📚 Formula & Key Principles Quick Reference for Year 12 OCR Biology | Year 12 OCR 生物：公式定理速查手册
This reference handbook brings together the essential equations, principles and statistical tests you are expected to know and apply in Year 12 of the OCR A Biology specification. Each section gives the formula, explains when to use it, and provides a concise worked example or key point for revision.
本速查手册汇总了你在 OCR A 生物学 Year 12 阶段必须掌握并应用的核心公式、原理与统计检验。每一节均给出公式，说明使用场景，并提供简明示例或关键要点以供复习。
1. Magnification & Image Size | 放大倍数与图像尺寸
The relationship between magnification, image size and actual size is fundamental for microscopy. Magnification is how many times larger an image appears compared with the real object.
放大倍数、图像大小与实际大小之间的关系是显微技术的基础。放大倍数是指图像看起来比实物大多少倍。
Magnification = Image size ÷ Actual size
放大倍数 = 图像大小 ÷ 实际大小
e ÷ Magnification. Always convert all measurements to the same unit, usually micrometres (µm) or nanometres (nm). Remember: 1 mm = 1000 µm, and 1 µm = 1000 nm.
将公式变形可得：实际大小 = 图像大小 ÷ 放大倍数。务必先将所有测量值换算为相同的单位，通常是微米（µm）或纳米（nm）。注意：1 mm = 1000 µm，1 µm = 1000 nm。
s 36 mm across at a magnification of ×400, the actual size is (36 mm ÷ 400) = 0.09 mm = 90 µm. Express your final answer to an appropriate number of significant figures.
若一个细胞的图像宽度为 36 mm，放大倍数为 ×400，则实际大小为 (36 mm ÷ 400) = 0.09 mm = 90 µm。最终答案要保留适当有效数字。
2. Water Potential (Ψ) | 水势
Water potential determines the direction of water movement. Water always moves from a region of higher (less negative) water potential to a region of lower (more negative) water potential across a partially permeable membrane.
水势决定水分运动的方向。水总是通过部分透性膜从水势较高（负值较小）的区域向水势较低（负值较大）的区域移动。
Ψ = Ψₛ + Ψₚ
plant cells owing to turgor pressure). In a fully turgid cell, Ψ = 0 as Ψₚ cancels Ψₛ. In pure water at atmospheric pressure, Ψ = 0.
式中 Ψ 为总水势，Ψₛ 为溶质势（始终为零或负值），Ψₚ 为压力势（植物细胞内因膨压通常为正值）。在完全饱满的细胞中，Ψ = 0，因为 Ψₚ 抵消了 Ψₛ。在标准大气压下的纯水中，Ψ = 0。
the protoplast shrinks and the pressure potential becomes zero, so Ψ = Ψₛ (very negative).
该公式有助于解释质壁分离：将植物细胞置于低水势溶液中，水离开细胞，原生质体缩小，压力势降为零，因此 Ψ = Ψₛ（负值很大）。
3. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle per minute. It is a key measure of heart performance.
心输出量是指一个心室每分钟泵出的血液体积，是衡量心脏功能的关键指标。
Cardiac Output = Stroke Volume × Heart Rate
心输出量 = 每搏输出量 × 心率
Stroke volume is the volume of blood ejected by a ventricle during one contraction (typically 70 cm³). Heart rate is the number of beats per minute (bpm). Cardiac output is typically expressed in dm³ min⁻¹ or L min⁻¹.
每搏输出量是一次心室收缩射出的血液体积（通常约为 70 cm³）。心率是每分钟心跳次数（bpm）。心输出量通常以 dm³ min⁻¹ 或 L min⁻¹ 表示。
¹. This value can change during exercise, when both stroke volume and heart rate increase.
若每搏输出量为 75 cm³，心率为 72 bpm，则心输出量 = 75 × 72 = 5400 cm³ min⁻¹ = 5.4 dm³ min⁻¹。运动时，每搏输出量和心率均会增加，此值随之改变。
4. Respiratory Quotient (RQ) | 呼吸商
The respiratory quotient indicates which respiratory substrate is being metabolised. It is obtained from the ratio of carbon dioxide produced to oxygen consumed.
呼吸商指示正在代谢的呼吸底物种类，通过产生的二氧化碳与消耗的氧气之比求得。
RQ = CO₂ produced ÷ O₂ consumed
RQ = 产生的 CO₂ ÷ 消耗的 O₂
Carbohydrate (glucose) yields an RQ of 1.0 because the numbers of CO₂ and O₂ molecules are equal. Lipid has an RQ of about 0.7, as fatty acids contain more hydrogen relative to oxygen. Protein gives an RQ around 0.9. A mixed diet usually produces an RQ between 0.8 and 0.9.
碳水化合物（葡萄糖）的 RQ 为 1.0，因为 CO₂ 与 O₂ 的分子数相等。脂质的 RQ 约为 0.7，因脂肪酸含氢相对较多而氧较少。蛋白质的 RQ 约 0.9。混合膳食通常产生 0.8–0.9 的 RQ。
In respirometer experiments, RQ helps identify the substrate used by an organism. A RQ greater than 1.0 suggests anaerobic respiration is occurring alongside aerobic respiration, because extra CO₂ is released without consuming O₂.
在呼吸计实验中，RQ 有助于识别生物体使用的底物。RQ 大于 1.0 表示在需氧呼吸的同时发生了厌氧呼吸，因为释放了额外的 CO₂ 而没有消耗 O₂。
5. Chi-squared Test (χ²) | 卡方检验
The chi-squared test is a statistical test used to compare observed and expected frequencies. In Year 12, it is commonly applied to genetics crosses or ecological distribution data.
卡方检验是一种用于比较观察频率与预期频率的统计检验方法。在 Year 12，它常用于遗传杂交或生态分布数据。
χ² = Σ ( (O – E)² / E )
O represents the observed number, E the expected number. Σ means 'sum of' 0.05) means the difference is unlikely to be due to chance; we reject the null hypothesis.
O 代表观察值，E 代表预期值，Σ 表示对所有类别求和。若结果具有显著性（χ² 大于 p = 0.05 时的临界值），表明差异不太可能由偶然造成，我们拒绝零假设。
Always state your null hypothesis and compare your calculated χ² against the appropriate critical value from the table.
拟合优度检验的自由度 df = 类别数 − 1。对于列联表，df = (行数 − 1) × (列数 − 1)。务必陈述零假设，并将计算得到的 χ² 与表中相应的临界值进行比较。
6. Simpson's Index of Diversity | 辛普森多样性指数
Simpson's Index of Diversity measures the biodiversity of a habitat, taking into account both species richness and the evenness of species abundance. A higher value indicates greater diversity.
辛普森多样性指数用于衡量一个栖息地的生物多样性，同时兼顾物种丰富度和物种个体分配的均匀度。值越高，多样性越高。
D = 1 – Σ ( n/N )²
Here N is the total number of organisms of all species, and n is the total number of organisms of a particular species. You calculate (n/N)² for each species, sum these values, and subtract the total from 1. The resulting D ranges from 0 (low diversity) to almost 1 (very high diversity).
其中 N 是所有物种的个体总数，n 是某一特定物种的个体总数。计算出每个物种的 (n/N)² 并求和，再从 1 中减去该总和。所得的 D 值范围从 0（低多样性）到接近 1（极高多样性）。
sometimes encountered is D = 1 / Σ (n/N)². Check which version is given in your exam paper' lues is reversed. The OCR specification expects you to use and interpret D = 1 − Σ (n/N)².
有时会遇到另一种公式 D = 1 / Σ (n/N)²。请注意试卷公式表中提供的是哪个版本，高低值的解释是相反的。OCR 考纲要求你使用并解释 D = 1 − Σ (n/N)²。
7. Percentage Change | 百分比变化
Calculating percentage change is essential when comparing biological measurements before and after a treatment, or when recording mass changes in osmosis experiments.
计算百分比变化在比较处理前后生物学测量值，或记录渗透实验中质量变化时至关重要。
Percentage Change = ( (final value – initial value) ÷ initial value ) × 100%
百分比变化 = ( (终值 – 初值) ÷ 初值 ) × 100%
A positive result represents an increase, a negative result a decrease. Using percentage change allows fair comparison between samples of different initial sizes. For potato cylinder osmosis, the percentage change in mass is plotted to determine the water potential of the tissue.
正值表示增加，负值表示减少。使用百分比变化可以公平地比较不同初始大小的样本。在马铃薯条渗透实验中，绘制质量变化百分比图可确定组织的水势。
8. Rate of Reaction | 反应速率
In enzyme-controlled reactions, you often estimate the initial rate of reaction as the reciprocal of the time taken for a measurable change, such as the disappearance of a substrate or the appearance of a product.
在酶控反应中，你常以发生可测量变化所需的时长的倒数来估算初始反应速率，如底物消失或产物出现的时间。
Rate = 1 / time (units: s⁻¹)
速率 = 1 / 时间（单位：s⁻¹）
kdown of starch by amylase, record the time taken for the iodine test to show no colour change, then use rate = 1/time to compare treatments.
当通过产物浓度变化测量速率时，公式为速率 = 浓度变化 / 时间。在如淀粉酶分解淀粉的实验中，记录碘液测试不再变色的时间，然后使用 速率 = 1/时间 比较不同处理。
9. Dilution Factor | 稀释因子
Serial dilutions are used to create a range of known concentrations for a calibration curve. The dilution factor tells you how much the original solution has been diluted.
系列稀释用于制作一系列已知浓度的溶液，以绘制标准曲线。稀释因子告诉你原始溶液被稀释了多少倍。
Dilution Factor = Total volume ÷ Volume of stock solution
稀释因子 = 总体积 ÷ 原液体积
ration ÷ dilution factor. The equation C₁V₁ = C₂V₂ is also helpful for calculating volumes when preparing solutions of a desired concentration.
对于 1:10 稀释，取 1 份原液加入 9 份稀释液，稀释因子为 10。新溶液的浓度 = 原始浓度 ÷ 稀释因子。在配制所需浓度溶液时，等式 C₁V₁ = C₂V₂ 也可用于计算体积。
10. Hardy-Weinberg Principle | 哈代-温伯格定律
The Hardy-Weinberg principle predicts the allele and genotype frequencies in a population that is not evolving. It provides a mathematical baseline against which evolutionary change can be detected.
哈代-温伯格定律预测一个不进化种群中的等位基因和基因型频率，它提供了检测进化变化的数学基线。
p + q = 1 p² + 2pq + q² = 1
Where p is the frequency of the dominant allele, q is the frequency of the recessive allele. p² is the frequency of homozygous dominant genotype, 2pq the heterozygous frequency, and q² the homozygous recessive frequency. You are often given the frequency of the recessive phenotype (q²), from which you can calculate q, then p, then genotype frequencies.
式中 p 为显性等位基因频率，q 为隐性等位基因频率。p² 为纯合显性基因型频率，2pq 为杂合子频率，q² 为纯合隐性基因型频率。题目常给出隐性表型频率 (q²)，由此可计算出 q，然后 p，进而求出各基因型频率。
The principle holds only when: the population is large, mating is random, there is no mutation, no migration and no selection. In reality these conditions are rarely met, so deviations indicate that evolution is occurring.
该定律成立的条件是：种群很大、随机交配、无突变、无迁移且无自然选择。现实中这些条件很少全部满足，因此偏离就表明进化正在发生。
11. Lincoln Index (Capture-Mark-Recapture) | 林肯指数（标记重捕法）
The Lincoln Index estimates the size of a mobile population. It is based on the assumption that the proportion of marked individuals in a second sample reflects the proportion of marked individuals in the whole population.
林肯指数用于估计移动种群的个体数量，其假设是：第二次样本中标记个体的比例反映了整个种群中标记个体的比例。
N = (M × C) ÷ R
ed in the second sample, R = number of marked individuals recaptured in the second sample.
N = 估测种群数量，M = 第一次捕获并标记的个体数，C = 第二次捕获的总数，R = 第二次捕获中有标记的个体数。
Assumptions: the marks do not harm the organisms or affect their survival; marked individuals mix randomly with the rest of the population; there is no significant birth, death, immigration or emigration between samples; and marks are not lost. The greater the discrepancy between sampling events, the less reliable the estimate.
假设条件：标记不会伤害生物或影响其生存；标记个体与种群其余部分充分随机混合；两次采样之间无显著出生、死亡、迁入或迁出；且标记不脱落。两次采样间隔越久，估计值的可靠性越低。
12. Calculating Uncertainties | 计算误差
Every measurement carries an uncertainty. Being able to quantify absolute and percentage uncertainty is vital for evaluating the reliability of results.
每一次测量都含有误差。能够量化绝对误差和百分误差对于评价结果的可靠性至关重要。
Absolute Uncertainty = ± half the smallest division of the measuring instrument
绝对误差 = ± 量器最小刻度值的一半
Percentage Uncertainty = (Absolute Uncertainty ÷ Measurement) × 100%
百分误差 = (绝对误差 ÷ 测量值) × 100%
ou measure a temperature of 22.0 °C, the percentage uncertainty = (0.5 ÷ 22.0) × 100 ≈ 2.3% rating instruments; random errors can be reduced by taking repeats and calculating a mean.
对于分度值为 1 °C 的温度计，绝对误差为 ±0.5 °C。若测得温度为 22.0 °C，则百分误差 = (0.5 ÷ 22.0) × 100 ≈ 2.3%。系统误差应通过校准仪器最小化；偶然误差可通过重复测量并计算平均值来减小。
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