📚 Year 8 CIE Geography: Formula & Theorem Quick Reference Handbook | 八年级 CIE 地理：公式定理速查手册
Welcome to your go-to revision handbook for essential formulas, equations and key relationships in Year 8 CIE Geography. Whether you are interpreting a topographic map, analysing population data or calculating river discharge, this guide gives you the core mathematical tools you need – all paired with clear explanations. Use it to check facts, practise calculations and build confidence before the exam.
欢迎使用八年级 CIE 地理核心公式与定理速查手册。无论你正在判读地形图、分析人口数据还是计算河流流量，这份指南将为你提供所有必要的数学工具，并配上清晰的解释。你可以用它来核对事实、练习计算，并在考试前建立信心。
1. Map Scale Conversion | 地图比例尺换算
The relationship between distance on a map and distance on the ground is given by the map scale. For a scale stated as 1 : X, 1 cm on the map represents X cm on the ground. To convert to metres, divide by 100; to kilometres, divide by 100,000.
地图上的距离与地面实际距离之间的关系由比例尺给出。对于标注为 1 : X 的比例尺，地图上 1 cm 代表实地 X cm。换算成米需除以 100，换算成公里需除以 100,000。
Real distance (km) = map distance (cm) × X ÷ 100,000
实地距离 (km) = 图上距离 (cm) × X ÷ 100,000
2. Gradient (Slope) Calculation | 坡度计算
n (distance). It is often written as 1 : R, where R = horizontal distance ÷ vertical rise.
坡度表示斜坡的陡峭程度，用垂直高差与水平距离之比表示。通常写成 1 : R 的形式，其中 R = 水平距离 ÷ 垂直高差。
Gradient = Vertical Rise (m) ÷ Horizontal Run (m) = 1 : (Horizontal Run ÷ Vertical Rise)
坡度 = 垂直高差 (m) ÷ 水平距离 (m) = 1 : (水平距离 ÷ 垂直高差)
xample, a rise of 50 m over a run of 2000 m gives a gradient of 50/2000 = 1/40, or 1 : 40.
例如，高差 50 m，水平距离 2000 m，坡度为 50/2000 = 1/40，即 1 : 40。
3. Contour Interval Interpretation | 等高距判读
The contour interval is the vertical difference between two adjacent contour lines on a topographic map. It is constant for a given map and is stated in the margin. Height of any point can be estimated by counting contours from a known spot height.
等高距是地形图上相邻两条等高线之间的垂直高差。同一幅地图中的等高距是固定的，并在图边注明。任何地点的高度都可以通过从一个已知高程点开始计数等高线来估算。
Elevation change = number of contours crossed × contour interval
高程变化 = 跨越的等高线条数 × 等高距
4. Population Density | 人口密度
Population density measures how crowded an area is. It is the number of people per unit area, usually per square kilometre (km²). This formula helps compare different regions.
人口密度用于衡量一个地区的拥挤程度。它是单位面积上的人口数量，通常以每平方公里 (km²) 为单位。该公式有助于比较不同地区。
Population Density = Total Population ÷ Total Area (km²)
人口密度 = 总人口 ÷ 总面积 (km²)
5. Crude Birth Rate and Crude Death Rate | 粗出生率与粗死亡率
Birth and death rates are vital demographic indicators, usually expressed per 1000 people per year. They ignore age structure but allow quick comparisons between countries.
出生率和死亡率是重要的人口统计指标，通常以每年每千人为单位表示。它们不考虑年龄结构，但可用于国家间的快速比较。
Crude Birth Rate (CBR) = (Number of live births ÷ Total population) × 1000
粗出生率 (CBR) = (活产婴儿数 ÷ 总人口) × 1000
Crude Death Rate (CDR) = (Number of deaths ÷ Total population) × 1000
粗死亡率 (CDR) = (死亡人数 ÷ 总人口) × 1000
6. Natural Increase Rate (NIR) | 自然增长率 (NIR)
Natural increase rate shows whether a population is growing or shrinking without migration. It is derived from the difference between birth rate and death rate, and can be expressed as a percentage.
自然增长率显示在没有迁移的情况下人口是增长还是萎缩。它由出生率与死亡率的差值计算得出，可以用百分比表示。
NIR (%) = (CBR – CDR) ÷ 10
自然增长率 (%) = (CBR – CDR) ÷ 10
Alternatively, NIR per 1000 = CBR – CDR.
或者，每千人的自然增长率 = CBR – CDR。
7. Doubling Time (Rule of 70) | 人口倍增时间 (70 法则)
The 'Rule of 70' estimates the number of years it takes for a population to double, given a constant annual growth rate. This is a quick approximation used in demography.
“70 法则”用于估算在年增长率保持不变的情况下人口翻倍所需的年数。这是人口学中常用的快速近似方法。
Doubling Time (years) ≈ 70 ÷ Annual Growth Rate (%)
倍增时间 (年) ≈ 70 ÷ 年增长率 (%)
8. Urbanisation Rate | 城市化率
The level of urbanisation shows the proportion of a country's total population living in areas classified as urban. It helps geographers track the movement from rural to urban living.
城市化水平表示一个国家总人口中居住在被划分为城市区域的人口比例。它帮助地理学家追踪从农村到城市的生活转变。
Urbanisation Rate (%) = (Urban Population ÷ Total Population) × 100
城市化率 (%) = (城市人口 ÷ 总人口) × 100
9. Dependency Ratio | 抚养比
The dependency ratio compares the economically dependent population (young and old) to the working-age population. It indicates the pressure on the productive population to support the non-productive.
抚养比将受抚养人口（少年和老年）与劳动年龄人口进行比较。它能反映劳动人口供养非劳动人口的压力。
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
10. River Discharge | 河流流量
Discharge is the volume of water flowing through a river channel cross-section per unit time. It is a fundamental measurement in hydrology, linking channel shape and flow speed.
流量是单位时间内流过河道横截面的水体积。它是水文学中的基本测量参数，将河道形态与流速联系起来。
Discharge (Q) = Cross-sectional Area (A) × Mean Velocity (V)
流量 (Q) = 横截面积 (A) × 平均流速 (V)
Units: m³/s. Area is usually in m², velocity in m/s.
单位：m³/s。面积通常以 m² 计，流速以 m/s 计。
11. Drainage Basin Area and Stream Order | 流域面积与水道等级
Drainage basin area is commonly calculated from a map using a grid square method or planimeter. Stream order, following Strahler's method, increases when two streams of the same order join. These concepts help predict discharge and flooding potential.
流域面积通常利用地图上的方格法或求积仪计算。水道等级（斯特拉勒方法）在两条相同等级的河流汇合时提升一级。这些概念有助于预测流量和洪水风险。
Strahler's rule: when two 1st-order streams join, they form a 2nd-order stream; two 2nd-order form a 3rd, and so on.
斯特拉勒规则：两条 1 级河流汇合成 2 级河流；两条 2 级汇合成 3 级，依此类推。
12. Time Zone Calculation | 时区计算
Time zones are based on 15° longitude intervals, since Earth rotates 360° in 24 hours. Knowing the longitude of two places allows you to calculate their time difference. East is ahead of time, West is behind.
时区以经度 15° 为间隔划分，因为地球 24 小时自转 360°。知道两地的经度就可以计算出时差。东边的时间更早，西边的时间更晚。
Time difference (hours) = Longitude difference ÷ 15
时差 (小时) = 经度差 ÷ 15
For every 1° eastward, add 4 minutes; for westward, subtract 4 minutes.
每向东 1° 加 4 分钟；向西 1° 减 4 分钟。
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