📚 Year 9 CAIE Biology: Quick Reference Handbook for Formulas and Theorems | Year 9 CAIE 生物：公式定理速查手册
This quick reference handbook gathers all the essential formulas, principles, and rules you need for Year 9 CAIE Biology. From magnification calculations in microscopy to photosynthesis word equations, from enzyme activity laws to genetic ratios, every key quantitative relationship and conceptual theorem is presented in a clear, paired English–Chinese format. Use it to revise efficiently and build a solid foundation for your IGCSE studies.
这本速查手册汇集了 Year 9 CAIE 生物学所需的所有重要公式、原理和定律。从显微镜放大倍数的计算到光合作用的文字方程，从酶活性规律到遗传比例，每一个关键的量化关系和概念定理都以清晰的中英对照形式呈现。用来高效复习，为 IGCSE 学习打下扎实的基础。
1. Magnification and Units in Microscopy | 显微镜放大倍数与单位
Magnification = Image size ÷ Actual size. Always convert all measurements to the same unit before calculation. The formula can be rearranged: Actual size = Image size ÷ Magnification; Image size = Actual size × Magnification.
放大倍数 = 图像尺寸 ÷ 实际尺寸。计算前务必将所有测量值转换为相同单位。公式可变形为：实际尺寸 = 图像尺寸 ÷ 放大倍数；图像尺寸 = 实际尺寸 × 放大倍数。
Common unit conversions: 1 cm = 10 mm; 1 mm = 1000 µm; 1 µm = 1000 nm. Use micrometres (µm) for cell structures. Always check the scale bar on a micrograph – if the scale bar measures 20 mm and represents 5 µm, then Magnification = 20 000 µm ÷ 5 µm = ×4000.
常用单位换算：1 厘米 = 10 毫米；1 毫米 = 1000 微米；1 微米 = 1000 纳米。细胞结构使用微米（µm）作单位。务必查看显微照片上的比例尺——如果比例尺量出 20 毫米，代表 5 微米，那么放大倍数 = 20 000 µm ÷ 5 µm = ×4000。
- Magnification triangle: cover the quantity you want, and the relationship remains: I = A × M.
- 放大倍数三角：遮住你需要求的量，公式关系不变：I = A × M。
2. Diffusion and Factors Affecting Rate | 扩散及其速率影响因素
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration, down a concentration gradient, as a result of random movement. It is a passive process (no energy required).
扩散是粒子由于随机运动，从高浓度区域向低浓度区域，沿着浓度梯度进行的净移动。它是一种被动过程（不需能量）。
The rate of diffusion increases with: larger concentration gradient, higher temperature (more kinetic energy), larger surface area, and shorter diffusion distance. The relationship is summarised by Fick’s Law: Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Thickness of membrane.
扩散速率随以下因素增大而加快：更大的浓度梯度、更高的温度（动能增大）、更大的表面积、以及更短的扩散距离。这种关系可由菲克定律概括：扩散速率 ∝（表面积 × 浓度差）÷ 膜厚度。
In living organisms, adaptations like flattened shape (e.g. red blood cells), thin exchange surfaces (alveoli), and rich blood supply all maximise the rate of diffusion.
在生物体内，扁平形状（如红细胞）、薄壁交换面（肺泡）和丰富的血液供应等适应特征，都最大程度地提高扩散速率。
3. Osmosis and Water Potential | 渗透作用与水势
Osmosis is the net diffusion of water molecules across a partially permeable membrane, from a region of higher water potential (dilute solution) to a region of lower water potential (concentrated solution). Water potential is measured in pressure units (kPa); pure water has the highest water potential (0 kPa), and adding solute lowers the water potential (becomes more negative).
渗透作用是水分子通过选择性半透膜的净扩散，从水势较高的区域（稀溶液）向水势较低的区域（浓溶液）移动。水势以压强单位（千帕）表示；纯水水势最高（0 kPa），加入溶质会降低水势（变得更负）。
In plant cells, turgor pressure develops when water enters by osmosis, pushing the cell membrane against the cell wall. In animal cells, too much water uptake leads to bursting (lysis); too much water loss causes shrinking (crenation).
在植物细胞中，水分通过渗透进入，产生的膨压将细胞膜推向细胞壁。在动物细胞中，过多的水分进入会导致破裂（溶血）；水分过度流失会导致皱缩（细胞退缩）。
General rule: water moves from less negative (higher) water potential to more negative (lower) water potential.
一般规律：水总是从水势较不负（较高）的区域流向水势更负（较低）的区域。
4. Enzyme Action and the Lock-and-Key Model | 酶的作用与锁钥模型
Enzymes are biological catalysts that speed up chemical reactions without being used up. Each enzyme has an active site that is complementary in shape to a specific substrate – the lock-and-key hypothesis. The substrate fits into the active site, forming an enzyme-substrate complex; products are then released.
酶是生物催化剂，能加速化学反应而自身不被消耗。每种酶都有与特定底物形状互补的活性位点——锁钥假说。底物嵌入活性位点，形成酶–底物复合物；随后产物释放。
Enzyme activity is affected by temperature and pH. As temperature rises, activity increases until an optimum (human enzymes usually around 37 °C). Above the optimum, the enzyme denatures (active site shape is permanently changed). Similarly, each enzyme has an optimum pH; extremes of pH denature the enzyme.
酶活性受温度和 pH 的影响。随着温度升高，活性增加直至最适温度（人体酶通常在 37 °C 左右）。超过最适温度，酶会变性（活性位点形状永久改变）。同样，每种酶有最适 pH；极端的 pH 会使酶变性。
Substrate concentration also affects rate: at low concentration, rate increases proportionally; at high concentration, rate plateaus as active sites become saturated.
底物浓度同样影响速率：低浓度时，速率成正比增加；高浓度时，活性位点饱和，速率达到平台期。
5. Food Tests: Reagents and Positive Results | 食物测试：试剂与阳性结果
You must remember four main biochemical tests.
你必须记住四种主要的生化测试。
| Food substance 食物成分 | Reagent 试剂 | Positive result 阳性结果 |
|---|---|---|
| Starch 淀粉 | Iodine solution 碘液 | Blue-black 蓝黑色 |
| Reducing sugars 还原糖 | Benedict’s solution + heat 本尼迪克特试剂 + 加热 | Brick-red precipitate 砖红色沉淀 |
| Protein 蛋白质 | Biuret reagent 双缩脲试剂 | Purple / lilac 紫色 |
| Lipids (fats) 脂类（脂肪） | Ethanol + water, shake 乙醇+水，振荡 | Cloudy white emulsion 乳白色乳浊液 |
The principle behind lipid test: lipids dissolve in ethanol and come out of solution when water is added, forming a permanent cloudy emulsion.
脂类测试的原理：脂类溶于乙醇，加水后从溶液中析出，形成持久的乳白色乳浊液。
6. Digestion: Enzymes and Their Products | 消化：酶及其产物
Digestion is the breakdown of large insoluble food molecules into small soluble ones that can be absorbed. Three main digestive enzymes catalyse specific reactions.
消化是将大块不溶性食物分子分解为可吸收的小分子的过程。三种主要的消化酶催化特定反应。
Amylase: Starch → Maltose (in the mouth and duodenum). Protease (e.g. pepsin, trypsin): Protein → Amino acids (stomach and duodenum). Lipase: Lipids → Fatty acids + Glycerol (duodenum, after emulsification by bile).
淀粉酶：淀粉 → 麦芽糖（口腔和十二指肠）。蛋白酶（如胃蛋白酶、胰蛋白酶）：蛋白质 → 氨基酸（胃和十二指肠）。脂肪酶：脂类 → 脂肪酸 + 甘油（十二指肠，胆汁乳化后）。
Bile is produced by the liver, stored in the gall bladder; it is not an enzyme but emulsifies fats and neutralises stomach acid.
胆汁由肝脏生成，储存在胆囊中；它不是酶，但能乳化脂肪并中和胃酸。
Rule: each enzyme acts on a specific substrate, and the reaction occurs at the enzyme’s optimum pH. For example, pepsin in the stomach works best at pH 2, while trypsin in the small intestine works best at around pH 8.
规律：每种酶作用于特定的底物，并在该酶的最适 pH 下发生反应。例如，胃中的胃蛋白酶在 pH 2 时最佳，而小肠中的胰蛋白酶在 pH 8 左右最佳。
7. Photosynthesis: Word and Chemical Equation | 光合作用：文字与化学方程式
Photosynthesis is the process by which green plants make glucose from carbon dioxide and water, using light energy absorbed by chlorophyll. Oxygen is released as a by-product.
光合作用是绿色植物利用叶绿素吸收光能，将二氧化碳和水转化为葡萄糖的过程。副产物释放氧气。
Word equation: Carbon dioxide + Water → Glucose + Oxygen
Conditions: light and chlorophyll required.
文字方程：二氧化碳 + 水 → 葡萄糖 + 氧气
条件：需要光和叶绿素。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This balanced chemical equation shows that 6 molecules of carbon dioxide combine with 6 molecules of water to produce 1 molecule of glucose and 6 molecules of oxygen. It is the reverse of aerobic respiration.
这个配平的化学方程式表明 6 个二氧化碳分子与 6 个水分子结合，产生 1 个葡萄糖分子和 6 个氧气分子。它是有氧呼吸的逆反应。
The rate of photosynthesis is limited by: light intensity, carbon dioxide concentration, and temperature. The limiting factor is the one in shortest supply; increasing other factors has no effect until the limiting factor is raised.
光合作用速率受限于：光照强度、二氧化碳浓度和温度。限制因素是指供应最少的那一个；只有提高限制因素，其他因素增加才会产生效果。
8. Respiration: Aerobic and Anaerobic Equations | 呼吸作用：有氧与无氧方程式
Respiration is the release of energy from glucose, occurring continuously in all living cells. It is not the same as breathing.
呼吸作用是细胞从葡萄糖中释放能量的过程，持续发生在所有活细胞中。呼吸作用不等于呼吸（气体交换）。
Aerobic respiration (requires oxygen): Glucose + Oxygen → Carbon dioxide + Water (+ energy)
有氧呼吸（需要氧气）：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ energy in the form of ATP)
Anaerobic respiration in muscles (during vigorous exercise, no oxygen): Glucose → Lactic acid (+ some energy)
肌肉中的无氧呼吸（剧烈运动时，无氧气）：葡萄糖 → 乳酸（+ 少量能量）
Anaerobic respiration in yeast (fermentation): Glucose → Ethanol + Carbon dioxide (+ some energy)
酵母中的无氧呼吸（发酵）：葡萄糖 → 乙醇 + 二氧化碳（+ 少量能量）
Key rule: aerobic respiration yields much more energy per glucose molecule (around 19 times more) than anaerobic respiration. Oxygen debt is the amount of oxygen needed to break down lactic acid after exercise.
关键规律：每分子葡萄糖，有氧呼吸释放的能量远多于无氧呼吸（约为 19 倍）。氧债是运动后分解乳酸所需的额外氧气量。
9. Gas Exchange and the Mechanics of Breathing | 气体交换与呼吸力学
In humans, gas exchange takes place in the alveoli. Oxygen diffuses from alveolar air into blood; carbon dioxide diffuses from blood into alveolar air, down their concentration gradients.
人体气体交换发生在肺泡。氧气沿浓度梯度从肺泡气向血液扩散；二氧化碳从血液向肺泡气扩散。
The breathing movements create pressure changes: during inhalation, the diaphragm contracts and moves down, the intercostal muscles contract to lift the ribs up and out – this increases the thoracic volume, lowering pressure below atmospheric pressure, so air rushes in. During exhalation, the muscles relax, volume decreases, pressure increases, and air is forced out.
呼吸运动产生压力变化：吸气时，膈肌收缩下移，肋间肌收缩将肋骨上提外展——胸容积增大，压力降至大气压以下，空气进入。呼气时，肌肉放松，容积减小，压力升高，空气排出。
Key theorem: Volume is inversely proportional to pressure in a sealed container (Boyle’s law applied to thoracic cavity).
关键定理：在密闭容器中，容积与压力成反比（波义耳定律在胸腔的应用）。
Lung volume can be measured using a spirometer; tidal volume is the volume of air moved in and out during normal breathing.
肺容量可用肺活量计测量；潮气量是正常呼吸时吸入或呼出的气体量。
10. Blood Circulation and the Heart | 血液循环与心脏
The heart is a double pump. The right side pumps deoxygenated blood to the lungs (pulmonary circulation); the left side pumps oxygenated blood to the rest of the body (systemic circulation). Blood passes through the heart twice in one complete circuit – this is called double circulation.
心脏是双泵。右侧将缺氧血泵至肺部（肺循环）；左侧将含氧血泵至全身（体循环）。血液在一次完整循环中两次经过心脏——这称为双循环。
Flow order: Body → Vena cava → Right atrium → Right ventricle → Pulmonary artery → Lungs → Pulmonary vein → Left atrium → Left ventricle → Aorta → Body.
流动顺序：身体 → 腔静脉 → 右心房 → 右心室 → 肺动脉 → 肺 → 肺静脉 → 左心房 → 左心室 → 主动脉 → 身体。
Valves prevent backflow: atrioventricular valves (tricuspid on right, bicuspid/mitral on left) lie between atria and ventricles; semilunar valves are at the base of the pulmonary artery and aorta.
瓣膜防止倒流：房室瓣（右侧三尖瓣，左侧二尖瓣/僧帽瓣）位于心房与心室之间；半月瓣位于肺动脉和主动脉基部。
The wall of the left ventricle is much thicker because it must generate higher pressure to pump blood all around the body.
左心室壁厚得多，因为它必须产生更高的压力，将血液泵至全身。
11. Genetics: Monohybrid Crosses and Ratios | 遗传：单基因杂交与比例
The basic rules of inheritance were discovered by Gregor Mendel. A gene is a section of DNA that codes for a protein; different forms of a gene are called alleles. A dominant allele (represented by a capital letter, e.g. T) masks the effect of a recessive allele (lowercase, e.g. t).
遗传的基本规律由孟德尔发现。基因是编码蛋白质的 DNA 片段；同一基因的不同形式称为等位基因。显性等位基因（用大写字母表示，如 T）能掩盖隐性等位基因（小写，如 t）的效应。
Genotype = the alleles present (TT, Tt, tt). Phenotype = the observable characteristic. Homozygous (TT or tt); Heterozygous (Tt).
基因型 = 携带的等位基因（TT、Tt、tt）。表现型 = 可观察的特征。纯合（TT 或 tt）；杂合（Tt）。
In a monohybrid cross between two heterozygous parents (Tt × Tt), the expected phenotypic ratio in offspring is 3 dominant : 1 recessive.
在两个杂合亲本（Tt × Tt）之间的单基因杂交中，后代预期表现型比例为 3 显性 : 1 隐性。
Punnett square summarises the probability:
庞氏方格总结概率：
| T | t | |
| T | TT | Tt |
| t | Tt | tt |
Genotypic ratio = 1 TT : 2 Tt : 1 tt.
基因型比例 = 1 TT : 2 Tt : 1 tt。
12. Energy Flow and Pyramids in Ecology | 生态中的能量流动与金字塔
In a food chain, energy is transferred from one trophic level to the next. Only about 10% of the energy is passed on; the rest is lost as heat, respiration, movement, and waste. This is the 10% energy rule.
在食物链中，能量从一个营养层级传递到下一级。通常大约只有 10% 的能量被传递过去；其余以热、呼吸、运动和排泄物等形式散失。这就是“百分之十能量定律”。
Pyramids of numbers show the number of organisms at each trophic level; pyramids of biomass show the dry mass of living material; pyramids of energy always show a narrowing shape because energy decreases at each level.
数量金字塔显示每一营养层级生物的数量；生物量金字塔显示生命的干物质质量；能量金字塔总是呈收缩的形状，因为能量在每一层级都减少。
A simple food chain: Producer (e.g. grass) → Primary consumer (herbivore) → Secondary consumer (carnivore) → Tertiary consumer. Arrows represent the direction of energy flow.
简单食物链：生产者（如草）→ 初级消费者（食草动物）→ 次级消费者（食肉动物）→ 三级消费者。箭头代表能量流动的方向。
The Sun is the principal source of energy for almost all ecosystems.
太阳是几乎所有生态系统的主要能量来源。
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