📚 A-Level CIE Biology: Formula Summary Handbook | A-Level CIE 生物：公式汇总手册
Mastering the key mathematical relationships in CIE A-Level Biology is essential for success in both Paper 2 (AS) and Paper 4 (A2). This handbook brings together all the core equations you need to apply in microscopy, physiology, ecology, genetics and data analysis, with clear explanations and paired bilingual commentary. Use it alongside past‑paper practise to build confidence in quantitative skills.
掌握 CIE A‑Level 生物学中的核心数学关系对于在 Paper 2（AS）和 Paper 4（A2）中取得成功至关重要。本手册汇集了显微镜学、生理学、生态学、遗传学及数据分析中你需要应用的所有关键公式，并提供清晰的解释和配对的中英双语注释。配合历年真题练习使用，能有效提升你的定量分析信心。
1. Magnification and Actual Size | 放大倍数与实际大小
The fundamental microscope formula links image size, actual size and magnification. Always convert all lengths to the same unit before substituting values into the equation.
Magnification (M) = Image size (I) ÷ Actual size (A)
基础显微镜公式将图像大小、实际大小和放大倍数联系起来。在将数值代入方程之前，务必把所有长度换算成相同的单位。
Rearranging gives the actual size: A = I ÷ M. A typical task is to calculate the real length of a cell from an image measured in millimetres, converting to micrometres (µm) for biological relevance.
Actual size (A) = Image size (I) ÷ Magnification (M)
变形后可求实际大小：A = I ÷ M。典型的考题是根据以毫米为单位的图像测量值，计算细胞的实际长度，并换算为生物学中常用的微米（µm）。
| Unit conversions | 换算关系 |
|---|---|
| 1 mm = 1000 µm | 1 毫米 = 1000 微米 |
| 1 µm = 1000 nm | 1 微米 = 1000 纳米 |
2. Calibrating the Eyepiece Graticule | 目镜测微尺校准
An eyepiece graticule must be calibrated for each objective lens using a stage micrometer. The calibration factor is the length represented by one eyepiece division.
目镜测微尺必须在每一个物镜下用镜台测微尺进行校准。校准系数即一个目镜分度所代表的实际长度。
One eyepiece unit (µ e divisions counted × Length of one stage division) ÷ Number of eyepiece divisions matched
一个目镜分度 (µm) = (计数的镜台分度数 × 单个镜台分度的长度) ÷ 所对应的目镜分度数
For example, if 10 stage micrometer divisions (each 10 µm) align with 40 eyepiece graticule divisions, one eyepiece unit = (10 × 10 µm) ÷ 40 = 2.5 µm. This value is then used to measure specimens.
例如，如果 10 个镜台测微尺分度（每个 10 µm）与 40 个目镜分度对齐，则一个目镜分度 = (10 × 10 µm) ÷ 40 = 2.5 µm。之后用该数值测量样本。
3. Cardiac Output and Minute Ventilation | 心输出量与每分通气量
Cardiac output is the volume of blood pumped by one ventricle per minute. It depends on heart rate and stroke volume.
Cardiac output (CO) = Heart rate (HR) × Stroke volume (SV)
心输出量是一个心室每分钟泵出的血液体积。它依赖于心率和每搏输出量。
心输出量 (CO) = 心率 (HR) × 每搏输出量 (SV)
Units: CO is usually expressed in litres per minute (L min⁻¹), HR in beats per minute (bpm), SV in millilitres per beat (mL). To convert SV to litres, divide by 1000.
单位：心输出量通常用升/分钟（L min⁻¹）表示，心率以次/分钟（bpm）计，每搏输出量以毫升/次（mL）计。要将每搏输出量换算为升，需除以 1000。
Minute ventilation (pulmonary ventilation) is the volume of air moved into the lungs per minute.
Minute ventilation = Tidal volume (TV) × Breathing rate (f)
每分通气量（肺通气量）是每分钟进出肺部的气体体积。
每分通气量 = 潮气量 (TV) × 呼吸频率 (f)
Typical units: litre per minute (L min⁻¹) for ventilation, litre (L) for tidal volume, breaths per minute for breathing rate.
典型单位：通气量用升/分钟（L min⁻¹），潮气量用升（L），呼吸频率用次/分钟。
4. Respiratory Quotient (RQ) | 呼吸商
Respiratory quotient reveals the type of respiratory substrate being metabolised. It is the ratio of carbon dioxide produced to oxygen consumed, measured over a given time.
RQ = Volume of CO₂ produced ÷ Volume of O₂ consumed
呼吸商揭示了正在被代谢的呼吸底物类型。它是一定时间内产生的二氧化碳体积与消耗的氧气体积之比。
呼吸商 = 产生的 CO₂ 体积 ÷ 消耗的 O₂ 体积
| Substrate | RQ value | 底物 | RQ 值 |
|---|---|---|---|
| Carbohydrate | 1.0 | 碳水化合物 | 1.0 |
| Lipid | ~0.7 | 脂质 | 约0.7 |
| Protein | ~0.9 | 蛋白质 | 约0.9 |
RQ values below 1.0 are often recorded during prolonged exercise or germination of oil‑rich seeds, when lipids are the main fuel.
在进行长时间运动或富含油脂的种子萌发时，常记录到低于 1.0 的 RQ 值，此时脂质是主要燃料。
5. Water Potential in Plant Cells | 植物细胞水势
ment. Pure water at standard pressure has Ψ = 0; solutions have negative water potentials.
Ψ = Ψₛ + Ψₚ
水势 (Ψ) 决定水分移动的方向。标准压力下纯水的 Ψ = 0；溶液的水势为负值。
水势 = 溶质势 + 压力势
Solute potential (Ψₛ) is always negative or zero; it becomes more negative as solute concentration increases. Pressure potential (Ψₚ) is positive inside turgid cells and zero in an open solution.
溶质势 (Ψₛ) 总是负值或零；溶质浓度越高，溶质势越低（越负）。压力势 (Ψₚ) 在膨胀的细胞内部为正值，在开放溶液中为零。
Water enters a plant cell when the external water potential is higher (less negative) than the internal water potential. The relationship is also described by Ψₛ = −iCRT, where i is the ionisation constant, C is molar concentration, R is the pressure constant and T is temperature in kelvin, but the simplified addition rule is sufficient for CIE calculations.
当外界水势高于（负值更小）细胞内部水势时，水分进入植物细胞。其中的关系也可用 Ψₛ = −iCRT 描述，其中 i 是解离常数，C 是摩尔浓度，R 是压力常数，T 是开尔文温度，但在 CIE 的计算中，简化的加法规则已足够。
6. Productivity and Ecological Efficiency | 生产力与生态效率
Gross primary production (GPP) is the total light energy converted into chemical energy by photosynthesis. Net primary production (NPP) is the energy remaining after plant respiration.
NPP = GPP − R (plant respiration)
总初级生产力 (GPP) 是通过光合作用转换为化学能的总光能。净初级生产力 (NPP) 是植物呼吸作用后剩余的能量。
NPP = GPP − R（植物呼吸作用）
Ecological efficiency describes the percentage of energy transferred from one trophic level to the next or the efficiency with which consumers convert assimilated food into new biomass.
Ecological efficiency (%) = (Energy used for growth / Energy assimilated) × 100
生态效率描述了能量从一个营养级传递到下一营养级的百分比，或者消费者将同化食物转化为新生生物量的效率。
生态效率 (%) = (用于生长的能量 / 同化的能量) × 100
In food chains, the trophic transfer efficiency is often given as (Energy at higher level ÷ Energy at lower level) × 100. Values are usually between 5 % and 20 %.
在食物链中，营养级传递效率通常表示为 （较高营养级的能量 ÷ 较低营养级的能量）× 100，数值通常在 5 % 至 20 % 之间。
7. Hardy‑Weinberg Equilibrium | 哈代‑温伯格平衡
The Hardy‑Weinberg principle predicts allele and genotype frequencies in a non‑evolving population. It allows you to calculate the frequency of carriers of recessive alleles.
p + q = 1
p² + 2pq + q² = 1
哈代‑温伯格定律用来预测非进化种群中等位基因频率和基因型频率。可以利用它计算隐性等位基因携带者的频率。
p + q = 1
p² + 2pq + q² = 1
recessive, and 2pq = frequency of heterozygotes. Given the incidence of a recessive phenotype (q²), take the square root to find q, then compute p = 1 − q.
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，q² = 隐性纯合子频率，2pq = 杂合子频率。知道了隐性表型的发生率 (q²)，求平方根得到 q，然后计算 p = 1 − q。
8. Chi‑Squared (χ²) Test | 卡方检验
The chi‑squared test compares observed and expected frequencies in categorical data. It is widely used in genetics and ecology to test for significant differences.
χ² = Σ (O − E)² ÷ E
卡方检验比较分类数据中的观察频数与期望频数。它广泛用于遗传学和生态学中，以检验差异是否显著。
χ² = Σ (O − E)² ÷ E
sen probability (p = 0.05) and degrees of freedom (df = number of categories − 1). If χ² > critical value, reject the null hypothesis.
O = 观察值，E = 期望值，Σ 表示对所有类别求和。将计算得到的 χ² 值与所选概率（p = 0.05）下的 χ² 表格临界值以及自由度（df = 类别数 − 1）进行比较。若 χ² > 临界值，则拒绝零假设。
9. Simpson’s Index of Diversity | 辛普森多样性指数
Simpson’s index quantifies the biodiversity of a habitat. A high value indicates high diversity because the community is not dominated by one species.
D = 1 − Σ (n / N)²
辛普森指数用于衡量一个栖息地的生物多样性。指数值越高，表示多样性越高，因为群落没有被某一个物种所主导。
