📚 Biology Formula & Theorem Quick Reference Handbook | 生物公式定理速查手册
This handbook compiles the essential formulas, theorems, and principles covered in the Year 8 CAIE Biology curriculum. Each entry is presented with a concise English explanation immediately followed by its Chinese translation, helping bilingual learners build a solid foundation in biological concepts and calculations.
本手册汇编了 Year 8 CAIE 生物学课程中的关键公式、定理和原理。每个条目先提供简明英文解释，紧接着给出对应中文翻译，帮助双语学习者牢固掌握生物学概念和相关计算。
1. Magnification Formula | 显微镜放大倍数公式
When using a microscope, the total magnification of the image you see can be calculated using a simple formula. It is important to use the same units for both image size and actual size, typically micrometres (µm) or millimetres (mm).
使用显微镜时，你看到的图像总放大倍数可以通过一个简单公式计算。务必确保图像尺寸和实际尺寸使用相同单位，通常是微米 (µm) 或毫米 (mm)。
Magnification = Image Size ÷ Actual Size
放大倍数 = 图像尺寸 ÷ 实际尺寸
easures 20 mm across at a magnification of ×400, the actual cell size is 20 ÷ 400 = 0.05 mm, which equals 50 µm.
如果已知放大倍数和图像尺寸，你可以变换该公式来求物体的实际大小。例如，一个细胞图像在 400 倍放大下测量跨度为 20 mm，那么实际细胞尺寸为 20 ÷ 400 = 0.05 mm，即 50 µm。
2. Photosynthesis Word Equation | 光合作用文字方程式
Photosynthesis is the process by which green plants make their own food. The overall reaction can be summarised as a word equation that captures the reactants and products. Light energy and chlorophyll are necessary conditions but are not consumed in the reaction itself.
光合作用是绿色植物制造自身养料的过程。总反应可以用一个文字方程式来概括，标明反应物和生成物。光能和叶绿素是必需条件，但本身不参与消耗。
Carbon Dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
This equation tells us that plants absorb carbon dioxide from the air and water from the soil, then using sunlight captured by chlorophyll, they convert them into glucose (a sugar used for energy and growth) and release oxygen as a by‑product.
该方程式表明，植物从空气中吸收二氧化碳，从土壤中吸收水分，然后利用叶绿素捕获的阳光，将它们转化为葡萄糖（用于供能和生长的糖类），并释放出氧气作为副产品。
3. Aerobic Respiration Word Equation | 需氧呼吸文字方程式
Aerobic respiration is the process that releases energy from food in the presence of oxygen. It occurs continuously in the cells of most organisms, including plants and animals. The word equation summarises how glucose and oxygen are used to produce energy.
需氧呼吸是在有氧条件下从食物中释放能量的过程。它在大多数生物体（包括植物和动物）的细胞中持续进行。文字方程式概括了葡萄糖和氧气如何被用来产生能量。
Glucose + Oxygen → Carbon Dioxide + Water
葡萄糖 + 氧气 → 二氧化碳 + 水
Note that energy is released as ATP, which is not shown in this simplified word equation. You can remember that aerobic respiration is essentially the reverse of photosynthesis in terms of raw materials exchanged with the environment.
注意能量以 ATP 形式释放，这个简化的文字方程式并未显示出来。你可以记住，需氧呼吸在与环境交换的物质上，本质上是光合作用的逆过程。
4. Anaerobic Respiration Equations | 无氧呼吸方程式
When oxygen is limited or absent, some organisms can still release energy through anaerobic respiration. The products differ between organisms such as yeast and human muscle cells. These equations are vital for understanding fermentation and muscle fatigue.
当氧气有限或缺乏时，某些生物体仍能通过无氧呼吸释放能量。酵母和人体肌肉细胞等生物产生的产物有所不同。这些方程式对理解发酵和肌肉疲劳至关重要。
In yeast: Glucose → Ethanol + Carbon Dioxide
在酵母中：葡萄糖 → 乙醇 + 二氧化碳
In muscles: Glucose → Lactic Acid
在肌肉中：葡萄糖 → 乳酸
Anaerobic respiration releases much less energy per glucose molecule than aerobic respiration. The build‑up of lactic acid during vigorous exercise causes muscle cramps and eventually needs to be broken down by supplying oxygen.
与需氧呼吸相比，无氧呼吸每个葡萄糖分子释放的能量要少得多。剧烈运动中乳酸的积累会导致肌肉痉挛，最终需要通过供氧来分解。
5. Energy Content of Food (Calorimetry) | 食物能量含量（量热法）
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 experiment assumes that all the heat released is absorbed by the water, allowing the energy per gram to be calculated.
储存在食物中的化学能可以通过燃烧样品并测量已知体积水的温升来估算。该实验假设所有释放的热量都被水吸收，从而计算出每克食物所含的能量。
ergy per gram (J/g) = (Mass of water (g) × 4.2 × Temperature rise (°C)) ÷ Mass of food (g)
每克能量 (J/g) = (水的质量 (g) × 4.2 × 温度上升值 (°C)) ÷ 食物质量 (g)
The constant 4.2 represents the specific heat capacity of water (Joules required to raise 1 g of water by 1 °C). Always ensure the food is completely burned and stir the water gently for a more accurate result.
常数 4.2 表示水的比热容（1 克水升高 1 °C 所需的焦耳数）。为确保结果更准确，要保证食物完全燃烧，并轻轻搅拌水。
6. Population Density | 种群密度
Population density describes how many individuals of a species live in a defined area. It is a useful measurement for ecologists studying habitats and comparing different environments. The formula is straightforward but requires careful counting and measurement.
种群密度描述了在一个确定区域内某个物种的个体数量。这对于研究栖息地和比较不同环境的生态学家来说是一个有用的测量指标。公式简单，但要求仔细计数和测量。
Population Density = Number of Individuals ÷ Area
种群密度 = 个体数量 ÷ 面积
ies per square metre. For aquatic environments, volume is sometimes used instead of area, giving individuals per litre or per cubic metre.
如果你在一个 4 平方米的样地中数出 36 朵雏菊，那么种群密度是 36 ÷ 4 = 9 朵/每平方米。对于水生环境，有时会使用体积而不是面积，单位为每升或每立方米的个体数。
7. Percentage Cover in Quadrat Sampling | 样方调查中的覆盖百分率
When organisms are difficult to count individually, such as grass or moss, ecologists estimate percentage cover using a grid quadrat. The quadrat is divided into smaller squares, and you record whether a particular species touches each square.
当生物难以逐个计数时（比如草或苔藓），生态学家会使用网格样方来估计覆盖百分率。样方被划分成许多小方格，你记录某个物种是否接触到每个方格。
Percentage Cover = (Number of squares covered ÷ Total number of squares) × 100
覆盖百分率 = （被覆盖的方格数 ÷ 总方格数）× 100
If a plant touches 25 out of 100 squares, the percentage cover is 25%. This method reduces bias and gives a quicker estimate than counting hundreds of tiny leaves. Remember that total cover can exceed 100% if plants overlap.
如果一种植物覆盖了 100 个方格中的 25 个，覆盖百分率就是 25%。这种方法能减少偏差，比点数几百片小叶子更快地给出估算值。记住，如果植物有重叠，总覆盖百分率可能超过 100%。
8. The Lock and Key Hypothesis | 锁钥假说
Enzymes are biological catalysts that speed up reactions in living cells. The lock and key model is a theorem that explains how enzymes work. According to this hypothesis, the active site of an enzyme has a specific shape that is complementary to its substrate, just as a key fits a specific lock.
酶是生物催化剂，能加速活细胞中的反应。锁钥模型是一种解释酶如何工作的定理。根据这一假说，酶的活性部位具有与其底物互补的特定形状，就像一把钥匙对一把特定的锁一样。
Enzyme + Substrate → Enzyme‑Substrate Complex → Enzyme + Products
酶 + 底物 → 酶-底物复合物 → 酶 + 产物
This theorem explains enzyme specificity: each enzyme only catalyses one type of reaction. If the shape of the active site is altered by high temperature or extreme pH (denaturation), the substrate can no longer bind and the reaction stops.
该定理解释了酶的专一性：每种酶只催化一种类型的反应。如果活性部位的形状因高温或极端 pH 值而改变（变性），底物就无法与之结合，反应随即停止。
9. Cell Theory | 细胞学说
Cell theory is one of the fundamental unifying theorems in biology. It states three core principles that apply to all living organisms. Understanding these principles helps you grasp the shared nature of life, from bacteria to blue whales.
细胞学说是生物学中统一性的基本定理之一。它陈述了三个适用于所有生物的核心原理。理解这些原理有助于你把握生命的共同本质，从细菌到蓝鲸。
All living things are made up of one or more cells. / 所有生物都由一个或多个细胞构成。
The cell is the basic unit of structure and function in organisms. / 细胞是生物体结构和功能的基本单位。
All cells arise from pre‑existing cells by division. / 所有细胞都通过分裂来自已有的细胞。
This theory was developed in the 19th century by scientists such as Schleiden, Schwann, and Virchow, and it underpins all modern biological study. It also implies that viruses are not considered living because they are not made of cells.
该学说在 19 世纪由施莱登、施旺和魏尔肖等科学家建立，它是所有现代生物学研究的基础。它也意味着病毒不被视为生物，因为它们不是由细胞构成的。
10. Diffusion and Osmosis Principles | 扩散与渗透原理
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration down a concentration gradient. This process is passive and does not require additional energy. Several factors affect the rate of diffusion.
扩散是粒子沿着浓度梯度从高浓度区域向低浓度区域的净移动。这一过程是被动的，不需要额外能量。有几个因素会影响扩散速率。
A simplified relationship shows that the rate of diffusion is proportional to the surface area and the concentration difference, and inversely proportional to the thickness of the exchange surface. Increasing temperature also speeds up diffusion because particles have more kinetic energy.
一个简化的关系表明，扩散速率与表面积和浓度差成正比，与交换面的厚度成反比。温度升高也会加速扩散，因为粒子获得了更多动能。
Osmosis is a special form of diffusion: it is the movement of water molecules from a dilute solution (more water, less solute) to a more concentrated solution (less water, more solute) through a partially permeable membrane. Osmosis is crucial for water uptake in plant roots and for maintaining cell turgor.
渗透是一种特殊的扩散：它是水分子通过部分透性膜，从稀溶液（水多、溶质少）向更浓的溶液（水少、溶质多）的移动。渗透对于植物根部的吸水以及维持细胞膨压至关重要。
11. Heart Rate and Breathing Rate | 心率与呼吸频率
Measuring heart rate and breathing rate provides valuable information about the body’s responses to exercise and rest. These rates are simple to calculate and are often recorded during investigations on fitness or the effects of activity.
测量心率和呼吸频率能为身体在运动和休息时的反应提供有价值的信息。这些频率计算简单，常在关于体能或活动影响的探究中记录。
Heart Rate (beats per minute) = Number of heartbeats ÷ Time (min)
心率 (次/分钟) = 心跳次数 ÷ 时间 (分钟)
Breathing Rate (breaths per minute) = Number of breaths ÷ Time (min)
呼吸频率 (次/分钟) = 呼吸次数 ÷ 时间 (分钟)
During exercise, both rates increase to deliver more oxygen to the muscles and remove carbon dioxide faster. After exercise, measuring how quickly these rates return to resting levels is an indicator of cardiovascular fitness.
运动期间，两项频率都会增加，以便向肌肉输送更多氧气并更快地清除二氧化碳。运动后，测量这些频率恢复到静息水平的速度可作为心血管健康的指标。
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