📚 Year 9 OCR Geography: Quick Reference Handbook of Formulas and Theorems | Year 9 OCR 地理：公式定理速查手册
This handbook provides a concise collection of essential formulas and theorems for Year 9 OCR Geography. Master these to strengthen your map skills, demographic analysis, river studies, and weather data interpretation. Each entry is presented with a clear formula and practical application tips.
本手册为 Year 9 OCR 地理整理了必背公式与定理。掌握这些内容将提升你在地图技能、人口分析、河流研究和气象数据解读中的解题能力。每个条目均包含公式和实用技巧。
1. Map Scale Conversion | 地图比例尺换算
The relationship between map distance and real ground distance is fundamental. Use this formula to convert between the two using the scale factor.
地图距离与实地距离的换算关系是基础技能。使用该公式可通过比例尺进行双向转换。
Ground Distance = Map Distance × Scale Factor
实地距离 = 图上距离 × 比例尺分母
h is 1 km. Always ensure consistent units, converting centimetres to metres or kilometres for readability.
例如，在 1:25,000 地图上，4 厘米代表 4 × 25,000 = 100,000 厘米，即 1 公里。务必统一单位，将厘米转换为米或公里以便理解。
2. Gradient (Slope) Calculation | 坡度计算
Gradient expresses the steepness of a slope as a ratio of vertical rise to horizontal run. It is often written as 1:n, where n is the run divided by the rise.
坡度表示斜坡的陡峭程度，为垂直高差与水平距离的比值，常写成 1:n 的形式，n 为水平距离除以高差。
Gradient = Vertical Rise / Horizontal Run
坡度 = 垂直高差 / 水平距离
20:500 = 1:25. This means for every 25 metres horizontally, elevation changes by 1 metre.
要得到 1:n 格式，将高差和水平距离同时除以高差值。若山丘在 500 米水平距离内上升 20 米，坡度为 20:500 = 1:25。即每水平移动 25 米，高度变化 1 米。
3. Area Measurement on Maps | 地图面积测量
Estimating the area of an irregular feature on a map often uses grid square counting. For regular shapes, apply geometric formulas after converting map dimensions to ground distances.
估算地图上不规则区域的面积常采用方格计数法。规则图形则在将图上尺寸换算为实地距离后套用几何面积公式。
Area (km²) = (Number of Grid Squares × Area of One Square) or (Length × Width)
面积（平方千米）=（方格数 × 单个方格面积）或（长 × 宽）
e equals 1 km² on the ground. Count full squares and combine partial squares to approximate the total area. For a rectangular field measuring 3 cm by 2 cm on the map, ground dimensions would be 1.5 km by 1.0 km, giving an area of 1.5 km².
在 1:50,000 地图上，每个 2 厘米 × 2 厘米方格代表实地 1 平方千米。统计完整方格，合并部分方格估算总面积。若矩形田地在地图上长 3 厘米、宽 2 厘米，实地尺寸为 1.5 千米 × 1.0 千米，面积 1.5 平方千米。
4. Natural Increase Rate (NIR) | 人口自然增长率
Natural increase measures how a population changes due to births and deaths alone, excluding migration. The result is usually expressed as a percentage.
人口自然增长率仅依据出生和死亡衡量人口变化，不含迁移，结果通常以百分比表示。
NIR (%) = (Crude Birth Rate − Crude Death Rate) / 10
自然增长率 (%) = (粗出生率 − 粗死亡率) / 10
irth rate of 30 per 1,000 and a death rate of 10 per 1,000 has a NIR of (30 − 10) / 10 = 2% itive NIR indicates population growth; a negative NIR suggests decline, barring migration.
出生率与死亡率以每千人计。若某国出生率为 30‰，死亡率为 10‰，自然增长率为 (30 − 10) / 10 = 2%。正值为人口增长，负值若无移民补充则意味着减少。
5. Population Density | 人口密度
Population density describes how crowded an area is. It is a simple ratio of total population to land area, helping to compare settlement patterns.
人口密度描述某一区域的拥挤程度，为总人口与土地面积的比例，有助于对比聚落模式。
Population Density = Total Population / Land Area (km²)
人口密度 = 总人口 / 土地面积（平方千米）
For instance, a city with 500,000 people living in an area of 100 km² has a density of 5,000 people per km². This is considered high density. Low densities are typical of rural areas with scattered populations.
例如，某市 50 万人居住在 100 平方千米范围内，人口密度为每平方千米 5000 人，属于高密度。低密度常见于人口分散的农村地区。
6. Urbanisation Rate | 城市化率
Urbanisation rate is the percentage of a country's population living in urban areas. Tracking changes over time reveals the pace of urban growth.
城市化率指一国居住在城市区域的人口百分比。观察其历年变化可揭示城市化速度。
Urbanisation Rate (%) = (Urban Population / Total Population) × 100
城市化率 (%) = (城市人口 / 总人口) × 100
llion urban residents out of a total 50 million, its urbanisation rate is (30/50)×100 = 60% increase in this rate indicates the speed of rural-to-urban migration and urban expansion.
若某国总人口 5000 万，其中城市人口 3000 万，城市化率为 (3000万/5000万)×100 = 60%。城市化率的年增长量反映了农村向城市迁移与城市扩张的速度。
7. Drainage Density | 河网密度
Drainage density indicates how well a basin is drained by its stream network. It is the total length of all stream channels divided by the drainage basin area.
河网密度反映流域内河网的疏密程度，为所有河道总长度除以流域面积。
Drainage Density = Total Stream Length (km) / Basin Area (km²)
河网密度 = 河道总长度（千米） / 流域面积（平方千米）
High drainage density (e.g., > 2 km/km²) suggests impermeable rock, intense rainfall, or sparse vegetation, promoting rapid runoff and a fine network of channels. Low density occurs in permeable landscapes where water infiltrates easily.
高河网密度（如 >2 千米/平方千米）通常意味着岩层不透水、暴雨集中或植被稀疏，促使快速径流并形成密集河道。低密度出现在透水性好的地区，水分易下渗。
8. River Gradient (Long Profile) | 河流比降（纵剖面）
The river gradient measures the steepness of a river channel over a given reach. It influences flow velocity and erosive power.
河流比降衡量特定河段的陡峭程度，影响流速与侵蚀能力。
Gradient = Vertical Drop (m) / Channel Length (m)
比降 = 垂直落差（米） / 河段长度（米）
teeper gradients occur in upper courses; lower gradients characterise floodplains near the mouth.
通常表示为无量纲比值或每千米落差。若 5 千米河段内下降 50 米，比降为 50/5000 = 0.01，即 10 米/千米。上游比降大，下游近河口冲积平原比降平缓。
9. Mean (Average) Temperature | 平均气温
Mean temperature summarises the typical thermal condition of a place over a day, month, or year. It smooths out daily extremes to reveal climate patterns.
平均气温概括了一地某日、某月或某年的典型热量状况，平滑了日极值以显示气候特征。
Mean Daily Temp = (Max Temp + Min Temp) / 2
日平均气温 = (最高气温 + 最低气温) / 2
To calculate mean monthly temperature, average all daily means for the month. Mean annual temperature is the average of the twelve monthly means. For example, a day with a high of 24 °C and a low of 14 °C has a mean of 19 °C.
计算月平均气温时，需将当月每日平均气温求和再除以天数。年平均气温则为十二个月平均气温的平均。若某日最高 24 °C，最低 14 °C，日均温为 19 °C。
10. Temperature Range | 气温较差
Temperature range shows the difference between the highest and lowest values in a given period. It indicates climate variability or continentality.
气温较差表示给定时段内最高值与最低值的差，反映气候变率或大陆度。
Temperature Range = Maximum Temp − Minimum Temp
气温较差 = 最高气温 − 最低气温
A large annual range (e.g., 30 °C) often signifies an inland continental location away from the moderating influence of oceans. Coastal regions typically have smaller ranges. When analysing climate graphs, calculate diurnal (daily) and annual ranges to infer location characteristics.
年较差大（如 30 °C）常表明地处内陆，远离海洋调节。沿海地区较差通常较小。分析气候图时，可计算日较差和年较差，推断该地特征。
11. Total Annual Precipitation | 年总降水量
Total precipitation is the sum of all rainfall (and snow melt equivalent) recorded over a year. It is essential for classifying climate types and assessing water availability.
总降水量为一年内记录的降雨（及融雪当量）总和，对于气候分类和评估水资源至关重要。
Annual Precipitation = Σ Monthly Rainfall Totals
年降水量 = 各月降水量总和
Always express in millimetres (mm). A station receiving monthly totals of 50, 40, 30, 45, 60, 70, 80, 90, 100, 110, 90, 80 mm would have an annual total of 845 mm. Coupled with temperature, this helps identify equatorial, desert, or temperate climates.
单位始终用毫米（mm）。若某站各月降水量分别为 50, 40, 30, 45, 60, 70, 80, 90, 100, 110, 90, 80 mm，年总量即为 845 mm。结合气温数据即可判别赤道、沙漠或温带气候。
12. Wave Frequency and Energy | 波浪频率与能量
In coastal geography, wave frequency affects erosion and sediment transport. It is the number of waves breaking per unit time, often per minute.
在海岸地理中，波浪频率影响侵蚀与泥沙输运，指单位时间内的拍岸次数，通常以每分钟计。
Wave Frequency = Number of Waves / Time (minutes)
波浪频率 = 波浪数 / 时间（分钟）
High-frequency destructive waves (e.g., 12-15 per minute) have a strong backwash and are common in stormy conditions, eroding beaches. Low-frequency constructive waves (6-8 per minute) build up beaches with a stronger swash. Field measurements of wave frequency support analysis of coastal change.
高频破坏性波浪（如每分钟 12-15 次）回冲强，常见于暴风天气，侵蚀海滩。低频建设性波浪（每分钟 6-8 次）冲流强，可堆积海滩。实地测量波浪频率有助于分析海岸变化。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图