📚 Year 10 CCEA Geography Formula & Theorem Quick Reference | CCEA 十年级地理公式定理速查手册
This quick-reference guide presents the essential formulas and quantitative concepts required for Year 10 CCEA Geography. Whether you are working on map skills, population studies, or physical geography, having these equations at your fingertips will strengthen your data-response answers and fieldwork calculations.
本速查手册汇总了 CCEA 十年级地理必需的核心公式与定量概念。无论你在练习地图技能、人口研究还是自然地理，熟悉这些方程都能增强你的数据分析题作答和实地考察计算能力。
1. Map Scales | 地图比例尺
A map scale expresses the ratio between a distance on the map and the corresponding distance on the ground. It can be stated as a representative fraction (e.g. 1:50,000), a linear scale, or a verbal statement.
地图比例尺表示图上距离与对应实地距离的比值。它可以表现为数字比例尺（如 1:50 000）、直线比例尺或文字说明。
Key formula: If the scale is 1 : X, then Ground Distance = Map Distance × X. Always ensure both measurements are in the same units before multiplying.
核心公式：若比例尺为 1 : X，则实地距离 = 图上距离 × X。计算前务必确保两者单位一致。
Example: On a 1:25,000 map, a 4 cm road represents 4 cm × 25,000 = 100,000 cm, which converts to 1 km.
示例：在 1:25 000 地图上，一条 4 cm 的道路代表 4 cm × 25 000 = 100 000 cm，换算为 1 km。
2. Measuring Straight-Line Distance | 测量直线距离
Straight-line distance is measured with a ruler and converted using the map scale. This is often the first step in describing the relative location of features.
直线距离用直尺量测，再通过比例尺换算。这通常是描述地物相对位置的第一步。
Calculation: Straight-Line Distance (km) = (Measured Length in cm × Scale Factor) ÷ 100,000. The scale factor is the denominator of the representative fraction.
计算方法：直线距离 (km) = (量测长度 cm × 比例尺分母) ÷ 100 000。
On a 1:50,000 map, 5.2 cm gives: Ground Distance = 5.2 × 50,000 = 260,000 cm = 2.6 km.
在 1:50 000 地图上，5.2 cm 即：实地距离 = 5.2 × 50 000 = 260 000 cm = 2.6 km。
3. Curved-Line Distance | 曲线距离
For winding roads or rivers, use a piece of string or an opisometer. Lay the string along the curve, straighten it, then measure its length with a ruler and apply the scale.
测量蜿蜒道路或河流时，使用细线或曲线计。让细线贴合曲线，拉直后用直尺量取长度，再按比例尺换算。
Procedure: Curved Distance = (Length of string in cm × Scale denominator) ÷ 100,000 to get km. This is essential for river long profiles or coastal routes.
步骤：曲线距离 = (线段长度 cm × 比例尺分母) ÷ 100 000，得出公里数。这对河流纵剖面或沿海路径测量至关重要。
4. Area Calculation | 面积计算
Area on a map is found by overlaying a grid or by dividing the shape into regular polygons. The calculated map area is then scaled up using the square of the scale factor.
地图上的面积可通过网格覆盖或将图形分割为规则多边形求得。计算出的图面面积再用比例尺的平方进行放大。
Formula: Ground Area = Map Area (cm²) × (Scale denominator)². Convert to m² or km² by dividing by 10,000 or 10,000,000,000 respectively.
公式：实地面积 = 图上面积 (cm²) × (比例尺分母)²。再分别除以 10 000 或 10 000 000 000，换算为 m² 或 km²。
On 1:10,000, a lake covering 3 cm² on the map has a ground area of 3 × 10,000² = 3 × 100,000,000 = 300,000,000 cm² = 30,000 m².
在 1:10 000 地图上，一个面积 3 cm² 的湖泊，实地面积为 3 × 10 000² = 300 000 000 cm² = 30 000 m²。
5. Gradient (Slope) | 坡度（梯度）
Gradient expresses the steepness of a slope as a ratio, fraction, or percentage. It is commonly used in contour analysis and river valley profiles.
坡度以比、分数或百分数表示斜坡的陡峭程度，常用于等高线分析和河谷剖面。
Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE)
坡度 = 垂直高差 (VI) ÷ 水平距离 (HE)
The vertical interval is the difference in height between two points, and the horizontal equivalent is the ground distance between them. Both must be in the same units. A slope of 1:10 means for every 10 metres horizontally, the land rises 1 metre.
垂直高差是两点间的高程差，水平距离是两点间的实地距离，两者单位须一致。1:10 的坡度表示水平每前进 10 米，高度上升 1 米。
6. Population Density | 人口密度
Population density measures how crowded an area is. It is one of the most common demographic statistics in human geography.
人口密度衡量一个地区的拥挤程度，是人文地理中最常用的人口统计指标之一。
Population Density = Total Population ÷ Total Land Area (km²)
人口密度 = 总人口 ÷ 土地总面积 (km²)
Population is usually given as a mid-year estimate, and land area excludes inland water bodies. Result is expressed in persons per square kilometre.
人口通常采用年中估计值，土地面积不含内陆水域。结果表示为每平方公里人数。
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If a region has 250,000 people and an area of 500 km², density = 500 persons/km².
若某地区有 25 万人，面积 500 km²，则人口密度为 500 人/km²。
7. Birth Rate and Death Rate | 出生率与死亡率
The crude birth rate (CBR) and crude death rate (CDR) are fundamental measures of natural population change, expressed per 1,000 people per year.
粗出生率 (CBR) 与粗死亡率 (CDR) 是衡量人口自然变动的基本指标，通常表示为每千人每年的数值。
Crude Birth Rate = (Number of live births ÷ Total population) × 1,000
粗出生率 = (活产婴儿数 ÷ 总人口) × 1 000
Crude Death Rate = (Number of deaths ÷ Total population) × 1,000
粗死亡率 = (死亡人数 ÷ 总人口) × 1 000
These rates allow comparison between countries of different sizes. CBR minus CDR gives the rate of natural increase (excluding migration).
这两个率值便于不同规模国家之间比较。CBR 减 CDR 得出自然增长率（不含迁移）。
8. Rate of Natural Increase and Migration Rate | 自然增长率与迁移率
Natural increase reflects the balance between births and deaths, while net migration rate accounts for movement of people in and out of an area.
自然增长反映出生与死亡的平衡，而净迁移率则表示人口迁入与迁出的净变化。
Rate of Natural Increase = (CBR – CDR) / 10 (to convert from per 1,000 to a percentage)
自然增长率 = (CBR – CDR) / 10 （从千分比转换为百分比）
Net Migration Rate = ((Immigration – Emigration) ÷ Total population) × 1,000
净迁移率 = ((迁入人数 – 迁出人数) ÷ 总人口) × 1 000
Population growth rate (%) = (Natural increase % + Net migration %) rounded to two decimal places. These formulas underpin the Demographic Transition Model.
人口增长率 (%) = (自然增长率 % + 净迁移率 %)，保留两位小数。这些公式是人口转变模型的基础。
9. Dependency Ratio | 抚养比
The dependency ratio compares the economically dependent population (young and old) to the working-age population. It is essential for understanding pressures on services and taxation.
抚养比将经济依赖人口（幼年与老年）与劳动年龄人口进行比较，这对理解公共服务压力和税收负担至关重要。
Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
抚养比 = [(0–14 岁人口 + 65 岁以上人口) ÷ 15–64 岁人口] × 100
A result of 55 means there are 55 dependents for every 100 working-age people. Youth dependency and old-age dependency can also be calculated separately.
结果为 55 表示每 100 名劳动年龄人口对应 55 名受抚养者。少龄抚养比和老年抚养比也可分别计算。
10. River Discharge | 河流流量
Discharge is the volume of water flowing past a given point in a river channel per unit time. It combines channel geometry with flow velocity and is a key variable in flood studies.
流量是单位时间内通过河道某一断面的水体体积，结合了断面几何形态与流速，是洪水研究中的关键变量。
Discharge (Q) = Cross-Sectional Area (A) × Mean Velocity (V)
流量 (Q) = 过水断面面积 (A) × 平均流速 (V)
Cross-sectional area is calculated by multiplying average depth by channel width (for a rough rectangle). Discharge is expressed in cubic metres per second (cumecs).
过水断面面积可用平均水深乘以河宽估算（近似矩形）。流量以立方米每秒 (cumecs) 表示。
11. Drainage Density | 河网密度
Drainage density describes how closely spaced streams are within a basin. It reflects climate, geology, and soil permeability, and helps predict flood response.
河网密度描述流域内水流的密集程度，反映气候、地质和土壤渗透性，并可辅助预测洪水响应。
Drainage Density = Total length of all stream channels (km) ÷ Drainage basin area (km²)
河网密度 = 全部河道总长度 (km) ÷ 流域面积 (km²)
A high drainage density (e.g. >2.5 km/km²) indicates rapid runoff and a flashy hydrograph, while low density suggests permeable ground and a lagged response.
高河网密度（如 >2.5 km/km²）意味着径流迅速、洪水过程线陡急，低密度则说明地面透水性强、水文响应迟缓。
12. Temperature Range and Annual Precipitation | 气温较差与年降水量
Climate graphs require two simple calculations: annual temperature range and total annual precipitation. These help classify climate types in CCEA fieldwork and exam questions.
气候图表需要两个简单计算：年气温较差和年总降水量。在 CCEA 实地考察和考试中，这些数值有助于判断气候类型。
Annual Temperature Range = Hottest month mean temperature – Coldest month mean temperature
年气温较差 = 最热月平均气温 – 最冷月平均气温
Total Annual Precipitation = Sum of all monthly precipitation totals (mm)
年降水量 = 各月降水量总和 (mm)
Temperature is recorded in °C, and precipitation in millimetres. These statistics underpin the Koppen-Geiger climate classification often referenced at Year 10 level.
温度以 °C 为单位，降水以毫米记。这些统计量支撑着十年级常引用的柯本气候分类。
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