A-Level OCR Biology: Formula Summary Handbook | A-Level OCR 生物：公式汇总手册

📚 A-Level OCR Biology: Formula Summary Handbook | A-Level OCR 生物：公式汇总手册

This comprehensive guide brings together the essential formulas you need to master for the OCR A-Level Biology specification. From microscopy calculations to statistical tests and ecological equations, each formula is presented with clear explanations and worked examples to support your revision. Understanding when and how to apply these formulas is critical for success in both written examinations and practical assessments.

本全面指南汇集了 OCR A-Level 生物考试中必须掌握的核心公式。从显微镜计算到统计检验和生态学方程，每个公式都配有清晰的解释和计算示例，助力你的复习。理解何时以及如何应用这些公式对于笔试和实践评估的成功至关重要。

1. Microscopy: Actual Size Calculation | 显微镜：实际大小计算

The relationship between magnification, image size and actual specimen size is fundamental in cell biology. The formula Actual Size = Image Size / Magnification allows you to work out the true dimensions of an object from a scaled image. Always ensure that image size and actual size share the same units, converting millimetres to micrometres by multiplying by 1000 as necessary. You must be able to use an eyepiece graticule and stage micrometer to calibrate the microscope and then measure cell structures accurately.

放大倍数、图像大小和实际样本大小之间的关系是细胞生物学的基础。公式实际大小 = 图像大小 / 放大倍数可让你从比例图像中计算出物体的真实尺寸。务必确保图像大小与实际大小单位相同，必要时将毫米乘以1000转换为微米。你必须能够使用目镜测微尺和镜台测微尺校准显微镜，然后精确测量细胞结构。

Actual Size = Image Size (measured) ÷ Magnification

实际大小 = 测量图像大小 ÷ 放大倍数

Example: If the image of a cell measures 56 mm and the magnification is ×400, then actual size = 56 ÷ 400 = 0.14 mm = 140 µm. For a scale bar, calculate magnification length first: Magnification = Scale bar length / scale bar label. Then use actual size formula.

示例：如果细胞的图像测量为56毫米，放大倍数为×400，则实际大小 = 56 ÷ 400 = 0.14 毫米 = 140 微米。对于比例尺，先计算放大倍数：放大倍数 = 比例尺长度 / 比例尺标签。然后使用实际大小公式。

2. Magnification and Scale | 放大倍数与比例尺

Magnification is vital for interpreting micrographs and scientific drawings. You can calculate magnification using Magnification = Size of image / Size of real object. When a scale line is provided, you measure its length on the image and divide by the distance it represents in reality. This method is frequently tested in the OCR practical skills question (PAGs), especially when you must draw cells observed under a microscope.

放大倍数对于解读显微照片和科学绘图至关重要。可以使用公式放大倍数 = 图像大小 / 实际物体大小进行计算。当提供比例尺线段时，测量其图像上的长度再除以它代表的实际距离。这种方法常在OCR实验技能题（PAGs）中考查，尤其是需要绘制显微镜下观察到的细胞时。

Magnification = Length of the line on the image ÷ Length the line represents

放大倍数 = 图像上线段长度 ÷ 线段代表的实际长度

Always express magnification to the nearest whole number and the actual size in appropriate units (nm, µm, mm). For electron micrographs, magnifications often reach ×100 000, so careful unit conversion is critical to avoid errors.

放大倍数始终取整数，实际大小用合适的单位（纳米、微米、毫米）表示。对于电子显微照片，放大倍数常达到×100 000，因此仔细的单位换算对于避免错误至关重要。

3. Rate of Reaction | 反应速率

Enzyme kinetics and other biological processes are frequently assessed by calculating the rate of reaction. The formula Rate = 1 / Time (or Rate = Change in quantity / Time) appears in questions on photosynthesis, respiration, enzyme activity and transport. If the time taken for a substrate to disappear or product to appear is measured, rate is expressed in s⁻¹. If the change in concentration or volume is recorded, rate has units such as cm³ min⁻¹ or g min⁻¹.

酶动力学和其他生物过程常通过计算反应速率来评估。公式速率 = 1 / 时间（或速率 = 变化量 / 时间）出现在光合作用、呼吸作用、酶活性和运输等问题中。如果测量底物消失或产物出现所需的时间，速率单位为 s⁻¹。如果记录了浓度或体积的变化，速率单位如 cm³ min⁻¹ 或 g min⁻¹。

Rate = 1 ÷ Time taken

速率 = 1 ÷ 所需时间

Example: If a piece of potato catalase produces 12 cm³ of oxygen in 300 seconds, the rate = 12 cm³ / 300 s = 0.04 cm³ s⁻¹. You can also convert this to min⁻¹ by multiplying by 60.

示例：如果一块马铃薯过氧化氢酶在300秒内产生12 cm³氧气，则速率 = 12 cm³ / 300 s = 0.04 cm³ s⁻¹。你也可以乘以60将其转换为 min⁻¹。

4. Percentage Change | 百分比变化

Percentage change is used to standardise comparisons, particularly in osmosis experiments where you measure mass or length change. The formula Percentage change = (Final value – Original value) / Original value × 100. A negative result indicates a decrease. This is essential for calculating water uptake or loss in plant tissue and for interpreting data on population or heart rate changes.

百分比变化用于标准化比较，特别是在渗透作用实验中测量质量或长度变化时。公式百分比变化 = （最终值 – 初始值）/ 初始值 × 100。负值表示减少。这对于计算植物组织的水分吸收或损失以及解读种群或心率变化数据至关重要。

% Change = (Final – Original) / Original × 100

百分比变化 = （最终值 – 初始值） / 初始值 × 100

When plotting osmosis graphs, % change in mass is plotted against solute concentration. The point where the line crosses zero corresponds to the water potential of the tissue. You must be confident with this calculation to identify isotonic points.

绘制渗透作用曲线时，质量变化百分比相对于溶质浓度作图。直线穿越零点的位置对应于组织的水势。你必须熟练掌握这一计算才能确定等渗点。

5. Mean, Median and Mode | 平均数、中位数和众数

Central tendency measures summarise data sets. The mean (x̄) is the sum of all values divided by the number of values, x̄ = Σx / n. The median is the middle value when data are arranged in order, useful for skewed distributions. The mode is the most frequent value. In A‑level Biology, you calculate the mean to represent average enzyme activity, biodiversity indices, or population estimates. Remember to quote the mean to an appropriate number of significant figures.

集中趋势量数可以概括数据集。平均数（x̄）是所有数值之和除以数据个数，x̄ = Σx / n。中位数是将数据排序后的中间值，适用于偏态分布。众数是最常出现的数值。在A‑level生物中，你计算平均数来代表平均酶活性、生物多样性指数或种群估计。记住平均数要保留适当位数的有效数字。

Mean (x̄) = Σx ÷ n

平均数（x̄） = Σx ÷ n

When data are normally distributed, the mean is the best measure. If outliers are present, the median is more robust. Always justify your choice in exam questions.

当数据呈正态分布时，平均数是最佳量度。如果存在异常值，中位数更为稳健。在考试题中始终要说明你选择的理由。

6. Standard Deviation | 标准差

Standard deviation measures the spread of data around the mean. A small standard deviation means data points are clustered closely around the mean; a large one indicates wide variation. The formula is s = √[Σ(x – x̄)² / (n – 1)]. While you are not always required to calculate it from raw data in the exam, you must be able to interpret standard deviation bars on graphs to determine whether differences between means are likely to be significant.

标准差衡量数据围绕平均数的分散程度。标准差小意味着数据点紧密聚集在平均数周围；标准差大则表示变异较大。公式为 s = √[Σ(x – x̄)² / (n – 1)]。虽然你并不总需要在考试中根据原始数据计算它，但你必须能够解读图表上的标准差条，以确定平均数之间的差异是否可能显著。

s = √[ Σ(x – x̄)² / (n – 1) ]

If the standard deviation bars of two means overlap, the difference is usually not statistically significant. If they do not overlap, there may be a significant difference. This is a quick way to assess data without complex calculations.

如果两个平均数的标准差条重叠，差异通常不具统计显著性。如果不重叠，则可能存在显著差异。这是一种无需复杂计算即可快速评估数据的方法。

7. Chi-Squared Test (χ²) | 卡方检验 (χ²)

The chi-squared test is used to compare observed frequencies with expected frequencies in categorical data, such as genetic crosses or ecological distribution. The formula is χ² = Σ [ (O – E)² / E ], where O is the observed count and E is the expected count. After calculating χ², you compare it to a critical value from a table at a given probability (usually p = 0.05) and degrees of freedom (number of categories minus 1). If χ² (calculated) > χ² (critical), the null hypothesis is rejected and the difference is significant.

卡方检验用于比较分类数据（如遗传杂交或生态分布）中的观测频数与期望频数。公式为 χ² = Σ [ (O – E)² / E ]，其中O是观测计数，E是期望计数。计算χ²后，将其与给定概率（通常p = 0.05）和自由度（类别数减1）下的表中临界值进行比较。如果计算χ² > 临界χ²，则拒绝零假设，差异显著。

χ² = Σ (O – E)² / E

Always state your null hypothesis clearly. For a genetic cross expecting a 9:3:3:1 ratio, the expected numbers are calculated from the total. Show all working in a table with columns for O, E, O–E, (O–E)² and (O–E)²/E.

始终清楚地陈述你的零假设。对于期望比例为9:3:3:1的遗传杂交，期望数由总数计算得出。在表格中列出O、E、O–E、(O–E)²和(O–E)²/E各列，展示所有计算步骤。

8. Student’s t-Test | 学生t检验

The independent sample t-test is used to compare the means of two sets of normally distributed data to see if they are significantly different from each other. The formula is t = (x̄₁ – x̄₂) / √ [ (s₁²/n₁) + (s₂²/n₂) ], where x̄₁ and x̄₂ are the means, s² the variances, and n the sample sizes. You then compare your calculated t value with a critical t value at the 5% significance level and appropriate degrees of freedom. If calculated t > critical t, the difference is significant.

独立样本t检验用于比较两组正态分布数据的平均数之间是否存在显著差异。公式为 t = (x̄₁ – x̄₂) / √ [ (s₁²/n₁) + (s₂²/n₂) ]，其中x̄₁和x̄₂是平均数，s²是方差，n是样本量。然后将计算的t值与5%显著性水平及相应自由度下的临界t值进行比较。如果计算t > 临界t，差异显著。

t = (x̄₁ – x̄₂) / √( s₁²/n₁ + s₂²/n₂ )

You are provided with the formula in the OCR examination, but you must know how to select the correct test and interpret the result. Paired t‑tests are used for repeated measures on the same individuals, whereas the unpaired version is for two separate groups.

OCR考试会提供公式，但你必须知道如何选择正确的检验方法并解读结果。配对t检验用于对同一个体进行重复测量，而非配对版本适用于两个独立组。

9. Hardy-Weinberg Equation | 哈代-温伯格方程

The Hardy‑Weinberg principle predicts allele and genotype frequencies in a population that is not evolving. The two equations are p + q = 1 (allele frequencies) and p² + 2pq + q² = 1 (genotype frequencies), where p is the frequency of the dominant allele, q is the frequency of the recessive allele, p² is the frequency of homozygous dominant, 2pq heterozygous, and q² homozygous recessive. In exam problems, you are often given the number of individuals with the recessive phenotype to calculate q² first, then q, p and the heterozygote proportion.

哈代‑温伯格原理预测一个不进化的种群中的等位基因频率和基因型频率。两个方程为 p + q = 1（等位基因频率）和 p² + 2pq + q² = 1（基因型频率），其中p是显性等位基因频率，q是隐性等位基因频率，p²为显性纯合子频率，2pq为杂合子频率，q²为隐性纯合子频率。在考试问题中，通常给出具有隐性表型的个体数目，据此先计算q²，再算q、p及杂合子比例。

p + q = 1

p² + 2pq + q² = 1

Ensure you understand the conditions required for the Hardy‑Weinberg equilibrium: large population, random mating, no mutations, no selection and no migration. The formula helps to estimate the percentage of a population carrying a recessive disease allele.

确保你理解哈代‑温伯格平衡所需的条件：大种群、随机交配、无突变、无选择和无迁移。该公式有助于估算种群中携带隐性遗传病等位基因的百分比。

10. Capture-Mark-Recapture (Lincoln Index) | 标记重捕法（林肯指数）

The Lincoln Index estimates population size for motile organisms. The formula is N = (M × C) / R, where N = estimated total population, M = number caught and marked in first sample, C = total caught in second sample, and R = number of marked individuals recaptured in the second sample. This method assumes that marked individuals mix randomly, marking does not affect survival and there is no migration or birth/death between samples. You may also be asked to evaluate the assumptions and suggest refinements.

林肯指数用于估算移动生物的种群大小。公式为 N = (M × C) / R，其中N = 估计种群总数，M = 第一次取样标记并释放的数量，C = 第二次取样捕获的总数，R = 第二次取样中已标记个体的数量。该方法假设标记个体随机混合，标记不影响生存，两次取样之间没有迁移或出生/死亡。你可能还需评估这些假设并提出改进建议。

N = M × C / R

Worked example: If 40 beetles are marked and released, and a second sample of 50 contains 10 marked beetles, then N = (40 × 50) / 10 = 200. This is only an estimate; confidence limits can be calculated using statistical tables.

计算示例：如果40只甲虫被标记并释放，第二次取样50只中有10只带标记，则N = (40 × 50) / 10 = 200。这只是一个估计值；置信区间可以使用统计表计算。

11. Net Primary Productivity (NPP) | 净初级生产力 (NPP)

Net primary productivity measures the energy stored in plant biomass after respiratory losses. The equation is NPP = GPP – R, where GPP is gross primary productivity (total energy fixed by photosynthesis) and R is respiratory heat loss. NPP is the energy available to the next trophic level. Units are typically kJ m⁻² year⁻¹ or g m⁻² year⁻¹. You may be given GPP and R and asked to calculate NPP, or to work out the efficiency of energy transfer.

净初级生产力衡量植物生物量中扣除呼吸消耗后储存的能量。方程为 NPP = GPP – R，其中GPP是总初级生产力（光合作用固定的总能量），R是呼吸热损失。NPP是可供下一营养级利用的能量。单位通常为 kJ m⁻² year⁻¹ 或 g m⁻² year⁻¹。你可能会得到GPP和R并计算NPP，或计算能量传递效率。

NPP = GPP – R

Ecological efficiency between trophic levels is calculated as: Efficiency (%) = (Energy available after transfer ÷ Energy available before transfer) × 100. Typically only about 10% of energy is transferred. The remaining 90% is lost as heat, movement, respiration, or indigestible material.

营养级之间的生态效率计算为：效率（%）=（传递后可利用的能量 ÷ 传递前可利用的能量）× 100。通常只有约10%的能量被传递。其余90%以热、运动、呼吸或难消化的物质形式损失。

12. Respiration Quotient (RQ) | 呼吸商 (RQ)

The respiration quotient is the ratio of carbon dioxide produced to oxygen consumed during respiration. It provides information about the respiratory substrate being used. RQ = Volume of CO₂ produced / Volume of O₂ consumed. For carbohydrates, RQ = 1.0; for lipids, RQ ≈ 0.7; for proteins, RQ ≈ 0.9. Values greater than 1.0 indicate some anaerobic respiration is occurring. You can measure RQ using a respirometer with soda lime to absorb CO₂.

呼吸商是呼吸作用中产生的二氧化碳与消耗的氧气之比。它提供了关于所用呼吸底物的信息。RQ = 产生的CO₂体积 / 消耗的O₂体积。对于碳水化合物，RQ = 1.0；对于脂类，RQ ≈ 0.7；对于蛋白质，RQ ≈ 0.9。数值大于1.0表明发生了一定程度的无氧呼吸。你可以使用带有碱石灰吸收CO₂的呼吸计来测量RQ。

RQ = CO₂ produced / O₂ consumed

RQ = 产生的CO₂ / 消耗的O₂

In respirometer experiments, the movement of the manometer fluid reflects oxygen consumption after CO₂ is absorbed. To calculate RQ, you must measure both oxygen uptake and carbon dioxide production, often requiring two respirometers – one with and one without KOH.

在呼吸计实验中，压力计液体的移动反映CO₂被吸收后的耗氧量。要计算RQ，你必须测量氧气吸收和二氧化碳产生，通常需要两个呼吸计——一个含KOH，另一个不含。

Published by TutorHao | Biology Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

A-Level OCR Biology: Formula Summary Handbook | A-Level OCR 生物：公式汇总手册