📚 KS3 CAIE Biology: Quick Reference Handbook of Formulas and Theorems | KS3 CAIE 生物：公式定理速查手册
This handbook brings together the essential formulas, equations, and key scientific principles you will encounter in the KS3 CAIE Biology course. Whether you are revising cell structure, mastering the equations of life processes, or recalling the laws of inheritance, this quick reference provides clear statements and balanced equations in one place. Use it to reinforce your understanding and to check your knowledge before tests.
本手册汇集了你在 KS3 CAIE 生物课程中将遇到的基本公式、方程和关键科学原理。无论你是在复习细胞结构、掌握生命过程的方程式，还是在回顾遗传规律，这份速查资料都为你提供了清晰的表述和配平的方程式。用它来巩固理解，并在测验前检查你的知识。
1. The Cell Theory | 细胞学说
All living organisms are composed of cells, and all cells arise from pre-existing cells. This is the foundation of biology.
所有生物体都由细胞构成，且所有细胞都来自已存在的细胞。这是生物学的基础。
The three statements of cell theory are: (1) All living things are made up of cells. (2) The cell is the basic unit of structure and function in living things. (3) All cells come from other cells by cell division.
细胞学说的三个要点是：(1) 所有生物都由细胞构成。(2) 细胞是生物体结构和功能的基本单位。(3) 所有细胞都通过细胞分裂从其他细胞产生。
2. Magnification Formula | 放大倍数公式
To calculate the magnification of a drawing, photograph or microscope image, use the relationship between image size and actual size.
要计算绘图、照片或显微镜图像的放大倍数，请使用图像尺寸与实际尺寸之间的关系。
Magnification = Image size ÷ Actual size
放大倍数 = 图像尺寸 ÷ 实际尺寸
Rearrange it to find actual size:
变换公式可求实际尺寸：
Actual size = Image size ÷ Magnification
实际尺寸 = 图像尺寸 ÷ 放大倍数
- Image size is measured with a ruler in mm or µm.
- 图像尺寸用尺子以毫米或微米为单位测量。
- Keep the units the same for both sizes.
- 两个尺寸的单位要保持一致。
3. Photosynthesis Equation | 光合作用方程式
Photosynthesis is the process by which green plants make glucose using light energy. The balanced word and chemical equations are fundamental.
光合作用是绿色植物利用光能制造葡萄糖的过程。配平的文字方程式和化学方程式是基础。
Word equation:
文字方程式：
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
条件：光照和叶绿体 (in the presence of light and chlorophyll)。
Chemical equation:
化学方程式：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Light energy is absorbed by chlorophyll inside chloroplasts. The rate of photosynthesis is affected by light intensity, carbon dioxide concentration and temperature.
光能被叶绿体中的叶绿素吸收。光合作用的速率受光照强度、二氧化碳浓度和温度的影响。
4. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration releases energy from glucose using oxygen. It occurs in the mitochondria of cells.
有氧呼吸利用氧气从葡萄糖中释放能量。它发生在细胞的线粒体中。
Word equation:
文字方程式：
Glucose + Oxygen → Carbon dioxide + Water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
Chemical equation:
化学方程式：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Energy is released in the form of ATP, which is used for muscle contraction, growth, and keeping warm.
能量以 ATP 的形式释放，用于肌肉收缩、生长和维持体温。
5. Anaerobic Respiration (Yeast and Muscle) | 无氧呼吸（酵母和肌肉）
When oxygen is absent, organisms can still release a small amount of energy through anaerobic respiration.
当缺氧时，生物体仍可通过无氧呼吸释放少量能量。
In yeast and some plants:
在酵母和某些植物中：
Glucose → Ethanol + Carbon dioxide
葡萄糖 → 乙醇 + 二氧化碳
In animal muscles during vigorous exercise:
在剧烈运动时的动物肌肉中：
Glucose → Lactic acid
葡萄糖 → 乳酸
Anaerobic respiration produces much less ATP than aerobic respiration. The accumulation of lactic acid causes muscle fatigue and cramps.
无氧呼吸产生的 ATP 远少于有氧呼吸。乳酸的积累会导致肌肉疲劳和抽筋。
6. Enzyme Activity and Lock-and-Key Model | 酶活性与锁钥模型
Enzymes are biological catalysts that speed up chemical reactions. The lock-and-key model describes how a substrate fits into the active site of an enzyme.
酶是加速化学反应的生物催化剂。锁钥模型描述了底物如何嵌入酶的活性位点。
No universal formula describes enzyme rate, but the key principles are:
没有通用公式描述酶促反应速率，但关键原则是：
- Each enzyme has an optimum temperature and pH. Above the optimum, the enzyme denatures and the active site changes shape.
- 每种酶都有一个最适温度和最适 pH。超过最适值，酶会变性，活性位点形状改变。
- The rate of reaction increases with substrate concentration up to a saturation point, after which all active sites are occupied (Vmax).
- 反应速率随底物浓度增加而加快，直至饱和点，之后所有活性位点都被占据（Vmax）。
Enzymes are used in digestion: amylase breaks down starch into maltose; protease breaks down proteins into amino acids; lipase breaks down lipids into fatty acids and glycerol.
酶用于消化过程：淀粉酶将淀粉分解为麦芽糖；蛋白酶将蛋白质分解为氨基酸；脂肪酶将脂质分解为脂肪酸和甘油。
7. Diffusion, Osmosis and Active Transport | 扩散、渗透和主动运输
Substances move across cell membranes by three main processes. No single equation governs them at KS3, but understanding the direction and energy requirements is vital.
物质通过三种主要方式穿过细胞膜。在 KS3 阶段没有单一方程式主导它们，但理解方向和能量需求至关重要。
| Process | Direction | Energy |
| Diffusion | High to low concentration | No energy (passive) |
| Osmosis (water only) | Across a partially permeable membrane, from high water potential to low water potential | No energy (passive) |
| Active transport | Low to high concentration | Energy from ATP (active) |
| 过程 | 方向 | 能量 |
| 扩散 | 高浓度到低浓度 | 无需能量（被动） |
| 渗透（仅水） | 穿过部分透性膜，从高水势到低水势 | 无需能量（被动） |
| 主动运输 | 低浓度到高浓度 | 来自 ATP 的能量（主动） |
8. Gas Exchange and Breathing Mechanics | 气体交换与呼吸机制
The respiratory system ensures oxygen enters the blood and carbon dioxide is removed. Lung volumes follow simple relationships.
呼吸系统确保氧气进入血液，二氧化碳被排出。肺容量遵循简单的关系。
Inhaled air: ~21% O₂, 0.04% CO₂
吸入气：约 21% O₂，0.04% CO₂
Exhaled air: ~16% O₂, 4% CO₂
呼出气：约 16% O₂，4% CO₂
During inhalation, the diaphragm contracts and moves down, the intercostal muscles contract, the rib cage moves up and out, and lung volume increases, lowering pressure so air rushes in.
吸气时，膈肌收缩并下移，肋间肌收缩，胸腔上提外扩，肺容积增大，压力降低，空气涌入。
During exhalation, the diaphragm relaxes and moves up, the intercostal muscles relax, the rib cage moves down and in, lung volume decreases, pressure increases, and air is pushed out.
呼气时，膈肌舒张并上移，肋间肌舒张，胸腔下移内收，肺容积减小，压力升高，空气被压出。
9. Circulatory System and Heart Rate Formula | 循环系统与心率公式
The circulatory system transports substances around the body. Cardiac output can be calculated using heart rate and stroke volume.
循环系统将物质输送到全身。心输出量可以通过心率和每搏输出量计算。
Cardiac output = Heart rate × Stroke volume
心输出量 = 心率 × 每搏输出量
- Heart rate is the number of beats per minute (bpm).
- 心率是每分钟心跳次数（bpm）。
- Stroke volume is the volume of blood pumped out of the left ventricle per beat (ml).
- 每搏输出量是每搏从左心室泵出的血液体积（毫升）。
- Typical resting values: heart rate ~70 bpm, stroke volume ~70 ml, so cardiac output ~4900 ml/min (about 5 L/min).
- 典型静息值：心率约 70 bpm，每搏输出量约 70 ml，因此心输出量约为 4900 ml/min（约 5 L/min）。
10. Inheritance: Mendel’s Laws and Monohybrid Cross | 遗传：孟德尔定律和单因子杂交
Genetics follows predictable patterns. A monohybrid cross between two heterozygous individuals gives a 3:1 phenotypic ratio in the F2 generation.
遗传遵循可预测的模式。两个杂合子个体间的单因子杂交在 F2 代中产生 3:1 的表型比。
Using a Punnett square for one gene with two alleles (A = dominant, a = recessive):
使用庞纳特方格处理一个基因两个等位基因（A = 显性，a = 隐性）：
| A | a | |
| A | AA | Aa |
| a | Aa | aa |
Genotypic ratio: 1 AA : 2 Aa : 1 aa. Phenotypic ratio: 3 dominant : 1 recessive.
基因型比：1 AA : 2 Aa : 1 aa。表型比：3 显性 : 1 隐性。
Key definitions:
关键定义：
- Allele: a version of a gene.
- 等位基因：基因的一种形式。
- Homozygous: having two identical alleles for a gene.
- 纯合子：对于某一基因拥有两个相同等位基因。
- Heterozygous: having two different alleles for a gene.
- 杂合子：对于某一基因拥有两个不同等位基因。
- Genotype: the genetic makeup.
- 基因型：遗传组成。
- Phenotype: the observable characteristics.
- 表型：可观察到的性状。
11. Energy Flow and Efficiency in Food Chains | 食物链中的能量流动与效率
Energy is transferred along food chains, but only a small percentage is passed from one trophic level to the next. Energy transfer efficiency can be calculated.
能量沿食物链传递，但只有一小部分从一个营养级传递到下一个。能量传递效率可以计算。
Efficiency = (Energy available to the next level ÷ Energy available to the previous level) × 100%
效率 = （下一营养级可用的能量 ÷ 上一营养级可用的能量）× 100%
Typically, this is around 10% because organisms use most of the energy for respiration, movement, growth, and lost as heat. Energy is not recycled; it flows through ecosystems. Biomass pyramids show the dry mass at each trophic level and are usually pyramid-shaped.
通常情况下，这个效率约为 10%，因为生物体将大部分能量用于呼吸、运动、生长，并以热的形式散失。能量不可循环；它在生态系统中流动。生物量金字塔显示每个营养级的干质量，通常呈金字塔形。
12. Food Tests and Reagent Reactions | 食物检测与试剂反应
Although not mathematical formulas, the following chemical tests are core practical skills. You need to remember the reagents and expected colour changes.
虽然这不是数学公式，但以下化学检测是核心实验技能。你需要记住试剂及预期的颜色变化。
| Nutrient | Reagent | Positive result |
| Starch | Iodine solution | Blue-black |
| Glucose (reducing sugar) | Benedict’s solution (heat) | Green → yellow → brick-red precipitate |
| Protein | Biuret solution | Violet/purple |
| Lipid | Ethanol then water (emulsion test) | Cloudy white emulsion |
| 营养物质 | 试剂 | 阳性结果 |
| 淀粉 | 碘液 | 蓝黑色 |
| 葡萄糖（还原糖） | 本尼迪克特溶液（加热） | 绿色 → 黄色 → 砖红色沉淀 |
| 蛋白质 | 双缩脲溶液 | 紫罗兰色/紫色 |
| 脂质 | 乙醇然后水（乳剂测试） | 云雾状白色乳剂 |
These tests confirm the presence of key biological molecules in foods and are often examined alongside digestion and nutrition.
这些检测可确认食物中关键生物分子的存在，通常与消化和营养一起考查。
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