📚 WJEC Year 11 Biology: Formula & Theorem Quick Reference Handbook | WJEC 11年级生物：公式定理速查手册
This quick reference handbook brings together all the essential formulas, equations, and key principles you need to master for WJEC Year 11 Biology. It is designed to help you revise efficiently, practise calculations, and understand the core theorems that underpin topics from cell biology to ecology. Keep it handy while working through past papers or reviewing your class notes.
本速查手册汇集了WJEC 11年级生物课程中所有必须掌握的重要公式、方程式和核心原理。它旨在帮助你高效复习、练习计算，并理解从细胞生物学到生态学等主题背后的基本定理。在做历年真题或复习课堂笔记时，随时翻阅它吧。
1. Magnification Formula | 放大倍数公式
ide; Actual size. Remember to convert all measurements to the same unit before calculation. If you are given the magnification and one length, you can rearrange the equation to find the missing value. In microscopy, units are often converted between millimetres (mm), micrometres (μm), and nanometres (nm). Note that 1 mm = 1000 μm and 1 μm = 1000 nm.
放大倍数是指图像的尺寸相较于物体实际尺寸被放大的倍数。公式为：放大倍数 = 图像尺寸 ÷ 实际尺寸。计算前记得将所有测量值转换成相同的单位。如果已知放大倍数和其中一个长度，可以通过变形公式求出未知值。在显微镜观察中，常用单位包括毫米(mm)、微米(μm)和纳米(nm)。注意 1 mm = 1000 μm，1 μm = 1000 nm。
M = I ÷ A where M = magnification, I = image size, A = actual size
M = I ÷ A 其中 M 为放大倍数，I 为图像尺寸，A 为实际尺寸
2. Rate of Enzyme-Controlled Reactions | 酶控反应速率
A common method is to record the volume of gas produced (e.g., oxygen from catalase breaking down hydrogen peroxide) and use the formula: Rate = Change in volume ÷ Time. The units could be cm³/s or cm³/min. You may also calculate the rate at a specific point on a graph by drawing a tangent.
酶控反应的速率可以通过测量在给定时间内产物出现的速度或底物消失的速度来计算。常用方法是记录产生的气体体积（例如过氧化氢酶分解过氧化氢产生的氧气），并使用公式：速率 = 体积变化量 ÷ 时间。单位可以是 cm³/s 或 cm³/min。你也可以通过在曲线图上画切线来计算某一特定时刻的速率。
Rate = Change in product (or substrate) ÷ Time
速率 = 产物（或底物）变化量 ÷ 时间
3. Photosynthesis Rate | 光合作用速率
n dioxide. The formula follows the same pattern as reaction rates: Photosynthesis rate = Volume of O&sub2; produced ÷ Time. Factors such as light intensity, carbon dioxide concentration, and temperature affect this rate. Remember that the rate often levels off when another factor becomes limiting.
光合作用速率可以通过测量水生植物单位时间内产生的氧气体积，或追踪二氧化碳的吸收量来估算。其公式遵循与反应速率相同的模式：光合作用速率 = 产生的 O&sub2; 体积 ÷ 时间。光照强度、二氧化碳浓度和温度等因素都会影响这一速率。请记住，当另一个因素成为限制因素时，速率往往会趋于平稳。
Photosynthesis rate = Oxygen volume ÷ Time (e.g., cm³/min)
光合作用速率 = 氧气体积 ÷ 时间 （例如 cm³/min）
4. Cardiac Output Equation | 心输出量公式
(volume of blood pumped out per beat). The equation is: Cardiac output = Heart rate × Stroke volume. A typical resting value for an adult is around 5 litres per minute. During exercise, both heart rate and stroke volume can increase, raising cardiac output significantly.
心输出量是指心脏每分钟泵出的血液体积。它取决于心率（每分钟心跳次数）和每搏输出量（每次心跳泵出的血液体积）。公式为：心输出量 = 心率 × 每搏输出量。成年人静息时的典型数值约为每分钟5升。运动时，心率和每搏输出量都会增加，从而显著提高心输出量。
CO = HR × SV (CO in litres/min, HR in beats/min, SV in litres/beat)
CO = HR × SV （CO 单位为升/分钟，HR 单位为次/分钟，SV 单位为升/次）
5. Body Mass Index (BMI) | 身体质量指数
(kg) ÷ [Height (m)]². For example, a person weighing 70 kg and 1.75 m tall has a BMI of 70 ÷ (1.75 × 1.75) ≈ 22.9. This value alone does not distinguish between muscle and fat, but it is widely used in epidemiology and health assessments.
身体质量指数是一种筛查工具，用于将个体分类为体重过轻、健康体重、超重或肥胖。公式为：BMI = 体重(kg) ÷ [身高(m)]²。例如，一个体重70公斤、身高1.75米的人，其 BMI = 70 ÷ (1.75 × 1.75) ≈ 22.9。该数值本身无法区分肌肉与脂肪，但在流行病学和健康评估中被广泛使用。
BMI = Mass (kg) ÷ [Height (m)]²
BMI = 体重(kg) ÷ [身高(m)]²
6. Percentage Change in Mass (Osmosis) | 质量变化百分比（渗透作用）
s results and makes comparisons fairer, especially when initial masses differ. The formula is: Percentage change = (Final mass − Initial mass) ÷ Initial mass × 100. A positive value means the tissue gained mass (water entered by osmosis); a negative value indicates water loss.
在研究渗透作用时，你经常要计算浸泡在不同溶液中的植物组织质量变化百分比。这样做可以标准化结果，使比较更加公平，特别是当初始质量不同时。公式为：质量变化百分比 = (最终质量 − 初始质量) ÷ 初始质量 × 100。正值表示组织质量增加（水通过渗透进入）；负值则表示水分流失。
% Change = (Final mass − Initial mass) ÷ Initial mass × 100%
质量变化百分比 = (最终质量 − 初始质量) ÷ 初始质量 × 100%
7. Genetic Crosses & Probability | 遗传杂交与概率
Mendel's laws form the basis of inheritance studies. The law of segregation states that each individual has two alleles for a gene, which separate during gamete formation so each gamete carries only one allele. The law of independent assortment explains that alleles of different genes are distributed to gametes independently. You can predict the outcome of monohybrid crosses using a Punnett square. The probability of a particular genotype or phenotype appearing in offspring is expressed as a fraction, percentage, or ratio. For a heterozygous cross (Aa × Aa), the expected genotypic ratio is 1 AA : 2 Aa : 1 aa, and the phenotypic ratio is 3 : 1 if the allele is completely dominant.
孟德尔定律构成了遗传研究的基础。分离定律指出，每个个体对于某个基因都有两个等位基因，在配子形成过程中它们会分离，因此每个配子只携带一个等位基因。自由组合定律说明，不同基因的等位基因独立地分配到配子中。你可以使用庞纳特方格预测单基因杂交的结果。后代出现特定基因型或表型的概率可以表示为分数、百分比或比例。对于杂合子杂交（Aa × Aa），预期的基因型比例为 1 AA : 2 Aa : 1 aa，如果等位基因完全显性，则表型比例为 3 : 1。
ype = (Number of squares showing that genotype) ÷ 4 (in a 2×2 Punnett square)
某种基因型的概率 = (显示该基因型的方格数) ÷ 4（在 2×2 庞纳特方格中）
8. Efficiency of Biomass Transfer | 生物量传递效率
gh respiration, egestion, and excretion. Efficiency of biomass transfer is calculated as: Efficiency = (Biomass transferred to the next trophic level ÷ Biomass available at the previous level) × 100. This value is rarely above 10% lains why food chains are usually short and why pyramid-shaped diagrams of biomass appear.
在食物链中，一个营养级摄入的生物量中，只有一小部分能转化为下一个营养级的新生物量。大部分通过呼吸作用、排遗和排泄而损失。生物量传递效率的计算公式为：效率 = （传递到下一营养级的生物量 ÷ 上一营养级可用的生物量） × 100。该数值通常不超过10%，这就解释了为什么食物链一般较短，以及为何会出现金字塔形的生物量图。
Efficiency (%) = (Biomass&sub2; ÷ Biomass&sub1;) × 100
效率(%) = （生物量&sub2; ÷ 生物量&sub1;） × 100
9. Surface Area to Volume Ratio | 表面积与体积比
rfaces. For a cube, surface area = 6 × (side length)² and volume = (side length)³. As an object increases in size, its volume grows faster than its surface area, so the SA:V ratio decreases. This principle dictates the efficiency of diffusion, heat exchange, and transport. Organisms like alveoli, villi, and root hair cells have adaptations that maximise surface area for exchange.
表面积与体积比（SA:V）是解释为什么细胞是微观的、以及为什么较大生物需要特化的交换表面的关键概念。对于立方体，表面积 = 6 × (边长)²，体积 = (边长)³。随着物体尺寸增大，其体积增长快于表面积增长，因此 SA:V 比值下降。这一原理制约着扩散、热交换和运输的效率。像肺泡、绒毛和根毛细胞等结构都具有增大交换表面积的特化适应特征。
ace area ÷ Volume (units often μm²/μm³ = μm−¹)
SA:V 比值 = 表面积 ÷ 体积 （单位常为 μm²/μm³ = μm−¹;）
10. Bacterial Population Growth | 细菌群体增长
calculate the number of bacteria after a given period. The formula is: Number of bacteria = Initial number × 2𝕟, where n is the number of generations (divisions). To find n, divide the total time by the mean division time. For instance, starting with 1 bacterium with a division time of 20 minutes, after 2 hours (6 divisions) there will be 1 × 2&sup6; = 64 bacteria.
细菌通过二分裂繁殖，在条件适宜时呈现指数增长。如果知道平均分裂时间，你就能计算经过一段时间后的细菌数量。公式为：细菌数量 = 初始数量 × 2𝕟，其中 n 为代数（分裂次数）。要计算 n，用总时间除以平均分裂时间。例如，从1个细菌开始，分裂时间为20分钟，2小时后（6次分裂），数量为 1 × 2&sup6; = 64 个细菌。
N = N&sub0; × 2𝕟 where n = total time ÷ mean division time
N = N&sub0; × 2𝕟 其中 n = 总时间 ÷ 平均分裂时间
11. Population Estimation (Capture-Recapture) | 种群数量估算（标记重捕法）
. Later, a second sample is captured, and the number of marked individuals in it is recorded. The population size is estimated using the Lincoln Index: Population size = (Number of animals in first sample × Number in second sample) ÷ Number of marked animals recaptured. This method assumes that marked individuals mix randomly, marks are not lost, and there is no significant migration or mortality between samples.
为了估算移动动物种群的大小，生态学家采用标记重捕法。首先捕捉一份样本，标记后释放。随后再捕捉第二份样本，并记录其中带有标记的个体数。种群数量通过林肯指数估算：种群数量 = （第一次样本个体数 × 第二次样本个体数） ÷ 重捕的标记个体数。该方法假定标记个体随机混合，标记不会丢失，且两次采样之间没有显著的迁入、迁出或死亡。
Population size (N) = (M × C) ÷ R
种群数量 (N) = (M × C) ÷ R
total number captured in second sample; R = number of marked individuals in second sample.
M = 第一次捕捉并标记的个体数；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。
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