸大 (VE) 用于绘制地形剖面，使起伏更加明显。它是垂直比例尺与水平比例尺的比值，两者均用数字比例尺或每厘米表示的单位。
VE = Horizontal scale denominator ÷ Vertical scale denominator
If the map' divide; 10,000 = 5. This means the heights appear five times steeper than they really are.
若地图的水平比例尺为 1:50,000，剖面图的垂直比例尺为 1 cm 代表 100 m（即 1:10,000），则 VE = 50,000 ÷ 10,000 = 5。这意味着高度被放大了五倍。
3. Cross-Section Area of a Channel | 河道横截面积
During a river fieldwork investigation, the channel cross-sectional area is needed to compute discharge. The simplest method multiplies the average width of the channel by its average depth. If the channel shape is irregular, you can divide it into several vertical sections (segments) and sum their areas.
在河流野外调查中，计算河道横截面积是为了求取流量。最简单的方法是用河道平均宽度乘以平均水深。如果河床形状不规则，可以将其分为若干垂直小段，分别计算面积并求和。
Cross-sectional area (m²) = Average width (m) × Average depth (m)
The average depth is obtained by measuring the water depth at regular intervals across the channel and dividing the sum of these depths by the number of measurements. Always use the same unit (metres) for width and depth.
平均水深是在河道上等间距测量水深，再将所有深度之和除以测量次数。宽度与深度必须使用相同单位（米）。
4. River Discharge & Velocity | 河流流量与流速
Discharge is the volume of water passing a point in the river per second. It is a fundamental measure of a river's capacity. To find it, you must first measure the surface velocity using a float or a flowmeter and then calculate the cross-sectional area of the channel.
径流量是每秒流过河道某一点的水体积，是衡量河流输水能力的基本指标。计算时需先用浮标或流速仪测出表面流速，再求出河道的横截面积。
Velocity (m/s) = Distance travelled by float (m) ÷ Time taken (s)
Because surface velocity is usually faster than the average velocity in the whole column, a correction factor of about 0.85 is often multiplied to convert surface velocity to mean velocity in IGCSE fieldwork.
由于表面流速通常快于整个水柱的平均流速，在 IGCSE 野外考察中常乘以 0.85 的校正系数，将表面流速转换为平均流速。
Discharge, Q (m³/s) = Cross-sectional area (m²) × Mean velocity (m/s)
A river with a large cross-sectional area and fast flow will have a high discharge. This equation helps explain why discharge increases downstream as more tributaries join and the channel deepens.
横截面积大且流速快的河流，径流量也大。该方程可解释下游因更多支流汇入、河槽加深而流量增加的现象。
5. Drainage Density & Stream Order | 排水密度与河流分级
Drainage density gives an idea of how well a basin is drained. It is the total length of all stream channels divided by the area of the drainage basin. A high drainage density indicates rapidly dissected terrain with many tributaries; a low density often occurs on permeable rocks.
排水密度反映流域内水系发育的程度，等于所有河道总长度除以流域面积。高排水密度表示地形切割强烈、支流众多；低排水密度常出现在透水性好的岩石区。
km², or km&supminus;¹) = Total stream length (km) ÷ Basin area (km²)
Stream ordering helps describe the hierarchy of a river network. The Strahler method is widely used: first-order streams are those without tributaries. When two streams of the same order join, the resulting stream becomes the next order. If streams of different orders meet, the order remains the higher one.
河流分级有助于描述河网的层次。普遍采用 Strahler 分级法：一级河流是没有支流的源头。两条同级河流汇合，河流等级升高一级；若不同级河流汇合，等级取较高者。
This remains a numbering theorem rather than a formula, but it allows geographers to compare the complexity of drainage networks and relate order to discharge or catchment area.
这是一种编号定理而非公式，但它使地理学者能够比较河网复杂度，并将河道等级与径流量或流域面积联系起来。
6. Population Density | 人口密度
Population density measures how crowded an area is. It is the number of people per unit of area, normally expressed as people per square kilometre. You may need to convert the total land area
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