Formula & Theorem Quick Reference Handbook | 公式定理速查手册

📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册

This handbook brings together all the key formulas, models and concepts you need for Year 9 CCEA Geography. Keep it close for quick revision — from map skills and population statistics to river processes and urban patterns. Each section pairs an English explanation with a matching Chinese translation so you can learn actively and accurately.

本手册汇集了 CCEA 九年级地理所有关键公式、模型和概念，方便你快速复习——内容涵盖地图技能、人口统计、河流过程和城市模式。每个部分都提供英文说明与对应中文翻译，帮助你主动、精准地学习。

1. Map Scale and Distance | 地图比例尺与距离

A map scale shows the relationship between distance on the map and actual distance on the ground. It can be expressed as a statement, a ratio or a linear bar.

地图比例尺表示图上距离与实际地面距离之间的关系。它可以用文字说明、数字比例或直线比例尺表示。

Formula: Actual Distance = Map Distance × Scale Denominator

公式: 实际距离 = 图上距离 × 比例尺分母

If the scale is 1:50 000, then 1 cm on the map represents 50 000 cm (0.5 km) on the ground.
如果比例尺为 1:50000，那么图上 1 厘米代表地面 50000 厘米（0.5 公里）。

2. Gradient Calculation | 坡度计算

Gradient describes the steepness of a slope. It is the ratio of vertical rise to horizontal distance.

坡度描述斜坡的陡峭程度，是垂直升高与水平距离的比值。

Gradient = Vertical Height Difference ÷ Horizontal Distance

坡度 = 垂直高差 ÷ 水平距离

Both measurements must be in the same unit. A gradient of 1:10 means the land rises 1 metre for every 10 metres travelled horizontally.

两个测量值必须使用相同单位。1:10 的坡度意味着每水平前进 10 米，地面上升 1 米。

3. Area Measurement on a Map | 地图上的面积测量

To estimate the area of an irregular shape on a map, use a grid square method. Count full squares and combine partial squares.

估算地图上不规则形状的面积，可使用网格法。计算完整的方格，并合并不完整的部分。

Formula: Area on ground = Area on map × (Scale Denominator)²

公式: 地面面积 = 图上面积 × (比例尺分母)²

For a scale of 1:25 000, 1 cm² on the map equals 6.25 hectares in reality (since 1 cm² = (25 000 cm)² = 625 000 000 cm² = 6.25 ha).

对于 1:25000 的比例尺，图上 1 平方厘米等于实际 6.25 公顷（因为 1 cm² = (25000 cm)² = 625000000 cm² = 6.25 ha）。

4. Population Density | 人口密度

Population density measures how crowded an area is. It shows the average number of people living per square kilometre.

人口密度衡量一个地区的拥挤程度，显示每平方公里平均居住人数。

Population Density = Total Population ÷ Total Land Area (km²)

人口密度 = 总人口 ÷ 总土地面积（平方公里）

Remember to use the correct unit — if area is given in hectares, convert to km² first (1 km² = 100 ha).

注意使用正确单位 —— 如果面积以公顷给出，请先转换为平方公里（1 km² = 100 ha）。

5. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率和自然增长率

These vital rates help analyse population change in a country over time.

这些关键比率有助于分析一个国家随时间变化的人口变化。

Birth Rate = (Number of live births ÷ Total population) × 1 000

出生率 = (活产婴儿数 ÷ 总人口) × 1000

Death Rate = (Number of deaths ÷ Total population) × 1 000

死亡率 = (死亡人数 ÷ 总人口) × 1000

Natural Increase = Birth Rate − Death Rate (per 1 000 per year)

自然增长率 = 出生率 − 死亡率（每年每千人）

A positive natural increase means the population is growing; a negative value indicates a natural decrease.

自然增长率为正则表示人口增长；为负则表示自然减少。

6. Population Change (Including Migration) | 人口变化（含迁移）

Total population change considers both natural change and net migration.

总人口变化同时考虑自然变动和净迁移。

Population Change = (Births − Deaths) + (Immigrants − Emigrants)

人口变化 = (出生 − 死亡) + (迁入 − 迁出)

Net migration is the difference between the number of people moving in and out of an area.

净迁移是指迁入与迁出某地区的人数之差。

7. Urban Land Use Models | 城市土地利用模型

Two classic models explain how cities are structured: the Burgess concentric zone model and the Hoyt sector model. No single formula exists, but recognising the patterns is essential.

有两种经典模型解释城市结构：伯吉斯同心圆模型和霍伊特扇形模型。虽然没有具体的公式，但识别这些模式至关重要。

Burgess (1925): City grows outward in rings – CBD, transition zone, low‑class housing, medium‑class housing, high‑class housing.

伯吉斯（1925）：城市呈环状向外扩展——中央商务区、过渡带、低阶层住宅区、中阶层住宅区、高阶层住宅区。

Hoyt (1939): City develops in wedges or sectors along transport routes; industry and housing follow rail lines and roads.

霍伊特（1939）：城市沿交通路线呈楔形或扇形发展；工业和住宅沿铁路和公路分布。

These models help students link urban form to accessibility and land values.

这些模型帮助学生将城市形态与可达性和地价联系起来。

8. River Discharge | 河流流量

Discharge is the volume of water flowing through a cross‑section of a river per second. It helps understand flood risk.

流量是河流每秒通过某一断面的水量，有助于理解洪水风险。

Discharge (m³/s) = Cross‑sectional Area (m²) × Velocity (m/s)

流量（立方米/秒） = 横截面积（平方米） × 流速（米/秒）

Cross‑sectional area is calculated as width × mean depth for a simple rectangular channel.

对于简单的矩形河道，横截面积可以按宽度乘以平均水深计算。

9. Temperature Range and Total Precipitation | 气温较差与降水总量

When analysing climate graphs, two quick calculations show the temperature variability and total moisture input.

分析气候图表时，有两项快速计算可以显示气温变化幅度和总降水量。

Annual Temperature Range = Hottest Month Mean − Coldest Month Mean

年较差 = 最热月平均温度 − 最冷月平均温度

Total Annual Precipitation = Sum of all monthly precipitation values (mm)

年降水总量 = 所有月降水量之和（毫米）

A small range suggests a maritime climate; a large range points to continentality.

气温较差小表明是海洋性气候；较差大则指向大陆性气候。

10. Development Indicators | 发展指标

Development is measured using economic and social statistics. Two common indicators are GDP per capita and the Human Development Index (HDI).

发展水平使用经济和社会统计数据衡量。两个常用指标是人均 GDP 和人类发展指数（HDI）。

GDP per capita = Total GDP ÷ Total Population

人均 GDP = 国内生产总值 ÷ 总人口

HDI combines life expectancy, education (mean years of schooling) and standard of living (GNI per capita) into a single score between 0 and 1.

人类发展指数将预期寿命、教育（平均受教育年限）和生活水平（人均国民总收入）综合成一个介于 0 到 1 之间的分数。

No simple DIY formula is required at this level — just understand that higher values mean greater development.

本阶段不需掌握详细的计算公式——只需理解数值越高代表发展程度越高。

11. Erosion and Weathering Types | 侵蚀与风化类型

Although these are processes rather than formulas, remembering their types is vital for exam answers on landscape change.

尽管这些是自然过程而非公式，但记忆其类型对于有关地貌变化的考试答案至关重要。

River erosion: Hydraulic action, abrasion, attrition, solution.

河流侵蚀：水力作用、磨蚀、磨损、溶蚀。

Coastal erosion: The same four, plus wave pounding and longshore drift.

海岸侵蚀：相同的四种，再加上波浪冲击和沿岸漂移。

Weathering: Physical (freeze‑thaw, exfoliation), chemical (carbonation, oxidation), biological (root action).

风化：物理风化（冻融作用、剥离作用）、化学风化（碳酸化、氧化）、生物风化（根系作用）。

No equations here, but consistently pairing the process with a landform earns marks.

此处没有方程式，但将过程与地貌始终配对描述能赢得分数。

12. Plate Boundary Theorem | 板块边界定理

The Earth’s crust is divided into tectonic plates that move because of convection currents in the mantle. The type of boundary — constructive, destructive, conservative — determines the associated hazards and landforms.

地壳分为若干构造板块，因地幔对流而移动。板块边界类型——建设型、破坏型、守恒型——决定了相关的灾害和地貌。

Plate Boundary 边界类型	Movement 运动方式	Landforms / Hazards 地貌/灾害
Constructive (Divergent) 建设型	Plates move apart 板块分离	Mid‑ocean ridges, rift valleys, gentle earthquakes 洋中脊、裂谷、轻微地震
Destructive (Convergent) 破坏型	Oceanic plate subducts under continental 大洋板块俯冲到大陆板块之下	Deep ocean trenches, volcanic arcs, powerful earthquakes, tsunamis 深海沟、火山弧、强震、海啸
Conservative (Transform) 守恒型	Plates slide past each other 板块水平滑动	Frequent earthquakes, no volcanoes 频繁地震，无火山

Remembering this theorem means you can explain why hazards occur where they do.

记住这个定理，你就能解释灾害为何发生在特定地点。

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Formula & Theorem Quick Reference Handbook | 公式定理速查手册