📚 Year 7 SQA Geography: Formulae & Theorems Quick-Reference Guide | Year 7 SQA 地理：公式定理速查手册
This quick-reference guide is designed for Year 7 SQA Geography learners. It brings together essential map-work formulae, calculation methods, and key geographic 'theorems' (principles) that you will use when reading Ordnance Survey maps, interpreting climate data, and understanding population patterns. Keep it handy for fieldwork, homework, and revision.
本速查手册专为 Year 7 SQA 地理学生编写。它汇集了在判读军械测量局地图、解释气候数据以及理解人口分布时需要用到的核心地图公式、计算方法以及关键的地理‘定理’（原理）。请在做野外调查、家庭作业和复习时随时翻阅。
1. Map Scale Types and Conversions | 地图比例尺类型与换算
A map scale shows the relationship between a distance on the map and the corresponding distance on the ground. The three common ways to express it are: statement scale (e.g. "1 cm to 0.5 km"), linear (bar) scale, and representative fraction (RF) scale, such as 1:50 000.
地图比例尺表示图上距离与对应的实际地面距离之间的关系。它通常有三种表达方式：文字比例尺（如“1厘米代表0.5千米”）、直线比例尺（图示比例尺）和分数比例尺（RF），例如1:50 000。
To calculate the real-world distance, multiply the map distance by the denominator of the scale. For a 1:50 000 map, 1 cm on the map equals 50 000 cm on the ground, which is 500 m or 0.5 km.
要计算实际距离，将图上距离乘以比例尺的分母即可。对于1:50 000的地图，图上1厘米等于实地50 000厘米，即500米或0.5千米。
Real Distance (cm) = Map Distance (cm) × Scale Denominator
实际距离（厘米）= 图上距离（厘米） × 比例尺分母
Example: On a 1:25 000 map, a 4 cm line represents 4 × 25 000 = 100 000 cm, which is 1 km.
例题：在1:25 000的地图上，一条4厘米的线段代表4 × 25 000 = 100 000厘米，即1千米。
2. Measuring Straight and Curved Distances | 直线与曲线距离测量
For a straight line between two points, simply place a ruler edge along the line, measure the centimetres, and convert to real distance using the scale formula.
测量两点之间的直线距离时，只需将直尺边缘对准直线，读出厘米数，再根据比例尺公式换算成实际距离即可。
To measure a curved distance, such as a winding road or river, use a piece of string or the edge of a scrap of paper. Lay it carefully along the curve, mark the end point, then straighten it against a ruler to get the map length before converting.
测量弯曲距离（例如蜿蜒的道路或河流）时，可以使用一根细绳或一张纸条的边缘。将其小心地沿着曲线摆放，在终点处做个记号，然后拉直并移到直尺上读出图上长度，再进行换算。
Curved Distance (real) = Measured String Length (cm) × Scale Factor
曲线距离（实际）= 测得的绳长（厘米） × 比例尺系数
3. Area Estimation on Grid Maps | 网格地图面积估算
area of a feature, count the number of whole squares and part-squares it covers. Count a part-square as half a full square if more than half is inside the feature; ignore tiny areas smaller than half.
军械测量局的地图通常有1千米 × 1千米的网格。要估算某个地物的面积，需数清它覆盖的完整方格和不完整方格的数量。若超过一半在特征内部，则将不完整方格计为半个完整方格；小于一半的微小区域可以忽略不计。
Estimated Area (km²) = Whole Squares + (½ × Part-Squares)
估算面积（平方千米）= 完整方格数 + (0.5 × 不完整方格数)
he unit as square kilometres (km²) or convert to hectares (1 km² = 100 hectares) if asked.
单位始终要写成平方千米（km²），或根据题目要求换算成公顷（1 km² = 100公顷）。
4. Gradient (Slope) Formula | 坡度公式
Gradient describes the steepness of a slope. It is calculated by dividing the vertical height change (the difference in height between two points) by the horizontal distance between them. The result can be expressed as a ratio (e.g. 1:10) or a percentage (% rise).
坡度描述斜坡的陡峭程度。它由两点之间的垂直高度变化（高差）除以它们之间的水平距离来计算。结果可用比（如1:10）或百分比（上升百分比）表示。
Gradient = Vertical Height Change (m) ÷ Horizontal Distance (m)
坡度 = 垂直高差（米） ÷ 水平距离（米）
he gradient is 1 in 10 (or 1:10). For a percentage, multiply by 100: (20 ÷ 200) × 100 = 10%.
若要以比的形式表示坡度，可将垂直高度化为1：例如，垂直高差为20米，水平距离为200米，则坡度为1比10（或1:10）。如果换成百分比，则乘以100：（20 ÷ 200）× 100 = 10 %。
5. Compass Directions and Bearings | 罗盘方位与方位角
The four cardinal points are North (0° or 360°), East (90°), South (180°), and West (270°). Between them are the intercardinal points: NE (45°), SE (135°), SW (225°), and NW (315°). Finer divisions give North-North-East (22.5°) and so on.
四个基本方位是北（0° 或 360°）、东（90°）、南（180°）和西（270°）。它们之间是间方位：东北（45°）、东南（135°）、西南（225°）和西北（315°）。更细的划分还有东北偏北（22.5°）等等。
A bearing is a precise angle measured clockwise from North, always given with three figures, e.g. 045° or 225°. Always place your protractor with the centre on the starting point and the 0° line pointing exactly to grid north.
方位角是从正北方向按顺时针方向量测的精确角度，始终用三位数字表示，例如045°或225°。使用量角器时，一定要将量角器的中心对准起点，并将0°刻度线准确地指向网格北。
6. Four- and Six-Figure Grid References | 四位与六位数字网格参考
A four-figure grid reference locates the whole grid square in which an object lies. It is the easting (horizontal line first), then the northing (vertical line second). Always go "along the corridor and up the stairs". For example, 2453 refers to square 24 across and 53 up.
四位数字网格参考能确定物体所在的整个网格方格。先读取东向坐标（沿横轴），再读取北向坐标（沿纵轴）。一定要记住“先横后纵，从左到右，从下到上”的原则。例如，2453表示东列24、北排53所在的方格。
A six-figure grid reference pinpoints the exact position within that square. Divide the square into tenths and estimate the extra digit for both the easting and the northing. For example, 246532 means 24 and 6 tenths east, 53 and 2 tenths north. Six-figure references are much more precise for individual buildings, bridges or footpath junctions.
六位数字网格参考能更精确地定位方格内的具体位置。将方格等分为十份，为东向和北向各添加一位估算的数字。例如，246532表示东列24再加十分之六个方格，北排53再加十分之二个方格。对单个建筑物、桥梁或步行道交叉口来说，六位参考要精确得多。
7. Contour Lines: Steepness and River Valleys | 等高线：坡度与河谷
Contour lines connect points of equal height above sea level. The 'contour theorem' to remember is: the closer together the contours, the steeper the slope. Widely spaced contours indicate a gentle slope; no contours or very wide spacing suggests a flat area or plateau.
等高线连接地面上高度相同的点。要记住的“等高线定理”是：等高线越密集，坡度越陡。等高线稀疏处表示缓坡；没有等高线或间距极大则表明为平地或高原。
When a contour line crosses a river or stream, it forms a 'V' shape. The 'V' always points upstream, towards the higher ground. This is a vital clue for interpreting river valleys and the direction of river flow on a map.
当等高线跨过河流或溪流时，会形成“V”字形。这个“V”字形的尖端永远指向河流的上游，即地势较高的方向。这是在地图上判读河谷和河流流向的重要线索。
8. Population Density Formula | 人口密度公式
Population density measures how crowded a place is. It is calculated as the total population of an area divided by the total land area, usually expressed in people per square kilometre (people/km²).
人口密度衡量一个地方的拥挤程度。它等于该地区的总人口除以土地总面积，通常以每平方千米的人口数（人/km²）表示。
Population Density = Total Population ÷ Area (km²)
人口密度 = 总人口 ÷ 面积（km²）
s like city centres typically have high densities, while rural farmland has low densities.
例如，如果一个苏格兰小镇有15 000人，面积为3 km²，那么它的人口密度就是15 000 ÷ 3 = 5000 人/km²。市中心等地区通常密度很高，而乡村农田的密度很低。
9. Climate Temperature Statistics | 气候温度统计
Three basic statistics help describe temperature data: the mean, the range, and the extremes. The mean temperature is found by adding up all the temperatures and dividing by the number of readings.
三个基本的统计量能帮助描述温度数据：平均数、较差和极端值。平均气温是将所有的温度值相加，再除以读数的个数而得到的。
The diurnal (daily) temperature range is the difference between the maximum and minimum temperatures recorded in a day. The annual temperature range is the difference between the mean temperature of the warmest month and the mean temperature of the coldest month.
日气温较差是一天中记录的最高气温与最低气温之差。年气温较差是最热月份的月平均气温与最冷月份的月平均气温之差。
Mean = Sum of Values ÷ Number of Values
平均数 = 数值总和 ÷ 数值个数
Range = Maximum – Minimum
较差 = 最大值 – 最小值
Always include the unit, e.g. °C, and check whether you need to give the daily or annual range in a climatic graph question.
务必要带上单位，如°C，并且在气候图表问题中，注意题目要求的是日较差还是年较差。
10. Measuring Precipitation and Rainfall Totals | 降水量与总降雨量
Rainfall is measured using a rain gauge and
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