📚 OCR A-level Biology Formula & Theorem Quick Reference | OCR A-level 生物公式定理速查手册
This quick reference handbook pulls together the essential formulas, statistical tests and mathematical relationships that you will encounter in the second year of the OCR A-level Biology course (Year 13). It is designed as a fast-revision tool – each entry states the formula, explains where it is used and highlights common examiner pitfalls.
本速查手册汇集了 OCR A-level 生物学第二年（13年级）课程中必须掌握的公式、统计检验和数学关系。它可以作为快速复习工具，每个条目给出了公式、使用场景以及考官常考的易错点。
1. Magnification and Actual Size | 放大倍数与实际大小
Magnification is the ratio of the size of an image to the actual size of the specimen. The equation is Magnification = Image size ÷ Actual size, often rearranged to Actual size = Image size ÷ Magnification. Always convert both measurements to the same unit (usually micrometres or millimetres) before dividing. If you are given a scale bar, measure its length on the image and divide by the length it represents.
放大倍数是图像大小与标本实际大小的比值。公式为 放大倍数 = 图像大小 ÷ 实际大小，通常变形为 实际大小 = 图像大小 ÷ 放大倍数。计算前一定要将两个测量值换算成相同的单位（通常为微米或毫米）。若给出比例尺，先测量比例尺在图上的长度，再除以其代表的实际长度。
2. Hardy‑Weinberg Principle | 哈代‑温伯格定律
Used to estimate allele and genotype frequencies in a large, randomly mating population that is not subject to mutation, migration or natural selection. The two equations are:
p + q = 1
p² + 2pq + q² = 1
where p = frequency of the dominant allele, q = frequency of the recessive allele, p² = frequency of homozygous dominant, 2pq = frequency of heterozygous, q² = frequency of homozygous recessive. You will usually be given the number of individuals showing the recessive phenotype, from which you calculate q², then q, then p.
该定律用于估算一个不存在突变、迁移和自然选择影响的随机交配大群体中的等位基因频率和基因型频率。两个核心方程为：
p + q = 1
p² + 2pq + q² = 1
其中 p = 显性等位基因频率，q = 隐性等位基因频率，p² = 显性纯合子频率，2pq = 杂合子频率，q² = 隐性纯合子频率。题目通常给出表现为隐性性状的个体数目，你可以据此求出 q²、q，再求 p。
3. Chi‑squared Test (χ²) | 卡方检验
The chi‑squared test compares observed results with expected results to determine whether any difference is due to chance or a significant factor. The formula is:
χ² = Σ (O − E)² / E
where O = observed frequency, E = expected frequency, and Σ means sum over all categories. You must state a null hypothesis, calculate degrees of freedom (number of categories − 1 for goodness‑of‑fit, or (rows − 1) × (columns − 1) for contingency tables), and compare your χ² value with the critical value at p = 0.05. Reject the null hypothesis if χ² exceeds the critical value.
卡方检验用于比较观察值与期望值，以判断差异是由偶然因素还是显著因子造成。公式为：
χ² = Σ (O − E)² / E
其中 O 代表观察频数，E 代表期望频数，Σ 表示对各类别求和。必须明确提出零假设，计算自由度（拟合优度检验为类别数−1，列联表为（行数−1）×（列数−1）），并将计算出的 χ² 值与 p=0.05 时的临界值比较。如果 χ² 大于临界值，则拒绝零假设。
4. Student’s t‑test (Unpaired) | 学生t检验（非配对）
The unpaired t‑test is used to compare the means of two independent samples to see if they differ significantly. The formula is:
t = (x̄₁ − x̄₂) / √ (s₁²/n₁ + s₂²/n₂)
where x̄₁ and x̄₂ are the sample means, s₁² and s₂² are the sample variances, and n₁ and n₂ are the sample sizes. Calculate degrees of freedom as n₁ + n₂ − 2. Compare the calculated t value with the critical value at p = 0.05; if t is larger, the difference is statistically significant.
非配对t检验用于比较两个独立样本的平均值是否存在显著差异。公式为：
t = (x̄₁ − x̄₂) / √ (s₁²/n₁ + s₂²/n₂)
其中 x̄₁ 和 x̄₂ 分别为两个样本的平均值，s₁² 和 s₂² 为样本方差，n₁ 和 n₂ 为样本容量。自由度为 n₁ + n₂ − 2。将计算得到的 t 值与 p=0.05 时的临界值比较，若 t 更大则差异具有统计学意义。
5. Simpson’s Index of Diversity | 辛普森多样性指数
Simpson’s index measures biodiversity by accounting for both species richness and evenness. As used in OCR, the formula is:
D = 1 − Σ (n/N)²
where n = total number of organisms of a particular species, and N = total number of organisms of all species. The value of D ranges from 0 (low diversity) to 1 (high diversity). A high value indicates a stable, complex ecosystem.
辛普森指数通过同时考虑物种丰度和均匀度来衡量生物多样性。OCR 考纲中使用的公式为：
D = 1 − Σ (n/N)²
其中 n 为某一特定物种的个体总数，N 为所有物种的个体总数。D 值介于0（低多样性）到1（高多样性）之间。高数值代表一个稳定、复杂的生态系统。
6. Energy Transfer and Productivity | 能量传递与生产力
Primary productivity is the rate at which producers convert light energy into chemical energy. The fundamental relationship is:
NPP = GPP − R
where GPP = gross primary production, R = respiratory losses, and NPP = net primary production – the energy available to the next trophic level. For consumers, net production is given by:
N = I − (F + R)
where I = ingested energy, F = energy lost in faeces, and R = respiratory losses. Efficiency of energy transfer between trophic levels is:
Efficiency (%) = (energy available after transfer / energy available before transfer) × 100
初级生产力是生产者将光能转化为化学能的速率。基本关系为：
NPP = GPP − R
其中 GPP 为总初级生产量，R 为呼吸损失，NPP 为净初级生产量——即可供下一营养级利用的能量。消费者的净生产量公式为：
N = I − (F + R)
其中 I 为摄入能量，F 为粪便能量损失，R 为呼吸损失。营养级之间的能量传递效率为：
效率(%) = (传递后的有效能量 / 传递前可用的能量) × 100
7. Respiratory Quotient (RQ) | 呼吸商
RQ indicates the type of substrate being respired. It is calculated as:
RQ = CO₂ produced / O₂ consumed
Carbohydrate respiration gives an RQ of 1.0, lipid respiration about 0.7, and protein about 0.9. Values above 1.0 suggest anaerobic respiration in some contexts. RQ is commonly measured using a respirometer.
呼吸商用来推测被呼吸消耗的底物类型。计算公式为：
RQ = CO₂产生量 / O₂消耗量
碳水化合物的呼吸商约为1.0，脂肪约为0.7，蛋白质约为0.9。在某些情境下，RQ大于1.0可能提示无氧呼吸的参与。呼吸商通常用呼吸计进行测定。
8. Cardiac and Ventilation Calculations | 心输出量与肺通气量计算
These straightforward multiplicative relationships are commonly tested in data‑response questions:
Cardiac output = Stroke volume × Heart rate
CO = SV × HR
Pulmonary ventilation = Tidal volume × Breathing rate
PV = TV × BR
Units: cardiac output is usually measured in L min⁻¹, stroke volume in L beat⁻¹, heart rate in beats min⁻¹. Pulmonary ventilation is typically in dm³ min⁻¹; tidal volume in dm³ and breathing rate in breaths min⁻¹.
这些简单的乘法关系常出现在数据分析题中：
心输出量 = 每搏输出量 × 心率
CO = SV × HR
肺通气量 = 潮气量 × 呼吸频率
PV = TV × BR
单位：心输出量常用 L min⁻¹，每搏输出量为 L beat⁻¹，心率为 beats min⁻¹。肺通气量通常用 dm³ min⁻¹，潮气量为 dm³，呼吸频率为 breaths min⁻¹。
9. Q₁₀ Temperature Coefficient | Q₁₀ 温度系数
Q₁₀ measures the rate of change of a biological process when the temperature increases by 10 °C. The formula is:
Q₁₀ = rate at (T + 10) °C / rate at T °C
Most enzyme‑controlled reactions have a Q₁₀ of about 2, meaning the rate doubles with a 10 °C rise, provided the enzyme has not begun to denature. Q₁₀ can be used to interpret temperature effects on respiration, photosynthesis and heartbeat in ectotherms.
Q₁₀ 表示温度每升高 10 °C 时生物过程速率的变化倍数。公式为：
Q₁₀ = (T + 10) °C 时的速率 / T °C 时的速率
大多数酶促反应的 Q₁₀ 约为2，即温度升高10 °C速率翻倍，前提是酶尚未开始变性。Q₁₀ 常用于解析温度对呼吸、光合作用以及变温动物心率的影响。
10. Mark‑Release‑Recapture (Lincoln Index) | 标记重捕法（林肯指数）
This method estimates the size of a mobile animal population. The equation is:
N = (n₁ × n₂) / n₃
where N = estimated total population size, n₁ = number captured and marked in the first sample, n₂ = total number captured in the second sample, and n₃ = number of marked individuals recaptured in the second sample. Key assumptions include: marks are not lost, marked individuals mix randomly, and there is no significant migration, birth or death between samples.
该方法用于估算移动动物种群的大小。公式为：
N = (n₁ × n₂) / n₃
其中 N 为估算的总种群数量，n₁ 为第一次捕获并标记的个体数，n₂ 为第二次捕获的总个体数，n₃ 为第二次捕获中带有标记的个体数。关键假设包括：标记不会丢失，标记个体与未标记个体充分混合，两次取样之间没有显著迁移、出生或死亡。
11. Rate of Enzyme‑Controlled Reactions | 酶促反应速率
In OCR practicals, the rate of an enzyme‑controlled reaction is often determined by measuring the time taken for a change to occur (e.g. starch disappearance or colour change). The simplest expression is:
Rate = 1 / time
If you measure product formation or substrate consumption over time, the rate can be expressed as:
Rate = Δ[product] / Δt
When describing initial rate, always draw a tangent to the curve at time zero. Units will depend on the variable measured, e.g. cm³ O₂ min⁻¹ or absorbance units s⁻¹.
在 OCR 实验操作中，酶促反应速率常通过测量发生变化所需的时间来确定（例如淀粉消失或颜色变化）。最简单的表达式为：
速率 = 1 / 时间
如果测量了产物生成或底物消耗的进程，速率可表示为：
速率 = Δ[产物] / Δt
描述初始速率时，一定要在时间为零的曲线处作切线。速率单位取决于所测变量，如 cm³ O₂ min⁻¹ 或吸光度单位 s⁻¹。
12. Fick’s Law of Diffusion | 菲克扩散定律
Fick’s law describes the factors affecting the rate of diffusion across a membrane. It is expressed as:
Rate of diffusion ∝ (Surface area × Concentration difference) / Thickness of membrane
A high surface area, a steep concentration gradient and a thin exchange surface all increase diffusion rate. This law underpins the structure of alveoli, gill lamellae and villi. You may be asked to explain how data on surface‑area‑to‑volume ratio relates to Fick’s law.
菲克定律描述了影响物质跨膜扩散速率的各种因素，表达为：
扩散速率 ∝ (表面积 × 浓度差) / 扩散距离（膜厚度）
较大的表面积、陡峭的浓度梯度和较薄的交换面都能加快扩散速率。这一定律是肺泡、鳃片和小肠绒毛结构的基础。考试中可能会要求你结合表面积与体积比的数据，解释菲克定律。
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