📚 Year 9 WJEC Geography: Formula & Theorem Quick Reference Guide | Year 9 WJEC 地理：公式定理速查手册
This quick reference guide covers essential formulas, calculations and key geographical skills required for Year 9 WJEC Geography. Mastering these will help you interpret maps, analyse population data, carry out fieldwork and understand physical processes with confidence. Keep this handbook handy for homework, class tests and revision.
本速查手册涵盖 Year 9 WJEC 地理课程所需的必备公式、计算方法和关键地理技能。掌握这些内容将有助你自信地解读地图、分析人口数据、开展野外调查并理解自然过程。请将这本手册放在手边，方便做作业、课堂测验和复习时查阅。
1. Map Scale Conversion | 地图比例尺换算
Map scale expresses the relationship between a distance on a map and the corresponding distance on the ground. It is usually given as a representative fraction (e.g., 1:50 000), meaning 1 unit on the map equals 50 000 of the same units on the ground. To find the true distance, simply multiply the map distance by the scale denominator.
地图比例尺表示图上距离与实地距离的比例关系。它通常以分数形式给出（如 1:50 000），意为地图上 1 个单位长度代表实地 50 000 个相同单位长度。计算实地距离时，只需将图上距离乘以比例尺分母。
True Distance = Map Distance × Scale Denominator
Example: 1:25 000 map, a footpath measures 8 cm. True distance = 8 cm × 25 000 = 200 000 cm = 2 km.
示例：在 1:25 000 地图上，一条步道长 8 厘米。实地距离 = 8 cm × 25 000 = 200 000 cm = 2 km。
2. Measuring Straight-line Distance | 直线距离测量
Straight-line distance ('as the crow flies') is measured with a ruler, then converted using the map scale. Ensure you measure carefully and note the units. On a paper map, always align the ruler with the grid lines for accuracy.
直线距离（“空中直线距离”）用直尺量测，然后通过地图比例尺换算。测量时需要仔细，并注意单位。在纸质地图上，为求精确，应始终将直尺与网格线对齐。
Straight-line Ground Distance = Ruler Distance × Scale Denominator
Tip: If the scale is 1:50 000, 1 cm on the map equals 50 000 cm on the ground, which is 500 m or 0.5 km. Memorising these quick conversions saves time.
技巧：若比例尺为 1:50 000，图上 1 厘米等于实地 50 000 厘米，即 500 米或 0.5 公里。记住这些快速换算能节省时间。
3. Measuring Curved-line Distance | 曲线距离测量
Curved features such as rivers, roads or coastlines cannot be measured accurately with a ruler. Instead, lay a piece of string along the curve on the map, mark the end point, then straighten the string and measure its length against a ruler. Finally, apply the scale conversion.
河流、道路或海岸线等弯曲地物无法用直尺精确测量。可以改用细线沿地图曲线摆放，在终点做好标记，然后将细线拉直并用直尺测量其长度，最后按比例尺进行换算。
True Curved Distance = Length of String × Scale Denominator
Example: stream measures 12 cm on a 1:50 000 map. True length = 12 cm × 50 000 = 600 000 cm = 6 km.
示例：用细线沿蜿蜒小溪测量，在 1:50 000 地图上细线长 12 厘米。实际长度 = 12 cm × 50 000 = 600 000 cm = 6 km。
4. Area Calculation Using Grid Squares | 利用方格计算面积
On topographic maps, area can be estimated using the grid square method. Count the number of complete squares within the boundary, then add half the number of incomplete squares. Multiply by the ground area represented by one square to obtain the total area.
在地形图上，可以利用方格法估算面积。先计算边界内完整方格的数量，再加上不完整方格数量的一半，最后乘以每个方格所代表的实地面积，即可得出总面积。
Area = (Whole Squares + ½ × Partial Squares) × Ground Area of One Square
Example: quares and 12 partial squares, area = (38 + ½ × 12) × 0.25 km² = (38 + 6) × 0.25 = 11 km².
示例：在 1:25 000 地图上，一个 2 cm × 2 cm 的方格代表 0.25 km²。若某湖泊覆盖 38 个完整方格和 12 个不完整方格，面积 = (38 + ½ × 12) × 0.25 km² = 44 × 0.25 = 11 km²。
5. Gradient Calculation | 梯度计算
Gradient describes the steepness of a slope. It is the ratio of vertical interval (VI) – the difference in height between two points – to horizontal equivalent (HE) – the horizontal distance between them. Both must be in the same units, and the gradient is usually simplified to a ratio such as 1:10.
梯度描述斜坡的陡峭程度。它是垂直间距（VI，两点间高差）与水平等距（HE，两点间水平距离）的比值。两者单位必须相同，梯度通常简化为 1:10 之类的比例。
Gradient = Vertical Interval (VI) / Horizontal Equivalent (HE) [same units]
Worked example: n a 1:10 000 map is 5 cm (i.e. 500 m on the ground). Gradient = 100 m / 500 m = 1/5 = 1:5.
计算示例：两点间等高线高差为 100 米，在 1:10 000 地图上量得水平距离为 5 厘米（即实地 500 米）。梯度 = 100 m / 500 m = 1/5 = 1:5。
6. Population Density | 人口密度
Population density measures how crowded an area is. It is found by dividing the total population by the total land area. The result is usually expressed as persons per square kilometre (persons/km²).
人口密度衡量一个地区的拥挤程度。用总人口除以土地总面积即可得出，结果通常以人/平方公里（人/km²）表示。
Population Density = Total Population ÷ Land Area (km²)
Example: ple and an area of 125 000 km². Population density = 5 000 000 ÷ 125 000 = 40 persons/km².
示例：某国有 500 万人口，面积 125 000 平方公里。人口密度 = 5 000 000 ÷ 125 000 = 40 人/km²。
7. Birth Rate and Death Rate | 出生率与死亡率
Birth and death rates are vital indicators for studying population change. The crude birth rate (CBR) is the number of live births per 1000 people per year. The crude death rate (CDR) is the number of deaths per 1000 people per year. Both are multiplied by 1000 to give a whole number for easy comparison.
出生率和死亡率是研究人口变化的重要指标。粗出生率 (CBR) 指每年每 1000 人中的活产婴儿数。粗死亡率 (CDR) 指每年每 1000 人中的死亡人数。两者都乘以 1000，以便得出整数进行比较。
Birth Rate (‰) = (Number of live births / Total population) × 1000
Death Rate (‰) = (Number of deaths / Total population) × 1000
Example: e, there were 2400 births and 1800 deaths last year. Birth rate = 2400/200 000 × 1000 = 12‰. Death rate = 1800/200 000 × 1000 = 9‰.
示例：某城镇人口 20 万，去年有 2400 名婴儿出生，1800 人死亡。出生率 = 2400/200 000 × 1000 = 12‰。死亡率 = 1800/200 000 × 1000 = 9‰。
8. Natural Increase Rate | 自然增长率
Natural increase (or natural decrease) shows whether a population is growing from births and deaths alone, ignoring migration. It is simply the birth rate minus the death rate, and is expressed per 1000 population.
自然增长（或自然减少）反映仅由出生和死亡造成的人口变化，不考虑迁移因素。计算方法为出生率减去死亡率，并以每 1000 人为单位表示。
Natural Increase Rate (‰) = Birth Rate – Death Rate
Example: Using the figures above, natural increase = 12‰ – 9‰ = +3‰, meaning the population grows by 3 people for every 1000 per year (excluding migration).
示例：承接上例数据，自然增长率 = 12‰ – 9‰ = +3‰，这意味着若不考虑迁移，该地每年每 1000 人增加 3 人。
9. Net Migration Rate | 净迁移率
Net migration rate accounts for the difference between the number of immigrants (people moving in) and emigrants (people moving out). It is expressed per 1000 population per year and can be positive (net in-migration) or negative (net out-migration).
净迁移率指迁入人口（移民）与迁出人口（移出）的差额，以每年每 1000 人为单位表示，可以是正值（净迁入）或负值（净迁出）。
Net Migration Rate (‰) = ((Immigrants – Emigrants) / Total population) × 1000
Example: ceived 15 000 immigrants and lost 5000 emigrants in one year. Net migration rate = (15 000 – 5000)/500 000 × 1000 = +20‰.
示例：某地区人口 50 万，一年内迁入 15 000 人，迁出 5000 人。净迁移率 = (15 000 – 5000)/500 000 × 1000 = +20‰。
10. Dependency Ratio | 依赖比率
The dependency ratio compares the economically dependent population (ages 0–14 and 65+) with the working-age population (ages 15–64). A higher ratio indicates greater pressure on the productive workforce to support dependents.
依赖比率比较经济依赖人口（0–14 岁和 65 岁以上）与劳动适龄人口（15–64 岁）的比例。比率越高，说明劳动人口赡养负担越重。
Dependency Ratio (%) = [(Population 0–14 + Population 65+) / Population 15–64] × 100
Example: A settlement has 3000 children (0– ng-age adults and 1000 elderly (65+). Dependency ratio = (3000 + 1000) / 6000 × 100 = 66.7%. This means for every 100 workers, there are about 67 dependents.
示例：某居民点有 3000 名儿童（0–14 岁）、6000 名劳动适龄人口和 1000 名老人（65 岁以上）。依赖比率 = (3000 + 1000) / 6000 × 100 = 66.7%。这意味着每 100 名劳动者需抚养约 67 名非劳动人口。
11. River Discharge | 河流流量
River discharge (streamflow) is the volume of water flowing through a channel cross-section per second. It is a key measurement in hydrology, calculated by multiplying the cross-sectional area of the channel by the average flow velocity. Discharge is measured in cubic metres per second (m³/s or cumecs).
河流流量（径流）是每秒通过河道横断面的水量。它是水文学中的关键测量指标，由河道横截面积乘以平均流速计算得出。流量单位为立方米/秒（m³/s 或 cumecs）。
Discharge (Q) = Cross-sectional Area (A) × Average Velocity (V)
Q = Width × Mean Depth × Velocity
Example: m, and the water flows at 0.8 m/s. A = 12 × 1.5 = 18 m². Q = 18 m² × 0.8 m/s = 14.4 m³/s.
示例：某河道宽 12 米，平均水深 1.5 米，水流速度为 0.8 米/秒。横截面积 A = 12 × 1.5 = 18 m²。流量 Q = 18 m² × 0.8 m/s = 14.4 m³/s。
12. Interquartile Range (IQR) | 四分位数间距
The interquartile range is a measure of dispersion used in fieldwork to describe the spread of the middle 50% of data. It is found by subtracting the lower quartile (Q₁, 25th percentile) from the upper quartile (Q₃, 75th percentile). IQR reduces the influence of extreme values and is ideal for comparing variables like pebble sizes or pedestrian counts.
四分位数间距是野外调查中用于描述数据中间 50% 离散程度的统计量。由上四分位数（Q₃，第 75 百分位数）减去下四分位数（Q₁，第 25 百分位数）得出。IQR 能减少极端值的影响，非常适合比较卵石粒径或行人流量等变量。
IQR = Q₃ – Q₁
Quick steps: (1) Order data from smallest to largest. (2) Find the median (Q₂). (3) Q₁ is the median of the lower half; Q₃ is the median of the upper half. (4) Subtract Q₁ from Q₃.
快速步骤：（1）将数据从小到大排序。（2）找出中位数（Q₂）。（3）Q₁ 为下半部分数据的中位数，Q₃ 为上半部分数据的中位数。（4）用 Q₃ 减去 Q₁。
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