📚 Year 10 AQA Geography: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook compiles the essential formulae, equations and key quantitative relationships that Year 10 students need to master for the AQA GCSE Geography course. From river discharge calculations to demographic measures, every formula is presented with clear definitions and worked examples. Mastering these tools will sharpen your analytical skills and boost your confidence in both physical and human geography examinations.
这本速查手册汇集了 Year 10 学生在 AQA GCSE 地理课程中必须掌握的核心公式、方程和关键定量关系。从河流流量计算到人口测量，每个公式都配有清晰的定义和计算实例。熟练掌握这些工具将增强你的分析能力，并提升你在自然地理与人文地理考试中的信心。
1. River Discharge | 河流流量
Discharge is the volume of water flowing through a river channel per unit of time. It is the most important measure of a river's capacity to transport sediment. The fundamental formula is:
流量是指单位时间内流过河道某一横截面的水体体积，是衡量河流输沙能力最重要的指标。基本公式为：
Q = A × V
where Q represents discharge (cubic metres per second, m3/s), A is the cross-sectional area of the channel (m2) and V is the mean velocity of the water (m/s). In the field, velocity is measured with a flowmeter at 0.6 of the depth from the surface to obtain a representative average.
其中 Q 表示流量（立方米每秒，m3/s），A 为河道横截面积（m2），V 为水流平均流速（m/s）。野外测量时常用流速仪在水面下 0.6 倍水深处测速，以获取代表性的平均流速。
To find the cross-sectional area, multiply channel width (w) by mean depth (d): A = w × d. For instance, a river 10 m wide with an average depth of 1.2 m has an area of 12 m2. If the mean velocity is 0.5 m/s, discharge Q = 12 × 0.5 = 6.0 m3/s (often called cumecs).
计算横截面积时，用水面宽度（w）乘以平均水深（d）：A = w × d。例如，某河道宽 10 米，平均水深 1.2 米，则 A = 12 m2。若平均流速为 0.5 m/s，流量 Q = 12 × 0.5 = 6.0 m3/s（常称作“立米每秒”）。
2. Cross-sectional Area and Hydraulic Radius | 横截面积与水力半径
Beyond simple width and depth, the efficiency of a river channel is often described by its hydraulic radius. The hydraulic radius (R) is the ratio of cross-sectional area (A) to wetted perimeter (P):
除了简单的宽度与深度，河道的输水效率常通过水力半径来描述。水力半径（R）为横截面积（A）与湿周（P）之比：
R = A ÷ P
The wetted perimeter is the length of the channel bed and banks in contact with the water. A larger hydraulic radius means less friction relative to the flow, so the river can move water more efficiently. In wide, shallow channels, the wetted perimeter is approximately equal to the width, so R approaches the mean depth.
湿周是指水流与河床、河岸接触线的长度。水力半径越大，意味着相对于水量的摩擦阻力越小，河道输水效率越高。在宽而浅的河道中，湿周近似等于水面宽度，此时水力半径接近于平均水深。
e, a rectangular channel 8 m wide with a water depth of 1.5 m has A = 8 × 1.5 = 12 m2 ius R = 12 ÷ 11 ≈ 1.09 m. This value is often used to compare channel shapes.
例如，一条宽 8 米的矩形河道，水深 1.5 米，A = 8 × 1.5 = 12 m2。其湿周 P = 宽度 + 2 × 水深 = 8 + 3 = 11 米。由此水力半径 R = 12 ÷ 11 ≈ 1.09 米。该值常用于比较不同的河道断面形态。
3. River Gradient | 河流梯度
Gradient describes the steepness of a river channel, which strongly influences flow velocity and erosive power. It is calculated as the vertical fall divided by the horizontal distance over a measured reach:
梯度描述河道的陡峭程度，对流速和侵蚀力影响极大。它通过测量河段的垂直高差除以其水平距离来计算：
Gradient = Vertical Rise (m) ÷ Horizontal Distance (m)
The result can be expressed as a ratio (e.g. 1 : 50), as a fraction or as a percentage. A gradient of 0.02 means a 2 m drop for every 100 m of along-channel distance. In upland areas, gradients are often steep, whereas lowland rivers typically have gradients below 1 in 1000.
结果可用比值（如 1:50）、分数或百分数表示。梯度为 0.02 意味着沿河道每 100 米下降 2 米。上游山区河段梯度通常较大，而平原河流的梯度往往低于 1/1000。
200 = 0.025, or expressed as 1 : 40. This steep reach is likely to have high velocity and coarse bedload.
实地测量示例：沿河道两点间水平距离为 200 米，高差为 5 米。梯度 = 5 ÷ 200 = 0.025，可表示为 1:40。这样陡的河段流速较高，河床沉积物粒径也较大。
4. Drainage Density | 河流密度
Drainage density reflects how well a basin is drained by surface streams. It is the total length of all stream channels divided by the area of the drainage basin:
河流密度反映流域内河道对地表水的疏干能力，等于流域内所有河道总长度除以流域面积：
Dd = ΣL ÷ Ab
where ΣL is the sum of the lengths of all stream segments (km) and Ab is the total basin area (km2). The unit is km/km2 (or km-1). High drainage density, typically found on impermeable rocks or steep slopes, indicates rapid runoff and a high peak discharge. Low density occurs on permeable substrates with more infiltration.
式中 ΣL 为所有河道总长度（km），Ab 为流域总面积（km2）。单位为 km/km2（或 km-1）。高河流密度常见于不透水岩石或陡坡地区，意味着径流快、洪峰流量大；低密度则出现在透水性好、下渗强烈的区域。
Example: a basin of 25 km2 contains 80 km of streams. Dd = 80 ÷ 25 = 3.2 km/km2. This relatively high value suggests that the basin responds quickly to rainfall, with a short lag time. On an AQA exam, you might be asked to compare drainage densities from map evidence.
示例：某流域面积 25 km2，河道总长 80 千米，则 Dd = 80 ÷ 25 = 3.2 km/km2。这个较高的数值表明流域对降水的响应迅速，滞后时间短。在 AQA 考试中，你可能需要依据地图资料来比较不同流域的河流密度。
5. Population Density | 人口密度
Population density is a fundamental measure in human geography, expressing how crowded an area is. The formula is straightforward:
人口密度是人文地理学的基本量度，表示一个地区的拥挤程度，计算公式非常简单：
Population Density = Total Population ÷ Land Area (km2)
It is usually given as persons per square kilometre. This statistic helps explain patterns of settlement, resource pressure and service provision. Areas with high density, such as city centres, often have high-rise buildings and intensive land use, while low-density rural areas may struggle to sustain public transport or schools.
通常以每平方公里人口数表示。该指标有助于说明聚落形态、资源压力和公共服务供给。高密度地区如市中心往往楼层高、土地利用强度大，而低密度的乡村地区可能难以维持公共交通或学校运转。
For instance, a ward with 8,400 residents covering 3 km2 has a density of 8,400 ÷ 3 = 2,800 people per km2. When interpreting data, remember that crude density does not show internal variations; a city might have an average density far lower than that of its central ward.
例如，某选区居住 8,400 人，面积 3 km2，其人口密度为 8,400 ÷ 3 = 2,800 人/km2。解读数据时要注意，粗密度无法反映内部差异；一座城市的平均密度可能远低于其中心选区的密度。
6. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率与自然增长
Demographic rates are crucial for population dynamics. The Crude Birth Rate (CBR) and Crude Death Rate (CDR) are expressed per 1,000 people per year:
人口统计率对人口动态至关重要。粗出生率（CBR）和粗死亡率（CDR）以每年每千人为单位：
CBR = (Number of Live Births ÷ Total Population) × 1000
CDR = (Number of Deaths ÷ Total Population) × 1000
The Rate of Natural Increase (RNI) can be calculated directly as a percentage:
自然增长率（RNI）可直接按百分比计算：
RNI (%) = (CBR - CDR) ÷ 10
f a country has a CBR of 24 and a CDR of 8 per 1,000, the RNI = (24 - 8) ÷ 10 = 1.6% per year. This means, ignoring migration, the population grows by 1.6% annually.
另一种算法为 RNI = ((出生数 - 死亡数) ÷ 总人口) × 100。若某国 CBR 为 24‰，CDR 为 8‰，则 RNI = (24 - 8) ÷ 10 = 1.6% / 年。这表明，在不考虑迁移的情况下，人口每年增长 1.6%。
In Year 10, you will also meet the total fertility rate and life expectancy; while they are not formula-based, the arithmetic of natural increase underpins most population models, including the Demographic Transition Model.
在 Year 10 阶段你还会接触到总和生育率和预期寿命；尽管它们并非公式，但自然增长的算术是大多数人口模型（包括人口转变模型）的基础。
7. Dependency Ratio | 抚养比
The dependency ratio is an economic indicator showing the pressure on the productive population. It compares those typically not in the labour force (young and old) to the working-age population:
抚养比是一个反映生产性人口所受经济压力的指标，它对比了通常不在劳动力市场中的群体（年轻人和老年人）与劳动年龄人口：
[(Population aged 0-14 + Population aged 65+) ÷ Population aged 15-64] × 100
The result is a percentage, with 100 meaning there is exactly one dependent for every person of working age. A high ratio, common in both youthful populations (many children) and ageing societies, implies greater demand for schools, healthcare and pensions.
结果以百分数表示，100 意味着每 1 名劳动年龄人口对应 1 名被抚养者。高抚养比常见于年轻型人口（儿童多）和老龄化社会，意味着对学校、医疗和养老金的更大需求。
100 = (40 ÷ 60) × 100 ≈ 66.7. This indicates that for every 100 working-age people, there are about 67 dependents.
例如，某国 0-14 岁人口 3,000 万，65 岁及以上 1,000 万，15-64 岁 6,000 万。抚养比 = [(30 + 10) ÷ 60] × 100 = 66.7。这意味着每 100 名劳动年龄人口需抚养约 67 名非劳动年龄人口。
8. Urban Growth Rate | 城市化增长率
Urbanisation can be measured as the change in the percentage of people living in urban areas, or as the growth rate of the urban population itself. A common formula for annual urban population growth rate is:
城市化既可用城镇人口占总人口百分比的变动来衡量，也可用城镇人口本身的增长率表示。城镇人口年增长率常用公式为：
Urban Growth Rate (%) = [(Urban Popnew - Urban Popold) ÷ Urban Popold] × 100
When calculated over a number of years, this can be averaged to show an annual rate. High urban growth rates, often seen in emerging economies, are driven by rural-urban migration and natural increase.
若计算多年情况，可求平均值得到年均增长率。高城镇人口增长率常见于新兴经济体，由乡城迁移和城镇人口自然增长共同驱动。
ercentage growth over the period = [(650,000 - 500,000) ÷ 500,000] × 100 = 30%. The average annual growth rate is roughly 30% ÷ 5 = 6% per year, although compound growth would provide a more exact figure.
考虑某城镇人口在 5 年内从 50 万增至 65 万。该时段总增长百分比 = [(650,000 - 500,000) ÷ 500,000] × 100 = 30%。年平均增长率约为 30% ÷ 5 = 6%，但复利计算会更精确。
You may also be asked to calculate the rate of change in the percentage urban, e.g. from 45% urban to 60% urban over a decade; simply subtract to find a percentage point change of 15.
你也可能被要求计算城镇化率的百分比变化，例如城镇化率从 45% 提高到 60%，直接相减得到 15 个百分点的增幅。
9. Map Scale and Real-World Distance | 地图比例尺与实际距离
Working with Ordnance Survey maps and other scaled representations requires the ability to convert measured distances into real-world equivalents. The scale tells you the ratio between map distance and ground distance. For a 1 : 25,000 map:
使用 Ordnance Survey 地图和其他比例图时，需要将图上量测的距离换算为实地距离。比例尺表示图上距离与地面距离的比值。以 1:25,000 地图为例：
Real Distance = Map Distance × Scale Factor
tor and convert to metres or kilometres. For example, a 4 cm measurement on a 1:50,000 map equals 4 × 50,000 cm = 200,000 cm = 2,000 m = 2 km.
因此，图上 1 厘米代表实地 25,000 厘米，即 250 米。实地上距离 = 图上长度（厘米）× 比例尺分母，再换算为米或公里。例如，在 1:50,000 地图上量得 4 厘米，则实地距离为 4 × 50,000 cm = 200,000 cm = 2,000 m = 2 km。
When using a linear scale (bar scale), no arithmetic is needed: simply compare your map measurement against the bar and read the distance directly. For curved routes, use a piece of string or a map measurer, then lay it against the scale bar.
使用直线比例尺（图示比例尺）时，无需通过算式：用分规或纸条量取图上长度后直接在比例尺上读数即可。对于弯曲路径，可用棉线或曲线量测仪测量后再与比例尺比对。
10. Contour Interval and Slope Calculation | 等高线间距与坡度计算
Contour lines allow you to calculate the steepness of a slope without visiting the site. Slope can be expressed as a gradient ratio or as an angle. The basic relationship is: Published by TutorHao | Year 10 Geography Revision Series | aleveler.com
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