📚 Year 12 Edexcel Biology: Formula & Theorem Quick Reference Handbook | Year 12 Edexcel 生物：公式定理速查手册
In Year 12 Edexcel Biology, quantitative skills and formula-based reasoning are integral to topics ranging from cell structure to ecosystems. This handbook consolidates the essential formulas, theorems, and relationships you will encounter in your AS-level exams. Each entry presents the equation in a clear, centred format, accompanied by variable definitions, practical examples, and key exam tips. Use this resource to practise calculations, interpret data, and embed these principles into your longer written responses.
在 Edexcel Year 12 生物学中，定量技能与基于公式的推理贯穿从细胞结构到生态系统的多个主题。本速查手册汇总了 AS 阶段考试中最核心的公式、定理与数量关系。每个条目均以醒目的居中式给出公式，并配有变量说明、实用示例与备考要点。通过这一手册，你可以高效地练习计算、分析数据，并将这些原理融入到开放型答题中。
1. Magnification | 放大倍数
ys convert all lengths to the same unit before substituting into the formula. Common unit conversions: 1 cm = 10 mm, 1 mm = 1000 µm, 1 µm = 1000 nm.
生物绘图、显微照片或图像的放大倍数是图像比实物增大的倍数。代入公式前必须将所有长度换算为相同单位。常见单位换算：1 厘米 = 10 毫米，1 毫米 = 1000 微米，1 微米 = 1000 纳米。
Magnification = Image size / Actual size
eter is 0.05 mm, magnification = 25 / 0.05 = ×500. Remember to report magnification with a '×' sign and no units.
例如，若一个细胞在图像中的长度为 25 毫米，实际直径为 0.05 毫米，则放大倍数 = 25 / 0.05 = ×500 倍。注意放大倍数须带 '×' 符号，没有单位。
2. Fick's Law | 菲克定律
Fick's Law describes the rate of diffusion across a membrane or tissue. It helps explain adaptations of gas exchange surfaces, such as the large surface area of alveoli, the thin diffusion barrier in capillaries, and the steep concentration gradients maintained by ventilation and blood flow.
菲克定律描述了物质跨膜或组织的扩散速率。它有助于解释气体交换表面的适应特征，例如肺泡的巨大表面积、毛细血管极薄的扩散屏障，以及通过通气和血流维持的陡峭浓度梯度。
Rate of diffusion ∝ (Surface area × Concentration difference) / Diffusion distance
The proportional symbol (∝) means that diffusion rate increases when surface area or concentration difference increases, and decreases when diffusion distance becomes larger. In an exam, you may need to use this relationship to predict how changes in lung structure affect gas exchange.
比例符号 (∝) 表示当表面积或浓度差增大时扩散速率增加，当扩散距离变大时速率减小。在考试中你可能需要运用这一关系，预测肺部结构变化如何影响气体交换。
3. Water Potential | 水势
Water potential (ψ) determines the direction of water movement by osmosis. Water moves from a region of higher water potential (less negative) to a region of lower water potential (more negative). Pure water at atmospheric pressure has a water potential of zero.
水势 (ψ) 决定了渗透作用中水分的运动方向。水分从水势较高（负得较少）的区域流向水势较低（负得更多）的区域。标准大气压下的纯水水势为零。
ψ = ψₛ + ψₚ
Where ψₛ is the solute potential (always negative or zero) and ψₚ is the pressure potential (usually positive inside turgid plant cells). In plant cells, the cell wall exerts a pressure potential that increases the overall water potential, opposing the entry of water and preventing bursting.
其中 ψₛ 为溶质势（总是负值或零），ψₚ 为压力势（在膨压植物细胞中通常为正值）。在植物细胞中，细胞壁产生压力势，提升总水势，从而对抗水分进入，防止细胞胀破。
4. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle per minute. It is a key indicator of the heart's efficiency and is regulated by changes in heart rate and stroke volume during exercise or disease.
心输出量是指一侧心室每分钟泵出的血液体积。它是衡量心脏效率的关键指标，在运动或疾病状态下通过心率和每搏输出量的变化来调节。
Cardiac output = Heart rate × Stroke volume
³ min⁻¹. During exercise, both heart rate and stroke volume can increase, raising cardiac output significantly.
单位通常为 dm³ min⁻¹ 或 L min⁻¹。若静息心率为 70 次/分，每搏输出量为 75 cm³ (0.075 dm³)，则心输出量 = 70 × 0.075 = 5.25 dm³ min⁻¹。运动时心率和每搏输出量均可增加，从而大幅提升心输出量。
5. Body Mass Index (BMI) | 身体质量指数
BMI is used to classify adults into weight categories and to assess health risks associated with being underweight, overweight, or obese. It is a simple but useful screening tool in epidemiological studies, though it does not distinguish between muscle and fat mass.
BMI 用于将成人划分为不同的体重类别，并评估与过轻、超重或肥胖相关的健康风险。它是一种简单实用的流行病学筛查工具，但无法区别人体肌肉与脂肪的质量。
BMI = mass (kg) / (height in m)²
ht of 1.70 m, BMI = 68 / (1.70)² ≈ 23.5 kg m⁻², which falls within the healthy range (18.5–24.9). Values of 25.0–29.9 indicate overweight, and 30.0 or above indicate obesity.
一位体重 68 公斤、身高 1.70 米的人，BMI = 68 / (1.70)² ≈ 23.5 kg m⁻²，属于健康范围 (18.5–24.9)。BMI 在 25.0–29.9 之间为超重，30.0 及以上为肥胖。
6. Temperature Coefficient (Q10) | 温度系数 (Q10)
The Q10 coefficient measures the rate of change of a biological process when the temperature is increased by 10°C. It is most commonly applied to enzyme‑controlled reactions and metabolic rates. A Q10 value of around 2–3 is typical for many enzyme reactions within their optimum temperature range.
Q10 系数衡量温度每升高 10°C 时生物过程速率的变化程度。它最常应用于酶控反应和代谢速率。在酶的最适温度范围内，典型的 Q10 值通常为 2–3。
Q10 = Rate at (T + 10)°C / Rate at T°C
If the rate of an enzyme reaction is 12 µmol min⁻¹ at 25°C and 30 µ 5. A Q10 less than 1 would indicate that the rate decreases with warming, which can happen if the temperature exceeds the enzyme's optimum and denaturation begins.
若某酶促反应在 25°C 时速率为 12 µmol min⁻¹，在 35°C 时速率为 30 µmol min⁻¹，则 Q10 = 30 / 12 = 2.5。Q10 小于 1 则表示升温导致速率下降，这可能发生在温度超过酶的最适点、开始变性时。
7. Hardy-Weinberg Equilibrium | 哈代-温伯格平衡
The Hardy-Weinberg principle provides a mathematical baseline for studying allele and genotype frequencies in a population that is not evolving. It is a null model that assumes random mating, no mutation, no gene flow, large population size, and no natural selection. You will use the two equations to estimate carrier frequencies and to test whether evolution is occurring.
哈代-温伯格原理为研究非进化群体中的等位基因频率和基因型频率提供了数学基线。它是一个零模型，假设随机交配、无突变、无基因流动、群体规模大且无自然选择。你将使用这两个方程来估算携带者频率，并检验种群是否在进化。
p + q = 1
p² + 2pq + q² = 1
Here, p is the frequency of the dominant allele, q is the frequency of the recessive allele; p², 2pq and q² represent the frequencies of the homozygous dominant, heterozygous, and homozygous recessive genotypes respectively. A typical exam question gives the frequency of a recessive phenotype (q²) and asks you to determine the percentage of heterozygous carriers.
这里，p 为显性等位基因频率，q 为隐性等位基因频率；p²、2pq 和 q² 分别代表纯合显性、杂合和纯合隐性基因型的频率。典型考题会给出隐性表型的频率 (q²)，要求你计算杂合携带者的百分比。
8. Simpson’s Diversity Index | 辛普森多样性指数
Simpson’s Diversity Index (D) quantifies the biodiversity of a community by considering both species richness and the relative abundance of each species. A higher D value indicates greater diversity, meaning the community is more stable and resilient to environmental changes.
辛普森多样性指数 (D) 通过同时考虑物种丰富度和各物种的相对多度来量化群落生物多样性。D 值越高代表多样性越大，意味着群落更稳定，对环境的抵抗力也更强。
D = 1 – ∑ (n/N)²
In this formula, n is the number of individuals of a particular species, and N is the total number of individuals of all species. Σ (n/N)² is the sum of the squared proportion of each species. Because D is expressed as 1 minus this sum, it can range from 0 (very low diversity) to almost 1 (very high diversity). Use this index when comparing two habitats or monitoring the impact of an environmental disturbance.
公式中，n 为某一特定物种的个体数，N 为所有物种的个体总数。Σ (n/N)² 是每一个物种所占比例的平方和。D 表示为 1 减去该平方和，因此其取值范围从 0（多样性极低）到接近 1（多样性极高）。在比较两个栖息地或监测环境扰动影响时，可应用该指数。
9. Net Primary Productivity (NPP) | 净初级生产力
Net primary productivity is the rate at which energy is incorporated into organic matter by producers after accounting for the energy used in their own respiration. It represents the energy available to the next trophic level (consumers) and is a fundamental measure of ecosystem efficiency.
净初级生产力是指生产者经自身呼吸消耗后，将能量固定到有机物中的速率。它代表了可供给下一营养级（消费者）的能量，是衡量生态系统效率的基本指标。
NPP = GPP – R
GPP (gross primary productivity) is the total energy fixed by photosynthesis, and R is the respiratory energy loss. Units are usually given as energy per unit area per unit time, e.g. kJ m⁻² year⁻¹. When analysing a food chain, NPP explains why the amount of energy transferred to herbivores is much smaller than the total energy captured by plants.
GPP（总初级生产力）是光合作用固定的总能量，R 为呼吸作用的能量损失。单位通常表示为每单位面积每单位时间的能量，例如 kJ m⁻² year⁻¹。在分析食物链时，NPP 解释了为什么传递到植食动物的能量远少于植物捕获的总能量。
10. Lincoln Index (Mark–Release–Recapture) | 林肯指数（标记重捕法）
The Lincoln Index estimates population size for motile organisms that cannot easily be counted directly. It relies on capturing, marking and releasing a sample, then recapturing a second sample and recording how many marked individuals appear. Several assumptions must be met: the marks are not lost, marking does not affect survival or behaviour, the population is closed, and marked individuals mix randomly with the rest of the population.
林肯指数用于估算不易直接计数的活动动物的种群规模。它基于捕获、标记并释放一批个体，之后进行第二次捕获并记录其中已标记个体出现的数量。必须满足若干假设：标记不会脱落，标记不影响生存或行为，种群是封闭的，且标记个体与未标记个体在种群中随机混合。
N = (M × C) / R
r of marked individuals recaptured in the second sample. For example, if 80 beetles are marked and released, and a later sample of 60 beetles contains 15 marked ones, the estimate is N = (80 × 60) / 15 = 320 beetles. Always evaluate whether the assumptions are likely to hold in the specific context of the question.
式中，M = 第一次捕获、标记并释放的个体数；C = 第二次捕获的总个体数；R = 第二次捕获中已标记的个体数。例如，80 只甲虫被标记释放，随后捕获的 60 只中有 15 只带有标记，则种群估值为 N = (80 × 60) / 15 = 320 只甲虫。答题时始终要评估这些假设在给定情境下是否可能成立。
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