📚 GCSE WJEC Biology: Formula Summary Handbook | GCSE WJEC 生物：公式汇总手册
This comprehensive handbook brings together every essential formula and calculation required for GCSE WJEC Biology. Mastering these relationships will strengthen your ability to interpret data, tackle mathematical questions with confidence, and secure high marks across topics ranging from cell biology to ecology. Each formula is explained in clear terms, followed by its Chinese translation, so you can memorise and apply them effectively in any exam context.
本手册汇集了 GCSE WJEC 生物学所需的所有重要公式和计算方法。掌握这些关系式将帮助您解读数据、自信应对计算题，并在从细胞生物学到生态学的各个主题中斩获高分。每个公式都用简明的语言加以解释，并附中文翻译，方便您记忆并在任何考试情境中熟练运用。
1. Magnification Formula | 放大倍数公式
Magnification describes how much larger an image appears compared to the real specimen. The formula is central to microscopy work. Remember that both measurements must share the same unit, typically millimetres or micrometres.
放大倍数描述的是图像相比实际标本放大了多少。这个公式是显微镜工作的核心。请记住，两个测量值必须使用相同的单位，通常为毫米或微米。
Magnification = Image size ÷ Actual size
放大倍数 = 图像尺寸 ÷ 实际尺寸
You can rearrange this to find actual size: Actual size = Image size ÷ Magnification. When working with a scale bar, measure its length on the image, read the true length it represents, and calculate magnification from those values.
您可以变形公式求出实际尺寸：实际尺寸 = 图像尺寸 ÷ 放大倍数。使用比例尺时，先测量比例尺在图像上的长度，读取它代表的真实长度，再根据这些数值计算放大倍数。
For example, if a cell image measures 24 mm across and the magnification is ×400, the actual width is 24 ÷ 400 = 0.06 mm, which converts to 60 µm.
例如，如果一个细胞图像测得的宽度为 24 mm，放大倍数为 ×400，那么实际宽度为 24 ÷ 400 = 0.06 mm，换算后为 60 µm。
2. Rate of Enzyme-Controlled Reactions | 酶促反应速率
Enzyme activity is often expressed as the rate of product formation or substrate disappearance over time. The simplest measure is the reciprocal of time for a fixed event, such as the disappearance of a starch spot.
酶活性通常用单位时间内产物的生成量或底物的消失量表示。最简单的量度是完成某个固定事件所需时间的倒数，例如淀粉斑点消失的时间。
Rate = 1 ÷ Time
速率 = 1 ÷ 时间
Alternatively, when a measurable product accumulates, use Rate = Quantity of product formed ÷ Time. Ensure you match units, for instance cm³ of oxygen per minute. This flexible approach supports investigations using catalase, amylase or protease.
另一种方法是当有可测量的产物积累时，使用速率 = 生成的产物量 ÷ 时间。确保单位匹配，例如每分钟产生多少 cm³ 氧气。这种灵活的方式适用于过氧化氢酶、淀粉酶或蛋白酶的研究。
3. Fick’s Law and Diffusion | 菲克定律与扩散
Fick’s Law describes the factors affecting the rate of diffusion across a membrane. It is a qualitative relationship at GCSE level, but you are expected to understand how each variable influences diffusion and to use the proportional form in explanations.
菲克定律描述了影响跨膜扩散速率的因素。在 GCSE 阶段，它是一条定性关系式，但要求您理解每个变量如何影响扩散，并能够用比例形式进行解释。
Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Thickness of membrane
扩散速率 ∝ (表面积 × 浓度差) ÷ 交换面的厚度
A larger surface area, a steeper concentration gradient, and a thinner diffusion distance all increase the rate of diffusion. This law applies directly to gas exchange in the lungs, gills, and leaves, where adaptations maximise these three factors.
更大的表面积、更陡的浓度梯度和更短的扩散距离都会加快扩散速率。该定律直接适用于肺、鳃和叶片中的气体交换，这些器官的适应性特征旨在最大化这三个因素。
4. Surface Area to Volume Ratio | 表面积与体积比
As an organism increases in size, its surface area to volume ratio (SA:V) decreases. This ratio governs how quickly substances can enter or leave cells and explains why large, active organisms need specialised exchange surfaces and transport systems.
随着生物体体积增大，其表面积与体积之比（SA:V）会减小。这个比值决定了物质进出细胞的快慢，也解释了为什么大型活跃生物需要专门的交换表面和运输系统。
SA:V = Surface area ÷ Volume
表面积与体积比 = 表面积 ÷ 体积
Calculate surface area and volume using simple geometry for cubes or spheres. Then simplify the ratio so that the volume number becomes 1, e.g. 6:1 or 1.5:1. An amoeba has a massive SA:V, while a whale has a tiny one, making diffusion alone inadequate for the whale.
可使用简单的几何公式计算立方体或球体的表面积与体积。然后简化比值，使体积数值化为 1，例如 6:1 或 1.5:1。变形虫具有极大的 SA:V，而鲸鱼的 SA:V 极小，因此仅靠扩散无法满足鲸鱼的需求。
5. Photosynthesis Rate | 光合速率
The rate of photosynthesis can be estimated by measuring oxygen production, carbon dioxide uptake, or biomass increase over a set time. The most common class practical uses an aquatic plant and counts oxygen bubbles per minute.
光合速率可通过测量单位时间内的氧气产量、二氧化碳吸收量或生物量的增加来估算。最常见的课堂实践是利用水生植物，记录每分钟产生的氧气气泡数。
Photosynthesis rate = Volume of oxygen produced ÷ Time
光合速率 = 产生的氧气体积 ÷ 时间
When investigating light intensity, you may also calculate the inverse square relationship to understand how distance from a lamp affects photosynthesis rate. The measurement period must be long enough for accuracy, and you should control temperature and carbon dioxide concentration.
在研究光照强度时，您可能还会计算平方反比关系，以理解光源距离如何影响光合速率。测量时间需足够长以保证准确性，同时应控制温度和二氧化碳浓度。
6. Respiration Rate and Respiratory Quotient (RQ) | 呼吸速率与呼吸商
Respiration rate reflects metabolic activity and is measured by the volume of carbon dioxide released or oxygen consumed per unit time. This can be done with a respirometer in living organisms such as seeds or small invertebrates.
呼吸速率反映代谢活性，可通过单位时间释放的二氧化碳量或消耗的氧气量来衡量。这可以用呼吸计对种子或小型无脊椎动物等活体进行测量。
Respiration rate = Volume of CO₂ produced ÷ Time
呼吸速率 = 产生的 CO₂ 体积 ÷ 时间
The Respiratory Quotient (RQ) indicates which substrate is being respired. It is calculated as the ratio of carbon dioxide produced to oxygen consumed over the same period. Values typically lie between 0.7 for lipids and 1.0 for carbohydrates.
呼吸商（RQ）指示被呼吸的底物类型。它等于同一时间内产生的二氧化碳与消耗的氧气之比。其数值一般介于脂质的 0.7 和碳水化合物的 1.0 之间。
RQ = CO₂ produced ÷ O₂ consumed
呼吸商 = 产生的 CO₂ ÷ 消耗的 O₂
7. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle per minute. It is a fundamental measure of circulatory efficiency and increases during exercise to deliver more oxygen and glucose to muscles.
心输出量是一个心室每分钟泵出的血液体积。它是衡量循环效率的基本指标，运动时会增加，以向肌肉输送更多氧气和葡萄糖。
Cardiac output (cm³/min) = Heart rate (beats/min) × Stroke volume (cm³)
心输出量 (cm³/min) = 心率 (次/分) × 每搏输出量 (cm³)
Stroke volume is the volume of blood ejected by a ventricle in one beat. A typical resting cardiac output for an adult is around 5 dm³ per minute. Well-trained athletes achieve larger stroke volumes and can sustain higher cardiac outputs during intense activity.
每搏输出量是一个心室每次搏动射出的血液体积。成年人静息时心输出量典型值约为每分钟 5 dm³。训练有素的运动员每搏输出量更大，在剧烈运动时能维持更高的心输出量。
8. Population Size – Lincoln Index | 种群大小 – 林肯指数
The Lincoln Index is a capture-mark-recapture technique used to estimate the population size of motile organisms. It assumes random mixing, no migration or deaths, and that marks are not lost.
林肯指数是一种标记重捕法，用于估算活动生物种群的大小。假设条件包括随机混合、没有迁移或死亡，并且标记不会脱落。
Population size = (Number in first sample × Number in second sample) ÷ Number of marked recaptured in second sample
种群大小 = (首次样本个体数 × 第二次样本个体数) ÷ 第二次样本中标记个体数
For example, if 30 woodlice are caught and marked, then released, and later 40 woodlice are caught of which 10 are marked, the estimated population is (30 × 40) ÷ 10 = 120 woodlice. Ethical handling and minimal disturbance are essential.
例如，捕获 30 只潮虫并标记后放回，稍后再次捕获 40 只，其中 10 只带有标记，则估算种群大小为 (30 × 40) ÷ 10 = 120 只潮虫。操作中必须遵循伦理规范，尽量降低干扰。
9. Inverse Square Law for Light Intensity | 光强度反平方律
Light intensity decreases with the square of the distance from a point source. This principle is used to investigate the effect of light on photosynthesis and transpiration.
光强度随与点光源距离的平方成反比下降。这一原理常用于研究光照对光合作用和蒸腾作用的影响。
Light intensity ∝ 1 ÷ (Distance)²
光强度 ∝ 1 ÷ (距离)²
If you double the distance, light intensity falls to one quarter, not one half. In laboratory investigations, you may plot rate of photosynthesis against 1/d² to verify the linear relationship, provided other factors like carbon dioxide and temperature are not limiting.
若将距离增加一倍，光强度会降至原来的四分之一，而非一半。在实验室研究中，只要二氧化碳和温度等其他因素未成为限制因素，您可以绘制光合速率与 1/d² 的关系图来验证这种线性关系。
10. Energy Transfer Efficiency and Biomass Transfer | 能量传递效率与生物量传递
In food chains, a large amount of energy is lost between trophic levels through respiration, excretion, and uneaten parts. Efficiency of energy or biomass transfer can be calculated to compare the productivity of different systems.
在食物链中，大量能量会在营养级之间因呼吸、排泄和未被取食的部分而损失。可以计算能量或生物量的传递效率，以比较不同系统的生产力。
Efficiency (%) = (Energy in higher trophic level ÷ Energy in lower trophic level) × 100
效率 (%) = (上营养级能量 ÷ 下营养级能量) × 100
The same formula applies to biomass transfer, with dry mass replacing energy. Typical efficiencies range from 10% to 20%. Shorter food chains are more efficient for human food production because fewer trophic levels mean less cumulative energy loss.
同样的公式也适用于生物量传递，只需将能量替换为干质量即可。典型效率在 10% 到 20% 之间。较短的食品链对人类食品生产来说更为高效，因为营养级越少，累计能量损失就越小。
11. Energy Content of Food | 食物能量含量
The chemical energy stored in food can be estimated by burning a sample and measuring the heat transferred to a known mass of water. This calorimetry experiment links nutrition directly to respiration and energy balance.
食物中储存的化学能可以通过燃烧样品并测量传递给已知质量水的热量来估算。这一量热实验将营养与呼吸以及能量平衡直接联系起来。
Energy per gram (J/g) = (Mass of water (g) × 4.2 J/g°C × Temperature rise (°C)) ÷ Mass of food burned (g)
每克能量 (J/g) = (水的质量 (g) × 4.2 J/g°C × 温度升 (°C)) ÷ 燃烧的食物质量 (g)
The factor 4.2 is the specific heat capacity of water; it is the energy needed to raise 1 g of water by 1°C. Stir the water thoroughly and shield the apparatus from drafts to minimise heat loss. Results are usually quoted in kilojoules per gram (÷1000).
系数 4.2 是水的比热容，即每克水升高 1°C 所需的能量。实验时应充分搅拌水并遮挡气流，以减少热量损失。结果通常以千焦每克（÷1000）表示。
12. Body Mass Index and Waist-to-Hip Ratio | 身体质量指数与腰臀比
Body Mass Index (BMI) and waist-to-hip ratio are simple metrics used to assess whether an individual’s weight is associated with health risks. They link diet, exercise, and lifestyle to the biology of obesity-related diseases.
身体质量指数 (BMI) 和腰臀比是用来评估个体体重是否与健康风险相关的简易指标。它们将饮食、运动与生活方式同肥胖相关疾病的生物学联系起来。
BMI = Mass (kg) ÷ (Height (m))²
BMI = 体重 (kg) ÷ (身高 (m))²
Waist-to-hip ratio = Waist circumference ÷ Hip circumference
腰臀比 = 腰围 ÷ 臀围
A BMI between 18.5 and 24.9 is generally considered healthy. Waist-to-hip ratio provides additional information about fat distribution: a ratio above 0.9 for males and 0.85 for females indicates central obesity, which carries a higher risk of cardiovascular disease and type 2 diabetes.
BMI 在 18.5 至 24.9 之间通常被视为健康。腰臀比提供了关于脂肪分布的额外信息：男性高于 0.9、女性高于 0.85 表明中心性肥胖，这会增加心血管疾病和 2 型糖尿病的风险。
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