📚 Year 7 WJEC Geography: Formula & Theorem Quick Reference Guide | Year 7 WJEC 地理：公式定理速查手册
This quick reference handbook brings together the essential formulas, key theorems, and numerical skills you need for Year 7 WJEC Geography. From map scales to population density, each entry is presented in both English and Chinese with clear step‑by‑step explanations. Keep this guide handy when tackling homework, fieldwork calculations, and revision.
这本速查手册汇集了 Year 7 WJEC 地理课程中必备的公式、关键定理和数字技能。从地图比例尺到人口密度，每个条目都配有英中双语对照和清晰的分步讲解。在完成作业、野外实地计算和复习时，都可以随时查阅。
1. Map Scale Formula | 地图比例尺公式
A map scale tells you how many times the real world has been reduced. It is usually written as a ratio, for example 1:25 000, meaning 1 cm on the map represents 25 000 cm on the ground.
地图比例尺反映了实地被缩小的倍数，通常用比例表示，如 1:25 000，即图上 1 厘米代表实际 25 000 厘米。
Actual Distance = Map Distance × Scale Denominator
实际距离 = 图上距离 × 比例尺分母
als 3 km. Always convert centimetres to metres or kilometres: 100 cm = 1 m, 1000 m = 1 km.
在 1:50 000 的地图上，如果一条小径的图上长度为 6 厘米，实际步行距离就是 6 × 50 000 = 300 000 厘米，即 3 公里。务必进行单位换算：100 厘米 = 1 米，1000 米 = 1 公里。
2. Calculating Gradient | 计算坡度
Gradient describes how steep a slope is. It can be given as a percentage, a ratio or an angle. The most common method in geography to find the percentage gradient is:
坡度表示斜坡的陡峭程度，可以用百分比、比、或角度来表示。地理学中最常用的百分比坡度计算公式为：
Gradient (%) = (Vertical Rise ÷ Horizontal Distance) × 100
坡度 (%) = (垂直高差 ÷ 水平距离) × 100
t increases by 15 m over a horizontal distance of 200 m. Gradient = (15 ÷ 200) × 100 = 7.5% tio, divide both numbers by the vertical rise: 200 ÷ 15 ≈ 13.3, giving approximately 1:13.
假设一座山丘的水平距离为 200 米，垂直高度上升了 15 米。坡度 = (15 ÷ 200) × 100 = 7.5%。若用比表示，将两者同时除以垂直高差：200 ÷ 15 ≈ 13.3，坡度比约为 1:13。
3. Population Density | 人口密度
Population density tells us how crowded an area is. It is the average number of people living in each square kilometre (or square mile).
人口密度用来衡量一个地区的拥挤程度，指每平方千米（或平方英里）平均居住的人口数。
Population Density = Total Population ÷ Area
人口密度 = 总人口数 ÷ 面积
its population density is 320 000 ÷ 40 = 8000 people per km². Always check the area units—map areas are often measured in km², but fieldwork areas may be in m².
如果一个城市有 32 万人，面积为 40 平方千米，人口密度 = 320 000 ÷ 40 = 8000 人/平方千米。注意检查面积单位——地图上的面积通常以 km² 为单位，而实地测量可能使用 m²。
4. Birth and Death Rates | 出生率与死亡率
The crude birth rate (CBR) and crude death rate (CDR) are calculated per 1000 people per year, allowing comparison between places of different sizes.
粗出生率（CBR）和粗死亡率（CDR）按每年每千人计算，便于对不同规模的地区进行比较。
Birth Rate = (Number of Live Births ÷ Total Population) × 1000 ‰
出生率 = (活产婴儿数 ÷ 总人口数) × 1000‰
Death Rate = (Number of Deaths ÷ Total Population) × 1000 ‰
死亡率 = (死亡人数 ÷ 总人口数) × 1000‰
Natural increase is simply the difference: Birth Rate – Death Rate, often expressed in the same per‑thousand units. When the birth rate exceeds the death rate, the population grows naturally.
人口自然增长即出生率减去死亡率，同样以千分比表示。当出生率高于死亡率时，人口出现自然增长。
5. Mean Annual Temperature & Temperature Range | 年均温与气温年较差
Climate graphs require you to calculate the average temperature for the whole year and the spread between the hottest and coldest months.
在分析气候图表时，需要计算全年平均气温以及最热月与最冷月之间的气温变化幅度。
Mean Annual Temperature = Sum of 12 Monthly Mean Temperatures ÷ 12
年均温 = 12 个月月均温之和 ÷ 12
Temperature Range = Hottest Month Mean – Coldest Month Mean
气温年较差 = 最热月月均温 – 最冷月月均温
For a Welsh coastal town, January might average 5 °C and July 17 °C. The annual range would be 17 – 5 = 12 °C, indicating a mild maritime climate.
假设威尔士某沿海小镇 1 月均温 5 °C，7 月均温 17 °C，其年较差 = 17 – 5 = 12 °C，表明这里属于温和的海洋性气候。
6. Total Annual Precipitation | 年总降水量
Total precipitation is the sum of all the rainfall (and melted snow) recorded in a year. It is usually measured in millimetres (mm).
年总降水量是指一年内记录到的所有降雨（和融雪）量的总和，通常以毫米 (mm) 为单位。
Total Annual Precipitation = Sum of Monthly Precipitation Values
年总降水量 = 各月降水量之和
You may also be asked for average monthly precipitation: divide the total by 12. A station recording 1200 mm annually has an average of 100 mm per month, though seasons vary greatly.
有时也需要计算月均降水量，用总量除以 12 即可。若某个测站年降水量为 1200 mm，月均降水量为 100 mm，但季节分布可能差异很大。
7. Grid References (4‑figure & 6‑figure) | 网格参考（四位数与六位数）
Grid references are used to pinpoint locations on Ordnance Survey maps. The rule to remember is "along the corridor and up the stairs": read the easting first, then the northing.
网格参考用来在英国地形测量局的地图上精确定位。口诀 “沿走廊走，再上楼”，即先读取东向数值，再读取北向数值。
A 4‑figure grid reference, such as 24 km square. The two digits 24 are the easting, and 31 are the northing. Think of the bottom‑left corner of that square.
四位数的网格参考如 24 31，表示一个 1 km × 1 km 的方格。24 是东向坐标值（easting），31 是北向坐标值（northing），定位到该方格左下角。
For greater precision, a 6‑figure grid reference divides the square into tenths. In 246 315, the third digit '6' estimates how many tenths east inside the square, and the sixth digit '5' estimates how many tenths north.
为了更精确，六位数网格参考会把方格细分为十等份。例如在 246 315 中，第三位数字 '6' 表示在方格内向东移动了十分之六，第六位数字 '5' 表示向北移动了十分之五。
8. Contour Interval & Height | 等高线间距与高度
Contour lines connect points of equal elevation. The contour interval is the vertical difference in height between two adjacent contour lines, stated in the map legend.
等高线连接海拔高度相等的各点。等高线间距是相邻两条等高线之间的垂直高差，通常会在地图图例中标出。
Contour Interval = Height of Upper Contour – Height of Lower Contour
等高线间距 = 较高等高线的海拔高度 – 较低等高线的海拔高度
To estimate the height of a summit that lies between two contours, use the midpoint assumption or check if there is a spot height or triangulation pillar. If the interval is 10 m and the summit sits halfway between the 220 m and 230 m contours, its approximate height is 225 m.
若要估算位于两条等高线之间的山峰高度，可采用中间值假设，或者查看是否有标注点高程或三角测量点。如果间距为 10 m，且山顶位于 220 m 和 230 m 等高线的正中间，则其估算高度约为 225 m。
9. River Discharge (Simple) | 河流流量（简易版）
River discharge is the volume of water flowing past a point in a given time. The basic formula links the channel's cross‑sectional area and the water's velocity.
河流流量是指单位时间内流过某一断面的水体体积。基本公式将河道横截面积与水流速度联系起来。
Discharge (m³/s) = Cross‑sectional Area (m²) × Velocity (m/s)
流量 (m³/s) = 横截面积 (m²) × 流速 (m/s)
In simple fieldwork, the cross‑ age depth of 0.5 m, and the water flows at 2 m/s, its discharge is (4 × 0.5) × 2 = 4 m³/s.
在简易野外观测中，横截面积可用平均水深乘以河宽来估算。假设一条溪流宽 4 m，平均水深 0.5 m，流速 2 m/s，其流量 = (4 × 0.5) × 2 = 4 m³/s。
10. Bearing & Compass Directions | 方位角与指南针方向
A bearing is a precise way of stating direction, measured in degrees clockwise from true north, and always written as a three‑digit number (e.g. 045°, 210°).
方位角是一种精确表示方向的方法，从正北开始顺时针量算，并用三位数字表示（如 045°、210°）。
Using a protractor on a map: place the centre on the starting point, line up 0° with the north line, and read the angle where the line to the destination cuts the protractor.
在地图上使用量角器时：将量角器的中心对准出发点，0° 刻度线与地图的北线对齐，然后读取指向目标点的直线所切割的角度。
The eight‑point compass directions (N, NE, E, SE, S, SW, W, NW) can be expressed as bearings: NE is 045°, SE is 135°, SW is 225°, NW is 315°. This theorem helps you convert between cardinal directions and bearings.
八方位指南针方向（北、东北、东、东南、南、西南、西、西北）可以用方位角表示：东北是 045°，东南是 135°，西南是 225°，西北是 315°。这个定理帮助你实现方位与方位角之间的转换。
11. Distance & Travel Time | 距离与旅行时间
The relationship between speed, distance and time is fundamental in many geographical investigations, such as planning a route or estimating journey length from a transport timetable.
速度、距离和时间之间的关系是许多地理探究的基础，如规划路线或根据交通时刻表估算行程时间。
Speed = Distance ÷ Time
速度 = 距离 ÷ 时间
If a train travels at 120 km/h for 1.5 hours, the distance covered is 120 × 1.5 = 180 km.
将公式变形可得到：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。若某列车以 120 km/h 的速度行驶 1.5 小时，所行驶的距离 = 120 × 1.5 = 180 km。
12. River Flow Rate | 河流流速
To measure the velocity of a river without flow meters, you can use a float (an orange or a tennis ball) and a stopwatch. This gives the surface velocity, which is then adjusted to get the mean velocity.
在没有流速仪的情况下，可以用浮标（如一个橙子或网球）和秒表来测量流速。这得到的是表面流速，再进行校正即可得出平均流速。
Velocity (m/s) = Distance Travelled by Float (m) ÷ Time Taken (s)
流速 (m/s) = 浮标漂移距离 (m) ÷ 所花时间 (s)
If it takes 8 seconds, the surface velocity is 10 ÷ 8 = 1.25 m/s. Because surface water moves faster, we often multiply by 0.85 to estimate the mean velocity.
选取一段 10 m 长的笔直河段，在上游起点放下浮标，记录它到达下游标记所用的秒数。如果耗时 8 秒，表面流速 = 10 ÷ 8 = 1.25 m/s。由于表层水流动较快，通常乘以 0.85 来估算平均流速。
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