📚 IGCSE CCEA Biology: Formula Summary Handbook | IGCSE CCEA 生物：公式汇总手册
This handbook collects all the essential mathematical formulas and calculations you need for IGCSE CCEA Biology. Every formula is presented with a clear explanation of what each symbol means, followed by a straightforward example. Using these formulas correctly in practical questions and data analysis tasks is vital for achieving top marks.
本手册汇集了 IGCSE CCEA 生物学所需的所有基本数学公式和计算方法。每个公式都附有清晰说明，解释每个符号的含义，并配有一个简单的例子。在实验题和数据分析题中正确运用这些公式，对于获得高分至关重要。
1. Magnification Formula | 放大倍数公式
Magnification is how many times larger an image appears compared to the object’s real size. The formula is: Magnification = Image size ÷ Actual size of object. Always make sure both measurements are in the same units.
放大倍数是图像比物体实际尺寸大多少倍。公式为：放大倍数 = 图像尺寸 ÷ 物体实际尺寸。务必确保两个测量值使用相同的单位。
Magnification = I ÷ A
- I = image size (measured with a ruler, in mm, µm, etc.)
- A = actual size of the specimen (usually given or calculated)
- I = 图像尺寸（用尺子测量，单位如 mm、µm 等）
- A = 标本的实际尺寸（通常题目给出或通过计算得出）
If an image of a cell is 60 mm wide and its real width is 0.06 mm, then Magnification = 60 ÷ 0.06 = ×1000.
如果一个细胞的图像宽度是 60 毫米，真实宽度是 0.06 毫米，那么放大倍数 = 60 ÷ 0.06 = ×1000。
2. Actual Size Formula | 实际尺寸公式
To find the real size of a specimen when magnification and image size are known, rearrange the formula: Actual size = Image size ÷ Magnification. This is often needed when using micrographs.
当知道放大倍数和图像尺寸时，求标本的实际尺寸可以变形公式：实际尺寸 = 图像尺寸 ÷ 放大倍数。使用显微照片时经常需要这个计算。
A = I ÷ M
If a mitochondrion in an electron micrograph measures 30 mm across and the magnification is ×50 000, actual size = 30 mm ÷ 50 000 = 0.0006 mm = 0.6 µm. Remember to convert units correctly: 1 mm = 1000 µm.
如果一张电子显微照片中线粒体的宽度是 30 毫米，放大倍数为 ×50 000，那么实际尺寸 = 30 mm ÷ 50 000 = 0.0006 mm = 0.6 µm。记得正确换算单位：1 毫米 = 1000 微米。
3. Percentage Change | 百分比变化
Percentage change is used to compare a final value to an initial value, for example in osmosis experiments measuring mass change of potato cylinders. The formula is:
百分比变化用于比较最终值与初始值，例如在渗透实验中测量土豆条的质量变化。公式如下：
Percentage change = (Final value − Initial value) ÷ Initial value × 100%
A negative result means a decrease. If a potato chip had an initial mass of 5.2 g and a final mass of 4.8 g, percentage change = (4.8 − 5.2) ÷ 5.2 × 100% = −7.69%, showing water loss.
负值表示减少。如果一根土豆条初始质量为 5.2 克，最终质量为 4.8 克，百分比变化 = (4.8 − 5.2) ÷ 5.2 × 100% = −7.69%，表示水分流失。
4. Rate of Reaction | 反应速率
Rates appear in enzyme-controlled reactions, photosynthesis and respiration investigations. The basic rate formula is:
速率出现在酶控制反应、光合作用和呼吸作用的研究中。基本速率公式是：
Rate = Change in quantity ÷ Time taken
For example, if an enzyme produces 24 cm³ of oxygen in 5 minutes, rate = 24 ÷ 5 = 4.8 cm³/min. Always include units.
例如，如果一种酶在 5 分钟内产生 24 立方厘米氧气，速率 = 24 ÷ 5 = 4.8 cm³/min。一定要带上单位。
5. Respiratory Quotient (RQ) | 呼吸商
The respiratory quotient indicates which substrate is being respired. It is used in respirometer experiments. The formula compares volumes of carbon dioxide produced to oxygen consumed:
呼吸商可以指示正在呼吸的底物类型。它用于呼吸计实验。公式比较产生的二氧化碳体积与消耗的氧气体积：
RQ = Volume of CO₂ produced ÷ Volume of O₂ consumed
For aerobic respiration of glucose, RQ = 6 ÷ 6 = 1.0. For lipids, RQ is about 0.7; for proteins, about 0.9. No units, as it is a ratio.
对于葡萄糖的有氧呼吸，RQ = 6 ÷ 6 = 1.0。脂类的 RQ 约为 0.7；蛋白质约为 0.9。它是一个比值，没有单位。
6. Energy Content of Food | 食物中的能量含量
The energy released when food is burned can be found using calorimetry. If the food is burned to heat water, the energy transferred is calculated as:
燃烧食物释放的能量可以通过量热法求得。如果燃烧食物加热水，转移的能量计算如下：
Energy (J) = mass of water (g) × 4.2 J/g°C × temperature rise (°C)
Then, energy per gram of food = Total energy (J) ÷ mass of food burned (g). For example, 0.5 g of a biscuit heated 20 g of water from 22 °C to 38 °C. Energy = 20 × 4.2 × 16 = 1344 J. Energy per gram = 1344 ÷ 0.5 = 2688 J/g.
那么，每克食物的能量 = 总能量 (J) ÷ 燃烧的食物质量 (g)。例如，0.5 克饼干使 20 克水从 22 °C 升至 38 °C。能量 = 20 × 4.2 × 16 = 1344 J。每克能量 = 1344 ÷ 0.5 = 2688 J/g。
7. Body Mass Index (BMI) | 身体质量指数
BMI is a simple estimate of body fat based on height and mass. It is one indicator of health.
BMI 是根据身高和体重估算体脂的简便方法，是健康指标之一。
BMI = Body mass (kg) ÷ (Height (m))²
A person of mass 70 kg and height 1.75 m has BMI = 70 ÷ (1.75)² = 70 ÷ 3.0625 ≈ 22.9 kg/m², which falls within the healthy weight range (18.5–24.9).
一个体重 70 千克、身高 1.75 米的人，BMI = 70 ÷ (1.75)² = 70 ÷ 3.0625 ≈ 22.9 kg/m²，属于健康体重范围（18.5–24.9）。
8. Cardiac Output and Stroke Volume | 心输出量与每搏输出量
Heart activity can be described by these linked formulas. Cardiac output is the volume of blood pumped by the heart per minute.
心脏活动可以用这些相互关联的公式来描述。心输出量是心脏每分钟泵出的血液体积。
Cardiac output (cm³/min) = Stroke volume (cm³/beat) × Heart rate (beats/min)
Stroke volume is the volume pumped out by the left ventricle in one beat. If heart rate is 75 bpm and stroke volume is 70 cm³, cardiac output = 75 × 70 = 5250 cm³/min.
每搏输出量是左心室每次心跳泵出的血液体积。如果心率为 75 次/分钟，每搏输出量为 70 立方厘米，心输出量 = 75 × 70 = 5250 cm³/min。
9. Ventilation Rate | 通气速率
Ventilation rate (or minute ventilation) is the volume of air moved into and out of the lungs per minute. It can be calculated using tidal volume and breathing rate.
通气速率（或每分钟通气量）是每分钟进出肺部的空气体积。可以用潮气量和呼吸频率计算。
Minute ventilation (dm³/min) = Tidal volume (dm³/breath) × Breathing rate (breaths/min)
If a person breathes 16 times per minute and each breath has a tidal volume of 0.5 dm³, minute ventilation = 16 × 0.5 = 8.0 dm³/min.
如果一个人每分钟呼吸 16 次，每次潮气量为 0.5 立方分米，那么每分钟通气量 = 16 × 0.5 = 8.0 dm³/min。
10. Surface Area to Volume Ratio | 表面积与体积之比
The surface area : volume ratio is crucial in explaining adaptations for exchange. It is not a single fixed formula but a comparison you must calculate and simplify.
表面积与体积的比值对于解释交换适应至关重要。它不是一个固定的公式，而是一个需要计算并简化的比较。
For a cube of side length 2 cm, surface area = 6 × (2)² = 24 cm², volume = (2)³ = 8 cm³, so ratio = 24:8 = 3:1. Smaller organisms have larger surface area : volume ratios, which aids diffusion.
对于一个边长为 2 厘米的立方体，表面积 = 6 × (2)² = 24 cm²，体积 = (2)³ = 8 cm³，因此比值 = 24:8 = 3:1。较小的生物具有较大的表面积与体积比，这有利于扩散。
11. Percentage Difference and Concentration in Dilutions | 百分比差异与稀释浓度
When comparing two values, percentage difference can help quantify accuracy. For dilutions, you may need to find the new concentration after adding solvent.
比较两个数值时，百分比差异有助于量化准确性。对于稀释，你可能需要求出添加溶剂后的新浓度。
Percentage difference = |Value₁ − Value₂| ÷ Average of values × 100%
For a simple dilution using a ratio, concentration after dilution = (Original concentration × Original volume) ÷ Total new volume. If you add 1 cm³ of 0.5% glucose to 4 cm³ of water, new concentration = (0.5 × 1) ÷ 5 = 0.1%.
对于简单的按比例稀释，稀释后浓度 = (原浓度 × 原体积) ÷ 新总体积。如果你把 1 立方厘米 0.5% 的葡萄糖溶液加入 4 立方厘米水中，新浓度 = (0.5 × 1) ÷ 5 = 0.1%。
12. Simpson’s Diversity Index (extension) | 辛普森多样性指数（拓展）
Although often covered in more detail at A level, some IGCSE CCEA courses introduce a simple measure of biodiversity such as the proportion of a species or Simpson index formula: D = 1 − Σ (n/N)². Here n = number of individuals of a particular species, N = total number of individuals of all species. A higher value indicates greater diversity.
虽然在 A Level 中会更详细地涉及，但一些 IGCSE CCEA 课程会引入简单的生物多样性测量方法，如物种比例或辛普森指数公式：D = 1 − Σ (n/N)²。其中 n = 某一特定物种的个体数，N = 所有物种的总个体数。数值越高，多样性越大。
For example, in a sample with 10 daisies, 5 buttercups and 5 clovers, N=20. D = 1 − [ (10/20)² + (5/20)² + (5/20)² ] = 1 − [0.25 + 0.0625 + 0.0625] = 0.625.
例如，在一个样本中有 10 株雏菊、5 株金凤花和 5 株三叶草，N=20。D = 1 − [ (10/20)² + (5/20)² + (5/20)² ] = 1 − [0.25 + 0.0625 + 0.0625] = 0.625。
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