📚 AS Eduqas Biology: Formula & Theorem Quick Reference Handbook | AS Eduqas 生物：公式定理速查手册
This handbook compiles the essential formulae, mathematical relationships and key theoretical principles required for the AS Eduqas Biology specification. Use it as a rapid revision tool to lock in the quantitative and conceptual foundations for your exam success.
这本速查手册汇编了 AS Eduqas 生物学课程中必备的公式、数学关系以及关键理论原理。请把它作为快速复习工具，牢牢掌握定量和概念基础，为考试成功做好铺垫。
1. Magnification and Cell Measurements | 放大率与细胞测量
The relationship between image size, actual size and magnification is foundational for any microscopy work.
图像大小、实际大小和放大率之间的关系是所有显微镜工作的基础。
Magnification = Image size ÷ Actual size
放大率 = 图像大小 ÷ 实际大小
Remember to convert all lengths to the same unit, usually micrometres (μm) or millimetres (mm), before calculation.
切记，在计算前需将所有长度转换为相同单位，通常使用微米（μm）或毫米（mm）。
nm = 0.001 μm. For scale bars, measure the bar length on the image and apply the formula.
1 毫米 = 1000 微米，1 纳米 = 0.001 微米。对于比例尺，先测量图像中比例尺的长度，再代入公式计算。
2. Biological Molecules and Units | 生物分子与单位换算
Monomers, polymers, and biochemical tests often require precise unit conversions and concentration checks.
单体、聚合物与生化检测常常需要精确的单位换算和浓度核对。
Mass concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³)
质量浓度（克/立方分米）= 溶质质量（克） ÷ 溶液体积（立方分米）
. When calculating percentage concentrations, use mass/volume or volume/volume relationships accordingly.
请记住 1 立方分米 = 1000 立方厘米 = 1 升。在计算百分比浓度时，使用对应的质量/体积或体积/体积关系。
For reducing sugar tests (Benedict's), quantitative comparisons can be made using colourimetry, with transmission or absorbance values compared to a calibration curve.
对于还原糖检测（本尼迪克特试剂），可使用比色法进行定量比较，将透射率或吸光度值与标准曲线进行对比。
3. Enzyme Activity and Rate Calculations | 酶活性与速率计算
Enzyme kinetics under controlled experiments rely on rate measurement. The initial rate of reaction is the steepest straight‑line portion of a product–time graph.
可控实验中的酶动力学依赖于速率测量。反应的初始速率是产物-时间曲线中最陡的直线部分。
Rate of reaction = Change in concentration (or volume) of product ÷ Time taken
反应速率 = 产物浓度（或体积）的变化量 ÷ 所用时间
Alternatively, rate can be expressed as 1 ÷ time to reach a fixed end point, provided the substrate concentration is not limiting.
或者，在底物浓度不构成限制的条件下，速率也可以表示为 1 ÷ 达到某一固定终点所需的时间。
ermination of rate uses absorbance changes; a tangent drawn at t=0 gives the initial rate.
通过比色法测定速率时使用吸光度变化；在 t=0 处绘制的切线斜率即为初始速率。
4. Cell Membrane and Transport Principles | 细胞膜与运输原理
Understanding diffusion, osmosis and active transport involves concentration gradients and water potential.
理解扩散、渗透和主动运输，需要掌握浓度梯度和水势的概念。
Water potential (Ψ) = Solute potential (Ψₛ) + Pressure potential (Ψₚ)
水势 (Ψ) = 溶质势 (Ψₛ) + 压力势 (Ψₚ)
negative solute potentials. Water moves from higher (less negative) to lower (more negative) water potential.
在开放容器中，压力势 Ψₚ 为零；纯水的水势 Ψ = 0 kPa。所有溶液均具有负的溶质势。水从水势较高（负值较小）的区域向水势较低（负值较大）的区域移动。
The rate of facilitated diffusion is proportional to the number of available transport proteins, showing saturation kinetics.
协助扩散的速率与可利用的转运蛋白数量成正比，呈现饱和动力学特征。
5. Surface Area to Volume Ratio | 表面积与体积比
Organisms exchange substances with their environment; SA:V ratio determines the efficiency of exchange.
生物体与环境进行物质交换；表面积与体积比（SA:V）决定了交换的效率。
SA:V ratio = Surface area ÷ Volume
SA:V 比值 = 表面积 ÷ 体积
As an organism or cell increases in size, volume rises more rapidly than surface area, so the SA:V ratio decreases. This is why large organisms need specialised exchange surfaces and transport systems.
随着生物体或细胞尺寸的增大，体积的增长比表面积更快，因此 SA:V 比值减小。这就是大型生物需要特化的交换表面和运输系统的原因。
For a cube with side length s: surface area = 6s², volume = s³, so SA:V = 6/s.
对于边长为 s 的立方体：表面积 = 6s²，体积 = s³，因此 SA:V = 6/s。
6. Gas Exchange and Fick's Law | 气体交换与菲克定律
Fick's law describes the factors affecting the rate of diffusion across a surface, crucial for alveolar and gill exchange.
菲克定律描述了影响物质通过表面扩散速率的因素，对肺泡和鳃的气体交换至关重要。
Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Thickness of exchange surface
扩散速率 ∝ (表面积 × 浓度差) ÷ 交换表面厚度
Maximising surface area (alveoli, gill filaments), maintaining a steep concentration gradient (ventilation + blood flow), and minimising barrier thickness (single squamous epithelial layer) are adaptations that increase diffusion rate.
最大化表面积（肺泡、鳃丝）、维持陡峭的浓度梯度（通气 + 血流）以及最小化屏障厚度（单层鳞状上皮），都是提高扩散速率的适应性特征。
For respiratory measurements, tidal volume, vital capacity, and minute ventilation are linked.
在呼吸测量中，潮气量、肺活量和每分通气量相互关联。
Minute ventilation (dm³/min) = Tidal volume (dm³) × Breathing rate (min⁻¹)
每分通气量（dm³/min）= 潮气量（dm³） × 呼吸频率（min⁻¹）
7. Circulatory System and Cardiac Output | 循环系统与心输出量
Cardiac output is a central measurement of heart performance, commonly expressed in dm³ min⁻¹.
心输出量是衡量心脏功能的核心指标，通常以 dm³ min⁻¹ 表示。
Cardiac output = Heart rate × Stroke volume
心输出量 = 心率 × 每搏输出量
Stroke volume is the volume of blood pumped out of the left ventricle per beat. Heart rate is beats per minute (bpm).
每搏输出量是指左心室每次收缩所泵出的血量。心率以每分钟心跳次数（bpm）表示。
For risk assessment, Body Mass Index (BMI) and waist‑to‑hip ratio may be calculated.
在风险评估中，可能需要计算身体质量指数（BMI）和腰臀比。
BMI = body mass (kg) ÷ (height (m))²
身体质量指数（BMI）= 体重（kg） ÷ （身高（m））²
8. Transport in Plants | 植物体内的运输
Transpiration and water movement through xylem are driven by water potential gradients. The rate of transpiration can be estimated with a potometer.
蒸腾作用以及水分在木质部中的运输由水势梯度驱动。蒸腾速率可用蒸腾计进行估算。
Rate of transpiration = Volume of water taken up ÷ Time
蒸腾速率 = 吸收的水量 ÷ 时间
The cohesion‑tension theory explains the continuous water column; adhesion to xylem walls helps support the column against gravity.
内聚力-张力假说解释了连续水柱的维持；水分子对木质部管壁的附着力有助于对抗重力作用。
Phloem translocation follows the pressure‑flow (mass flow) hypothesis; solute potential at source (loading) and sink (unloading) drives the pressure difference.
韧皮部的输导遵循压力流（集体流动）假说；源（装载端）与库（卸载端）之间的溶质势差异驱动了压力差。
9. Disease, Immunity and Public Health Metrics | 疾病、免疫与公共卫生指标
Epidemiological data can be analysed using incidence, prevalence, and mortality rates. Vaccination efficacy is evaluated through cohort studies.
流行病学数据可通过发病率、患病率和死亡率进行分析。疫苗效力通过队列研究进行评估。
Attack rate (%) = (Number of new cases in a group ÷ Total number in the group) × 100
罹患率（%）= （群组内新病例数 ÷ 该群组总人数） × 100
Antibody concentration in serum can be quantified via serial dilution and ELISA, using a calibration curve to interpolate data.
血清中的抗体浓度可通过连续稀释和酶联免疫吸附试验（ELISA）进行定量，利用标准曲线插值计算数据。
The membrane attack complex and opsonisation are functional consequences of the complement cascade, but no complex calculations are required in this topic beyond data interpretation.
膜攻击复合物和调理作用都是补体级联反应的功能性结果，但本主题除数据解释外无需进行复杂计算。
10. Ecology and Biodiversity Calculations | 生态学与生物多样性计算
Ecological studies require quantitative descriptions of communities. Species richness counts the number of different species; Simpson's Index of Diversity incorporates both richness and evenness.
生态学研究需要对群落进行定量描述。物种丰富度计算不同物种的数量；辛普森多样性指数则结合了丰富度和均匀度。
Simpson's Index (D) = 1 – Σ(n/N)²
辛普森指数（D）= 1 – Σ(n/N)²
r of organisms of all species. D ranges from 0 (low diversity) to nearly 1 (high diversity).
其中 n = 某一特定物种的个体总数，N = 所有物种的个体总数。D 的取值范围为 0（低多样性）到近乎 1（高多样性）。
For population growth, the rate of change depends on birth rate, death rate, immigration and emigration.
对于种群增长，其变化率取决于出生率、死亡率、迁入量和迁出量。
Population growth rate = (Births – Deaths) + (Immigrants – Emigrants)
种群增长率 =（出生数 – 死亡数）+（迁入个体数 – 迁出个体数）
11. Genetics and Probability Rules | 遗传学与概率规则
Monohybrid and dihybrid crosses rely on the laws of segregation and independent assortment. Probability rules simplify phenotypic ratio predictions.
单因子杂交和双因子杂交基于分离定律和自由组合定律。概率规则可简化表型比率的预测。
Product rule: the probability that two independent events both occur is the product of their individual probabilities. Sum rule: the probability that either of two mutually exclusive events occurs is the sum of their probabilities.
乘法定理：两个独立事件同时发生的概率等于各自概率的乘积。加法定理：两个互斥事件中任一个发生的概率等于各自概率之和。
erozygotes (Aa × Aa), the expected phenotypic ratio is 3:1 if dominance is complete. A chi‑squared (χ²) test can evaluate the goodness of fit between observed and expected values.
对于杂合子之间的单因子杂交（Aa × Aa），若为完全显性，预期表型比为 3:1。卡方（χ²）检验可用于评估观察值与期望值之间的拟合优度。
χ² = Σ (O – E)² / E
χ² = Σ (观察值 – 期望值)² / 期望值
cal value at p=0.05) indicates no significant difference; the null hypothesis is accepted.
较低的 χ² 值（与 p=0.05 水平的临界值相比）表示无显著差异；即接受原假设。
12. Key Theoretical Principles summarised | 关键理论原理总结
Several 'theorems' appear across the specification as overarching explanatory frameworks.
规范中有多个'定理'作为整体解释框架出现。
Fick's law: diffusion rate ∝ (area × concentration gradient) ÷ thickness – used for gas exchange, transpiration and absorption.
菲克定律：扩散速率 ∝（面积 × 浓度梯度）÷ 厚度 —— 适用于气体交换、蒸腾作用和吸收过程。
Competitive exclusion principle: two species competing for the same limited resource cannot coexist; one will outcompete the other.
竞争排斥原理：竞争同一有限资源的两个物种无法长期共存；其中一个会在竞争中胜出。
Pressure‑flow hypothesis (mass flow): organic solutes move from source to sink in phloem due to osmotically generated pressure gradients.
压力流假说（集体流动）：有机溶质由于渗透压产生的压力梯度，在韧皮部中由源向库移动。
Cohesion‑tension theory: transpiration pull generates tension, transmitted down continuous water columns held together by cohesion and adhesion.
内聚力-张力假说：蒸腾作用产生拉力，该拉力通过由内聚力和附着力维系的水柱向下传导。
Natural selection: individuals with advantageous alleles are more likely to survive and reproduce, increasing allele frequency in subsequent generations.
自然选择：携带有利等位基因的个体更可能生存并繁殖，从而使该等位基因在后续世代中频率增加。
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