📚 Year 10 OCR Geography: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook gathers the most frequently used formulas, equations, and geographical models you will encounter during your Year 10 OCR Geography course. Use it to sharpen your map skills, master population calculations, interpret river data, and recall urban land-use theories efficiently.
这本速查手册汇集了 Year 10 OCR 地理课程中最常用的公式、方程式和地理模型。用它来提升你的地图技能，掌握人口计算，解读河流数据，并高效回顾城市土地利用理论。
1. Map Scale and Real-World Distance | 地图比例尺与实际距离
Map scale expresses the relationship between a distance on the map and the corresponding distance on the ground. It is usually given as a representative fraction (1:50,000) or a linear scale.
地图比例尺表示图上距离与对应实地距离的关系，通常以分数比例尺（1:50,000）或直线比例尺给出。
Real distance = Map distance × Scale factor
实地距离 = 图上距离 × 比例尺分母
mple, on a 1:50,000 map, 4 cm between two points gives: 4 cm × 50,000 = 200,000 cm = 2 km.
例如，在 1:50,000 地图上两点相距 4 厘米，则实地距离为：4 cm × 50,000 = 200,000 cm = 2 km。
When using a linear scale, simply read the distance directly without calculation. For a fractional scale, ensure both distances are in the same unit before conversion.
使用直线比例尺时可直接读数，无需计算。使用分数比例尺时，转换前务必确保两个距离单位统一。
2. Vertical Exaggeration | 垂直夸大
Vertical exaggeration is used when drawing cross-sections to make relief more visible. It is the ratio of the vertical scale to the horizontal scale.
垂直夸大用于绘制剖面图时使地势起伏更明显，它是垂直比例尺与水平比例尺的比值。
Vertical Exaggeration (VE) = Horizontal scale ÷ Vertical scale
垂直夸大 (VE) = 水平比例尺 ÷ 垂直比例尺
scale is 1:50,000 and the vertical scale is 1:1,000, then VE = 50,000 / 1,000 = 50 times.
两个比例尺必须使用相同格式，通常化为数字比例（如 1 厘米代表 1 米写作 1:100）。若水平比例尺为 1:50,000，垂直比例尺为 1:1,000，则 VE = 50,000 / 1,000 = 50 倍。
3. Gradient (Slope) | 坡度
Gradient describes the steepness of a slope, often expressed as a ratio or a percentage. It relates the vertical change (rise) to the horizontal distance (run).
坡度描述斜坡的陡峭程度，常用比率或百分比表示，反映垂直变化（高差）与水平距离之间的关系。
Gradient (%) = (Vertical rise ÷ Horizontal distance) × 100
坡度 (%) = (垂直高差 ÷ 水平距离) × 100
15 m in height over a horizontal distance of 200 m, the gradient is (15 / 200) × 100 = 7.5%. As a ratio, it is 1:13.3. Always express the ratio with 1 on the left.
如果一条道路在水平距离 200 米内升高 15 米，坡度为 (15 / 200) × 100 = 7.5%。用比率表示为 1:13.3，确保左侧为 1。
4. River Discharge | 河流流量
Discharge is the volume of water flowing through a river channel per unit time. It increases downstream as tributaries add water and the channel grows.
流量是单位时间内流过河道某一断面的水体体积。由于支流汇入和河道拓宽，流量向下游增加。
Discharge (Q) = Cross-sectional area (A) × Mean velocity (v)
流量 (Q) = 横截面积 (A) × 平均流速 (v)
depth. Therefore, Q = w × d × v. Discharge is measured in cubic metres per second (m³/s).
横截面积由河宽乘以平均水深计算：A = 宽度 × 平均水深。因此 Q = w × d × v。流量单位为立方米每秒 (m³/s)。
5. Crude Birth Rate, Death Rate and Natural Increase | 粗出生率、死亡率与自然增长率
These vital rates are fundamental to population geography and help explain the demographic structure of a country.
这些生命率是人口地理学的基础指标，有助于解释一个国家的人口结构。
Crude Birth Rate (CBR) = (Live births ÷ Total population) × 1000
粗出生率 (CBR) = (活产婴儿数 ÷ 总人口) × 1000
Crude Death Rate (CDR) = (Deaths ÷ Total population) × 1000
粗死亡率 (CDR) = (死亡人数 ÷ 总人口) × 1000
Natural Increase Rate = CBR - CDR (per 1000)
自然增长率 = 粗出生率 - 粗死亡率 (每千人)
or example, CBR = 20/1000 and CDR = 8/1000 gives a natural increase of 12 per 1000, or 1.2%.
若将自然增长率转化为百分数，将结果除以 10。例如 CBR = 20/1000，CDR = 8/1000，自然增长率为每千人 12，即 1.2%。
6. Net Migration Rate | 净迁移率
Net migration accounts for the balance between people entering and leaving a country. It directly influences population change alongside natural increase.
净迁移考虑进入和离开一个国家的人口差额，与自然增长共同直接影响人口变动。
Net Migration = Number of immigrants - Number of emigrants
净迁移 = 迁入人数 - 迁出人数
Net Migration Rate = (Net Migration ÷ Total population) × 1000
净迁移率 = (净迁移 ÷ 总人口) × 1000
pulation growth rate = Natural increase rate + Net migration rate, all expressed per 1000.
总人口增长率 = 自然增长率 + 净迁移率，各项均以每千人表示。
7. Population Density | 人口密度
Population density shows how crowded a place is and helps compare settlement patterns or pressures on land.
人口密度显示一个地方的拥挤程度，有助于比较聚落格局或土地压力。
Population Density = Total population ÷ Land area (km²)
人口密度 = 总人口 ÷ 土地面积 (km²)
It is usually expressed as people per square kilometre. A high density does not automatically mean overcrowding because it depends on the type of land use and available resources.
通常以每平方公里人数表示。密度高并不一定意味着过度拥挤，因为这取决于土地利用类型和可用资源。
8. Doubling Time (Rule of 70) | 人口倍增时间（70 法则）
The doubling time estimates how many years it will take for a population to double in size, assuming a constant annual growth rate.
倍增时间用于估算在年增长率保持恒定的情况下，人口规模翻一番需要多少年。
Doubling time (years) ≈ 70 ÷ Annual growth rate (%)
倍增时间 (年) ≈ 70 ÷ 年增长率 (%)
For example, a growth rate of 2% per year gives a doubling time of approximately 35 years. This rule of thumb is widely used because it provides a quick, useful estimate without complex mathematics.
例如年增长率为 2% 时，倍增时间约 35 年。这一经验法则广泛使用，因为它能快速提供有用的估计，无需复杂计算。
9. Gross Domestic Product (GDP) per Capita | 人均国内生产总值
GDP per capita is a key economic indicator used to compare the average wealth or standard of living between countries.
人均 GDP 是一项关键的经济指标，用于比较不同国家的平均财富或生活水平。
GDP per capita = Total GDP ÷ Total population
人均 GDP = 国内生产总值总额 ÷ 总人口
It is usually expressed in US dollars. While useful, it does not account for income inequality within a country, so it can mask significant differences in quality of life.
通常以美元表示。尽管该指标有用，但它没有考虑国家内部收入不均，因此可能掩盖生活质量上的巨大差异。
10. The Bradshaw Model | 布拉德肖模型
The Bradshaw model describes how river characteristics change from the source to the mouth. It is often presented as a series of arrows showing downstream trends.
布拉德肖模型描述了从源头到河口河流特征的变化规律，通常用一系列箭头展示下游的变化趋势。
Mean velocity increases downstream, mainly due to a smoother channel bed and fewer obstacles.
平均流速向下游增加，主要原因是河床更平滑、障碍物减少。
Channel width and depth both increase because of greater discharge and lateral erosion.
由于流量增大和侧向侵蚀，河道宽度和深度都增加。
Discharge rises dramatically as tributaries contribute more water and the catchment area expands.
随着支流不断汇入和流域面积扩大，流量急剧升高。
Bedload particle size generally decreases, becoming more rounded and smaller due to attrition and abrasion.
由于磨蚀和磨损作用，河床沉积物粒径通常减小，变得更加圆润细小。
Channel bed roughness decreases, contributing to less friction and faster flow.
河床粗糙度降低，摩擦力减小，水流速度更快。
Gradient (slope) becomes less steep, which lowers the energy of the river but is offset by higher volume.
坡度变得平缓，河流能量有所下降，但被更大水量所抵消。
11. Burgess Concentric Zone Model | 伯吉斯同心圆模型
Developed in 1925 by Ernest Burgess, this urban land-use model explains the socio-spatial structure of cities as a series of concentric rings outward from the CBD.
1925 年由欧内斯特·伯吉斯提出，该城市土地利用模型将城市的社会空间结构描述为自 CBD 向外的一系列同心圆环。
Zone 1 – The Central Business District (CBD): commercial and retail core, high land values, tall buildings.
第一圈——中央商务区 (CBD)：商业与零售核心，地价高，高楼密集。
Zone 2 – The Transition Zone: mixed land uses with older housing, light industry, and often inner-city deprivation.
第二圈——过渡地带：土地利用混合，有旧住宅、轻工业，常出现内城贫困。
Zone 3 – Inner Suburbs / Working-Class Housing: terraced houses originally built for industrial workers, now often upgraded or redeveloped.
第三圈——内城郊区/工人阶级住房：最初为产业工人建造的排屋，现多经翻新或再开发。
Zone 4 – Middle-Class Housing: larger semi-detached houses with gardens, better environment.
第四圈——中产阶级住房：带有花园的半独立式大宅，环境较佳。
Zone 5 – Commuter Zone / High-Class Residential: suburbs and villages with spacious detached houses, residents commute to the city.
第五圈——通勤地带/上等住宅：郊区及村庄，有宽敞的独立式住宅，居民通勤至市区。
12. Hoyt Sector Model | 霍伊特扇区模型
Homer Hoyt proposed this model in 1939, arguing that cities develop in sectors or wedges radiating from the CBD along transport routes rather than in perfect rings.
霍默·霍伊特于 1939 年提出该模型，认为城市沿交通线路呈扇区或楔形自 CBD 向外发展，而非完美的环状。
High-rent residential areas occupy desirable sectors with environmental advantages and good transport, often on higher ground or next to open space.
高租金住宅区占据环境优越、交通便利的理想扇区，常位于高地或开放空间旁。
Industrial and low-cost housing sectors align along railway lines, rivers, or major roads, where land is cheaper and less attractive for residential use.
工业和低成本住房扇区沿铁路线、河流或主干道分布，此处土地便宜、对居住吸引力较弱。
Once a wedge-like pattern is established, similar land uses tend to expand outward within the same sector, reinforcing the pattern over time.
一旦形成楔形格局，同类土地利用倾向于在同一扇区内向外扩展，随时间不断强化这一模式。
The model helps explain why certain areas of a city retain their character for decades, unlike the concentric zone model which predicts uniform radial change.
该模型有助于解释城市某些区域为何数十年来保持其特徵，而同心圆模型预测的是均匀的放射状变化。
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