📚 KS3 CIE Biology: Formula & Theorem Quick Reference Handbook | KS3 CIE 生物：公式定理速查手册
This handbook provides a concise summary of the essential formulas, word equations, and calculation principles covered in the Cambridge Lower Secondary (KS3) Biology curriculum. Mastering these will help you tackle numerical problems, understand biological rates, and interpret experimental data with confidence.
本手册简明总结了剑桥初中（KS3）生物课程中的核心公式、词方程式和计算原理。掌握这些内容将帮助你轻松解决数值问题、理解生物学速率并有信心地解读实验数据。
1. Magnification Formula | 显微镜放大倍数公式
Magnification describes how many times larger an image appears compared to the real specimen. The formula is fundamental for any microscopy work.
放大倍数表示图像比实际样本放大了多少倍，这是所有显微镜工作的基础公式。
Magnification = Image size ÷ Actual size
放大倍数 = 图像大小 ÷ 实际大小
Always ensure image size and actual size are measured in the same units, such as millimetres (mm) or micrometres (µm).
务必确保图像大小和实际大小使用相同的单位，例如毫米（mm）或微米（µm）。
2. Calculating Actual Size of a Specimen | 计算标本的实际大小
Once you know the magnification and can measure the image size, you can rearrange the formula to find the real dimensions of a cell or organism.
一旦知道放大倍数并能够测量图像大小，就可以通过变形公式求出细胞或生物体的真实尺寸。
Actual size = Image size ÷ Magnification
实际大小 = 图像大小 ÷ 放大倍数
For example, if a cell image measures 40 mm and the magnification is ×400, the actual size is 40 mm ÷ 400 = 0.1 mm, which is 100 µm.
例如，如果一个细胞图像测量为 40 mm，放大倍数是 ×400，那么实际大小为 40 mm ÷ 400 = 0.1 mm，即 100 µm。
3. Rate of Reaction (Enzyme Activity) | 反应速率（酶活性）
Biological reactions, such as those catalysed by enzymes, often require measuring how quickly a product forms or a substrate disappears. The general rate formula is widely applicable.
生物反应，如酶催化的反应，常常需要测量产物生成或底物消失的快慢。通用速率公式适用性很强。
Rate of reaction = Change in amount of product (or substrate) ÷ Time taken
反应速率 = 产物（或底物）的变化量 ÷ 所用时间
The change can be measured in mass, volume, number, or any other suitable quantity. Common units include cm³/min or g/s.
变化量可以用质量、体积、数量或其他合适的量来测量。常见单位包括 cm³/min 或 g/s。
4. Rate of Photosynthesis | 光合作用速率
The rate of photosynthesis can be determined by measuring the volume of oxygen produced by a water plant, such as Elodea, over a set period of time.
光合作用速率可以通过测量水生植物（如黑藻）在固定时间内产生的氧气体积来确定。
Rate of photosynthesis = Volume of oxygen produced ÷ Time (min)
光合作用速率 = 产生的氧气体积 ÷ 时间（分钟）
You might also count the number of oxygen bubbles released per minute as a simpler method. Remember that light intensity, carbon dioxide concentration and temperature all affect this rate.
你也可以用每分钟释放的氧气气泡数作为更简单的方法。记住，光照强度、二氧化碳浓度和温度都会影响该速率。
5. Rate of Respiration | 呼吸作用速率
Respiration rate can be measured by tracking the production of carbon dioxide or the consumption of oxygen. A common lab method uses a respirometer or hydrogencarbonate indicator.
呼吸速率可以通过追踪二氧化碳的产生或氧气的消耗来测量。常见的实验方法使用呼吸计或碳酸氢盐指示剂。
Rate of respiration = Volume of CO₂ released (or O₂ consumed) ÷ Time (min)
呼吸速率 = 释放的 CO₂ 体积（或消耗的 O₂ 体积） ÷ 时间（分钟）
In germinating seeds or small invertebrates, this rate indicates metabolic activity. Keep temperature constant for fair comparisons.
在萌发的种子或小型无脊椎动物中，该速率反映了代谢活动。为了公平比较要保持温度恒定。
6. Body Mass Index (BMI) | 身体质量指数（BMI）
Body Mass Index is a useful numerical tool to assess whether a person has a healthy body mass for their height. It links biology with personal health.
身体质量指数是评估一个人体重相对于身高是否健康的有用数值工具，将生物学与个人健康联系起来。
BMI = Body mass (kg) ÷ [Height (m)]²
BMI = 体重（kg） ÷ 身高（m）的平方
A BMI between 18.5 and 24.9 is generally considered healthy. Values outside this range may indicate underweight, overweight or obesity, though the index has limitations for athletes and children.
BMI 在 18.5 到 24.9 之间通常被认为是健康的。超出此范围的数值可能表明体重过轻、超重或肥胖，不过该指数对运动员和儿童有一定的局限性。
7. Energy Content of Food | 食物中的能量含量
The chemical energy stored in food can be estimated by burning a sample and measuring the temperature rise of a known volume of water. This relates to the concept of kilojoules (kJ).
食物中储存的化学能可以通过燃烧样品并测量已知体积水的温度升高来估算，这涉及到千焦（kJ）的概念。
Energy per gram (J/g) = (Mass of water × 4.2 × Temperature rise) ÷ Mass of food sample
每克能量（J/g） = （水的质量 × 4.2 × 温度升高）÷ 食物样品质量
The constant 4.2 J/g/°C is the specific heat capacity of water. This experiment helps compare energy values in different foods, though it gives approximate results due to heat loss.
常数 4.2 J/g/°C 是水的比热容。该实验有助于比较不同食物的能量值，但因为有热量散失，结果只是近似值。
8. Word Equation for Photosynthesis | 光合作用词方程式
Photosynthesis is the process by which plants and algae convert light energy into chemical energy, producing glucose and oxygen. The word equation summarises the reactants and products.
光合作用是植物和藻类将光能转化为化学能、生成葡萄糖和氧气的过程。词方程式总结了反应物和产物。
Carbon dioxide + water → glucose + oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
This reaction takes place in chloroplasts and requires light energy, which is trapped by chlorophyll. It is the foundation of nearly all food chains on Earth.
该反应在叶绿体中进行，需要光能，光能被叶绿素捕获。它是地球上几乎所有食物链的基础。
9. Word Equation for Aerobic Respiration | 有氧呼吸词方程式
Aerobic respiration releases energy from glucose using oxygen. It occurs continuously in the cells of most organisms, supplying energy for all life processes.
有氧呼吸利用氧气从葡萄糖中释放能量。它在大多数生物体的细胞中持续进行，为所有生命过程提供能量。
Glucose + oxygen → carbon dioxide + water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
The energy released is used to synthesise ATP, which powers muscle contraction, cell division, active transport and maintaining body temperature in warm-blooded animals.
释放的能量用于合成 ATP，ATP 为肌肉收缩、细胞分裂、主动运输和恒温动物的体温维持提供动力。
10. Anaerobic Respiration in Yeast | 酵母的厌氧呼吸
When oxygen is absent, yeast cells switch to anaerobic respiration, producing ethanol and carbon dioxide. This process is economically important in baking and brewing.
在缺乏氧气时，酵母细胞转为厌氧呼吸，产生乙醇和二氧化碳。这个过程在烘焙和酿造中具有重要的经济价值。
Glucose → ethanol + carbon dioxide (+ a little energy)
葡萄糖 → 乙醇 + 二氧化碳（+ 少量能量）
Fermentation by yeast causes bread dough to rise due to CO₂ bubbles, and it produces the alcohol in beer and wine. The energy yield is much lower than aerobic respiration.
酵母的发酵产生了 CO₂ 气泡，使面团膨胀，同时制造出啤酒和葡萄酒中的酒精。它的能量产出远低于有氧呼吸。
11. Anaerobic Respiration in Muscles | 肌肉的厌氧呼吸
During vigorous exercise, human muscle cells may not receive enough oxygen, so they respire anaerobically for a short time, producing lactic acid.
在剧烈运动期间，人体肌肉细胞可能无法获得足够的氧气，因此它们会在短时间内进行厌氧呼吸，产生乳酸。
Glucose → lactic acid (+ a little energy)
葡萄糖 → 乳酸（+ 少量能量）
Lactic acid build-up causes muscle fatigue and cramps. After exercise, extra oxygen is needed to break down lactic acid in the liver – this is known as the oxygen debt.
乳酸的积累会导致肌肉疲劳和痉挛。运动后，需要额外的氧气在肝脏中分解乳酸——这被称为氧债。
12. Population Density and Percentage Change | 种群密度与百分比变化
Ecologists often estimate population size in a habitat. Population density describes how crowded a species is in a given area, while percentage change allows monitoring of population trends.
生态学家常会估算栖息地中种群的大小。种群密度描述了某一物种在给定区域中的拥挤程度，而百分比变化可用于监测种群变化趋势。
Population density = Number of individuals ÷ Area (m² or km²)
种群密度 = 个体数量 ÷ 面积（m² 或 km²）
Percentage change = [(Final value − Initial value) ÷ Initial value] × 100%
百分比变化 = [（最终值 − 初始值）÷ 初始值] × 100%
These tools help track whether a population is growing, declining or stable, and they are central to conservation and field studies.
这些工具有助于追踪种群是在增长、减少还是保持稳定，在保护和野外研究中居于核心地位。
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