Year 13 WJEC Biology: Formula & Theorem Quick-Reference Handbook | Year 13 WJEC 生物：公式定理速查手册

📚 Year 13 WJEC Biology: Formula & Theorem Quick-Reference Handbook | Year 13 WJEC 生物：公式定理速查手册

This handbook consolidates the essential quantitative relationships, equations, and statistical principles required for Year 13 WJEC Biology. It is designed as a rapid revision aid to support your understanding of topics ranging from microscopy and water potential to population genetics and ecological energetics. Each entry presents the core formula or theorem, a concise explanation, and paired bilingual commentary so you can cross-reference concepts with ease.

本手册汇集了 Year 13 WJEC 生物课程所需的基本定量关系、公式和统计原理。手册旨在作为快速复习工具，帮助你巩固从显微镜测量、水势到群体遗传学和生态能量学等主题的理解。每个条目都呈现了核心公式或定理、简要说明以及配套的双语解析，方便你对照学习。

1. Microscopy and Magnification | 显微测量与放大率

Magnification (M) relates the size of an image to the actual size of the specimen. The standard formula is M = I / A, where I is the measured image size and A is the actual object size. Both quantities must be expressed in the same unit.

放大率 (M) 将图像大小与标本的实际大小关联起来。标准公式为 M = I / A，其中 I 为测量图像大小，A 为实际物体大小。两个量必须使用相同单位。

M = I / A

To convert between units, recall: 1 mm = 1000 µm, and 1 µm = 1000 nm. Using a calibrated eyepiece graticule together with a stage micrometer allows you to determine the actual size, which you then substitute into the formula.

进行单位换算时请记住：1 mm = 1000 µm，1 µm = 1000 nm。使用已校准的目镜测微尺配合镜台测微尺可以确定实际大小，再代入公式即可。

An alternative arrangement is A = I / M, which is used when you know the magnification and need to find the true dimensions of a cell or organelle from a labelled micrograph.

另一种变形为 A = I / M，当已知放大率并需要从标记显微照片中求出细胞或细胞器的真实尺寸时会用到。

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2. Water Potential (Ψ) | 水势

Water potential (Ψ) determines the direction of water movement across membranes. In plant cells it is the sum of the solute potential (Ψₛ) and the pressure potential (Ψₚ). The unit is megapascals (MPa).

水势 (Ψ) 决定了水分跨膜运动的方向。在植物细胞中，水势等于溶质势 (Ψₛ) 与压力势 (Ψₚ) 之和，单位为兆帕 (MPa)。

Ψ = Ψₛ + Ψₚ

Solute potential is always negative or zero, becoming more negative as solute concentration increases. Pressure potential is typically positive inside turgid cells and zero in plasmolysed cells. Water moves from a region of higher (less negative) water potential to a region of lower (more negative) water potential.

溶质势总是负值或零，溶质浓度越高，溶质势越负。压力势在膨压细胞内通常为正值，在质壁分离细胞中为零。水总是从水势较高（负值较小）的区域流向水势较低（负值较大）的区域。

In WJEC problems you are often given Ψₛ and Ψₚ for two adjacent cells and asked to predict net water movement; simply calculate Ψ for each cell and compare.

在 WJEC 考题中，常给出两个相邻细胞的 Ψₛ 和 Ψₚ，要求预测净水分移动方向；只需分别计算每个细胞的 Ψ 并比较即可。

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

The ratio of surface area (SA) to volume (V) constrains the maximum size a cell or organism can attain. As an object increases in size, its volume rises faster than its surface area, so the SA:V ratio decreases.

表面积 (SA) 与体积 (V) 的比值限制了细胞或生物体所能达到的最大尺寸。随着物体变大，其体积的增长速度快于表面积，因此 SA:V 比值下降。

SA:V = surface area / volume

For a cube of side length L, surface area = 6L², volume = L³, so SA:V = 6/L. This illustrates why large organisms cannot rely solely on diffusion; they require specialised exchange surfaces and transport systems.

对于边长为 L 的立方体，表面积 = 6L²，体积 = L³，因此 SA:V = 6/L。这说明了为何大型生物不能仅依靠扩散，而需要特化的交换表面和运输系统。

When analysing data on oxygen uptake or heat loss, remember that a higher SA:V ratio promotes faster exchange but also greater heat loss per unit volume, which is critical in understanding adaptations of endotherms and ectotherms.

分析氧气吸收或散热数据时，请记住较高的 SA:V 比值促进更快的交换，但也导致单位体积散热量更大，这对理解恒温动物和变温动物的适应至关重要。

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4. Photosynthesis and Net Productivity | 光合作用与净生产力

Gross primary productivity (GPP) is the total energy captured by photosynthesis. Net primary productivity (NPP) is the energy remaining after subtracting the energy used in plant respiration (R). The fundamental relationship is NPP = GPP – R.

总初级生产力 (GPP) 是光合作用捕获的总能量。净初级生产力 (NPP) 是扣除植物呼吸消耗 (R) 后剩余的能量。基本关系式为 NPP = GPP – R。

NPP = GPP – R

NPP represents the biomass available to the next trophic level. Units are typically kJ m⁻² year⁻¹ or g m⁻² year⁻¹. To calculate the efficiency of energy capture, divide GPP by the total light energy incident on the plant.

NPP 代表可供下一营养级利用的生物量。单位通常为 kJ m⁻² year⁻¹ 或 g m⁻² year⁻¹。要计算能量捕获效率，可用 GPP 除以照射到植物上的总光能。

In WJEC contexts, you may also need to work with net exchange of CO₂ or O₂ in a closed chamber to infer GPP and R. Remember that in the light, net gas exchange = (GPP – R); in the dark, gas exchange gives an estimate of R alone.

在 WJEC 情境中，你可能还需要利用密闭容器内 CO₂ 或 O₂ 的净交换量来推断 GPP 和 R。记住，在光下净气体交换 = (GPP – R)；黑暗中气体交换仅反映 R 的估计值。

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5. Respiratory Quotient (RQ) | 呼吸商

The respiratory quotient (RQ) is the ratio of the volume of carbon dioxide produced to the volume of oxygen consumed during aerobic respiration. It provides insight into the respiratory substrate being metabolised.

呼吸商 (RQ) 是有氧呼吸过程中产生二氧化碳的体积与消耗氧气的体积之比。它能揭示正被代谢的呼吸底物类型。

RQ = volume of CO₂ produced / volume of O₂ consumed

Typical RQ values are: carbohydrate ≈ 1.0, lipid ≈ 0.7, protein ≈ 0.8–0.9. When RQ exceeds 1.0, some anaerobic respiration may be occurring, or the substrate is organic acid. In respirometer practicals, you calculate RQ using manometer readings of gas volume changes.

典型的 RQ 值：碳水化合物 ≈ 1.0，脂类 ≈ 0.7，蛋白质 ≈ 0.8–0.9。当 RQ 大于 1.0 时，可能发生了某些无氧呼吸，或者底物为有机酸。在呼吸计实验中，你利用气压计读数的气体体积变化来计算 RQ。

If CO₂ is absorbed by a chemical such as potassium hydroxide, the manometer movement reflects only O₂ consumption. Comparison with a control tube allows you to deduce both O₂ uptake and CO₂ production.

如果 CO₂ 被氢氧化钾等化学物质吸收，气压计液柱的移动仅反映 O₂ 的消耗。与对照管比较，即可推算出 O₂ 吸收量和 CO₂ 产生量。

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6. Microbial Growth Kinetics | 微生物生长动力学

In batch culture, exponential growth of a microbial population can be modelled by Nₜ = N₀ eʳᵗ, where N₀ is the initial number of cells, Nₜ is the number after time t, and r is the intrinsic growth rate. This applies during the log phase.

在分批培养中，微生物群体的指数生长可用 Nₜ = N₀ eʳᵗ 建模，其中 N₀ 为初始细胞数，Nₜ 为时间 t 后的细胞数，r 为内禀增长率。这适用于对数期。

Nₜ = N₀ eʳᵗ

The doubling time (g) is the time required for the population to double: g = ln 2 / r. Knowing the doubling time helps predict when a culture will reach a specific density or when food spoilage might occur.

倍增时间 (g) 是群体数量翻倍所需的时间：g = ln 2 / r。知道倍增时间有助于预测培养物何时达到特定密度或食物何时可能腐败。

When environmental resistance becomes significant, growth decelerates and eventually enters the stationary phase. The maximum specific growth rate (µmax) is obtained from the steepest portion of the semi-log plot of cell number versus time.

当环境阻力显著时，生长减速并最终进入稳定期。最高比生长速率 (µmax) 可从细胞数对时间的半对数图中最陡峭的部分获得。

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7. Population Growth Models | 种群增长模型

Unrestricted population growth is exponential: dN/dt = rN. However, most populations face resource limitations, which are described by the logistic growth model: dN/dt = rN(1 – N/K), where K is the carrying capacity.

无限制的种群增长为指数型：dN/dt = rN。但大多数种群面临资源限制，这可用逻辑生长模型描述：dN/dt = rN(1 – N/K)，其中 K 为环境容纳量。

dN/dt = rN(1 – N/K)

In the logistic curve, growth is fastest at intermediate population sizes (around K/2) and slows to zero as N approaches K. K is determined by factors such as food supply, nesting space and accumulation of waste.

在逻辑斯谛曲线中，种群规模适中时（约 K/2 处）生长最快，当 N 趋近 K 时生长速率降为零。K 由食物供应、筑巢空间和废物积累等因素决定。

Conservation biologists and pest managers use these models to set harvesting quotas or predict recovery times. If a population overshoots K, a die-off often follows before numbers stabilise around K.

保护生物学家和害虫管理者利用这些模型来设定捕捞配额或预测恢复时间。若种群数量超过 K，常会在数量降至 K 附近之前出现大量死亡。

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8. Ecological Energetics and Simpson’s Diversity Index | 生态能量学与辛普森多样性指数

The efficiency of energy transfer between trophic levels is calculated as: Ecological efficiency (%) = (energy available after transfer / energy available before transfer) × 100. Typically only about 10 % of energy is passed on, with the rest lost as heat, movement and undigested material.

营养级之间能量传递效率的计算公式为：生态效率 (%) = (传递后可利用的能量 / 传递前可利用的能量) × 100。通常仅有约 10% 的能量被传递，其余以热量、运动和未消化物质等形式损失。

Ecological efficiency = (Eₙ₊₁ / Eₙ) × 100%

Simpson’s Diversity Index (D) is a measure of biodiversity that accounts for both species richness and evenness. The formula used in WJEC is: D = 1 – [Σ n(n–1) / N(N–1)], where n is the total number of organisms of a particular species and N is the total number of organisms of all species.

辛普森多样性指数 (D) 是衡量生物多样性的指标，同时考虑了物种丰富度和均匀度。WJEC 所用的公式为：D = 1 – [Σ n(n–1) / N(N–1)]，其中 n 为某物种的个体总数，N 为所有物种的个体总数。

D = 1 – [Σ n(n–1) / N(N–1)]

A high D value (close to 1) indicates high diversity, while a low value signals dominance by one or a few species. When you calculate D, work stepwise: first find N, then compute n(n–1) for each species, sum those values, and finally apply the formula.

高 D 值（接近 1）表示多样性高，低值则表明一个或少数物种占优势。计算 D 时请分步进行：先求 N，再逐个物种计算 n(n–1)，求和后代入公式

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