Year 10 SQA Geography: Formula & Theorem Quick Reference Guide | Year 10 SQA 地理：公式定理速查手册

📚 Year 10 SQA Geography: Formula & Theorem Quick Reference Guide | Year 10 SQA 地理：公式定理速查手册

This quick reference handbook brings together the essential formulas, theorems and quantitative relationships that underpin the SQA Year 10 Geography course. From map skills and river dynamics to population indicators and climate statistics, these tools will help you tackle both examination questions and fieldwork tasks with confidence.

本速查手册汇总了支撑 SQA 10 年级地理课程的基本公式、定理和定量关系。从地图技能、河流动力到人口指标和气候统计，这些工具将帮助您自信地应对考试和野外作业。

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1. Map Scale and Distance | 地图比例尺与距离

Map scale expresses the ratio between a distance measured on a map and the true distance on the ground. It allows you to convert straight‑line map lengths into real‑world kilometres or metres.

地图比例尺表示图上量测距离与实地真实距离之间的比率，可将直线图上长度换算为实地公里或米。

Actual Distance = Map Distance × Scale Factor

实际距离 = 图上距离 × 比例系数

For example, on a 1:25 000 map the scale factor is 25 000. A 4 cm road on the map therefore represents 4 cm × 25 000 = 100 000 cm, or 1 km, in reality.

例如在 1:25 000 地图上，比例系数为 25 000。图上 4 cm 的道路代表实地 4 cm × 25 000 = 100 000 cm，即 1 km。

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2. Area Calculation on Maps | 地图面积计算

To estimate the area of an irregular feature (such as a lake or woodland) on a topographic map, overlay a grid and count the coloured squares. Full squares are added to a visual estimate of the partial squares.

估算地形图上不规则地物（如湖泊或林地）的面积时，可覆盖方格网并计算着色方格数。将完整方格与目估的部分方格相加。

Ground Area = (Number of Grid Squares × Area per Square) × (Scale Denominator)²

地面面积 = (方格数 × 每方格面积) × (比例尺分母)²

If a 1:50 000 map uses 1 cm × 1 cm grid squares, each square represents (50 000 cm)² = 0.25 km² on the ground. Counting 72 full and partial squares gives a ground area of 72 × 0.25 km² = 18 km².

如果一张 1:50 000 地图使用 1 cm × 1 cm 方格，每个方格代表实地 (50 000 cm)² = 0.25 km²。数得 72 个完整和部分方格，则地面面积为 72 × 0.25 km² = 18 km²。

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3. Gradient and Slope | 梯度与坡度

Gradient describes the steepness of a slope by comparing the vertical rise to the horizontal distance. It is a fundamental skill for interpreting contour patterns on OS maps.

梯度通过比较垂直上升高度与水平距离来描述坡的陡峭程度，是解读 OS 地图等高线形态的基本技能。

Gradient = Vertical Interval (V.I.) / Horizontal Equivalent (H.E.)

梯度 = 垂直高差 (V.I.) / 水平距离 (H.E.)

The result is usually expressed in the form 1 in n, where n = H.E. / V.I. For instance, a V.I. of 30 m over a horizontal distance of 600 m gives a gradient of 1 in 20.

结果通常表示为 1:n 的形式，其中 n = H.E. / V.I.。例如水平距离 600 m 上垂直高差 30 m，则梯度为 1:20。

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4. River Discharge and Hydraulic Geometry | 河流流量与水力几何

Discharge (Q) is the volume of water passing a given cross‑section of a river channel every second. It is a key indicator of a river’s energy and transport capacity.

流量 (Q) 是每秒通过河道某横截面的水量，是衡量河流能量与搬运能力的关键指标。

Q = Cross‑sectional Area (A) × Mean Velocity (V)

流量 = 横截面积 (A) × 平均流速 (V)

Units are cubic metres per second (m³/s). The cross‑sectional area is approximated by multiplying the average width by the mean depth. Mean velocity is normally measured at 0.6 of the depth using a flow meter, or corrected from a surface float (multiply by 0.85 for a rocky bed).

单位为立方米每秒 (m³/s)。横截面积近似为平均宽度乘以平均深度。平均流速通常使用流速仪在 0.6 水深处理测，或由水面浮标测速乘以校正系数（岩质河床取 0.85）获得。

Hydraulic geometry describes how a river’s width, depth and velocity change as discharge increases downstream. Width grows with discharge roughly as the square root (exponent ~0.5), depth as the 0.4 power, and velocity as the 0.1 power.

水力几何描述河流宽度、深度和流速如何随下游流量的增加而变化。宽度大致随流量的平方根增长（指数约 0.5），深度增长指数约 0.4，流速增长指数约 0.1。

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5. River Velocity | 河流流速

Water velocity can be determined by timing how long a float takes to travel a measured stretch of river. This simple field method is often used in geography investigations.

水流速度可通过测量浮标流经一段已知距离的时间来确定，这是地理调查中常用的简便野外方法。

Velocity (m/s) = Distance Travelled (m) / Time Taken (s)

流速 (m/s) = 流动距离 (m) / 所用时间 (s)

Always repeat the measurement at least three times and take an average. For discharge calculations, remember to convert the surface velocity to mean velocity using a correction factor

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