📚 GCSE AQA Geography: Formula & Theorem Quick Reference Handbook | GCSE AQA 地理：公式定理速查手册
This handbook compiles every key formula, theorem, and calculation skill required for the AQA GCSE Geography specification. Use it to master numerical questions across both physical and human topics, from population dynamics and river discharge to map skills and statistical analysis. Each entry is paired with a worked example to help you apply the formula under exam conditions.
本手册汇集了 AQA GCSE 地理考试大纲要求的每一个关键公式、定理和计算技能。无论人口动态、河流流量，还是地图技能与统计分析，你都能在这里找到对应的速查内容。每个条目都配有解析实例，帮助你在考试中准确运用公式。
1. Population Formulas | 人口公式
The crude birth rate (CBR) is the number of live births per 1000 people per year: CBR = (Number of births ÷ Total population) × 1000. A country with 800,000 births and a population of 40 million has a CBR of (800,000 ÷ 40,000,000) × 1000 = 20 per 1000.
粗出生率 (CBR) 是每年每千人中的活产婴儿数：CBR = (出生人数 ÷ 总人口) × 1000。例如，一个国家出生 80 万，总人口 4000 万，则 CBR = (800,000 ÷ 40,000,000) × 1000 = 20‰。
Similarly, the crude death rate (CDR) is (Number of deaths ÷ Total population) × 1000. If deaths are 600,000, CDR = (600,000 ÷ 40,000,000) × 1000 = 15 per 1000.
粗死亡率 (CDR) 为 (死亡人数 ÷ 总人口) × 1000。若死亡 60 万，则 CDR = (600,000 ÷ 40,000,000) × 1000 = 15‰。
Natural increase is calculated as CBR − CDR, and the rate of natural increase (RNI) is often expressed as a percentage: RNI (%) = (CBR − CDR) ÷ 10. Here, RNI = (20 − 15) ÷ 10 = 0.5%.
自然增长由 CBR − CDR 得出，自然增长率 (RNI) 常用百分数表示：RNI (%) = (CBR − CDR) ÷ 10。上述案例 RNI = (20 − 15) ÷ 10 = 0.5%。
Population density equals Total population ÷ Land area (km²). A city of 2.5 million people covering 500 km² has a density of 5000 people/km².
人口密度 = 总人口 ÷ 土地面积 (km²)。一座 250 万人口、面积 500 平方公里的城市，密度为 5000 人/平方公里。
The dependency ratio shows the pressure on the working population: [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100. It is a pure number, not a percentage, but often read as ‘X dependents per 100 working-age people’.
抚养比反映劳动人口承受的压力：[(0–14 岁人口 + 65 岁以上人口) ÷ 15–64 岁人口] × 100。它是一个比值，通常读作“每 100 名劳动年龄人口负担 X 名受抚养者”。
2. Urbanisation & Development Indicators | 城市化与发展指标
The urbanisation rate is the percentage of a country’s population living in urban areas. It is often given directly on a graph, but you can calculate it as (Urban population ÷ Total population) × 100. Use this to track changes over time, e.g., from 60% in 1990 to 75% in 2020.
城市化率指一国城镇人口占总人口的百分比，常直接从图表获取，也可通过 (城镇人口 ÷ 总人口) × 100 计算。用它追踪随时间的变化，比如从 1990 年的 60% 升至 2020 年的 75%。
Gross Domestic Product (GDP) per capita is Total GDP ÷ Total population. It is usually expressed in US$ and indicates average economic output per person. A rapid rise often signals a newly emerging economy (NEE).
人均国内生产总值 (GDP) 为 GDP 总额 ÷ 总人口，通常以美元表示，反映人均经济产出。快速上升往往预示着一个新兴经济体 (NEE) 的出现。
The Human Development Index (HDI) combines life expectancy, education, and GNI per capita into a number between 0 and 1. No simple formula is needed for the exam, but you must understand that a higher HDI means greater development. Thresholds: low (<0.550), medium (0.550–0.699), high (0.700–0.799), very high (≥0.800).
人类发展指数 (HDI) 综合了预期寿命、教育和人均国民总收入，数值在 0 到 1 之间。考试不要求具体公式，但需理解 HDI 越高发展水平越高。划分标准：低 (<0.550)、中 (0.550–0.699)、高 (0.700–0.799)、极高 (≥0.800)。
The Gini coefficient measures inequality within a country. A score of 0 means perfect equality, 1 means perfect inequality. It is not a calculation you perform, but you must interpret it: a coefficient of 0.25 indicates a more equal society than 0.60.
基尼系数衡量一国内部的不平等程度。0 表示完全平等，1 表示完全不平等。考试中不需计算，但要会解读：0.25 的社会比 0.60 更加平等。
3. River Discharge & Flow | 河流流量与流速
Discharge (Q) is the volume of water passing a point in a river per second: Q = A × v, where A is the cross‑sectional area (m²) and v is the mean velocity (m/s). Q is measured in cubic metres per second (cumecs).
流量 (Q) 是每秒钟流过河道某断面的水量：Q = A × v，其中 A 为横截面积 (m²)，v 为平均流速 (m/s)。Q 的单位为立方米/秒 (cumec)。
Cross‑sectional area A is found by multiplying channel width (w) by mean depth (d): A = w × d. If a stream is 8 m wide and has a mean depth of 1.2 m, A = 9.6 m².
横截面积 A 由河宽 (w) 与平均水深 (d) 相乘得到：A = w × d。如果河道宽 8 m，平均水深 1.2 m，A = 9.6 m²。
Velocity v is often measured with a flowmeter or float method. Using a float, v = Distance (m) ÷ Time (s). If a float travels 10 m in 25 seconds, v = 0.4 m/s. To estimate the mean velocity, multiply surface velocity by a correction factor (e.g., 0.8 for shallow streams).
流速 v 常用流速仪或浮标法测量。用浮标时，v = 距离 (m) ÷ 时间 (s)。若浮标 25 秒移动 10 米，v = 0.4 m/s。估算平均流速时，将表面流速乘以校正系数（如浅溪取 0.8）。
Hydraulic radius (R) is a measure of channel efficiency: R = A ÷ wetted perimeter (P). Wetted perimeter is the length of the channel bed and banks in contact with water. For a trapezoidal channel, P = w + 2d, but in a rectangular channel it simplifies to R = (w × d) ÷ (w + 2d).
水力半径 (R) 反映河道输水效率：R = A ÷ 湿周 (P)。湿周是水流与河床、河岸接触的长度。梯形河道中 P = w + 2d，在矩形河道中简化为 R = (w × d) ÷ (w + 2d)。
4. Coastal Processes | 海岸过程
The rate of coastal erosion is typically expressed as metres per year: Erosion rate = Distance eroded (m) ÷ Time period (years). If a cliff retreats 15 m over 30 years, the rate is 0.5 m/year. You can compare rates along a coastline to identify vulnerable zones.
海岸侵蚀速率通常以米/年表示：侵蚀速率 = 侵蚀距离 (m) ÷ 时间长度 (年)。如果悬崖 30 年后退 15 米，侵蚀速率为 0.5 米/年。可通过对比海岸各段的速率识别脆弱区域。
Longshore drift volume can be estimated when both the cross‑sectional area of the beach and the velocity of sediment movement are known, but no fixed formula is required for GCSE. Instead, focus on interpreting sediment size and movement direction from maps and field sketches.
沿岸漂移的沙量可通过海滩横截面积和沉积物移动速度估算，但 GCSE 不要求固定公式。重点是根据地图和实地草绘判断沉积物粒径和运动方向。
To calculate the percentage change in beach width after a storm event, use % change = [(New width − Original width) ÷ Original width] × 100. A beach that shrinks from 40 m to 32 m has a change of [(32 − 40) ÷ 40] × 100 = −20%.
计算风暴后海滩宽度的百分比变化：% 变化 = [(新宽度 − 原宽度) ÷ 原宽度] × 100。海滩从 40 米缩至 32 米，变化为 [(32 − 40) ÷ 40] × 100 = −20%。
5. Map Skills | 地图技能
Scale is a ratio that compares a distance on the map to the corresponding distance on the ground. For a 1:25,000 map, 1 cm represents 25,000 cm (250 m). To find actual distance D = map distance (cm) × scale factor ÷ 100,000 to convert to km. 4 cm on a 1:50,000 map gives 4 × 50,000 ÷ 100,000 = 2 km.
比例尺是图上距离与实地距离的比值。1:25,000 地图上，1 厘米代表 25,000 厘米 (250 米)。实际距离 D = 图上距离 (cm) × 比例尺 ÷ 100,000 得到公里数。1:50,000 图上 4 厘米 = 4 × 50,000 ÷ 100,000 = 2 公里。
Gradient is the steepness of a slope: Gradient = Vertical rise (m) ÷ Horizontal run (m). It is often written as a ratio 1:X, where X = horizontal run ÷ vertical rise. If a path climbs 30 m over a horizontal distance of 600 m, the gradient is 30/600 = 1:20.
坡度表示坡面的陡峭程度：坡度 = 垂直高差 (m) ÷ 水平距离 (m)。常用 1:X 的比例表示，X = 水平距离 ÷ 高差。如果一条路水平距离 600 米升高 30 米，坡度为 30/600 = 1:20。
Area on a map can be estimated by counting squares on a grid overlay or by treating a shape as a rectangle: Area (km²) = length × width, after converting map measurements to ground kilometres. For irregular shapes, use the dot‑grid method: each dot represents a known area.
地图上的面积可通过数网格或视为矩形估算：面积 (km²) = 长 × 宽，计算前需将图上长度换算为实地公里数。对不规则形状，可用点格法，每点代表已知面积。
Bearings are measured clockwise from north (0°) and given as three‑digit angles. Use a protractor to measure the angle between the north‑line and the line joining two points. Always align the protractor carefully with the grid north.
方位角从正北 (0°) 顺时针测量，用三位数表示。用量角器测量北向线与两点连线之间的夹角。务必使量角器与网格北对齐。
6. Statistical Measures | 统计测量
The mean is the arithmetic average: Mean = Sum of all values ÷ Number of values. If five pebble lengths are 12, 14, 10, 15, 9 cm, the mean is (12+14+10+15+9) ÷ 5 = 12 cm. The mean is sensitive to outliers.
平均值即算术平均数：平均值 = 所有数值之和 ÷ 数值个数。五颗卵石的长度是 12、14、10、15、9 厘米，平均值为 (12+14+10+15+9) ÷ 5 = 12 厘米。平均值易受异常值影响。
The median is the middle value when data are sorted. For an even number of values, take the mean of the two middle numbers. In the set 9, 10, 12, 14, 15, the median is 12 cm. It is less affected by extremes.
中位数是排序后位于中间的数值。若为偶数个数值，取中间两数的平均。集合 9, 10, 12, 14, 15 的中位数为 12 厘米，受极端值影响较小。
Range shows the spread: Range = Highest value − Lowest value. Here, range = 15 − 9 = 6 cm. Interquartile range (IQR) is the difference between the upper quartile (Q3) and lower quartile (Q1). Find Q1 as the median of the lower half, Q3 as the median of the upper half.
极差反映离散程度：极差 = 最大值 − 最小值。此处极差 = 15 − 9 = 6 厘米。四分位距 (IQR) 是上四分位数 (Q3) 与下四分位数 (Q1) 的差。下四分位数是下半部分的中位数，上四分位数是上半部分的中位数。
Percentage change is widely used in geography: % change = [(New value − Original value) ÷ Original value] × 100. The rate of urbanisation growth or decline in a river’s discharge can be compared this way.
百分比变化在地理中应用广泛：% 变化 = [(新值 − 原值) ÷ 原值] × 100。城市化增长率或河流流量的变化都可用此法比较。
7. Climate Calculations | 气候计算
Mean annual temperature is calculated by summing the 12 monthly mean temperatures and dividing by 12. For a climate graph, each monthly mean is the average of daily maximum and minimum temperatures.
年均温由 12 个月的月均温相加后除以 12 得到。气候图中，月均温是日最高温与日最低温的平均值。
Total annual precipitation is the sum of all 12 monthly rainfall totals. In a climate with monthly totals of 50, 40, 30, … mm, the annual total is the sum of those figures. Units must always be shown (mm).
年降水量是 12 个月降水量的总和。若某气候各月降水量分别为 50、40、30 … 毫米，年总量即为这些数字之和，单位必须标明 (mm)。
Temperature range is the difference between the highest and lowest monthly mean temperatures: Range = max monthly mean − min monthly mean. A large range suggests a continental climate, a small range a maritime climate.
气温年较差是最高月均温与最低月均温的差：年较差 = 最高月均温 − 最低月均温。年较差大表明大陆性气候，小则表明海洋性气候。
When comparing climate data for two locations, use the paired statistics—mean temperature, total precipitation, temperature range—and always round to one decimal place. Explain the results in terms of latitude, altitude, and distance from the sea.
比较两地气候数据时，使用成对的统计量——平均温度、总降水量、气温年较差，并始终保留一位小数。结合纬度、海拔、距海远近解释结果。
8. Fieldwork Techniques | 实地调查技术
Systematic and random sampling are the two main approaches. In systematic sampling, you collect data at regular intervals (e.g., every 5 metres along a transect); in random sampling, every location has an equal chance of being chosen, often using a random number generator.
系统抽样与随机抽样是两种主要方法。系统抽样按固定间隔收集数据（如沿样带每隔 5 米）；随机抽样中每个位置被选中的概率相同，通常借助随机数生成器。
Percentage cover is used in vegetation surveys and land‑use mapping. % cover = (Area covered by feature ÷ Total area of quadrat) × 100. If rocks cover 12 out of 25 squares in a 0.5 m × 0.5 m quadrat, percentage cover = (12 ÷ 25) × 100 = 48%.
覆盖百分比用于植被调查和土地利用制图。覆盖率 = (特征覆盖面积 ÷ 样方总面积) × 100。在一个 0.5 m × 0.5 m 样方 (25 格) 中，若岩石覆盖 12 格，覆盖率 = (12 ÷ 25) × 100 = 48%。
River depth measurements along a channel cross‑section allow you to calculate mean depth. Place the meter ruler at equal intervals, record depth, then Mean depth = Sum of depths ÷ Number of measurements. This feeds into discharge calculations.
沿河道横断面测量水深可计算平均水深。在等距点放置测深尺记录深度，平均水深 = 深度总和 ÷ 测量次数，该数据可进一步用于流量计算。
Spearman’s Rank Correlation Coefficient (rs) tests the relationship between two data sets. The formula is rs = 1 − [6 Σd² ÷ n(n²−1)], where d is the difference between ranks and n is the number of pairs. rs ranges from −1 (perfect negative) to +1 (perfect positive). A worked example is essential practice.
斯皮尔曼等级相关系数 (rs) 用于检验两数据集的关系。公式为 rs = 1 − [6 Σd² ÷ n(n²−1)]，其中 d 为等级差，n 为数据对数。rs 从 −1 (完全负相关) 到 +1 (完全正相关)，需通过实例熟练掌握。
9. Economic Indicators | 经济指标
Trade balance is the difference between a country’s exports and imports: Trade balance = Total value of exports − Total value of imports. A positive balance is a surplus, a negative balance a deficit. It is often measured in US$ billions.
贸易差额是一国出口与进口的差值：贸易差额 = 出口总额 − 进口总额。正值表示顺差，负值表示逆差，通常以十亿美元计。
Employment structure shows the percentage of the labour force in primary, secondary, tertiary, and quaternary sectors. To find the percentage in a sector: (Number employed in sector ÷ Total labour force) × 100. Compare pie charts to identify development stage.
就业结构反映了劳动力在第一、二、三、四产业中的百分比。部门占比 = (部门就业人数 ÷ 总劳动力) × 100。通过比较饼状图可判断所处的发展阶段。
Food miles and carbon footprint are often presented as totals or per capita values, but the calculation principle is similar to ratios. For carbon footprint per person: Total CO₂ emissions (tonnes) ÷ Population. A decrease indicates progress towards sustainability.
食物里程和碳足迹常以总量或人均值给出，计算原则与比值相似。人均碳足迹 = CO₂ 排放总量 (吨) ÷ 人口。数值下降代表向可持续方向进展。
10. Exam Application Tips | 考试应用技巧
Always present answers in the correct units and round to an appropriate number of decimal places—usually one or two unless stated otherwise. For percentage change, show the formula, the substitution, and the final answer clearly.
答案务必使用正确单位，并四舍五入至合适的小数位数——除非另有说明，一般保留一到两位。计算百分比变化时，清晰地写出公式、代入过程和最终结果。
When a question asks you to ‘calculate’, you must show all steps. For ‘describe the relationship’, use values from the graph, e.g., ‘As discharge increases from 5 to 25 cumecs, velocity increases from 0.2 to 1.1 m/s’. Link back to geographical theory.
遇到“计算”题必须展示全部步骤。遇到“描述关系”题，要用图表中的具体数值，例如“当流量从 5 增至 25 cumecs，流速从 0.2 m/s 增至 1.1 m/s”，并与地理理论挂钩。
Interpreting a scattergraph: if points form an upward‑sloping pattern, speak of a positive correlation. If you can draw a line of best fit, use it to estimate values. Never extend the line beyond the data range (extrapolation is unreliable).
解读散点图：若点大致呈上倾趋势，为正相关。若可画最佳拟合线，可用它估测数值。切勿将线延长至数据范围之外（外推不可靠）。
Finally, memorise the key formulas actively—write them on flashcards, practise them with past papers, and always double‑check your arithmetic under exam pressure. Accurate use of the formulas in this handbook can be the difference between a grade 6 and a grade 9.
最后，主动记忆关键公式——写在抽认卡上，用历年真题反复练习，且考试时一定再次核查运算。准确运用本手册中的公式，可能是从 6 分跃升至 9 分的关键。
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