📚 A-Level Edexcel Biology: Formula Summary Handbook | A-Level Edexcel 生物：公式汇总手册
This comprehensive summary handbook gathers all the essential mathematical formulae and quantitative relationships required for A-Level Edexcel Biology. From microscopic measurements to population genetics, every equation is presented with clear definitions, worked contexts, and links to specification topics. Keeping these formulae at your fingertips will boost your confidence in calculations and data-analysis questions across all exam papers.
这本全面的公式汇总手册收集了 A-Level Edexcel 生物课程所需的所有核心数学公式和数量关系。无论是显微镜测量还是群体遗传学，每个公式都附有清晰的定义、应用情境以及与考纲主题的链接。熟记这些公式将极大提升你在各试卷中应对计算和数据分析题型的信心。
1. Microscopy & Magnification | 显微镜与放大率
Magnification is the degree to which the size of an image is larger than the real object. The relationship linking magnification (M), image size (I), and actual size (A) is a core tool for interpreting micrographs and scientific drawings.
放大率是指图像比实物放大的倍数。联系放大率（M）、图像大小（I）和实际大小（A）的关系是解读显微照片和科学绘图的核心工具。
Magnification = Image size ÷ Actual size (M = I ÷ A)
The formula can be rearranged to Actual size = Image size ÷ Magnification and Image size = Magnification × Actual size. Always convert all measurements to the same unit before calculation, and express the final actual size in the most suitable unit (micrometres or nanometres as appropriate). In the exam, you may also need to calculate magnification from a scale bar: measure the bar length in the image and divide by the stated real length.
该公式可变形为实际大小 = 图像大小 ÷ 放大率和图像大小 = 放大率 × 实际大小。计算前务必将所有测量值转换为同一单位，最终的实际大小应以最合适的单位表示（微米或纳米）。考试中还可能要求根据比例尺计算放大率：测量图像中比例尺的长度，除以标注的真实长度即可。
2. Cell Counting & Mitotic Index | 细胞计数与分裂指数
The mitotic index is a measure of the proportion of cells actively undergoing mitosis in a population. It is used to assess tissue growth rates or the effect of treatments on the cell cycle.
分裂指数是衡量一个细胞群体中正在进行有丝分裂的细胞比例的指标，用于评估组织生长速率或处理因素对细胞周期的影响。
Mitotic index = (Number of cells in mitosis ÷ Total number of cells) × 100
When using a haemocytometer to estimate cell concentration, you count cells within a known volume. The concentration of cells per cm³ is given by (Average count per large square × Dilution factor) ÷ Volume of one large square (cm³). For a typical Neubauer chamber, the volume above one large square is 0.1 mm³ (10⁻⁴ cm³). Take care to count cells touching two boundaries only, to avoid bias.
使用血球计数板估算细胞浓度时，需对已知体积内的细胞进行计数。每立方厘米的细胞浓度 = （每个大方格的平均细胞数 × 稀释因子）÷ 一个大方格上方液体的体积（cm³）。典型 Neubauer 计数板中，每个大方格上方的体积为 0.1 mm³（10⁻⁴ cm³）。计数时注意只计及接触两条边界的细胞，以避免偏差。
3. Surface Area to Volume Ratio | 表面积与体积比
As an organism or cell increases in size, its surface area to volume ratio (SA:V) decreases. This ratio is fundamental to understanding the limitations on diffusion, heat exchange, and metabolic rate.
随着生物体或细胞体积的增大，其表面积与体积之比（SA:V）会降低。这一比值对于理解扩散、热交换和代谢速率的限制至关重要。
SA:V ratio = Surface area ÷ Volume
For simple shapes, you may be given the surface area and volume formulae and must compute the ratio. For a sphere, surface area = 4πr² and volume = ⁴⁄₃πr³, giving SA:V = 3/r. For a cube of side L, surface area = 6L² and volume = L³, so SA:V = 6/L. The biological significance is that small organisms (or single cells) with high SA:V ratios can rely on simple diffusion, whereas larger organisms need specialised exchange surfaces and transport systems.
对于简单几何形状，题目可能提供表面积和体积公式，要求你计算比值。球体表面积 = 4πr²，体积 = ⁴⁄₃πr³，得 SA:V = 3/r。边长为 L 的正方体表面积 = 6L²，体积 = L³，SA:V = 6/L。其生物学意义在于，具有高 SA:V 的小型生物（或单细胞）可依赖简单扩散，而大型生物则需要特化的交换表面和运输系统。
4. Cardiac Output & Heart Rate | 心输出量与心率
Cardiovascular calculations link heart activity to the delivery of oxygen and nutrients. The key equation relates cardiac output, stroke volume, and heart rate.
心血管计算将心脏活动与氧气和营养物质的输送联系起来。核心公式涉及心输出量、每搏输出量和心率。
Cardiac output (dm³ min⁻¹) = Stroke volume (dm³) × Heart rate (bpm)
Stroke volume is the volume of blood pumped by one ventricle per beat; cardiac output is the total volume pumped per minute. You may need to rearrange the equation to find heart rate or stroke volume from given data. Remember that the units must be consistent, and volumes are often expressed in dm³ or cm³ (1 dm³ = 1000 cm³). This relationship is especially relevant when interpreting data on exercise, training, or cardiovascular disease.
每搏输出量是单侧心室每次搏动泵出的血量；心输出量是每分钟泵出的总血量。你可能需要根据已知数据转换公式以求解心率或每搏输出量。注意单位必须一致，容积常用 dm³ 或 cm³ 表示（1 dm³ = 1000 cm³）。在解读运动、训练或心血管疾病数据时，这一关系尤为相关。
5. Respiratory Quotient (RQ) | 呼吸商
The respiratory quotient reveals which respiratory substrate is being metabolised by comparing the volumes of carbon dioxide produced and oxygen consumed.
呼吸商通过比较二氧化碳产生量与氧气消耗量的体积比，揭示正在被代谢的呼吸底物种类。
RQ = Volume of CO₂ produced ÷ Volume of O₂ consumed
Typical RQ values are 1.0 for carbohydrates, approximately 0.7 for lipids, and around 0.8–0.9 for proteins. A measured RQ can therefore indicate the dominant fuel source. In respirometer experiments, you must subtract any control readings to account for changes in pressure or temperature. RQ is calculated from the net volumes of gas exchanged over a specific time period, ensuring conditions are standardised.
典型的 RQ 值：碳水化合物约为 1.0，脂类约为 0.7，蛋白质约在 0.8–0.9 之间。因此，测得的 RQ 可以指示主要的燃料来源。在呼吸计实验中，必须减除对照组的读数，以校正压力或温度变化。RQ 是根据特定时间段内气体交换的净体积计算的，需确保条件标准化。
6. Productivity & Energy Transfer Efficiency | 生产力与能量传递效率
In ecosystems, energy enters through producers and passes along food chains. Productivity equations account for the energy fixed and lost at each trophic level.
在生态系统中，能量通过生产者进入，并沿食物链传递。生产力方程则计算每个营养级中固定的能量和损失的能量。
Net primary production (NPP) = Gross primary production (GPP) − Plant respiration (R)
For consumers, net production (N) is the energy retained after losses in faeces and respiration: N = I − (F + R), where I is the chemical energy in ingested food, F is energy lost in faeces, and R is energy lost through respiration. Efficiency of energy transfer between trophic levels is given by:
对于消费者，净生产量（N）是减去粪便和呼吸损失后保留的能量：N = I − (F + R)，其中 I 代表摄入食物中的化学能，F 代表粪便中损失的能量，R 代表呼吸损失的能量。营养级之间的能量传递效率计算公式为：
Efficiency (%) = (Energy or biomass after transfer ÷ Energy or biomass before transfer) × 100
Biomass values (kg, g m⁻² year⁻¹) are often used as a convenient proxy for energy, assuming uniform energy content. Exam questions frequently ask you to calculate missing values in productivity pyramids or to explain why efficiency is typically low (around 10%), referencing energy lost as heat, uneaten parts, and excretion.
生物量值（如 kg、g m⁻² year⁻¹）常作为能量的方便替代指标，前提是各物质的能量含量均匀。考题常要求计算生产力金字塔中的缺失值，或结合能量以热、未被取食的部分以及排泄物形式损失的原因，解释为何传递效率通常较低（约 10%）。
7. Mark-Release-Recapture (Lincoln Index) | 标记重捕法（林肯指数）
The Lincoln Index estimates the size of a motile animal population where a direct total count is impractical. It relies on the proportion of marked individuals in a second sample.
林肯指数用于估算活动能力强、无法直接计数的动物种群的大小，其原理基于第二次样本中标记个体所占的比例。
N = (M × C) ÷ R
N = estimated population size; M = number of animals captured, marked, and released in the first sample; C = total number captured in the second sample; R = number of marked animals recaptured in the second sample. This method assumes: mixing of marked and unmarked individuals is complete; no births, deaths, immigration, or emigration between samples; the mark does not affect survival or catchability; and the marking medium is not lost. Violations of these assumptions lead to over‑ or underestimation, and you should be prepared to discuss how changes affect the calculated N.
N = 估算种群大小；M = 第一次捕获、标记并释放的动物数量；C = 第二次捕获的总数；R = 第二次捕获中带有标记的个体数。该方法假设：标记与未标记个体经历了充分混合；两次采样期间没有出生、死亡、迁入或迁出；标记不影响生存或可捕性；标记物不会脱落。违反这些假设将导致高估或低估，你应准备讨论各项变化如何影响计算出的 N 值。
8. Hardy-Weinberg Equilibrium | 哈代-温伯格平衡
In a stable, large population where no evolutionary forces operate, allele and genotype frequencies remain constant across generations. The Hardy-Weinberg equations provide a null model for studying genetic change.
在一个没有进化力量作用的大而稳定的种群中，等位基因和基因型频率在世代间保持恒定。哈代-温伯格方程提供了研究遗传变迁的零模型。
p + q = 1
p² + 2pq + q² = 1
Here, p represents the frequency of the dominant allele and q the frequency of the recessive allele. p² is the frequency of homozygous dominant individuals, 2pq the frequency of heterozygotes, and q² the frequency of homozygous recessive individuals. In Edexcel questions, you are often given the frequency of either a recessive phenotype (which equals q²) or an allele frequency, and are asked to calculate the carrier frequency (2pq) or the proportion of the population that is homozygous dominant (p²). Remember to take the square root of a phenotype frequency to find the allele frequency when starting from q².
其中，p 代表显性等位基因的频率，q 代表隐性等位基因的频率。p² 表示显性纯合个体的频率，2pq 表示杂合个体的频率，q² 表示隐性纯合个体的频率。在 Edexcel 考题中，通常会给出隐性表型频率（等于 q²）或某个等位基因频率，要求计算携带者频率（2pq）或显性纯合子比例（p²）。从 q² 出发时，需将表型频率开平方以求得等位基因频率。
9. Dilution Calculations | 稀释计算
Serial dilutions are standard practice when preparing solutions of known concentration or when counting colonies on agar plates. Understanding dilution factors is essential for calculating original cell concentrations or solute masses.
连续稀释是制备已知浓度溶液或计数琼脂平板上菌落时的标准操作。理解稀释因子对于计算原始细胞浓度或溶质质量至关重要。
Dilution factor = Total final volume ÷ Volume of stock solution used
For a serial dilution, the overall dilution factor is the product of the individual steps. For example, a 10⁻² dilution followed by a 10⁻³ dilution yields an overall 10⁻⁵ dilution. To find the concentration of cells in the original suspension from a viable count: Original concentration = (Number of colonies ÷ Volume plated) × Dilution factor. Always express your final concentration with appropriate units (CFU cm⁻³). Ensure that the volumes match; if the volume plated is 0.1 cm³, you must account for this when scaling up to per cm³.
对于连续稀释，总稀释因子是各步骤因子的乘积。例如，先做 10⁻² 稀释，再做 10⁻³ 稀释，得到总稀释度为 10⁻⁵。根据活菌计数求原液中的细胞浓度：原始浓度 = (菌落数 ÷ 涂布体积) × 稀释因子。最终浓度必须以适当的单位表示（如 CFU cm⁻³）。确保体积统一；如果涂布体积为 0.1 cm³，在换算为每 cm³ 时必须纳入计算。
10. Rate Calculations in Biology | 生物学中的速率计算
Rate equations are encountered across the syllabus, from enzyme‑catalysed reactions to population growth and substrate uptake. They take the general form of a quantity change per unit time.
从酶催化反应到种群增长和底物吸收，速率方程贯穿整个考纲，其一般形式为单位时间内某个量的变化。
Rate = Change in measured quantity ÷ Time
In enzyme kinetics, you may calculate the initial rate of reaction as (Change in product concentration) ÷ Time or from the slope of a progress curve at time zero. For transpiration, rate = (Distance moved by bubble) ÷ (Time × Cross‑sectional area) when using a potometer. You might also need to compute percentage change: Percentage change = ((Final value − Initial value) ÷ Initial value) × 100. Always check the quantity being measured (absorbance, volume of gas, mass) and the time unit specified; if a graph is provided, draw a tangent at the required point to determine the instantaneous rate.
在酶动力学中，你可以计算初始反应速率：（产物浓度变化）÷ 时间，或根据进程曲线在零时的斜率求得。对于蒸腾作用，使用蒸腾计测量时，速率 = （气泡移动距离）÷（时间 × 茎截面积）。你可能还需要计算百分比变化：百分比变化 = ((终值 − 初值) ÷ 初值) × 100。务必确认被测量的量（吸光度、气体体积、质量）及规定的时间单位；若给出曲线图，应在指定点绘制切线以确定瞬时速率。
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