📚 Year 8 CAIE Biology: Formula & Theorem Quick Reference Handbook | Year 8 CAIE 生物：公式定理速查手册
Welcome to your quick reference guide for Year 8 CAIE Biology. This handbook collects the essential formulas, word equations, and foundational theorems you will encounter. Each principle is presented with a clear statement followed by an explanation, helping you to revise effectively and apply these ideas to exam questions.
欢迎使用 Year 8 CAIE 生物速查手册。本手册汇总了你将遇到的关键公式、文字方程式和基本定理。每条原理都配有清晰的表述和解释，帮助你高效复习，并在考试中灵活运用。
1. The Magnification Formula | 显微镜放大倍数公式
When using a light microscope, the total magnification is found by multiplying the magnifying power of the eyepiece lens by that of the objective lens. This formula is fundamental for all microscope work.
使用光学显微镜时，总放大倍数是目镜放大倍数与物镜放大倍数的乘积。这个公式是所有显微镜工作的基础。
Total magnification = Eyepiece magnification × Objective magnification
In addition, magnification can be defined as the ratio of the size of an image to the size of the real object. This relationship is used when drawing biological specimens to scale.
此外，放大倍数可定义为图像大小与实际对象大小之比。绘制生物标本比例图时会用到这个关系。
Magnification = Image size ÷ Actual size
2. Calculating Actual Size | 计算实际尺寸
Once you know the magnification and the measured size of an image, you can calculate the actual size of the specimen. Rearranging the magnification formula gives a direct expression. Always ensure your units are consistent.
知道放大倍数和图像的测量尺寸后，就可以计算标本的实际大小。变形放大倍数公式就能得到直接表达式。注意单位必须保持一致。
Actual size = Image size ÷ Magnification
iven in micrometres (μm). Use the conversion 1 mm = 1000 μm to switch between units.
显微镜图像常用毫米（mm）测量，但细胞尺寸通常以微米（μm）表示。单位换算使用 1 mm = 1000 μm。
| Measurement | Equivalent |
|---|---|
| 1 centimetre (cm) | 10 mm |
| 1 millimetre (mm) | 1000 μm |
| 1 micrometre (μm) | 1000 nanometres (nm) |
3. The Photosynthesis Word Equation | 光合作用文字方程式
Photosynthesis is the process by which green plants convert light energy into chemical energy stored in glucose. The overall reaction can be summarised as a word equation that also shows the necessary conditions.
光合作用是绿色植物将光能转化为储存在葡萄糖中的化学能的过程。总反应可用文字方程式概括，同时展示必需的条件。
carbon dioxide + water → glucose + oxygen
This reaction only occurs in the presence of light energy and chlorophyll. The glucose produced can be used immediately for respiration, converted to starch for storage, or used to build other organic molecules.
该反应只有在光能和叶绿体存在时才能发生。产生的葡萄糖可立即用于呼吸作用，转化为淀粉储存，或用于构建其他有机分子。
4. Aerobic Respiration Word Equation | 需氧呼吸文字方程式
Aerobic respiration is the process that releases energy from glucose using oxygen. This is the most efficient way for cells to generate ATP for all life functions.
需氧呼吸是利用氧气从葡萄糖中释放能量的过程。这是细胞为一切生命活动生成ATP的最高效方式。
glucose + oxygen → carbon dioxide + water (+ energy)
The 'energy' released is not a chemical substance but is used to power cellular work, such as muscle contraction, active transport, and maintaining body temperature. The carbon dioxide and water are waste products exhaled from the lungs.
释放的“能量”不是一种化学物质，而是用于驱动细胞工作，如肌肉收缩、主动运输和维持体温。二氧化碳和水是呼出的废物。
5. Anaerobic Respiration Equations | 厌氧呼吸方程式
When oxygen is scarce or absent, cells can still release a small amount of energy from glucose through anaerobic respiration. Different organisms produce different end products.
缺氧或无氧时，细胞仍能通过厌氧呼吸从葡萄糖中释放少量能量。不同生物体产生不同的终产物。
In yeast (fermentation):
glucose → ethanol + carbon dioxide (+ some energy)
In human muscle cells during vigorous exercise:
glucose → lactic acid (+ some energy)
Anaerobic respiration yields much less energy per glucose molecule than aerobic respiration. Lactic acid accumulation causes muscle fatigue and must later be oxidised back to harmless products once oxygen is available.
厌氧呼吸每分子葡萄糖产生的能量远少于需氧呼吸。乳酸积累导致肌肉疲劳，必须在供氧后氧化为无害产物。
6. Energy in Food and Calorimetry | 食物中的能量与量热法
The energy content of food can be measured by burning a sample and using the heat released to warm a known mass of water. The temperature rise of the water is then used in a formula.
通过燃烧食物样本并利用释放的热量加热已知质量的水，可以测定食物能量含量。再利用水温升高值代入公式计算。
d by water (J) = mass of water (g) × 4.2 J/g°C × temperature rise (°C)
To find the energy released per gram of food, divide the energy absorbed by the mass of the food burned. This simple calorimetry principle illustrates how we obtain figures like kilojoules per 100 g on nutrition labels.
要得到每克食物释放的能量，用吸收的能量除以燃烧的食物质量。这个简单的量热法原理解释了营养标签上的每100克千焦数是如何得出的。
Energy per gram (J/g) = Energy absorbed (J) ÷ mass of food burned (g)
7. Energy Loss Along Food Chains | 食物链中的能量损失原理
In every ecosystem, energy passes along food chains from producers to consumers. At each trophic level, a large proportion of the energy is lost, mainly as heat from respiration, movement and undigested waste.
在每个生态系统中，能量沿食物链从生产者传递到消费者。每个营养级都有大部分能量损失，主要以呼吸产热、运动和未消化废物的形式散失。
Typically, only about 10% of the energy is transferred from one trophic level to the next.
This low transfer efficiency explains why food chains are rarely more than four or five organisms long. It also means that there are far fewer top predators than producers in a community.
低下的传递效率解释了为什么食物链很少超过四五个生物。它也意味着群落中顶级捕食者的数量远少于生产者。
8. Heart Rate and Pulse Rate Calculation | 心率与脉搏率计算
Heart rate is the number of times the heart beats in one minute. It can be measured by taking the pulse at the wrist or neck. The formula converts a timed count into beats per minute (bpm).
心率是心脏每分钟跳动的次数。可通过测量手腕或颈部的脉搏获得。公式将计时计数转换为每分钟心跳次数（bpm）。
Heart rate (bpm) = Number of beats counted ÷ Time (minutes)
bpm. During exercise, heart rate increases to supply muscles with more oxygen and glucose.
例如，如果在15秒（0.25分钟）内计数17次，心率为17 ÷ 0.25 = 68 bpm。运动时心率上升，为肌肉提供更多氧气和葡萄糖。
9. Breathing Rate Formula | 呼吸频率公式
Breathing rate measures how many times you inhale and exhale in one minute. This simple calculation is important for understanding how the body responds to changing oxygen demands.
呼吸频率测量每分钟吸气和呼气的次数。这个简单计算对于理解身体如何响应变化的氧气需求十分重要。
Breathing rate (breaths/min) = Number of breaths ÷ Time (minutes)
At rest, a typical breathing rate for a Year 8 student is 12–16 breaths per minute. It increases during physical activity to expel extra carbon dioxide and take in more oxygen.
休息时，Year 8学生的典型呼吸频率为每分钟12–16次。体力活动时呼吸频率上升，以排出更多二氧化碳并吸入更多氧气。
10. Surface Area to Volume Ratio in Diffusion | 扩散中的表面积与体积比
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration. The efficiency of diffusion depends heavily on the surface area to volume ratio (SA:V) of the organism or cell.
扩散是粒子从高浓度区域向低浓度区域的净移动。扩散的效率很大程度上取决于生物体或细胞的表面积与体积比（SA:V）。
As size increases, the SA:V ratio decreases → diffusion becomes slower and less effective.
Single-celled organisms like amoeba have a very large SA:V ratio, allowing them to rely on simple diffusion across their surface. Large multicellular organisms need specialised exchange surfaces (e.g. lungs, gills) and transport systems to compensate for their small SA:V ratio.
像变形虫这样的单细胞生物拥有极大的SA:V比，可以完全依靠表面的简单扩散。大型多细胞生物则需要特化的交换面（如肺、鳃）和运输系统来弥补相对较小的SA:V比。
11. Cell Theory – The Fundamental Theorem | 细胞学说——基本定理
Cell theory is one of the central principles of biology. It unifies our understanding of living things and provides the framework for most topics in the subject.
细胞学说是生物学的核心原理之一。它统一了我们对生物的认识，为本学科大多数主题提供了框架。
The three statements of cell theory are:
细胞学说的三句话是：
- All living organisms are composed of one or more cells. / 所有生物体都由一个或多个细胞组成。
- The cell is the basic unit of structure and function in living things. / 细胞是生物体结构和功能的基本单位。
- All cells arise from pre-existing cells by cell division. / 所有细胞均来自已有细胞，通过细胞分裂产生。
This theorem explains why we study cells as the building blocks of life, from bacteria to plants and animals. It also underpins our understanding of growth, repair, and reproduction.
这条定理解释了为什么我们将细胞视为生命的构建块，从细菌到植物和动物。它也支撑着我们对生长、修复和生殖的理解。
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