📚 Year 11 SQA Geography: Quick Reference Handbook of Formulas and Theorems | Year 11 SQA 地理：公式定理速查手册
This handbook provides a concise summary of the key formulas, equations and calculation methods required for the Year 11 SQA Geography course. Understanding and applying these quantitative skills is essential for interpreting data, completing fieldwork tasks and answering exam questions with confidence. The guide covers physical geography, human geography, map skills and climate analysis, matching the National 5 specification.
本手册简要概括了 Year 11 SQA 地理课程中必备的关键公式、方程和计算方法。理解和应用这些量化技能对于解读资料、完成野外作业任务以及自信地应对考试题目至关重要。本指南涵盖自然地理、人文地理、地图技能和气候分析，与 National 5 课程规范相对应。
1. River Discharge Formula | 河流流量公式
Discharge is the volume of water flowing through a river channel per unit time. It is the fundamental measure of a river's capacity and is calculated using the continuity equation.
流量是单位时间内流过河道某一断面的水体体积。它是衡量河流输送能力的基本指标，可使用连续方程进行计算。
Q = A × V
Q is the discharge (cubic metres per second, m³/s). A represents the cross-sectional area of the channel (square metres, m²). V is the average flow velocity (metres per second, m/s).
Q 为流量（立方米每秒，m³/s）。A 表示河道横截面积（平方米，m²）。V 为平均流速（米每秒，m/s）。
To obtain reliable results, the cross-sectional area is usually subdivided into vertical sections where depth and velocity are measured at each interval. Discharge then becomes the sum of the products of area and velocity for all sections.
为了获得可靠的结果，横截面积通常被划分为若干垂直断面，在每个断面测量水深和流速。流量即所有断面的面积与流速乘积之和。
This formula underpins flood prediction, river management and fieldwork investigations such as measuring stream flow with a flowmeter.
该公式是洪水预测、河流管理以及实地调查（例如使用流速仪测量水流）的基础。
2. Cross-Sectional Area of a Channel | 河道横截面积
Calculating the channel cross-sectional area accurately is necessary for discharge measurement. The area can be estimated by treating the riverbed as a series of trapezoids.
准确计算河道横截面积对于流量测量是必需的。可以将河床视为一系列梯形来估算面积。
A = (w × d̄) or A = ∑(width of segment × mean depth of segment)
In a simplified field approach, the wetted perimeter width and average depth are used: A ≈ width × average depth. Where the channel is irregular, measure depth at several points across the width, calculate the mean depth, then multiply by the total width.
在简化的实地方法中，使用湿周宽度和平均水深：A ≈ 宽度 × 平均水深。若河道不规则，则在宽度方向上测量多个点的水深，计算平均水深，再乘以总宽度。
Units must be consistent. Width and depth are recorded in metres, giving area in square metres (m²). Field sketches and cross-sectional diagrams help to visualise bankfull and wetted dimensions.
单位必须一致。宽度和水深以米为单位记录，所得面积为平方米（m²）。实地草图和横截面示意图有助于直观显示满岸水位和湿周尺寸。
3. Stream Gradient | 河道坡度
Gradient describes the steepness of a river channel or valley. It influences velocity, erosion and sediment transport.
坡度描述河道或河谷的陡峭程度。它影响着流速、侵蚀和沉积物搬运。
Gradient = Vertical Drop ÷ Horizontal Distance
The vertical drop is the difference in height between two points along the river, measured using spot heights or contour lines on an OS map. The horizontal distance is the actual river length between the same two points, not the straight-line distance.
垂直落差是沿河流两点之间的高差，使用地形图上点位高程或等高线测量。水平距离是同一两点间的实际河道长度，而非直线距离。
Gradient is often expressed as a ratio (e.g. 1:50) or as the fall in metres per kilometre. For SQA exam questions, always check the required format. A steep gradient is found in upper course; a gentle gradient indicates lower course or floodplain.
坡度常以比率（如 1:50）或者米/千米的降幅表示。对于 SQA 考试题目，请始终检查所要求的格式。陡峭坡度见于上游；平缓坡度表示下游或洪泛平原。
4. Population Density | 人口密度
Population density indicates how crowded an area is and allows comparisons between regions. It is one of the most frequently used statistics in human geography.
人口密度表明一个区域的拥挤程度，并可用于地区间的比较。这是人文地理中最常用的统计量之一。
Population Density = Total Population ÷ Land Area (km²)
Ensure the land area is expressed in square kilometres. In the UK exam context, areas from grid squares can be calculated using map skills. A high density suggests urban or fertile agricultural zones; low density points to harsh environments or large-scale farming.
确保土地面积以平方公里表示。在英国考试情境中，可通过地图技能计算网格方格面积。高密度代表城市或肥沃农业区；低密度则指示恶劣环境或大规模农业。
When using this formula in fieldwork, be aware that administrative boundaries can distort the real picture of population clustering. Dot maps and choropleth maps often supplement density data.
在野外作业中使用该公式时，要注意行政边界可能会扭曲人口聚集的真实图景。点值图和等值区域图常被用于补充密度数据。
5. Birth, Death and Natural Increase Rates | 出生率、死亡率和自然增长率
Demographic rates are crucial for studying population change. They are expressed per 1000 people per year to standardise comparisons between countries of different sizes.
人口统计率对于研究人口变化至关重要。它们以每年每千人的方式表达，以便在不同规模的国家之间进行标准化比较。
Crude Birth Rate (CBR) = (Live Births ÷ Total Population) × 1000
Crude Death Rate (CDR) = (Deaths ÷ Total Population) × 1000
centage). Additionally, the absolute natural change = number of births - number of deaths.
自然增长可计算为出生率与死亡率之差，得出每千人的比率（常转换为百分数）。此外，绝对自然变化 = 出生人数 - 死亡人数。
Countries in the early stages of the demographic transition model have high CBR and CDR, resulting in low natural increase. The formula helps explain population projections and resource demands.
处于人口转变模型早期阶段的国家具有高出生率和高死亡率，自然增长较低。该公式有助于解释人口预测和资源需求。
6. Net Migration Rate | 净迁移率
Migration adds another dimension to population change. The net migration rate balances immigration and emigration relative to the mid-year population.
迁移为人口变化增加了另一个维度。净迁移率根据年中人口来平衡迁入和迁出人口。
Net Migration Rate = ((Immigrants - Emigrants) ÷ Total Population) × 1000
If the rate is positive, there is net in-migration; if negative, net out-migration. When combined with natural increase, the total population growth rate is obtained.
若比率为正值，则为净迁入；若为负值，则为净迁出。将它与自然增长结合，即可得到总人口增长率。
In SQA case studies, push and pull factors influence migration streams. Calculating the rate quantitatively reinforces explanations of urbanisation, counter-urbanisation and refugee movements.
在 SQA 案例研究中，推力和拉力因素影响着迁移流。定量计算该比率可加强对城市化、逆城市化和难民流动的解释。
7. Dependency Ratio | 抚养比率
The dependency ratio shows the proportion of the population that is not economically active compared with those of working age. It is a key indicator of the economic pressure on the productive part of society.
抚养比率显示了非经济活动人口与劳动适龄人口的比例。它是衡量社会生产性部分经济压力的关键指标。
((Population aged 0-14 + Population aged 65+) ÷ Population aged 15-64) × 100
A result over 60 is generally considered high, indicating a heavy burden on workers to support dependent young and elderly. Ageing populations in developed countries and youthful populations in developing countries each produce distinct dependency structures.
结果若超过 60，一般被认为较高，表明劳动人口在抚养幼年和老年人口方面负担沉重。发达国家的人口老龄化和发展中国家的年轻人口结构分别产生不同的抚养结构。
In exam answers, link the ratio to social services, healthcare and pension systems. It brings together demographic formulas and the consequences of population structure.
在考试答案中，要将该比率与社会服务、医疗和养老金体系联系起来。它把人口统计公式与人口结构的后果结合在一起。
8. Mean, Range and Moving Averages for Climate | 气候数据的平均值、较差和移动平均数
Climate graphs and statistics require the ability to calculate central tendency and variability. These techniques are applied to temperature and precipitation data.
气候图表和统计数据要求具备计算集中趋势和变异性的能力。这些技术被应用于温度和降水数据。
Mean = ∑ of all values ÷ Number of values
Range = Maximum value - Minimum value
For a moving average (e.g. a 3-point moving average), take sets of consecutive values, calculate their mean, and plot the result at the centre point. This smooths out short-term fluctuations and reveals longer-term trends.
对于移动平均数（例如 3 点移动平均），取连续数值组，计算其平均值，并在中点处绘制结果。这样可以平滑短期波动，揭示长期趋势。
These skills are tested when constructing and interpreting climate graphs in physical environments units. Always label axes, include units, and provide a key.
这些技能在自然地理单元中构建和解读气候图表时会受到考查。务必标注坐标轴、包含单位并提供图例。
9. Map Scale and Distance | 地图比例尺与距离
Ordnance Survey map skills are fundamental to SQA Geography. Scale conversion allows you to translate a line measured on the map into a real-world distance.
地形图技能是 SQA 地理的基础。比例尺换算使你能将图上量得的线段转化为现实世界的距离。
Real Distance = Map Distance × Scale Factor
For a scale of 1:25,000, 1 cm on the map represents 25,000 cm (250 m) on the ground. For 1:50,000, 1 cm represents 500 m. Always convert the answer into the unit requested in the question, typically metres or kilometres.
对于 1:25,000 的比例尺，图上 1 厘米代表实地 25,000 厘米（250 米）。对于 1:50,000，1 厘米代表 500 米。始终将答案转换为题目要求的单位，通常是米或千米。
Measure curved distances, such as a winding river, with a piece of string or by dividing the path into small straight segments. Present your working clearly to gain method marks.
用细线或将路径分割为若干小直线段的方法来测量如蜿蜒河流那样的曲线距离。清晰地展示计算过程以取得方法分。
10. Area Calculation from Maps | 地图面积计算
Estimating the area of a feature, such as a lake or forest, uses the map scale in two dimensions. Regular shapes can be calculated directly.
估算某一地物（如湖泊或森林）的面积，需在两个维度上使用地图比例尺。规则形状可直接计算。
Map Area (cm²) × (Scale Factor)² = Real Area
otal. On a 1:50,000 map, each 1 cm grid square represents 0.25 km² (since 1 cm = 500 m, area = 500 m × 500 m = 250,000 m² = 0.25 km²). Record the steps.
对于不规则区域，采用网格方格法。计算边界内完整的方格，并组合部分方格以估算总数。在 1:50,000 地图上，每个 1 厘米网格方格代表 0.25 平方公里（因为 1 厘米 = 500 米，面积 = 500 米 × 500 米 = 250,000 平方米 = 0.25 平方公里）。记录计算步骤。
The key is to maintain consistent units and always show the conversion from map area to ground area explicitly.
关键在于保持单位一致，并始终清晰地显示从图上面积到实地面积的转换过程。
11. Vertical Exaggeration of Cross-Sections | 横截面的纵向夸大
When drawing a cross-section from a contour map, vertical exaggeration helps to emphasise relief features. It must be calculated to allow fair comparison between profiles.
根据等高线地形图绘制横截面时，纵向夸大有助于凸显地形特征。必须进行计算，以便在剖面之间进行公平比较。
Vertical Exaggeration (VE) = Vertical Scale (VS) ÷ Horizontal Scale (HS)
presents 5 m). The VE = (1/5000) ÷ (1/50000) = 10 times. A VE of 1 means no exaggeration; values greater than 1 make slopes appear steeper.
两种比例尺均以数字比例表示，例如水平比例尺可能为 1:50,000，垂直比例尺为 1:5,000（1 毫米代表 5 米）。VE = (1/5000) ÷ (1/50000) = 10 倍。VE 为 1 表示无夸大；大于 1 的值使坡度显得更陡。
Always state the VE as 'times' (e.g. ×10). This calculation is a standard requirement in mapwork and field-sketch analysis.
始终将 VE 表示为“倍”（例如 ×10）。这个计算是地图作业和实地草图分析中的标准要求。
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