GCSE CCEA Geography: Formula & Theorem Quick Reference Handbook | GCSE CCEA 地理：公式定理速查手册

📚 GCSE CCEA Geography: Formula & Theorem Quick Reference Handbook | GCSE CCEA 地理：公式定理速查手册

This quick reference handbook brings together all the essential formulae, calculations and key relationships you need to master for GCSE CCEA Geography. From map skills and population indicators to river measurements and fieldwork statistics, being confident with these equations will help you handle data-response questions and geographical investigations with precision.

本速查手册汇集了 GCSE CCEA 地理课程中你需要掌握的所有重要公式、计算与关键关系。从地图技能、人口指标到河流测量和实地考察统计，熟练掌握这些方程式将帮助你在数据与分析题以及地理调查中更加精准地作答。

1. Map Scale and Distance | 地图比例尺与距离

Map scale expresses the ratio between a distance on a map and the corresponding distance on the ground. It is most commonly shown as a representative fraction (e.g. 1:25 000) or a linear scale. The basic formula for calculating real ground distance is:

Real Distance = Map Distance × Scale Denominator

地图比例尺表示图上距离与对应实际地面距离的比值，通常以数字比例尺（如 1:25 000）或直线比例尺标示。计算实际地面距离的基本公式为：实际距离 = 图上距离 × 比例尺分母。

When measuring a curved feature such as a river or road on a map, use a piece of string to trace the shape, then straighten the string and measure its length against the linear scale. Always convert your final answer to kilometres or metres and remember to give the unit.

测量地图上的曲线地物（如河流或道路）时，可用一根细线沿地物走向描摹，然后将线拉直，对照直线比例尺量取长度。最终答案务必换算为千米或米，并标明单位。

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2. Area Estimation Using Grid Squares | 利用网格方格估算面积

On Ordnance Survey maps and sketch maps, you can estimate irregular area by counting grid squares. The method combines full squares and partial squares:

Area = (Number of full squares + ½ × Number of partial squares) × Area represented by one grid square on the ground

在 Ordnance Survey 地图和草图上，可通过数方格的方法估算不规则图形的面积。计算公式为：面积 = (完整方格数 + ½ × 不完整方格数) × 每个方格代表的实际地面面积。

Each grid square on a 1:50 000 map normally represents 1 km² (10 mm × 10 mm = 1 km × 1 km), while on a 1:25 000 map one square typically represents 0.25 km². Always check the map’s scale before applying this technique.

在 1:50 000 地图上，每个方格通常代表 1 km²（10 mm × 10 mm 对应 1 km × 1 km）；在 1:25 000 地图上，一个方格一般代表 0.25 km²。使用该方法前，务必先确认地图比例尺。

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3. Gradient (Slope) Calculation | 坡度计算

Gradient describes the steepness of a slope and is frequently examined in map skills questions. It is the ratio of the vertical interval to the horizontal equivalent:

Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE)

坡度描述斜坡的陡峭程度，是地图技能题目中的常见考点。它的定义是垂直间隔与水平距离的比值：坡度 = 垂直间隔 (VI) ÷ 水平距离 (HE)。

The vertical interval is found by subtracting the lower contour value from the higher one. The horizontal equivalent is the distance between the two contours measured along the ground and converted using the map scale. Express the gradient as a ratio such as 1:5, or as a fraction, and always simplify.

垂直间隔由较高等高线读数減去较低等高线读数求得。水平距离是两条等高线之间沿地面的距离，需要根据地图比例尺换算。请将坡度表示为 1:5 或分数的形式并化简。

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4. Population Density | 人口密度

Population density shows how crowded an area is and is a fundamental measure in human geography. It is calculated very simply:

Population Density = Total Population ÷ Land Area (km²)

人口密度反映一个地区的拥挤程度，是人文地理中的基本指标。计算方法十分简单：人口密度 = 总人口 ÷ 土地面积（km²）。

The result is expressed as people per square kilometre. When using data, make sure the land area excludes large inland water bodies and that both figures refer to the same year. This measure helps compare urban, rural and national distributions.

结果以每平方千米人口数表示。使用数据时，要确保土地面积不含大面积内陆水域，且两项数据来自同一年份。该指标可用于比较城市、乡村和国家的人口分布。

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5. Birth Rate and Death Rate | 出生率与死亡率

Crude birth rate and crude death rate are vital signs of population change, both expressed per 1000 people per year:

Crude Birth Rate = (Number of live births ÷ Total population) × 1000

Crude Death Rate = (Number of deaths ÷ Total population) × 1000

粗出生率和粗死亡率是反映人口变化的关键指标，均以每年每千人为单位表示：粗出生率 = (活产婴儿数 ÷ 总人口) × 1000；粗死亡率 = (死亡人数 ÷ 总人口) × 1000。

These rates are termed ‘crude’ because they do not account for age or sex structure. Always write the answer with the unit ‘per 1000’ (‰) and make sure your numerator and denominator cover exactly the same 12‑month period and geographical area.

之所以叫“粗”率，是因为它们没有考虑人口的年龄和性别结构。答案必须带有“每千人”（‰）的单位，并确保分子与分母为同一年度、同一地理范围的统计。

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6. Natural Increase Rate | 人口自然增长率

Natural increase shows whether a population is growing or declining from births and deaths alone, ignoring migration. It can be expressed as a percentage or per 1000:

Natural Increase Rate (%) = [(Births − Deaths) ÷ Total population] × 100

人口自然增长反映仅由出生和死亡导致的人口增减变化（不考虑迁移），可用百分比或千分比表示：自然增长率 (%) = [(出生人数 − 死亡人数) ÷ 总人口] × 100。

If you are using the crude rates directly, simply subtract death rate from birth rate and divide by 10 to convert to a percentage: Natural increase (%) = (CBR − CDR) ÷ 10. A positive value means natural growth; a negative value signals natural decrease.

如果直接使用粗出生率和粗死亡率，只需用出生率減去死亡率再除以 10 转换为百分比即可：自然增长率 (%) = (CBR − CDR) ÷ 10。正值代表人口自然增长，负值则表示人口自然减少。

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7. Percentage Change and Growth Rate | 百分比变化与增长率

Percentage change is widely used in geography to compare how a variable such as population, GDP or rainfall has altered over time:

Percentage Change = [(New value − Old value) ÷ Old value] × 100%

百分比变化在地理中广泛用于比较人口、GDP 或降水量等变量随时间变化的幅度：百分比变化 = [(新值 − 旧值) ÷ 旧值] × 100%。

Be careful to identify the correct ‘old’ (baseline) value; the formula measures change relative to the starting point. A positive result indicates growth, while a negative result indicates decline. Always round sensibly and state the time interval being compared.

注意准确判断“旧值”（基准值），该公式衡量的是相对于起点的变化。结果为正值表示增长，负值表示下降。务必合理取整并说明对比的时间区间。

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8. Dependency Ratio | 抚养比

The dependency ratio compares the economically dependent population (young and elderly) with the working‑age population, signalling pressure on the productive part of society:

Dependency Ratio = [(Population 0‑14 + Population 65+) ÷ Population 15‑64] × 100

抚养比衡量经济依赖人口（少年儿童和老年人）与劳动年龄人口之间的比例关系，反映社会生产年龄群体承受的负担：抚养比 = [(0‑14 岁人口 + 65 岁及以上人口) ÷ 15‑64 岁人口] × 100。

The result is a pure number (sometimes written as ‘per 100 working‑age people’). A rising dependency ratio can indicate an ageing population or high youth dependency, which has implications for healthcare, education and pension policy.

计算结果是一个纯数字（有时表示为每 100 名劳动年龄人口抚养的人数）。抚养比上升可能意味着人口老龄化或较高的少儿抚养负担，对医疗保障、教育和养老金政策都有深远影响。

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9. River Discharge | 河流流量

River discharge (Q) is the volume of water flowing past a point in the river per unit time, a fundamental measure in fluvial geography and flood risk:

Discharge (Q) = Cross‑sectional Area (A) × Average Velocity (v)

河流流量 (Q) 是指单位时间内通过河流某断面的水体体积，是河流地貌和洪水风险中的基础指标：流量 (Q) = 横截面积 (A) × 平均流速 (v)。

Discharge is usually expressed in cubic metres per second (m³/s, or cumecs). Area is measured in m² and velocity in m/s. To obtain an accurate Q, you must measure velocity at several points across the channel and calculate a mean.

流量通常以立方米每秒（m³/s，即 cumec）为单位。面积单位为 m²，流速单位为 m/s。为得到准确的 Q，需要测量河道内若干个位置的流速并求取均値。

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10. River Cross‑Sectional Area | 河流横截面积

To find the cross‑sectional area (A) of a river channel, you need the channel width and the average depth at a sampling site:

A = Width (w) × Average Depth (d̄)

计算河道横截面积 (A) 需要测量采样点的河宽与平均水深：A = 河宽 (w) × 平均水深 (d̄)。

Average depth is obtained by dividing the sum of depth readings taken at regular intervals across the channel by the number of readings. If the river bed is uneven, the method can be refined by treating the cross‑section as a series of trapezoids, but the simple width × average depth formula is sufficient for GCSE investigations.

平均水深等于在河道宽度方向上等间距测得的一系列水深数值的总和除以测点个数。如果河床不平整，改进的方法是把横截面看成一系列梯形计算，但在 GCSE 调查中使用“河宽 × 平均水深”的简化公式就足够了。

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11. Flow Velocity (Float Method) | 流速（浮标法）

In fieldwork, river velocity is often measured by timing a floating object (e.g. an orange or a cork) over a known distance:

Velocity (v) = Distance (d) ÷ Time (t)

在野外考察中，常通过计测浮体（如橙子或软木塞）漂过一段已知距离所用时间来确定流速：流速 (v) = 距离 (d) ÷ 时间 (t)。

Measure a straight section of the river, mark start and finish lines, and record the time with a stopwatch. Because surface velocity is faster than average velocity in the channel, the result is usually multiplied by a correction factor (commonly 0.8 or 0.85) to estimate the mean velocity for discharge calculations.

应选择一段顺直河段，标出起点和终点线，并用秒表记录时间。由于水面流速通常大于断面平均流速，该结果一般需要乘上修正系数（常用 0.8 或 0.85），以便估算参与流量计算的平均流速。

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12. Mean, Median and Range for Fieldwork Data | 野外考察数据的平均值、中位数与范围

When analysing fieldwork results such as pebble sizes, infiltration rates or pedestrian counts, simple statistics help identify typical values and spread:

Mean = Sum of all values ÷ Number of values

Range = Highest value − Lowest value

在分析卵石粒径、下渗率或行人计数等野外数据时，简单的统计量有助于识别典型值和数据离散程度：平均值 = 所有数值的总和 ÷ 数值个数；范围 = 最大值 − 最小值。

Median is the middle value when data are arranged in order. It is useful when data contain extreme outliers. Always state the units for your results and, if comparing two sites, calculate both the mean and the range to describe difference and variability.

中位数是将数据排序后处于中间位置的数值，当数据含有极端异常值时尤其有用。给出结果时一定要注明单位；若要对比两个地点，应同时计算平均值和范围，以描述差异和变异程度。

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