📚 Year 11 AQA Biology: Formula & Theorem Quick Reference | Year 11 AQA 生物：公式定理速查手册
This quick reference handbook compiles the essential formulas, equations, and key theorems required for Year 11 AQA GCSE Biology. Mastery of these numerical skills and principles is vital for practical work, data analysis, and the written examinations. Use it alongside your revision notes to ensure you can confidently tackle any calculation or application question.
本速查手册汇编了 Year 11 AQA GCSE 生物学所需的核心公式、方程和关键定理。掌握这些计算技能和原理对实验操作、数据分析和笔试至关重要。请结合你的复习笔记使用本手册，确保能够自信、熟练地解决任何计算或应用题。
1. Magnification and Unit Conversions | 放大倍率与单位换算
In microscopy, the relationship between image size, actual size, and magnification is expressed by a simple formula. Always ensure that the image size and actual size are in the same units before substituting values.
在显微镜使用中，图像尺寸、实际尺寸和放大倍率之间的关系可由一个简单公式表达。代入数值前，务必确保图像尺寸和实际尺寸使用相同的单位。
Magnification = Image size / Actual size
放大倍率 = 图像尺寸 / 实际尺寸
When rearranging the formula, you may calculate actual size as Actual size = Image size / Magnification, or image size as Image size = Magnification × Actual size. It is common to be asked to convert between millimetres (mm), micrometres (µm), and nanometres (nm).
当重新排列公式时，你可以计算实际尺寸：实际尺寸 = 图像尺寸 / 放大倍率，或者图像尺寸 = 放大倍率 × 实际尺寸。考试中常要求你在毫米（mm）、微米（µm）和纳米（nm）之间进行转换。
| Unit | Equivalent | 中文 |
| 1 kilometre (km) | 1000 metres (m) | 1 千米 = 1000 米 |
| 1 metre (m) | 1000 millimetres (mm) | 1 米 = 1000 毫米 |
| 1 millimetre (mm) | 1000 micrometres (µm) | 1 毫米 = 1000 微米 |
| 1 micrometre (µm) | 1000 nanometres (nm) | 1 微米 = 1000 纳米 |
For example, if a cell image measures 5 mm on a drawing and the actual cell diameter is 0.05 mm, the magnification = 5 / 0.05 = 100 ×. If the image is given in mm and the actual size in µm, convert both to the same unit first.
例如，若细胞图像在图上测量为 5 mm，实际细胞直径为 0.05 mm，放大倍率 = 5 / 0.05 = 100 倍。如果图像以 mm 给出而实际尺寸以 µm 给出，请先将两者换算为同一单位。
2. Rate Calculations | 速率计算
Rate is a measure of how much something changes per unit of time. The general formula is used widely in biology to describe enzyme reaction rates, uptake of substances, and population growth.
速率是衡量某一变化量在单位时间内变化快慢的指标。该通用公式广泛应用于生物学中，用以描述酶促反应速率、物质吸收速率以及种群增长。
Rate = Change in quantity / Time taken
速率 = 变化量 / 所用时间
Common units for rate depend on the quantity being measured, for example cm³/s for gas production, g/s for mass change, or individuals per day for population growth. Ensure you read the axes of graphs carefully to identify the correct units when calculating gradient as a rate.
速率的常见单位取决于被测量的量，例如气体产生可用 cm³/s，质量变化用 g/s，种群增长用个体数/天。当通过计算斜率求解速率时，请仔细读取图表坐标轴上的单位，以确定正确的单位。
When a graph shows a straight line through the origin, the rate is constant. If the line curves, you may be asked to calculate a rate at a specific point by drawing a tangent and finding its gradient.
当图像显示一条过原点的直线时，速率为定值。若图像呈曲线，你可能需要在特定点作切线并求切线斜率，以计算该点的瞬时速率。
3. Photosynthesis Rate | 光合作用速率
The rate of photosynthesis can be measured by the volume of oxygen produced per unit time, or by the rate of carbon dioxide uptake. A common laboratory method uses pondweed to count bubbles of oxygen released.
光合作用速率可以通过单位时间内氧气的产生量或二氧化碳的吸收量来测定。一个常见的实验室方法是用水生植物（如水蕴草），通过计数释放的氧气气泡来测量。
Photosynthesis rate ≈ Volume of O₂ produced / Time (min)
光合作用速率 ≈ 产生的 O₂ 体积 / 时间（分钟）
Alternatively, the rate can be expressed as the change in mass of a plant (due to glucose synthesis) per unit time, but this is less direct. The limiting factors — light intensity, carbon dioxide concentration, and temperature — determine the actual rate, and the formula is used to calculate the rate at each condition.
或者，速率也可以表示为单位时间内植物质量的变化（因葡萄糖合成），但这种方式不够直接。限制因素——光照强度、二氧化碳浓度和温度——决定了实际速率；利用上述公式可以计算每种条件下的速率。
4. Respiration Rate | 呼吸速率
Cellular respiration can be measured using a respirometer or by monitoring the volume of oxygen consumed or carbon dioxide released over time. The rate of oxygen consumption is often used as an indicator of metabolic rate.
可以通过呼吸计测量细胞呼吸，或者监控一段时间内耗氧量或二氧化碳释放量。耗氧速率常被用作代谢率的指标。
Respiration rate = Volume of O₂ consumed / Time
呼吸速率 = 消耗的 O₂ 体积 / 时间
In experiments using a respirometer, you must also account for changes in temperature and pressure, often by using a control tube with glass beads instead of living organisms. The distance moved by a coloured liquid can be converted to volume consumed using the radius of the capillary tube.
在使用呼吸计的实验中，必须考虑温度和气压变化的影响，通常使用装有玻璃珠的对照管来代替生物。通过带入毛细管半径，有色液柱移动的距离可以换算为消耗的气体体积。
5. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by the heart per minute. It is determined by the heart rate and the stroke volume, and is a key measure of the circulatory system’s performance.
心输出量是指心脏每分钟泵出的血液量。它由心率和每搏输出量决定，是衡量循环系统功能的重要指标。
Cardiac output (cm³/min) = Heart rate (bpm) × Stroke volume (cm³)
心输出量（cm³/分钟）= 心率（每分钟心跳次数） × 每搏输出量（cm³）
For example, if a person’s heart rate is 70 bpm and stroke volume is 75 cm³, cardiac output = 70 × 75 = 5250 cm³/min. This value can increase dramatically during exercise to deliver more oxygen and glucose to muscles.
例如，若一个人的心率为 70 次/分钟，每搏输出量为 75 cm³，则心输出量 = 70 × 75 = 5250 cm³/分钟。该值在运动期间会显著升高，以向肌肉输送更多氧气和葡萄糖。
6. Population Size Estimation | 种群大小估算
When studying ecosystems, ecologists often need to estimate the population size of mobile organisms. The capture-recapture method uses the following formula, which assumes that marked and unmarked individuals mix randomly.
在研究生态系统时，生态学家常常需要估算活动性强的生物种群大小。捕捉-标记-重捕法使用以下公式，其前提假设是已标记和未标记个体随机混合。
Estimated population size = (n₁ × n₂) / m
估计种群大小 = （第一次捕捉数 × 第二次捕捉数） / 标记重捕数
Where n₁ = number captured and marked in the first sample, n₂ = total number captured in the second sample, and m = number of marked individuals recaptured in the second sample.
其中 n₁ = 第一次取样捕捉并标记的个体数，n₂ = 第二次取样捕捉的总个体数，m = 第二次取样中带有标记的个体数。
For sessile or slow-moving organisms, quadrats are used. Population density is calculated as: Density = Total number of individuals / Total area sampled. Quadrat results are often scaled up by multiplying the mean count per quadrat by the total area divided by the quadrat area.
对于固着或移动缓慢的生物，则使用样方。种群密度计算公式为：密度 = 个体总数 / 取样总面积。通常将每个样方的平均计数乘以（总面积 / 样方面积）来估算整个区域的种群大小。
7. Genetic Ratios and Probability | 遗传比例与概率
Monohybrid crosses in GCSE Biology involve predicting the probability of offspring genotypes and phenotypes using Punnett squares. The probability of a particular genotype can be expressed as a fraction or percentage.
GCSE 生物学中的单基因杂交涉及使用庞纳特方格预测后代的基因型和表型概率。特定基因型出现的概率可以用分数或百分数表示。
Probability of a genotype = (Number of squares with that genotype) / 4
某基因型的概率 = （包含该基因型的方格数） / 4
For a cross between two heterozygous parents (Aa × Aa), the expected genotypic ratio is 1 AA : 2 Aa : 1 aa, and the phenotypic ratio for a dominant-recessive trait is typically 3 : 1. You should be able to use these ratios to predict numbers in a given population and understand that observed ratios may deviate due to chance, especially in small sample sizes.
对于两个杂合亲本（Aa × Aa）的杂交，预期的基因型比为 1 AA : 2 Aa : 1 aa，在显性-隐性性状中表型比通常为 3 : 1。你应当能够利用这些比例来预测给定种群中的个体数，并理解由于随机因素，实际观察到的比例可能与理论值有偏差，尤其是在样本量较小时。
8. Percentage Change and Data Handling | 百分比变化与数据处理
Many biological investigations require you to calculate percentage change to compare results before and after a treatment, or to standardise differences between control and experimental groups.
许多生物实验都需要你计算百分比变化，以比较处理前后的结果，或对对照组与实验组之间的差异进行标准化。
Percentage change = ((Final value – Initial value) / Initial value) × 100%
百分比变化 = （（最终值 – 初始值） / 初始值） × 100%
A negative percentage change indicates a decrease. When processing data, you should also know how to calculate a mean: Mean = Sum of all data values / Number of data values. Outliers can be identified and excluded to improve the reliability of the mean.
负的百分比变化表示减少。在处理数据时，你还应掌握如何计算平均值：平均值 = 所有数据值之和 / 数据个数。可以识别并剔除异常值，以提高平均值的可靠性。
When plotting graphs, always choose scales that use at least half the grid, label axes with quantity and unit, and draw a line of best fit, which can be straight or curved depending on the trend.
绘制图表时，务必选择至少占据网格一半的刻度、在坐标轴上标注物理量和单位，并画出最佳拟合线，该线视趋势而定可能是直线或曲线。
9. Surface Area to Volume Ratio | 表面积与体积比
As an organism or a cell increases in size, its surface area to volume ratio decreases. This ratio affects the rate of diffusion, osmosis, and heat exchange, and explains why larger organisms need specialised exchange surfaces and transport systems.
当生物体或细胞体积增大时，其表面积与体积之比会减小。这一比率影响着扩散、渗透和热交换的速率，也解释了为什么较大的生物需要特化的交换表面和运输系统。
Surface area : Volume ratio = Surface area / Volume
表面积 : 体积比 = 表面积 / 体积
For a cube of side length L, surface area = 6L² and volume = L³, so SA:V = 6/L. As L increases, the ratio decreases. You may be asked to calculate these values and explain the consequences for diffusion distances and metabolic needs.
对于边长为 L 的立方体，表面积 = 6L²，体积 = L³，因此 SA:V = 6/L。随着 L 增大，该比值减小。你可能需要计算这些数值并解释其对扩散距离和代谢需求的影响。
10. Enzyme Activity and Limiting Factors | 酶活性与限制因素
Enzyme-controlled reactions are influenced by several factors. The rate of an enzyme reaction can be calculated using the general rate formula, and is often measured by the volume of product formed per minute or the time taken for a substrate to disappear (e.g., starch breakdown measured with iodine).
酶促反应受多种因素影响。酶反应速率可以用通用速率公式来计算，通常通过每分钟产物体积或底物消失所需时间来衡量（例如，用碘液测定淀粉分解）。
Rate of enzyme reaction = Amount of product formed / Time
酶反应速率 = 产物生成量 / 时间
The rate initially increases with temperature until it reaches an optimum; beyond this, the enzyme denatures and the rate drops sharply. pH also has an optimum, and deviations from this optimum reduce enzyme activity. Substrate concentration increases the rate up to a point where all enzyme active sites are saturated.
反应速率起初随温度升高而增加，直至最适温度；
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