AS CCEA Biology: Formula & Theorem Quick Reference Handbook | AS CCEA 生物：公式定理速查手册

📚 AS CCEA Biology: Formula & Theorem Quick Reference Handbook | AS CCEA 生物：公式定理速查手册

This handbook compiles all the essential formulas, equations, and key theoretical relationships that you will encounter in the AS CCEA Biology course. From microscope work to population ecology and statistical testing, each entry is presented with clear definitions, typical units, and worked examples so you can revise effectively before the exam.

这本手册汇编了你在 AS CCEA 生物课程中会遇到的所有的核心公式、方程式以及关键理论关系。从显微镜操作到种群生态学再到统计检验，每一条都配有清晰的定义、常用单位和计算示例，帮助你高效地进行考前复习。

1. Microscopy and Magnification | 显微镜与放大率

Magnification is the factor by which an image appears larger than the actual object. The formula relates image size and actual size, provided both are measured in the same units.

放大率是图像比实际物体看上去大多少倍的倍数。该公式将在同一单位下测量的图像大小与实际大小建立起联系。

M = I / A

where M = magnification, I = image size, and A = actual size. You may need to convert between millimetres (mm), micrometres (µm) and nanometres (nm) before substituting values.

其中 M 为放大率，I 为图像大小，A 为实际大小。代入数值之前通常需要先完成毫米 (mm)、微米 (µm) 与纳米 (nm) 之间的单位转换。

For example, if a cell measures 20 mm in a micrograph and its actual length is 0.02 mm, the magnification is 20 / 0.02 = 1000 ×. In CCEA exam questions, you are often required to measure images with a ruler and convert the reading to micrometres.

举例而言，如果一个细胞在显微照片中量得长度为 20 mm，而实际长度为 0.02 mm，则放大率为 20 / 0.02 = 1000 倍。在 CCEA 试卷中，经常要求你用尺子测量图像并将读数换算为微米。

Always remember that electron microscopes have much higher resolution and can achieve magnifications over 500 000 ×, while light microscopes are limited to about 1500 ×.

始终请记住，电子显微镜的分辨率远高于光学显微镜，其放大率可以达到 500 000 倍以上，而光学显微镜通常被限制在约 1500 倍。

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2. Surface Area to Volume Ratio | 表面积与体积比

Cells rely on diffusion to exchange materials, making the surface area to volume ratio crucial. As an object increases in size, its surface area grows more slowly than its volume, reducing this ratio and limiting cell efficiency.

细胞依赖扩散来完成物质交换，因此表面积与体积比至关重要。随着物体尺寸增大，表面积的增长慢于体积的增长，该比例便会下降，从而限制了细胞的工作效率。

SA : V ratio = Surface Area / Volume

For a cube of side length x, surface area = 6x² and volume = x³, so SA:V = 6/x. For a sphere of radius r, surface area = 4πr² and volume = ¾πr³, giving SA:V = 3/r.

对于边长为 x 的立方体，表面积 = 6x²，体积 = x³，因此 SA:V = 6/x。对于半径为 r 的球体，表面积 = 4πr²，体积 = ⁴⁄₃πr³，SA:V = 3/r。

You can calculate these ratios to explain why large organisms need specialised exchange surfaces (e.g. lungs, gills) and why unicellular organisms can survive by simple diffusion alone.

你可以通过计算这些比例来解释为什么体型较大的生物需要特化的交换表面（如肺、鳃），而单细胞生物仅靠简单扩散就能维持生存。

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3. Water Potential and Osmosis | 水势与渗透

Water potential (ψ) determines the direction of water movement across a partially permeable membrane. Water always moves from a region of higher water potential to a region of lower water potential.

水势 (ψ) 决定了水穿过部分透性膜的运动方向。水总是从水势较高的区域向水势较低的区域移动。

ψ = ψₛ + ψₚ

Here ψₛ is the solute potential (always negative or zero, with pure water having ψₛ = 0) and ψₚ is the pressure potential (positive in turgid plant cells, zero in an open beaker).

式中 ψₛ 为溶质势（总是为负值或零，纯水的 ψₛ = 0），ψₚ 为压力势（在膨压植物细胞中为正值，在开放烧杯中为零）。

Water potential is measured in kilopascals (kPa) or megapascals (MPa). For example, if a cell has ψₛ = -600 kPa and ψₚ = 200 kPa, then ψ = -400 kPa. A surrounding solution of ψ = -300 kPa would be hypertonic, causing water to leave the cell.

水势的单位为千帕 (kPa) 或兆帕 (MPa)。例如，某细胞的 ψₛ = -600 kPa，ψₚ = 200 kPa，则 ψ = -400 kPa。若周围溶液的 ψ = -300 kPa，该溶液相对呈高渗，会导致水从细胞向外流失。

Remember that plasmolysis occurs when a plant cell is placed in a hypertonic solution and the protoplast pulls away from the cell wall.

请记住，当植物细胞被置于高渗溶液中并导致原生质体与细胞壁脱离时，便发生了质壁分离。

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4. Respiratory Quotient (RQ) | 呼吸商

The respiratory quotient is the ratio of carbon dioxide produced to oxygen consumed during respiration. It indicates which respiratory substrate is being metabolised.

呼吸商 (RQ) 是指呼吸过程中产生的二氧化碳与消耗的氧气之间的比值，它能够指示正在代谢的呼吸底物的类型。

RQ = CO₂ produced / O₂ consumed

Standard RQ values: carbohydrate = 1.0, lipid = 0.7, protein = about 0.9. These values can be obtained from a simple respirometer experiment using a manometer and soda lime to absorb CO₂.

标准 RQ 值：碳水化合物为 1.0，脂肪为 0.7，蛋白质约为 0.9。这些数值可以用一个简单的呼吸计实验获得，该实验通过测压计和碱石灰来吸收 CO₂。

For example, if a germinating seed takes up 2.0 cm³ of oxygen and releases 1.4 cm³ of carbon dioxide, the RQ = 1.4 / 2.0 = 0.7, suggesting lipids are the main fuel.

例如，若发芽的种子吸收了 2.0 cm³ 氧气并释放了 1.4 cm³ 二氧化碳，则 RQ = 1.4 / 2.0 = 0.7，提示脂肪是主要燃料。

Anaerobic respiration in plants produces CO₂ without consuming O₂, giving an RQ that approaches infinity; in animals, anaerobic respiration produces lactic acid with no CO₂, so RQ cannot be calculated this way.

植物无氧呼吸会产生 CO₂ 而不消耗 O₂，导致 RQ 趋于无穷大；动物无氧呼吸产生乳酸且不释放 CO₂，因此无法用这种方式计算 RQ。

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5. Calorimetry and Energy Content of Food | 量热法与食物能量值

Burning a known mass of food to heat water allows you to estimate the energy content. The principle is based on the relationship between heat, mass, specific heat capacity and temperature change.

通过燃烧已知质量的食物来加热水，可以估算食物的能量值。其原理基于热量、质量、比热容和温度变化之间的关系。

Energy (J) = m_water × c × ΔT

where m_water is the mass of water in grams, c is the specific heat capacity of water (4.2 J g⁻¹ °C⁻¹), and ΔT is the temperature rise in °C. To find the energy per gram of food, divide the energy obtained by the mass of the food sample burned.

其中 m_water 为水的质量（克），c 为水的比热容 (4.2 J g⁻¹ °C⁻¹)，ΔT 为水升高的温度 (°C)。若要计算每克食物的能量，则将所得能量除以被燃烧的食物样品的质量。

Energy per gram = (m_water × 4.2 × ΔT) / m_food. You should always comment on heat loss to surroundings, incomplete combustion and other systematic errors that cause the result to be lower than the true value.

每克能量 = (m_water × 4.2 × ΔT) / m_food。你必须始终指出因周围环境热量散失、燃烧不充分以及其他系统误差所导致的结果低于真实值的情况。

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6. Enzyme Activity and Temperature Coefficient Q10 | 酶活性与温度系数 Q10

The temperature coefficient, Q10, is a measure of how much the rate of an enzyme-catalysed reaction increases when the temperature is raised by 10 °C.

温度系数 Q10 衡量的是当温度升高 10 °C 时，酶促反应速率增加的倍数。

Q10 = (rate at T+10 °C) / (rate at T °C)

For many biological reactions, Q10 is approximately 2, meaning the rate doubles with a 10 °C rise, up to an optimum temperature. Beyond the optimum, the enzyme denatures and the rate falls sharply.

对于许多生物反应，Q10 大约为 2，意味着在到达最适温度以前，温度每升高 10 °C，速率便翻一番。超过最适温度后，酶会变性，速率急剧下降。

If the rate of amylase activity at 20 °C is 0.5 mg starch broken down per minute, and at 30 °C it is 1.2 mg min⁻¹, then Q10 = 1.2 / 0.5 = 2.4. You would then relate this to the kinetic energy of molecules and the number of enzyme-substrate complexes formed.

若淀粉酶在 20 °C 下的速率为每分钟 0.5 mg 淀粉被分解，而在 30 °C 下为 1.2 mg/min，则 Q10 = 1.2 / 0.5 = 2.4。随后你应将其与分子的动能以及形成的酶–底物复合物数量联系起来分析。

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7. Mark, Release and Recapture (Lincoln Index) | 标记重捕法（林肯指数）

The Lincoln index estimates the size of a motile animal population. It depends on capturing, marking, releasing and then recapturing a sample of individuals.

林肯指数可用于估算活动性动物种群的大小，它依赖于对一群个体进行捕捉、标记、释放后再重新捕获一个样本的操作。

N = (M × C) / R

where N = estimated population size, M = number of animals marked in the first capture, C = total number captured in the second sample, and R = number of marked individuals recaptured.

其中 N = 估算的种群大小，M = 首次捕获并标记的动物数量，C = 第二次捕获的总数，R = 第二次捕获中含有标记的个体数。

This method assumes that the population is closed, there is no migration or death, marking does not affect survival, marked individuals mix randomly, and marks are not lost. You should discuss how violations of these assumptions bias the estimate.

该方法假设种群是封闭的，没有迁入、迁出或死亡，标记不影响生存，标记个体能随机混合，且标记不会丢失。你应该讨论这些假设被违反时会导致估计出现何种偏差。

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8. Chi-Squared (χ²) Test | 卡方检验

The chi-squared test is used to determine whether there is a significant difference between observed and expected frequencies in categorical data. It is commonly applied to genetics and ecological distributions.

卡方检验用于判断分类数据中观察频数与期望频数之间是否存在显著差异。它通常应用于遗传学和生态学分布的研究。

χ² = Σ (O – E)² / E

O is the observed value and E is the expected value for each category. Summed over all categories, the larger the χ² statistic, the more likely the difference is not due to chance alone.

O 为每个类别的观测值，E 为期望值。对所有类别求和后，χ² 统计量越大，差异越有可能并非仅因偶然因素所致。

You then compare the calculated χ² with a critical value from a table at a probability level of 0.05, using degrees of freedom = (number of categories – 1). If χ² calculated > χ² critical, you reject the null hypothesis and conclude a significant difference.

随后你将计算出的 χ² 与自由度等于（类别数 – 1）下、概率水平为 0.05 的临界值比较。若 χ² 计算值 > χ² 临界值，则拒绝零假设，认为存在显著差异。

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9. Mendelian Laws and Probability in Genetics | 孟德尔遗传规律与概率

Mendel’s law of segregation states that allele pairs separate during gamete formation, with each gamete carrying only one allele for each gene. The law of independent assortment applies to genes on different chromosomes.

孟德尔的分离定律指出，在配子形成过程中等位基因对发生分离，每个配子只携带某基因的一个等位基因。自由组合定律适用于位于不同染色体上的基因。

These laws allow you to predict genotype ratios using Punnett squares. The two key probability rules are the multiplication rule (chance of two independent events both occurring = product of individual probabilities) and the addition rule (chance of any of several mutually exclusive events = sum of their probabilities).

运用这些规律，你可以借助庞纳特方格预测基因型比例。两条关键的概率法则是：乘法法则（两个独立事件同时发生的概率 = 各自概率的乘积）和加法法则（若干互斥事件中任一事件发生的概率 = 各自概率之和）。

For a monohybrid cross between two heterozygotes (Aa × Aa), the probability of an offspring being homozygous recessive (aa) is ½ × ½ = ¼. The probability of being either AA or Aa (dominant phenotype) is ¼ + ½ = ¾.

对于两个杂合子 (Aa × Aa) 的单基因杂交，子代为隐性纯合子 (aa) 的概率是 ½ × ½ = ¼。表现为显性性状（AA 或 Aa）的概率为 ¼ + ½ = ¾。

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10. Counting Cells with a Haemocytometer | 血球计数板细胞计数

A haemocytometer allows you to count cells in a known volume of liquid, enabling the calculation of cell concentration. The improved Neubauer chamber is frequently used in CCEA practicals.

血球计数板能够让你在已知体积的液体中对细胞进行计数，从而计算出细胞浓度。改良牛鲍计数板在 CCEA 实验中经常被用到。

Cell concentration = N / (n × V × D)

where N = total number of cells counted, n = number of squares counted (e.g. 5 groups of 16 small squares), V = volume of one counted square (often 0.1 mm³ per main square, but check the specification), and D = dilution factor.

其中 N = 计数的细胞总数，n = 所计数的方格数（如 5 组 16 个小方格），V = 每个计数方格的体积（通常一个大方格为 0.1 mm³，需确认规格），D = 稀释倍数。

To obtain cells per cm³, convert mm³ to cm³ (1 cm³ = 1000 mm³). If you counted 200 cells in 0.5 mm³ of a 1:10 dilution, the concentration = 200 / (0.5 × 10) = 40 cells per mm³, which is 40 000 cells per cm³.

要得到每 cm³ 的细胞数，需将 mm³ 转为 cm³（1 cm³ = 1000 mm³）。若你在 0.5 mm³ 的 1:10 稀释液中数得 200 个细胞，则浓度为 200 / (0.5 × 10) = 40 cells/mm³，即 40 000 cells/cm³。

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11. Percentage Change and Rate Calculations | 百分比变化与速率计算

Calculations of percentage change are essential when analysing osmosis, plant growth or enzyme experiments. The formula compares the final value to the initial value.

在进行渗透、植物生长或酶学实验的数据分析时，百分比变化的计算是必不可少的。此公式将最终值与初始值进行比较。

Percentage change = (final value – initial value) / initial value × 100%

A positive value indicates an increase, while a negative value shows a decrease. For potato chip osmosis, a potato strip that gains mass from 2.0 g to 2.5 g has a percentage mass change of (2.5 – 2.0) / 2.0 × 100% = +25%.

正值表示增加，负值表示减少。就马铃薯条的渗透实验而言，若一根马铃薯条质量从 2.0 g 增加到 2.5 g，则质量变化百分比为 (2.5 – 2.0) / 2.0 × 100% = +25%。

Rate of reaction is simply the change in a measured variable divided by time. For instance, initial rate = (initial amount of product formed) / time taken. You often calculate this from a tangent drawn at time zero on a progress curve.

反应速率就是所测变量的变化量除以时间。例如，初始速率 = 最初产物的生成量 / 所用时间。你通常需要在进程曲线上通过时间零点处的切线来进行计算。

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