📚 Year 9 SQA Geography: Quick Reference Handbook of Formulas and Theorems | 九年级SQA地理：公式定理速查手册
In SQA Year 9 Geography, you will often be asked to read maps, calculate population statistics, measure slopes and interpret data. These tasks all rely on a small set of essential formulas and theorems. This handbook brings them together in one place, with clear definitions, worked examples and tips for the exam. Keep it handy when revising physical and human geography topics.
在SQA九年级地理课程中，你需要经常阅读地图、计算人口统计数据、测量坡度以及解读数据。这些任务都依赖于一套核心公式与定理。本手册将它们集中整理，提供清晰的定义、详细的例题和考试提示，方便你在复习自然地理与人文地理时随时查阅。
1. Map Scale | 比例尺
Map scale expresses the relationship between a distance on a map and the corresponding distance on the ground. It is given as a ratio, a written statement or a scale bar. The formula to convert a map distance to a real-world distance is straightforward if you know the scale.
比例尺表示地图上的距离与实地相应距离之间的关系。它可以用比例式、文字说明或线段比例尺来表示。如果已知比例尺，将图上距离转换为实地距离的公式非常简单。
Real distance = Map distance × Scale denominator
实地距离 = 图上距离 × 比例尺分母
0 = 0.5 km. So if two points are 4 cm apart on the map, the real distance is 4 × 0.5 = 2 km.
例如，在1:50 000的地图上，图上1厘米代表实地50 000厘米。要换算成千米，除以100 000即可：50 000 ÷ 100 000 = 0.5千米。因此，如果图上两点相距4厘米，实地距离就是4 × 0.5 = 2千米。
Always check the units required in your answer. Most exam questions expect the result in kilometres or metres, so you may need to convert centimetres carefully.
答题时一定要注意题目要求的单位。多数考题要求以千米或米作答，所以你可能需要小心地进行厘米的换算。
2. Bearings | 方位角
A bearing is an angle measured clockwise from north, expressed as a three‑digit number. Bearings are used to describe direction precisely. The bearing of a point is found using a protractor on a map.
方位角是从正北方向顺时针测量的角度，用三位数字表示。方位角用于精确描述方向。在地图上寻找某点的方位角需要使用量角器。
To measure the bearing from point A to point B, draw a straight line joining the two points. Place the centre of the protractor on A with 0° pointing north. Read the angle where the line AB crosses the protractor scale. If the angle is less than 100°, add leading zeros, e.g. 045°. The bearing of north itself is 000° (or 360°), east is 090°, south is 180° and west is 270°.
要测量从A点到B点的方位角，先画一条连接两点的直线。将量角器的中心放在A点，0°指向正北。读取直线AB与量角器刻度相交的角度。如果角度小于100°，在前面补零，如045°。正北的方位角是000°（或360°），正东为090°，正南为180°，正西为270°。
Remember: bearings are always given with three digits. Even a bearing of 5° is written as 005°, and your protractor reading must be taken from the north line moving clockwise.
请记住：方位角始终用三位数字表示。即使是5°的方位角也要写成005°，而且量角器的读数必须从正北方向顺时针读取。
3. Grid References | 网格坐标
erences allow you to locate places on an Ordnance Survey map using a numbered grid. A four‑figure grid reference gives a 1 km × 1 km square, while a six‑figure grid reference pinpoints a location to within 100 m.
网格坐标用于在军械测量地图上通过编号网格定位地点。四位数字的网格坐标给出一个1千米 × 1千米的方格，六位数字的网格坐标则可以将位置精确到100米之内。
Four‑ irst two digits = easting (along the corridor), last two digits = northing (up the stairs)
四位坐标：前两位 = 东向值（沿走廊走），后两位 = 北向值（上楼）
To find a six‑figure reference, divide the grid square mentally into ten equal parts along both the easting and northing. For example, if a school lies four‑tenths of the way across the square and three‑tenths up, the reference becomes easting + 4 + northing + 3, written as six digits without spaces: e.g. 123456 means easting 1234, northing 456?
要找出六位坐标，先将网格方格沿东向和北向各想象分成十等份。例如，一所学校位于方格横向十分之四处、纵向十分之三处，则坐标变成：东向值+4+北向值+3，连写成六位数字（无空格），如123456表示东向值1234、北向值456？严格来说，应该是网格左下角坐标加细分数字。
A correct six‑figure reference for a point whose grid square bottom‑left corner is 1234 (easting 12, northing 34) and the point is 4/10 across and 3/10 up would be 124343. Always quote the easting first and then the northing.
若某点所在方格左下角坐标为东向12、北向34，且该点在方格内横向4/10、纵向3/10处，正确的六位坐标是124343。务必先报东向值，再报北向值。
4. Gradient | 坡度
Gradient measures the steepness of a slope. It is the ratio between the vertical rise (change in height) and the horizontal distance. On a map, contours help you find the height difference, and the distance is measured from the map and converted to ground distance.
坡度衡量斜坡的陡峭程度。它是垂直高差（高度变化）与水平距离之比。在地图上，等高线能帮你找到高差，而水平距离需从图上量取再换算为实地距离。
Gradient = Rise ÷ Run, or Gradient = 1 : (Run ÷ Rise)
坡度 = 高差 ÷ 水平距离，或表示为 1 : (水平距离 ÷ 高差)
easured on a 1:25 000 map, is 6 cm, which equals 1500 m on the ground. The gradient is 150 ÷ 1500 = 0.1, simplified to 1 : 10.
例如，一座小山顶的高程为250米，底部为100米，高差为150米。在1:25 000地图上测得两点间水平距离为6厘米，相当于实地1500米。坡度 = 150 ÷ 1500 = 0.1，简化为1:10。
means a steeper slope. Always make sure both rise and run are in the same unit before dividing.
坡度常以1 : X的形式表示，其中X = 水平距离 ÷ 高差。X越小表明坡度越陡。计算前一定要确保高差和水平距离使用相同的单位。
5. River Discharge | 河流流量
Discharge is the volume of water passing a given point in a river every second. It links the cross‑sectional area of the channel with the velocity of the water. This formula is fundamental when studying river processes and flooding.
流量是指每秒钟流过河道某一点的水的体积。它将河槽的横截面积与水流速度联系起来。在研究河流作用和洪水时，这个公式是基础。
Discharge (Q) = Cross‑sectional area (A) × Velocity (V)
流量 (Q) = 横截面积 (A) × 流速 (V)
You can measure the cross‑ Velocity is often measured with a flow meter or by timing a float. If a stream has a cross‑ the water flows at 0.8 m/s, the discharge is 15 × 0.8 = 12 m³/s (cubic metres per second).
横截面积可以通过河宽和平均水深算出，但在多数九年级练习中面积是直接给出的。流速常用流速仪或通过浮标计时测得。如果一条河的横截面积为15平方米，水流速度为0.8米/秒，那么流量为15 × 0.8 = 12立方米/秒。
Units matter: area is in m², velocity in m/s, and discharge in m³/s. An increase in rainfall or snowmelt will increase discharge, which may lead to higher flood risk.
单位至关重要：面积以平方米计，流速以米/秒计，流量以立方米/秒计。降水或融雪增加会使流量增大，从而可能抬高洪水风险。
6. Population Density | 人口密度
Population density shows how crowded an area is. It is the number of people per unit of land, usually expressed per square kilometre. This formula is widely used in human geography to compare different regions.
人口密度反映一个地区的拥挤程度。它是单位面积土地上的人口数，通常以每平方千米的人数来表示。这个公式在人文地理中广泛用于比较不同区域。
Population density = Total population ÷ Land area (km²)
人口密度 = 总人口 ÷ 土地面积（平方千米）
ople / km². Large cities often have densities above 1000 people/km², while rural areas may be below 10 people/km².
例如，一个城镇有50 000人，面积为200平方千米，其人口密度为50 000 ÷ 200 = 250人/平方千米。大城市的人口密度往往超过1000人/平方千米，而农村地区可能低于10人/平方千米。
Population density must not be confused with overpopulation. A high density does not always mean the area cannot support its people – it depends on resources and technology.
人口密度不能和人口过剩混为一谈。高密度并不总意味着该地区无法供养其人口——这取决于资源和技术。
7. Birth Rate and Death Rate | 出生率与死亡率
Birth rate and death rate are key demographic indicators. They measure the number of live births and deaths per 1000 people per year. These rates allow fair comparisons between countries of different sizes.
出生率和死亡率是关键的人口统计指标。它们分别衡量每千人每年中的活产数和死亡数。有了这些比率，就能在不同大小的国家之间进行公平的比较。
Birth rate = (Number of live births ÷ Total population) × 1000
出生率 = (活产数 ÷ 总人口) × 1000
Death rate = (Number of deaths ÷ Total population) × 1000
死亡率 = (死亡数 ÷ 总人口) × 1000
, if there were 40 000 deaths, the death rate is (40 000 ÷ 5 000 000) × 1000 = 8 per 1000.
如果一个500万人口的国家一年内有10万活产，出生率 = (100 000 ÷ 5 000 000) × 1000 = 20‰。同样，如果死亡4万人，死亡率 = (40 000 ÷ 5 000 000) × 1000 = 8‰。
These rates are usually expressed per mille (‰). Factors like healthcare, contraception and nutrition strongly influence them, and in the exam you may be asked to explain why rates differ between MEDCs and LEDCs.
这些比率通常用千分比（‰）表示。医疗保健、避孕和营养等因素对它们影响很大；考试中可能要求你解释发达国家与欠发达国家之间比率差异的原因。
8. Natural Increase Rate | 自然增长率
Natural increase (or natural change) is the difference between the birth rate and the death rate. It shows whether a population is growing or shrinking without counting migration. The rate is normally given as a percentage or per 1000.
自然增长（或自然变动）是指出生率与死亡率之差。它显示在不考虑迁移的情况下，人口是在增长还是减少。该比率通常以百分比或千分比表示。
Natural increase = Birth rate − Death rate
自然增长 = 出生率 − 死亡率
Natural increase as a percentage = Natural increase ÷ 10
自然增长百分比 = 自然增长（每千人） ÷ 10
Using the earlier example, birth rate 20‰ and death rate 8‰ gives a natural increase of 12 per 1000. To express this as a percentage, divide by 10: 1.2%. Many developing countries have high natural growth, while some developed countries have very low or even negative natural change.
沿用前面的例子，出生率20‰，死亡率8‰，自然增长为12‰。换算为百分比，除以10得1.2%。许多发展中国家有较高的自然增长，而一些发达国家自然增长极低，甚至为负值。
This formula is central to understanding population pyramids and demographic transition models. Remember that the total population growth also includes net migration, but natural increase is just the balance of births and deaths.
这个公式对理解人口金字塔和人口转变模型至关重要。注意，总人口增长还包括净迁移，而自然增长仅仅是出生与死亡之差。
9. Doubling Time (Rule of 70) | 倍增时间（70法则）
Demographers use the rule of 70 to estimate how many years it will take for a population to double, given a constant growth rate. This simple rule is very powerful for comparing future population pressures.
人口学家使用70法则来估算，在固定的增长率下，人口翻一番需要多少年。这个简单法则在比较未来人口压力时非常有效。
Doubling time (years) = 70 ÷ Annual growth rate (%)
倍增时间（年） = 70 ÷ 年增长率（%）
For example, if a country's population is growing at 2% per year, the doubling time is 70 ÷ 2 = 35 years. If the growth rate falls to 1% because of logarithmic mathematics, but for geography you just need to apply the formula.
例如，如果一个国家的人口年增长率为2%，倍增时间就是70 ÷ 2 = 35年。如果增长率降到1%，倍增时间就延长到70年。70法则源于对数数学，但在地理课上你只需会运用这个公式即可。
It is important to use the annual growth rate that includes both natural increase and net migration. The rule of 70 can also be applied to other exponential changes, such as economic growth or resource consumption.
这里应使用包含自然增长和净迁移的整体年增长率。70法则也适用于其他指数变化，例如经济增长或资源消耗。
10. Temperature Range | 温度较差
Temperature range is a simple way to describe the variation in temperature over a day, a month or a year. It is often used when comparing climates and interpreting climatic graphs.
温度较差是描述一日、一月或一年内温度变化程度的简单方法，在比较气候和分析气候图表时经常使用。
Temperature range = Maximum temperature − Minimum temperature
温度较差 = 最高温度 − 最低温度
st and coldest months. In a June climate graph for London, the maximum temperature might be 21 °C and the minimum 12 °C, giving a monthly range of 9 °C. The annual range is calculated from the hottest month (say July, 23 °C) and the coldest month (January, 5 °C): 23 − 5 = 18 °C.
日较差是一天内最高温与最低温之差。年较差则是最热月与最冷月之差。在伦敦的六月气候图中，最高温可能为21 °C，最低温12 °C，月较差为9 °C。年较差需要用最热月（如七月23 °C）和最冷月（一月5 °C）计算：23 − 5 = 18 °C。
Coastal locations usually have smaller annual temperature ranges than inland places because the sea stores heat. Deserts often have very large diurnal ranges because of clear skies and dry air.
沿海地区由于海洋储热作用，年较差通常比内陆地区小。沙漠则因晴朗天空和干燥空气，日较差往往很大。
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