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

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

Mastering the essential formulae and quantitative relationships is key to success in AS WJEC Biology. This handbook gathers all the calculations, equations and theorems you need across microscopy, physiology, genetics, ecology and biochemistry, with worked examples and clear unit guidance. Use it alongside your practical work to build speed and accuracy.

掌握必要的公式和数量关系是取得 AS WJEC 生物考试成功的关键。本手册汇总了显微镜学、生理学、遗传学、生态学及生物化学中所需的所有计算、方程和定理，配有计算示例和明确的单位指导。请将其与实验操作结合使用，以提升速度和准确性。

1. Microscopy and Magnification | 显微镜与放大倍数

The total magnification of a compound light microscope is the product of the eyepiece lens magnification and the objective lens magnification. This is always written with a multiplication sign, not as a sum.

复式光学显微镜的总放大倍数是目镜放大倍数与物镜放大倍数的乘积。它始终用乘号书写，而非求和。

Total Magnification = Eyepiece magnification × Objective magnification

总放大倍数 = 目镜放大倍数 × 物镜放大倍数

To find the actual size of a specimen from a micrograph or drawing, you must rearrange the fundamental magnification equation. Remember that image size and actual size must be in the same units; typical conversions involve micrometres (µm), millimetres (mm) and nanometres (nm).

要从显微照片或手绘图求出标本的实际大小，必须变形基本的放大倍数方程。切记图像尺寸和实际尺寸必须使用相同单位；常见转换涉及微米 (µm)、毫米 (mm) 和纳米 (nm)。

Magnification = Image size ÷ Actual size

放大倍数 = 图像尺寸 ÷ 实际大小

Actual size = Image size ÷ Magnification

实际大小 = 图像尺寸 ÷ 放大倍数

A common worked example: if an image of a cell measures 30 mm in a photograph taken at ×2000 magnification, the actual length is 30 mm ÷ 2000 = 0.015 mm, which converts to 15 µm. Always convert to the most appropriate unit for the biological scale.

常见计算示例：若某细胞在放大 2000 倍的照片中图像长度为 30 mm，则实际长度为 30 mm ÷ 2000 = 0.015 mm，转换为 15 µm。始终转换为最适合生物学尺度的单位。

2. Cell Size and Surface Area to Volume Ratio | 细胞大小与表面积体积比

As a cell or organism increases in size, its surface area to volume ratio (SA:V) decreases. This ratio governs the rate of exchange of materials across the cell surface and is fundamental to understanding why organisms need specialised exchange surfaces, mass transport systems or adaptations like villi and alveoli.

当细胞或生物体体积增大时，其表面积与体积比 (SA:V) 会下降。该比值决定了物质穿过细胞表面的交换速率，是理解生物为何需要特化的交换表面、物质运输系统或诸如绒毛和肺泡等适应的基础。

Surface area to volume ratio = Surface area ÷ Volume

表面积与体积比 = 表面积 ÷ 体积

For simple geometric shapes, calculate surface area and volume separately then divide. For a cube of side length L, SA = 6L² and V = L³, so SA:V = 6/L. The larger L gets, the smaller the ratio becomes. You must be able to interpret and plot graphs of SA:V against size and relate the trend to heat loss and metabolic rate.

对于简单几何形状，可分别计算表面积和体积再相除。边长为 L 的立方体，SA = 6L²，V = L³，因此 SA:V = 6/L。L 越大，比值越小。你必须能够解读并绘制 SA:V 随大小变化的曲线图，并将该趋势与热量散失和代谢率关联起来。

3. Fick’s Law of Diffusion | 菲克扩散定律

Fick’s law describes the factors affecting the rate of diffusion across a membrane or an exchange surface. It is not a single equation to solve in most WJEC AS contexts, but a proportional relationship you must be able to explain and apply to adaptations of gas exchange and absorption.

菲克定律描述了影响物质通过膜或交换表面扩散速率的因素。在多数 WJEC AS 情境中，它并非一个用来计算的独立方程，而是一种比例关系，你必须能够解释并将其应用于气体交换和吸收的适应性分析。

Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Diffusion distance

扩散速率 ∝ (表面积 × 浓度差) ÷ 扩散距离

Large surface area (e.g. flattened alveoli, root hairs), short diffusion distance (thin alveolar walls, squamous epithelium) and maintenance of a steep concentration gradient (ventilation, blood flow) all increase the rate. For WJEC questions, always link numerical data or structural features back to these three components.

较大的表面积（如扁平的肺泡、根毛）、较短的扩散距离（薄的肺泡壁、扁平上皮）以及维持陡峭的浓度梯度（通气、血流）都能提高扩散速率。应对 WJEC 考题时，始终将数值数据或结构特征关联回这三个要素。

4. Cardiac Output and Ventilation | 心输出量与肺通气

Cardiac output is the volume of blood pumped by one ventricle per minute. It is determined by heart rate (beats per minute) and stroke volume (volume of blood pumped per beat). These values can be calculated from simple data or graphs of cardiac cycles.

心输出量是指一个心室每分钟泵出的血液体积。它由心率（每分钟心跳次数）和每搏输出量（每搏泵出的血量）决定。可以从简单数据或心动周期图形中计算出这些值。

Cardiac output (CO) = Heart rate (HR) × Stroke volume (SV)

心输出量 = 心率 × 每搏输出量

Units: CO in dm³ min⁻¹ or L min⁻¹, HR in beats min⁻¹ (bpm), SV in cm³ or mL. Typical resting values for a human: HR ≈ 70 bpm, SV ≈ 70 cm³, giving CO ≈ 4.9 dm³ min⁻¹. During exercise, both HR and SV increase, raising CO significantly.

单位：CO 为 dm³ min⁻¹ 或 L min⁻¹，HR 为 beats min⁻¹ (bpm)，SV 为 cm³ 或 mL。人类静息时的典型值：HR ≈ 70 bpm，SV ≈ 70 cm³，可得 CO ≈ 4.9 dm³ min⁻¹。运动期间，HR 与 SV 均增加，显著提高 CO。

Pulmonary ventilation is the volume of air moved into and out of the lungs per minute. It depends on tidal volume (volume of air per breath) and breathing rate.

肺通气量是每分钟进出肺部的空气体积。它取决于潮气量（每次呼吸的空气体积）和呼吸频率。

Pulmonary ventilation = Tidal volume × Breathing rate

肺通气量 = 潮气量 × 呼吸频率

Units: ventilation in dm³ min⁻¹ or L min⁻¹, tidal volume in dm³ or L, breathing rate in breaths min⁻¹. Use spirometer traces to read these values and calculate ventilation at rest and during exercise.

单位：通气量为 dm³ min⁻¹ 或 L min⁻¹，潮气量为 dm³ 或 L，呼吸频率为 breaths min⁻¹。利用肺量计描记图读取这些数值，并计算静止和运动时的通气量。

5. Water Potential | 水势

Water potential (ψ, psi) is the measure of the tendency of water to move from one place to another. It is used to predict the direction of osmosis in plant and animal cells. Water moves from a region of higher (less negative) water potential to a region of lower (more negative) water potential.

水势 (ψ) 用于衡量水从一处移动到另一处的趋势，可预测动植物细胞中渗透作用的方向。水会从水势较高（较不偏向负值）的区域移向水势较低（更偏向负值）的区域。

ψ = ψₛ + ψₚ

水势 = 溶质势 + 压力势

Solute potential (ψₛ) is always negative or zero; adding solutes lowers water potential. Pressure potential (ψₚ) is usually positive inside a turgid plant cell, but can be zero or negative in the xylem under tension. Units are usually megapascals (MPa) or kilopascals (kPa); pure water has ψ = 0 MPa at standard conditions.

溶质势 (ψₛ) 总为负值或零；加入溶质会降低水势。压力势 (ψₚ) 在膨胀的植物细胞中通常为正值，但在木质部张力的作用下可为零或负值。单位通常为兆帕 (MPa) 或千帕 (kPa)；纯水在标准条件下 ψ = 0 MPa。

When a plant cell is placed in a solution of known ψₛ, incipient plasmolysis occurs when ψₚ = 0, so ψ_cell = ψₛ of the external solution. This principle is used in experiments with sucrose solutions to estimate tissue water potential.

当植物细胞被置于已知 ψₛ 的溶液中时，初始质壁分离发生在 ψₚ = 0 时，因此此时细胞水势等于外界溶液的 ψₛ。这一原理用于利用蔗糖溶液估算组织水势的实验。

6. Respiratory Quotient (RQ) | 呼吸商

The respiratory quotient is a dimensionless number that reveals which respiratory substrate is being metabolised. It is calculated from the volumes of carbon dioxide produced and oxygen consumed over a specific time period, often measured using a respirometer.

呼吸商是一个无量纲数，可揭示正在代谢的呼吸底物类型。它根据特定时间段内产生的二氧化碳体积和消耗的氧气体积计算得出，常用呼吸计进行测量。

RQ = Volume of CO₂ produced ÷ Volume of O₂ consumed

呼吸商 = CO₂ 产生体积 ÷ O₂ 消耗体积

Substrate / 底物	RQ	Interpretation / 解释
Carbohydrate / 碳水化合物	1.0	Equal volumes of CO₂ and O₂
Lipid / 脂质	~0.7	More O₂ consumed than CO₂ released
Protein / 蛋白质	~0.8–0.9	Rarely sole fuel; RQ varies with amino acid composition

If an experimental RQ is >1.0, it suggests anaerobic respiration is also occurring, since CO₂ is produced without O₂ uptake. In a respirometer that absorbs CO₂, any pressure decrease reflects O₂ consumption, allowing RQ determination when a parallel tube without CO₂ absorber is used.

如果实验 RQ > 1.0，则表明存在无氧呼吸，因为产生了 CO₂ 却没有摄取 O₂。在使用能吸收 CO₂ 的呼吸计中，压力的下降反映了 O₂ 的消耗，配合一支不含 CO₂ 吸收剂的平行试管即可测定 RQ。

7. Photosynthesis Rate | 光合作用速率

The rate of photosynthesis can be measured indirectly as the rate of oxygen production, the rate of carbon dioxide uptake or the rate of biomass increase. In WJEC practical work, counting bubbles of oxygen from an aquatic plant such as Elodea is a common proxy, but the true volume of gas produced per unit time should be used for calculations.

光合作用速率可通过产氧速率、二氧化碳吸收速率或生物量增加速率间接测定。在 WJEC 实验操作中，计数水生植物（如伊乐藻）释放的氧气泡是常用替代方法，但计算时应使用单位时间内产生的实际气体体积。

Rate of photosynthesis = Volume of O₂ produced ÷ Time

光合作用速率 = 产生的 O₂ 体积 ÷ 时间

When using a photosynthometer, you may also be asked to calculate the rate of CO₂ uptake or the change in biomass over a growing season. Remember to control or account for respiration that occurs simultaneously. Net photosynthesis is gross photosynthesis minus respiration.

当使用光合作用计时，也有可能要求计算 CO₂ 吸收速率或一个生长季的生物量变化。记得控制或考虑同时进行的呼吸作用。净光合速率等于总光合速率减去呼吸速率。

Unit conversions are often needed: 1 cm³ of O₂ per hour per gram of leaf tissue. Always read the axis labels on graphs carefully — light intensity, temperature and carbon dioxide concentration are limiting factors whose impact can be quantified by the initial slope or plateau level of the rate curve.

经常需要进行单位换算：如每小时每克叶片组织产生多少 cm³ O₂。务必仔细阅读图表的坐标轴标签——光照强度、温度和二氧化碳浓度是限制因素，它们的影响可通过速率曲线的初始斜率或平台高度进行量化。

8. Genetic Probabilities and Hardy–Weinberg | 遗传概率与哈代–温伯格平衡

Monohybrid crosses produce predictable genotypic and phenotypic ratios. Probabilities can be calculated using Punnett squares or the product rule (AND rule) and sum rule (OR rule). For independent assortment, the probability of two independent events both occurring is the product of their individual probabilities.

单基因杂交可产生可预测的基因型比例和表型比例。概率可利用庞纳特方格或乘积法则（AND 法则）及加法法则（OR 法则）进行计算。对于自由组合，两个独立事件同时发生的概率等于各自概率的乘积。

Hardy–Weinberg principles are used to estimate allele frequencies in populations where the assumptions (no mutation, random mating, no gene flow, large population, no natural selection) are met. It is assessed as the ability to calculate allele and genotype frequencies from given data.

哈代–温伯格原理用于估算符合以下假设（无突变、随机交配、无基因流动、群体足够大、无自然选择）的种群中的等位基因频率。考查形式为根据给定数据计算等位基因和基因型频率。

p + q = 1

等位基因频率：p + q = 1

p² + 2pq + q² = 1

基因型频率：p² + 2pq + q² = 1

Where p = frequency of dominant allele, q = frequency of recessive allele. p² = frequency of homozygous dominant, 2pq = heterozygous, q² = homozygous recessive. If a question gives the number or proportion of recessive phenotypes (q²), take the square root to find q, then p = 1 − q. You can then compute heterozygote frequency 2pq — a common examination requirement.

其中 p = 显性等位基因频率，q = 隐性等位基因频率。p² = 纯合显性频率，2pq = 杂合子频率，q² = 纯合隐性频率。若题目给出隐性表型的个数或比例 (q²)，则开平方得到 q，再计算 p = 1 − q。随后可求出杂合子频率 2pq，这是常见的考试要求。

9. Chi-squared Test | 卡方检验

The chi-squared test is a statistical test used to determine whether observed frequencies differ significantly from expected frequencies. In AS WJEC Biology, it is commonly applied to genetics crosses, ecological distributions and behavioural studies when categorical data are collected.

卡方检验是一种用于判断观察频数与期望频数是否存在显著差异的统计检验方法。在 AS WJEC 生物中，它常用于遗传杂交、生态分布和行为研究中收集到的分类数据。

χ² = Σ (O − E)² ÷ E

O = observed frequency, E = expected frequency. For each category, calculate (O − E)²/E and sum all values. The degrees of freedom (df) = number of categories − 1 in tests of goodness of fit, or (rows − 1) × (columns − 1) for contingency tables where independence is tested.

O = 观察频数，E = 期望频数。对每一类别计算 (O − E)²/E 并求和。适合性检验中自由度 (df) = 类别数 − 1；在检验独立性的列联表中，df = (行数 − 1) × (列数 − 1)。

Compare the calculated χ² to a critical value from a table at the 0.05 probability level for the appropriate df. If χ² > critical value, the result is significant: reject the null hypothesis. In genetics, if a 3:1 or 9:3:3:1 ratio is not rejected, the data fit the expected Mendelian ratio.

将计算得到的 χ² 值与在 0.05 概率水平下相应自由度查表所得的临界值进行比较。若 χ² > 临界值，则结果显著：拒绝原假设。在遗传学中，若 3:1 或 9:3:3:1 比例未被拒绝，则数据符合预期的孟德尔比例。

10. Mark–Release–Recapture (Lincoln Index) | 标记重捕法（林肯指数）

The Lincoln index provides an estimate of population size for mobile organisms. It relies on the assumption that marked and unmarked individuals mix randomly and evenly in the population, and that no significant births, deaths, immigration or emigration occur between samples.

林肯指数用于估算活动能力强生物的种群大小。其前提假设为标记与未标记个体在种群中均匀随机混合，且两次取样之间不出现显著的出生、死亡、迁入或迁出。

N = (M × C) ÷ R

种群总数 N = (M × C) ÷ R

Where: N = estimated total population, M = number of individuals initially captured, marked and released, C = total number of individuals caught in the second sample, R = number of marked individuals recaptured in the second sample.

其中：N = 估算的种群总数，M = 初次捕获、标记并释放的个体数，C = 第二次捕捉的总个体数，R = 第二次捕捉中带有标记的个体数。

Worked example: If 40 woodlice are marked and released, and later a sample of 50 contains 10 marked individuals, then N = (40 × 50) ÷ 10 = 200. This is an estimate only; confidence depends on compliance with assumptions. WJEC may ask you to discuss the validity and limitations of the method.

计算示例：若标记并释放了 40 只潮虫，随后在 50 只的样本中发现 10 只带有标记，则 N = (40 × 50) ÷ 10 = 200。这只是一个估计值；其置信度取决于假设的满足程度。WJEC 可能会要求讨论该方法的有效性与局限性。

11. Simpson’s Diversity Index | 辛普森多样性指数

Biodiversity is measured using the Simpson’s index of diversity, which accounts for both species richness (number of species) and evenness (relative abundance of each species). A high value indicates high diversity; the maximum value is 1 minus correction for the number of species, but WJEC uses the 1 − Σ(n/N)² form.

生物多样性用辛普森多样性指数来测定，该指数同时考虑了物种丰富度（物种数目）和均匀度（每个物种的相对多度）。指数值高表明多样性高；最大值接近 1，WJEC 采用 1 − Σ(n/N)² 的形式。

D = 1 − Σ (n/N)²

n = total number of organisms of a particular species, N = total number of organisms of all species. For each species, calculate n/N, square it, sum all these squared values, and subtract from 1. The sum of n/N across all species equals 1.

n = 某一特定物种的个体总数，N = 所有物种的个体总数。对每一物种计算 n/N，平方，然后将所有这些平方值求和，最后从 1 中减去该和。所有物种的 n/N 之和等于 1。

For example, a community with two species, each with 5 out of 10 individuals, gives D = 1 − [(5/10)² + (5/10)²] = 1 − (0.25+0.25) = 0.5. If one species has 9 and the other 1, D = 1 − (0.81+0.01) = 0.18, which is much lower. Simpson’s index is more sensitive to changes in abundant species than rare ones — a point you may be asked to evaluate.

例如，某群落有两个物种，每个物种各有 5 个个体（共 10 个），则 D = 1 − [(5/10)² + (5/10)²] = 1 − (0.25+0.25) = 0.5。若一个物种有 9 个，另一个有 1 个，则 D = 1 − (0.81+0.01) = 0.18，数值低得多。辛普森指数对常见种的变化比对稀有种的变化更敏感——这可能作为评估要点。

Published by TutorHao | Biology Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

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