📚 Year 12 OCR Geography: Formulae & Theorems Quick Reference Handbook | 公式定理速查手册
This quick reference handbook brings together the essential formulae and theorems required for the Year 12 OCR Geography course. From demographic rates and urban growth to river discharge, statistical tests, and spatial models, these tools underpin both your physical and human geography investigations. Use this guide to revise key equations, understand their applications, and build confidence for your examinations and fieldwork write-ups.
本速查手册汇总了 Year 12 OCR 地理课程所需的关键公式和定理。从人口统计指标、城市增长到河流流量、统计检验以及空间模型，这些工具是自然地理与人文地理研究的基石。利用本手册复习重要方程，理解它们的应用，为考试和野外调查报告增添信心。
1. Demographic Rates and Population Change | 人口统计指标与人口变化
The Crude Birth Rate (CBR) measures the number of live births per 1000 population in a given year. It is a fundamental indicator of fertility.
CBR = (B ÷ P) × 1000
where B is the number of live births and P is the total mid-year population.
粗出生率（CBR）衡量每年每千人口中的活产数，是反映生育水平的基本指标。公式：CBR = (B / P) × 1000，其中B为活产总数，P为年中总人口。
The Crude Death Rate (CDR) shows the number of deaths per 1000 population per year. Together with CBR it frames natural population change.
CDR = (D ÷ P) × 1000
where D is the number of deaths.
粗死亡率（CDR）表示每年每千人口中的死亡数。与CBR结合可展示人口的自然变动。公式：CDR = (D / P) × 1000，其中D为死亡人数。
The rate of natural increase (RNI) is the difference between CBR and CDR. It is often expressed as a percentage by dividing the difference by 10.
RNI (%) = (CBR – CDR) ÷ 10
自然增长率（RNI）是出生率与死亡率之差，常转换为百分比：RNI (%) = (CBR − CDR) ÷ 10。
Infant mortality rate (IMR) focuses on deaths under one year old per 1000 live births, an important social development indicator.
IMR = (Deaths under 1 year ÷ Live births) × 1000
婴儿死亡率（IMR）指某年内每千名活产婴儿中未满周岁死亡的人数，是衡量社会发展的重要指标。
2. Rule of 70 and Doubling Time | 70法则与人口倍增时间
The doubling time estimates how many years it will take for a population to double in size, assuming a constant annual growth rate.
Doubling Time (years) = 70 ÷ r
where r is the annual growth rate expressed as a percentage (e.g., 2 for 2%).
人口倍增时间用于估算在年增长率恒定的条件下，人口规模翻一番所需的年数。公式：倍增时间 = 70 ÷ r，其中r是年增长率百分比（如2%取2）。
For a country with a 2.5% growth rate, doubling time = 70 / 2.5 = 28 years. This rule of thumb is widely used in demographic studies to project future population sizes quickly.
对于年增长率2.5%的国家，倍增时间 = 70 ÷ 2.5 = 28年。这一经验法在人口研究中被广泛用于快速推测未来人口规模。
3. Net Migration and the Demographic Equation | 净迁移与人口平衡方程
Net migration is the difference between the number of immigrants (I) and emigrants (E). It can be expressed as an absolute number or as a rate per 1000 population.
Net Migration = I – E
Net Migration Rate = ((I – E) ÷ P) × 1000
净迁移是指迁入（I）与迁出（E）人口数之差，可用绝对数或每千人口比率表示。
The demographic balancing equation combines natural change and net migration to calculate total population change over a time period.
ΔP = (B – D) + (I – E)
where ΔP is the change in total population, B = births, D = deaths, I = immigration, and E = emigration.
人口平衡方程将自然变动与净迁移结合，计算某一时期的人口总变化：ΔP = (B − D) + (I − E)，其中ΔP为人口变化量。
This equation is essential when constructing population projections and understanding the components driving population growth or decline in a specific region.
该方程在编制人口预测、理解区域人口增长或下降的驱动力方面至关重要。
4. Urbanisation Level and Growth Rate | 城市化水平与增长率
The urbanisation level measures the proportion of a population living in urban areas. It is expressed as a percentage.
Urbanisation Level (%) = (Urban population ÷ Total population) × 100
城市化水平衡量城镇人口占总人口的比例，以百分比表示。
Urban growth rate refers to the annual rate of change in the urban population. It helps distinguish between the speed of urbanisation and urban population growth per se.
Urban Growth Rate (%) = ((Ut – Ut-1) ÷ Ut-1) × 100
where Ut is the urban population in the current year and Ut-1 is the urban population in the previous year.
城市增长率指城市人口的年变化率，用于区分城市化速度与单纯的城市人口增长。
A high urban growth rate combined with a falling urbanisation level may indicate that rural areas are growing even faster, a nuance important for analysing settlement change in an AS Geography context.
当城市增长率高而城市化水平却下降时，可能意味着农村人口增长更快；这一细微之处对AS地理的定居点变化分析十分重要。
5. River Discharge and Hydraulic Geometry | 河流流量与水力几何
River discharge (Q) is the volume of water passing a cross-section per unit time. It is a core variable in fluvial studies.
Q = A × v
where A is the cross-sectional area (m2) and v is the mean flow velocity (m/s).
河流流量（Q）是单位时间内通过河道断面的水体体积，是河流研究的核心变量。公式：Q = A × v，其中A为过水断面面积（平方米），v为平均流速（米/秒）。
To calculate the mean velocity, geographers often use a flow meter or float method. The cross-sectional area is found by multiplying channel width by average depth.
地理学者通常采用流速仪或浮标法测算平均流速。过水断面面积由河宽乘以平均水深求得。
Hydraulic radius (R) describes the efficiency of a channel shape and is used in Manning’s equation.
R = A ÷ P
where P is the wetted perimeter (the length of channel cross-section in contact with water).
水力半径（R）反映河道形态的效率，用于曼宁公式。R = A / P，其中P为湿周（水流与河床接触的断面周长）。
6. Manning’s Equation for Channel Flow | 河道水流的曼宁公式
Manning’s equation estimates open-channel flow velocity under uniform flow conditions. It links channel roughness, hydraulic radius, and slope.
v = (1 ÷ n) × R2/3 × S1/2
where v = mean velocity (m/s), n = Manning’s roughness coefficient, R = hydraulic radius (m), and S = channel slope (dimensionless, often expressed as a gradient).
曼宁公式用于估算恒定均匀流条件下的明渠流速，它将河道糙率、水力半径和坡度联系在一起：v = (1/n) × R^(2/3) × S^(1/2)。
The roughness coefficient n varies from about 0.01 for smooth concrete to >0.05 for boulder-strewn natural channels. Manning’s equation is particularly powerful when predicting flood flow velocities or designing river management schemes.
糙率系数n范围从光滑混凝土的约0.01到布满巨砾
Published by TutorHao | Year 12 Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导