📚 IGCSE AQA Biology: Formula Summary Handbook | IGCSE AQA 生物：公式汇总手册
This guide brings together the essential mathematical relationships you will encounter in IGCSE AQA Biology. Whether you are working through microscope calculations, exploring enzyme kinetics, or tackling genetics problems, having these formulas at your fingertips will sharpen your exam technique and deepen your understanding of biological data.
本指南汇集了你在IGCSE AQA生物课程中会遇到的关键数学关系。无论是处理显微镜计算、探索酶动力学还是解决遗传学问题，随时掌握这些公式都能提升你的考试技巧，加深你对生物数据的理解。
1. The Magnification Equation | 放大率公式
Magnification describes how many times larger an image appears compared with the real object. It is a ratio without units.
放大率描述图像看起来比实际物体大多少倍。它是一个没有单位的比值。
Magnification = Image size ÷ Actual size
Both the image size and the actual size must be in the same length unit (e.g. mm, μm). If they differ, convert one so they match before dividing.
图像大小和实际大小必须使用相同的长度单位（例如 mm、μm）。如果它们不同，请在进行除法之前转换其中一个，使二者单位一致。
For example, a cell image measures 45 mm across under the microscope, and its real diameter is 0.015 mm. The magnification is 45 ÷ 0.015 = 3000 ×.
例如，一个细胞在显微镜下的图像宽度为 45 mm，而它的真实直径是 0.015 mm。则放大率为 45 ÷ 0.015 = 3000 ×。
2. Rearranging for Actual Size and Image Size | 计算实际大小与图像大小的变形公式
You can rearrange the magnification formula to find the actual size of a specimen or the size an image must be drawn.
你可以通过变形放大率公式来求出样本的实际大小或绘图所需图像大小。
Actual size = Image size ÷ Magnification
This is particularly useful when a scale bar is given and you need to measure a structure’s true dimensions in μm or mm.
当给出比例尺且你需要以 μm 或 mm 为单位测量某个结构的真实尺寸时，这个公式尤其有用。
Image size = Magnification × Actual size
Use this version when you have been told the actual length and the required magnification, and you need to determine how big the drawing should be.
当你已知实际长度和所需放大倍数，需要确定绘图应当多大时，可使用这个版本。
Remember to convert between millimetres (mm), micrometres (μm) and nanometres (nm) accurately: 1 mm = 1000 μm, 1 μm = 1000 nm.
记得准确换算毫米 (mm)、微米 (μm) 和纳米 (nm)：1 mm = 1000 μm，1 μm = 1000 nm。
3. Rate of Enzyme-Controlled Reactions | 酶促反应速率
One common way to measure enzyme activity is to time how long it takes for a substrate to be used up (or a product to appear). The initial rate is often taken as the reciprocal of time.
衡量酶活性的一种常用方法是记录底物被用完（或产物出现）所需的时间。初始速率通常取时间的倒数。
Rate (s−¹) = 1 ÷ Time taken for a standard change
For example, if a starch-iodine mixture turns from blue-black to colourless in 25 seconds with amylase, the relative rate is 1 ÷ 25 = 0.04 s−¹.
例如，如果淀粉酶使淀粉-碘混合物在 25 秒内从蓝黑色变为无色，则相对速率为 1 ÷ 25 = 0.04 s−¹。
In other investigations, you may measure a volume of product (e.g. oxygen) produced in a fixed time and use: Rate = Volume of product ÷ Time.
在其他探究中，你可能测量固定时间内产物的体积（如氧气），并使用：速率 = 产物体积 ÷ 时间。
Rate = Change in amount of product or substrate ÷ Time interval
Always include the units of rate, for instance cm³ min−¹ for gas volume over time, or s−¹ for a time-based reciprocal measure.
始终包含速率的单位，例如气体体积随时间变化使用 cm³ min−¹，基于时间的倒数测量则使用 s−¹。
4. Respiratory Quotient (RQ) | 呼吸商
The respiratory quotient tells you which respiratory substrate an organism is mainly using by comparing the volumes of carbon dioxide produced and oxygen consumed.
呼吸商通过比较产生的二氧化碳体积和消耗的氧气体积，告知你生物体主要正在利用哪种呼吸底物。
RQ = Volume of CO&sub2; produced ÷ Volume of O&sub2; consumed
Carbohydrate respiration gives an RQ close to 1.0, lipids typically give RQ values around 0.7, and proteins often produce values near 0.9.
碳水化合物的呼吸作用产生的 RQ 值接近 1.0，脂类的 RQ 值通常约为 0.7，蛋白质则往往产生接近 0.9 的数值。
RQ is most accurately measured using a respirometer that absorbs carbon dioxide, allowing you to calculate the change in gas volume.
最准确的 RQ 测量方法是使用能吸收二氧化碳的呼吸计，借此计算气体体积的变化。
5. Rate of Photosynthesis | 光合作用速率
Photosynthesis rate is often monitored by the production of oxygen or the uptake of carbon dioxide per unit time. A simple proxy is counting bubbles of oxygen evolved from an aquatic plant like Elodea.
光合作用速率通常通过单位时间内氧气的产生或二氧化碳的吸收来监测。一个简单的替代方法是计数水生植物（如伊乐藻）释放的氧气气泡。
Rate of photosynthesis = Volume of O&sub2; produced ÷ Time
Alternatively, if you use a pH indicator to track carbon dioxide changes, you can use the reciprocal of the time taken for the indicator to change colour as a measure of rate.
或者，如果你使用 pH 指示剂跟踪二氧化碳的变化，可以用指示剂变色所需时间的倒数作为速率指标。
Rate (s−¹) = 1 ÷ Time for colour change
Remember to control light intensity, temperature and carbon dioxide concentration when investigating one limiting factor, keeping the others constant.
在探究某个限制因素时，记得控制光照强度、温度和二氧化碳浓度，保持其他因素不变。
6. Ecological Efficiency | 生态效率
Energy is lost at each trophic level in a food chain. Ecological efficiency expresses how much energy is transferred from one level to the next as a percentage.
能量在食物链的每个营养级中都会损耗。生态效率以百分比表示能量从一个营养级传递到下一个营养级的量。
Ecological efficiency = (Energy in biomass at next level ÷ Energy in biomass at previous level) × 100%
Typical efficiencies are around 10%, because most energy is used for respiration, movement, heat loss and is not stored as new biomass.
典型的效率大约为 10%，因为大部分能量被用于呼吸作用、运动、热量散失，而未被储存为新生物质。
You might also use biomass (g m−²) or energy (kJ m−² year−¹) data from pyramids of biomass or energy to calculate efficiency.
你也可以使用生物量 (g m−²) 或能量 (kJ m−² year−¹) 金字塔的数据来计算效率。
7. Population Growth Rate | 种群增长率
Population growth rate quantifies how quickly a population is changing in size over a specific period, considering births, deaths and migration.
种群增长率定量描述了一个种群在特定时期内数量变化的快慢，考虑出生、死亡和迁移因素。
Population growth rate = (Change in population size) ÷ Time period
Change in population size = (Births + Immigration) − (Deaths + Emigration). You can present this as individuals per year or as a percentage growth rate. For a percentage growth rate: (Change ÷ Initial population) × 100% per time unit.
种群规模变化 = (出生数 + 迁入数) − (死亡数 + 迁出数)。你可以用每年个体数表示，或者用百分比增长率：每单位时间 (变化量 ÷ 初始种群) × 100%。
In IGCSE Biology, you might be given simple data from yeast cultures or bacterial colonies and asked to calculate the increase over fixed time intervals.
在 IGCSE 生物中，你可能会获得来自酵母培养物或细菌菌落的简单数据，并被要求计算固定时间间隔内的增长量。
8. Percentage Change in Mass (Osmosis Experiments) | 质量变化百分比（渗透实验）
When investigating osmosis with plant tissue (e.g. potato cylinders), you need to compare the change in mass in a standardised way. The percentage change formula accounts for the different starting masses.
在用植物组织（例如土豆块）研究渗透作用时，你需要以标准化的方式比较质量变化。质量变化百分比公式考虑到了不同的初始质量。
Percentage change in mass = ((Final mass − Initial mass) ÷ Initial mass) × 100%
A positive value indicates a net gain of water and an increase in mass; a negative value indicates net loss of water and a decrease in mass.
正值表示净吸水和质量增加；负值表示净失水和质量减少。
Plotting percentage change against solute concentration allows you to estimate the water potential of the tissue at the point where the graph crosses zero change.
绘制质量变化百分比随溶质浓度变化的曲线，可以在曲线与零变化线相交处估算组织的水势。
9. Surface Area to Volume Ratio | 表面积与体积比
Surface area to volume ratio (SA:V) is a crucial concept for explaining the limits of cell size and the adaptations of exchange surfaces. It is calculated by dividing the total surface area by the volume of an object.
表面积与体积比（SA:V）是解释细胞大小限制和交换表面适应性的关键概念。计算方法是用物体的总表面积除以体积。
SA:V ratio = Total surface area ÷ Volume
For a cube of side length L, surface area = 6L² and volume = L³, so the ratio = 6L² ÷ L³ = 6 / L. As the cube gets larger, its SA:V ratio decreases.
对于边长为 L 的立方体，表面积 = 6L²，体积 = L³，所以比值为 6L² ÷ L³ = 6 / L。随着立方体变大，其 SA:V 比值减小。
Small organisms or single cells have a high SA:V ratio, which allows efficient diffusion of substances; large organisms require specialised exchange systems with large surface areas.
小型生物或单细胞具有较高的 SA:V 比值，使物质能够高效扩散；大型生物则需要具有大表面积的特化交换系统。
10. Body Mass Index (BMI) | 身体质量指数
BMI is a screening tool used to classify underweight, healthy weight, overweight and obesity in humans. It is computed from mass and height.
BMI 是一种筛查工具，用于将人类体重分为偏瘦、健康体重、超重和肥胖。它由体重和身高计算得出。
BMI = Mass (kg) ÷ (Height (m))²
Mass must be in kilograms and height in metres. For an adult weighing 70 kg and measuring 1.75 m, BMI = 70 ÷ (1.75)² ≈ 22.9 kg m−².
体重必须以千克为单位，身高以米为单位。若一名成人体重 70 kg，身高 1.75 m，则 BMI = 70 ÷ (1.75)² ≈ 22.9 kg m−²。
The classification ranges for adults are: underweight < 18.5; normal 18.5-24.9; overweight 25-29.9; obese ≥ 30.0. BMI does not distinguish between muscle and fat, so it has limitations.
成人的分类范围是：偏瘦 < 18.5；正常 18.5-24.9；超重 25-29.9；肥胖 ≥ 30.0。BMI 无法区分肌肉和脂肪，因此存在局限性。
11. Genetic Probability and Ratios | 遗传概率与比例
In monohybrid crosses, you can predict the probability of an offspring inheriting a particular genotype or phenotype using Punnett squares and basic probability.
在单基因杂交中，你可以使用旁氏表（Punnett square）和基本概率来预测后代继承特定基因型或表现型的概率。
Probability of a genotype = (Number of offspring boxes with that genotype) ÷ (Total number of boxes)
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 3 : 1.
对于两个杂合亲本（Aa × Aa）之间的杂交，预期基因型比例为 1 AA : 2 Aa : 1 aa，显性-隐性性状的表现型比例为 3 : 1。
You can use a simple table to organise these outcomes:
你可以用一个简表来整理这些结果：
| A | a | |
| A | AA | Aa |
| a | Aa | aa |
The ratio can be expressed as a fraction (e.g. probability of dominant phenotype = 3/4), a percentage (75%) or a ratio (3:1). Always read the question to present the answer in the required form.
该比例可以用分数（例如显性表现型概率 = 3/4）、百分比（75%）或比值（3:1）来表示。答题时务必按照题目要求的形式呈现答案。
For co-dominance or sex-linked inheritance, the same probability principles apply; just adjust the allele notation and carefully track parental genotypes.
对于共显性或伴性遗传，相同的概率原则依然适用；只需调整等位基因的表示方法，并仔细追踪亲本基因型即可。
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