📚 Year 8 SQA Geography: Formula and Theorems Quick Reference | SQA 八年级地理公式定理速查手册
This quick reference guide brings together every essential formula, theorem and calculation method you need for Year 8 SQA Geography. It covers map skills, scale and distance, relief and gradient, population, climate, rivers and fieldwork, and each rule is given in words, in symbols and with a worked example so you can revise fast and solve geographical problems with confidence.
这本速查手册汇集了 SQA 八年级地理所需的全部核心公式、定理与计算方法，涵盖地图技能、比例尺与距离、地形与坡度、人口、气候、河流以及实地调查。每一条规则都以文字表述、符号公式和例题三种形式呈现，帮助你快速复习、自信解题。
1. Map Scale | 地图比例尺
A map scale shows the relationship between a distance measured on the map and the real distance on the ground. It can be written in three ways: as a ratio (1:50,000), as a fraction (1/50,000) or as a linear scale bar drawn along the bottom of the map.
地图比例尺表示图上量得的距离与实地真实距离之间的关系。它有三种写法：比率式（1:50,000）、分数式（1/50,000）以及画在地图下方的线段比例尺。
A scale of 1:50,000 means that 1 cm on the map represents 50,000 cm on the ground. The scale denominator is the number after the colon is called the scale denominator, and it is the number you multiply by. The larger the denominator, the smaller the scale of the map.
比例尺 1:50,000 意味着图上 1 厘米代表实地 50,000 厘米。冒号后面的数字称为比例尺分母，也是你要相乘的那个数。分母越大，地图比例尺越小。
- Large scale maps, such as 1:10,000 or 1:25,000, show more detail but cover a smaller area. | 大比例尺地图（如 1:10,000、1:25,000）细节更丰富，但覆盖范围较小。
- Small scale maps, such as 1:250,000 or 1:1,000,000, show less detail but cover a much larger region. | 小比例尺地图（如 1:250,000、1:1,000,000）细节较少，但覆盖范围大得多。
- A town centre plan is a large scale map; a map of the whole of Scotland is a small scale map. | 城镇中心平面图是大比例尺地图；整个苏格兰的地图则是小比例尺地图。
Ground distance = Map distance × Scale denominator
实地距离 = 图上距离 × 比例尺分母
2. Converting Between Map Distance and Ground Distance | 图上距离与实地距离的换算
To convert a map measurement into a real distance, measure the distance on the map in centimetres, multiply by the scale denominator, then divide by 100,000 to change centimetres into kilometres.
要把图上量得的长度换算成实地距离，先用厘米量出图上距离，乘以比例尺分母，再除以 100,000 把厘米换算成千米。
Real distance (km) = Map distance (cm) × Scale denominator ÷ 100,000
实地距离（千米）= 图上距离（厘米）× 比例尺分母 ÷ 100,000
as 4 cm. The real distance is 4 × 50,000 = 200,000 cm, which is 200,000 ÷ 100,000 = 2 km.
例题：在 1:50,000 的地图上，你量得一条笔直公路为 4 厘米。实地距离为 4 × 50,000 = 200,000 厘米，即 200,000 ÷ 100,000 = 2 千米。
You may also need to work backwards, from the ground distance to the map distance. In that case you divide instead of multiplying.
有时也需要反向计算，即由实地距离求图上距离，这时要用除法而不是乘法。
Map distance (cm) = Real distance (cm) ÷ Scale denominator
图上距离（厘米）= 实地距离（厘米）÷ 比例尺分母
t. On a 1:25,000 map this is 3.5 km = 350,000 cm, and 350,000 ÷ 25,000 = 14 cm on the map.
例题：两个村庄相距 3.5 千米。在 1:25,000 的地图上，3.5 千米 = 350,000 厘米，350,000 ÷ 25,000 = 图上 14 厘米。
| Unit | 单位 | Equivalent | 等值 |
| 1 km | 1,000 m = 100,000 cm |
| 1 m | 100 cm |
| 1 km² | 1,000,000 m² |
3. Measuring Straight and Curved Distances | 直线距离与曲线距离的测量
For a straight line distance, simply lay a ruler between the two points and read the measurement in centimetres before converting. Always measure from the centre of one symbol to the centre of the other.
测量直线距离时，只需用直尺连接两点并读出厘米数，再进行换算。记住要从一个符号的中心量到另一个符号的中心。
For a curved feature such as a road or a river, a ruler will underestimate the true length. Use one of these three methods instead.
对于公路、河流等曲线地物，用直尺会低估真实长度，应改用以下三种方法之一。
- String method: lay a piece of string along the curve, mark the ends, then straighten the string against a ruler. | 细绳法：把细绳沿着曲线摆放，标出两端，再把绳子拉直用直尺测量。
- Paper edge method: place the edge of a strip of paper along the curve, mark each bend with a pencil, then measure the total against a ruler. | 纸边法：用纸条边缘沿曲线摆放，在每个转弯处用铅笔做记号，最后对照直尺量出总长度。
- Segment method: divide the curve into a series of short straight sections, measure each one and add them together. | 分段法：把曲线分成若干小段近似直线，逐段测量后相加。
The scale bar printed on the map is the quickest check: place the paper edge against the bar and read the real distance directly, with no conversion needed.
地图上印的线段比例尺是最快的检查工具：把纸边直接对准比例尺读出实地距离，无需任何换算。
4. Area, Grid References and Direction | 面积、网格参考与方向
To estimate the area of an irregular feature, count the number of whole grid squares it covers, add half of the partially covered squares, then multiply by the real area of one square.
估算不规则地物的面积时，先数出它完整覆盖的网格数，再加上被部分覆盖网格的一半，最后乘以一个网格所代表的实地面积。
represents 2 km × 2 km = 4 km². For a rectangular feature, use the standard area formula.
在 1:25,000 的地图上，每个网格为 4 厘米 × 4 厘米，即实地 1 千米 × 1 千米 = 1 平方千米。在 1:50,000 的地图上，每个网格代表 2 千米 × 2 千米 = 4 平方千米。若地物为矩形，则直接套用面积公式。
Area of a rectangle = Length × Breadth
矩形面积 = 长 × 宽
A four-figure grid reference locates a whole square and is read eastings first, then northings. A six-figure grid reference locates a point within a square and is read to the nearest tenth of a square, again eastings first. The memory phrase is 'along the corridor, then up the stairs'.
四位网格参考（四位数坐标）用于定位整个网格，先读东距（横坐标）再读北距（纵坐标）。六位网格参考用于定位网格内的具体点，精确到十分之一格，同样先东后北。记忆口诀是"先沿走廊走，再顺楼梯上"。
Bearings are measured clockwise from north, in degrees from 0° to 360°. North is 000°, east is 090°, south is 180° and west is 270°. To find the bearing from A to B, draw a north line through A and measure the angle clockwise to the line AB.
方位角以正北为起点顺时针量取，用 0° 至 360° 的度数表示。正北为 000°，正东 090°，正南 180°，正西 270°。求 A 到 B 的方位角时，先在 A 点画一条正北方向线，再顺时针量到 AB 连线的夹角。
5. Relief, Contours and Gradient | 地形、等高线与坡度
Relief means the shape and height of the land. It is shown on a map by contour lines, spot heights and triangulation pillars. The contour interval is the vertical height between one contour line and the next, and it stays the same all over the map.
地形指陆地的形态与高度，在地图上通过等高线、高程点和三角测量点表示。等高距是相邻两条等高线之间的垂直高度差，在同一幅地图上保持不变。
- Closely spaced contours mean a steep slope. | 等高线密集表示坡度陡。
- Widely spaced contours mean a gentle slope. | 等高线稀疏表示坡度缓。
- Contours that cross a river form a V shape pointing upstream, that is, towards higher ground. | 等高线穿过河流时呈 V 形，V 字尖端指向上游，即指向高处。
Gradient, or slope, compares the vertical rise with the horizontal distance. Both measurements must be in the same unit before you divide.
坡度比较垂直升高量与水平距离，两者必须先化为同一单位才能相除。
Gradient = Vertical interval ÷ Horizontal distance
坡度 = 垂直高差 ÷ 水平距离
is 150 m ÷ 3,000 m = 1/20, which can be written as a ratio of 1:20 or as a percentage of 5%.
例题：一座山在 3 千米的水平距离内升高 150 米。换成同一单位后为 150 米 ÷ 3,000 米 = 1/20，可写作比值 1:20，也可写作百分数 5%。
To turn a fraction into a percentage, multiply by 100. To find the vertical rise when the gradient and distance are known, rearrange the formula.
把分数变成百分数要乘以 100。若已知坡度和距离求高差，只需对公式进行变形。
Vertical interval = Gradient × Horizontal distance
垂直高差 = 坡度 × 水平距离
6. Population Data and Density | 人口数据与人口密度
Population density tells you how crowded an area is. It is the average number of people living in each square kilometre, and it is always written as people per km².
人口密度反映一个地区的拥挤程度，指每平方千米平均居住的人数，单位始终写作"人/平方千米"。
Population density = Total population ÷ Area (km²)
人口密度 = 总人口 ÷ 面积（平方千米）
density is 240,000 ÷ 120 = 2,000 people per km², which makes it a densely populated area.
例题：某市辖区有 240,000 人，面积 120 平方千米。人口密度为 240,000 ÷ 120 = 2,000 人/平方千米，属于人口稠密区。
A densely populated area usually has a high density, often over 1,000 people per km². A sparsely populated area has a low density, sometimes fewer than 10 people per km². Physical factors such as relief, climate, soil and water supply, and human factors such as jobs, transport and services, both help to explain the pattern.
人口稠密区密度通常较高，常在 1,000 人/平方千米以上；人口稀疏区密度很低，有时不足 10 人/平方千米。地形、气候、土壤和水源等自然因素，以及就业、交通和服务等人文因素，共同解释了这种分布格局。
If the density and the area are known, you can rearrange the formula to find the total population.
若已知人口密度和面积，可对公式变形求出总人口。
Total population = Population density × Area
总人口 = 人口密度 × 面积
7. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率与自然增长
Birth rate and death rate are both calculated per 1,000 people per year, so the final answer must be multiplied by 1,000.
出生率和死亡率都按"每 1,000 人每年"计算，因此最后一步必须乘以 1,000。
Birth rate = (Births in a year ÷ Total population) × 1,000
出生率 = （一年出生人数 ÷ 总人口）× 1,000
Death rate = (Deaths in a year ÷ Total population) × 1,000
死亡率 = （一年死亡人数 ÷ 总人口）× 1,000
Natural increase is simply the birth rate minus the death rate. If the death rate is higher, the answer is negative and we call it natural decrease.
自然增长就是出生率减去死亡率。如果死亡率更高，结果为负值，我们称之为自然减少。
Natural increase = Birth rate − Death rate
自然增长 = 出生率 − 死亡率
,000 = 12 per 1,000, the death rate is (500,000 ÷ 50,000,000) × 1,000 = 10 per 1,000, and the natural increase is 12 − 10 = 2 per 1,000, or 0.2%.
例题：某国人口 5,000 万，一年内出生 600,000 人、死亡 500,000 人。出生率为（600,000 ÷ 50,000,000）× 1,000 = 12‰，死亡率为（500,000 ÷ 50,000,000）× 1,000 = 10‰，自然增长为 12 − 10 = 2‰，即 0.2%。
To convert a rate per 1,000 into a percentage, divide by 10. Total population change also takes migration into account.
把千分率换算成百分数，只需除以 10。总人口变化还要考虑人口迁移。
Population change = Natural increase + Net migration
人口变化 = 自然增长 + 净迁移
8. Climate Graphs and Rainfall Totals | 气候图与降水量计算
A climate graph shows average monthly temperature as a line and average monthly rainfall as bars for one location. Temperature is read on the right-hand axis in degrees Celsius, and rainfall on the left-hand axis in millimetres.
气候图用折线表示某地各月平均气温，用柱状表示各月平均降水量。气温读右侧坐标轴，单位为摄氏度；降水量读左侧坐标轴，单位为毫米。
Three calculations appear again and again in exam questions about climate.
在气候类考题中，以下三种计算反复出现。
- Temperature range = highest mean monthly temperature − lowest mean monthly temperature. | 气温年较差 = 最高月平均气温 − 最低月平均气温。
- Total annual rainfall = the sum of all twelve monthly rainfall figures. | 年降水量 = 十二个月降水量之和。
- Mean annual rainfall = Total annual rainfall ÷ 12. | 年平均降水量 = 年降水量 ÷ 12。
Temperature range = Max temperature − Min temperature
气温年较差 = 最高气温 − 最低气温
°C. If the twelve monthly rainfall totals add up to 840 mm, the total annual rainfall is 840 mm and the mean monthly rainfall is 840 ÷ 12 = 70 mm.
例题：某站 7 月平均气温最高为 21 °C，1 月最低为 3 °C，气温年较差为 21 − 3 = 18 °C。若十二个月降水量合计 840 毫米，则年降水量为 840 毫米，月平均降水量为 840 ÷ 12 = 70 毫米。
When you describe a climate graph, quote figures and use the correct vocabulary: a small temperature range means an equable or maritime climate, while a large range suggests a continental climate. A clear seasonal rainfall pattern, such as a wet winter and dry summer, should also be identified.
描述气候图时要引用具体数据并使用正确术语：气温年较差小说明气候温和，属海洋性气候；年较差大则说明是大陆性气候。若降水呈明显季节差异，如冬雨夏干，也应指出。
9. River Discharge, Velocity and Cross-Section | 河流流量、流速与横断面
Discharge is the volume of water passing a point in a river every second. It is measured in cubic metres per second (m³/s), a unit geographers also call cumecs.
流量指每秒通过河道某一点的水量，单位为立方米每秒（m³/s），地理学中也称"秒立方米"。
Discharge = Cross-sectional area × Velocity
流量 = 过水断面面积 × 流速
Cross-sectional area = Width × Mean depth
过水断面面积 = 河宽 × 平均水深
f the velocity measured with a flow meter is 0.6 m/s, the discharge is 4 × 0.6 = 2.4 m³/s.
例题：某河宽 8 米，平均水深 0.5 米，过水断面面积为 8 × 0.5 = 4 平方米。若用流速仪测得流速为 0.6 米/秒，则流量为 4 × 0.6 = 2.4 立方米/秒。
Discharge normally increases downstream because tributaries add water and because the channel becomes wider and deeper. Velocity also tends to increase downstream as the channel becomes smoother and more efficient, although friction is greatest along the bed and banks.
流量通常自上游向下游增大，因为支流汇入水量，且河床变得更宽更深。流速也往往向下游增大，因为河道更光滑、输水效率更高，不过河底与河岸的摩擦力最大。
To find velocity when discharge and area are known, divide discharge by area.
若已知流量和断面面积求流速，用流量除以面积即可。
Velocity = Discharge ÷ Cross-sectional area
流速 = 流量 ÷ 过水断面面积
10. Storm Hydrographs and Lag Time | 洪水过程线与滞后时间
A storm hydrograph plots river discharge against time after a rainfall event. It has a rising limb, a peak discharge, a falling limb and a base flow, which is the normal discharge of the river before the storm.
洪水过程线把降雨事件后河流流量随时间的变化绘成曲线，包含上升段、洪峰流量、退水段以及基流。基流是降雨前河流的常态流量。
Lag time is the delay between the peak of the rainfall and the peak of the discharge. A short lag time means a flashy river that responds quickly and can flood fast; a long lag time means a slower, steadier response.
滞后时间是降雨峰值与流量峰值之间的时间差。滞后时间短说明河流反应迅速、易突发洪水；滞后时间长则说明河流反应缓慢平稳。
Lag time = Time of peak discharge − Time of peak rainfall
滞后时间 = 洪峰出现时刻 − 降雨峰值出现时刻
Worked example: the heaviest rain falls at 14:00 and the river reaches its highest discharge at 19:30. The lag time is 5 hours 30 minutes.
例题：最强降雨出现在 14:00，河流流量在 19:30 达到最大，则滞后时间为 5 小时 30 分钟。
Several factors shorten the lag time and raise the flood peak: impermeable rock such as granite, steep slopes, thin or absent vegetation, urban surfaces and drains, and heavy, intense rainfall. Factors that lengthen the lag time include permeable rock such as limestone, gentle slopes, dense woodland and steady, light rainfall.
多种因素会缩短滞后时间并抬升洪峰：花岗岩等不透水岩层、陡峭坡面、植被稀薄或缺失、城市硬化地面与排水管网，以及强度大的暴雨。延长滞后时间的因素包括石灰岩等透水岩层、平缓坡面、茂密林地以及强度小的持续性降雨。
11. Fieldwork Sampling and Averages | 实地调查采样与平均值
Fieldwork data is only trustworthy if the sample is representative. Three sampling strategies are used at Year 8.
只有当样本具有代表性时，实地调查数据才可靠。八年级常用的采样方法有三种。
- Random sampling: use a random number generator to pick sites, which reduces bias but may miss key locations. | 随机采样：用随机数生成器选取样点，可减少偏差，但可能漏掉关键地点。
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