📚 Year 9 CIE Biology Formula & Theorem Quick Reference | 九年级CIE生物公式定理速查手册
This handbook pulls together the must-know formulas, word equations and core principles for Year 9 CIE Biology. Use it to revise microscope calculations, key metabolic equations, enzyme rules, inheritance patterns and the vital sign relationships that underpin human physiology. Each section presents the essential statement or formula, followed by a clear explanation and a matched Chinese translation so you can reinforce your understanding in both languages.
这本手册汇集了九年级CIE生物课程必须掌握的公式、词方程与核心原理。你可以用它复习显微镜计算、重要的代谢方程、酶的工作规律、遗传比例，以及支撑人体生理的重要指标关系。每一节先给出关键表述或公式，再提供清晰的解释和对应的中文翻译，帮助你在双语学习中巩固理解。
1. Magnification Formula | 放大倍率公式
When you observe a specimen through a light microscope, the total magnification is the product of the eyepiece (ocular) lens magnification and the objective lens magnification. The standard formula relates image size, actual size and magnification.
使用光学显微镜观察标本时，总放大倍率是目镜倍数与物镜倍数的乘积。标准公式将图像尺寸、实际尺寸和放大倍率联系在一起。
Magnification = Image size ÷ Actual size
放大倍率 = 图像尺寸 ÷ 实际尺寸
agnification. Always convert all measurements to the same unit (usually micrometres or millimetres) before calculating.
如果题目给出比例尺或标明的放大倍率，可以变形公式：实际尺寸 = 图像尺寸 ÷ 放大倍率。计算前务必把所有测量值换算成相同单位（通常用微米或毫米）。
30 mm across at a magnification of ×600. Actual size = 30 mm ÷ 600 = 0.05 mm, which is 50 µm.
例如，一个细胞的图像在×600放大下宽度为30 mm，实际尺寸 = 30 mm ÷ 600 = 0.05 mm，即 50 µm。
2. Photosynthesis: Word and Symbol Equations | 光合作用：词方程与符号方程
Photosynthesis is the process by which green plants manufacture glucose using light energy, carbon dioxide and water. Chlorophyll in chloroplasts traps the light energy. The overall word equation summarises the reactants and products.
光合作用是绿色植物利用光能、二氧化碳和水制造葡萄糖的过程。叶绿体中的叶绿素捕获光能。总的词方程概括了反应物和产物。
carbon dioxide + water → glucose + oxygen
(in the presence of light and chlorophyll)
二氧化碳 + 水 → 葡萄糖 + 氧气
（在光照和叶绿素存在下）
The balanced chemical equation is frequently used in exam answers:
考试答题时常使用配平后的化学方程式：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Glucose produced may be converted into starch for storage, cellulose for cell walls, or used in respiration to release energy. Oxygen is released as a by‑product, which is essential for aerobic life.
产生的葡萄糖可转化为淀粉储存、转化为纤维素构建细胞壁，或用于呼吸作用释放能量。氧气作为副产物释放，对有氧生物至关重要。
3. Respiration Equations | 呼吸作用方程
Respiration is the enzyme‑controlled release of energy from food molecules (usually glucose). Aerobic respiration requires oxygen and produces a large amount of energy. The word and symbol equations are fundamental.
呼吸作用是由酶控制的、从食物分子（通常是葡萄糖）中释放能量的过程。有氧呼吸需要氧气，产生大量能量。词方程和符号方程是基础。
Aerobic respiration word equation:
有氧呼吸词方程：
glucose + oxygen → carbon dioxide + water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水 (+ 能量)
Symbol equation:
符号方程式：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
In the absence of oxygen, some cells can perform anaerobic respiration. In yeast, this produces ethanol and carbon dioxide:
无氧条件下，某些细胞可以进行无氧呼吸。酵母进行无氧呼吸时产生乙醇和二氧化碳：
glucose → ethanol + carbon dioxide (+ some energy)
葡萄糖 → 乙醇 + 二氧化碳 (+ 少量能量)
In animal muscles, anaerobic respiration produces lactic acid, leading to oxygen debt. The word equation is:
在动物肌肉中，无氧呼吸产生乳酸，造成氧债。词方程为：
glucose → lactic acid (+ some energy)
葡萄糖 → 乳酸 (+ 少量能量)
4. Enzyme Action and the Lock‑and‑Key Model | 酶作用与锁钥模型
Enzymes are protein catalysts that speed up biochemical reactions without being used up. The lock‑and‑key model describes how a substrate fits exactly into the active site of its specific enzyme, forming an enzyme‑substrate complex before products are released.
酶是蛋白质催化剂，能加快生化反应而自身不被消耗。锁钥模型描述底物如何精确地嵌入特定酶的活性位点，形成酶‑底物复合物，随后释放产物。
Two key principles govern enzyme activity:
酶活性遵循两条关键原理：
Temperature rule: As temperature rises, kinetic energy increases and the rate of reaction rises until an optimum is reached (often around 37 °C in human enzymes). Beyond this temperature, the enzyme denatures — the active site loses its shape permanently, and the reaction rate falls sharply.
温度规则：温度升高时，动能增加，反应速率上升，直至达到最适温度（人体酶约为37 °C）。超过这一温度，酶变性——活性位点永久失去原有形状，反应速率急剧下降。
pH rule: Each enzyme works best at a specific optimum pH. For example, pepsin in the stomach works best at pH 2, while most other enzymes prefer near‑neutral pH. Extreme pH changes cause denaturation.
pH规则：每种酶只在特定最适pH下活性最高。例如胃蛋白酶在pH 2时活性最佳，而多数其他酶在中性附近活性最高。过激的pH变化会导致变性。
5. Digestive Enzymes at a Glance | 消化酶一览
Digestion breaks down large insoluble molecules into smaller soluble ones that can be absorbed. The main enzymes, their sources, substrates and products are summarised in the table below.
消化将大而不溶的分子分解为可吸收的小分子。下表总结了主要的消化酶及其来源、底物和产物。
| Enzyme (酶) | Source (来源) | Substrate (底物) | Products (产物) | Optimum pH (最适pH) |
|---|---|---|---|---|
| Amylase | Salivary glands, pancreas | Starch | Maltose | ~7 |
| Protease (pepsin) | Stomach | Protein | Peptides | ~2 |
| Protease (trypsin) | Pancreas | Protein | Peptides | ~8 |
| Lipase | Pancreas | Fats (lipids) | Fatty acids + glycerol | ~8 |
Note that bile (produced in the liver, stored in the gall bladder) is not an enzyme but emulsifies fats, increasing the surface area for lipase action. Acid in the stomach provides the optimum pH for pepsin and kills harmful microorganisms.
请注意，胆汁（肝产生、胆囊储存）并非酶，但能乳化脂肪，增大脂肪的表面积以利于脂肪酶作用。胃里的酸为胃蛋白酶提供最适pH，并杀死有害微生物。
6. Factors Influencing Diffusion Rate | 影响扩散速率的因素
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration, down a concentration gradient. The rate of diffusion is crucial for gas exchange and nutrient uptake. It can be summarised by a proportional relationship:
扩散是粒子从高浓度区域向低浓度区域净移动、顺浓度梯度的过程。扩散速率对气体交换和养分吸收至关重要。可以用一个比例关系来概括：
Rate of diffusion ∝ (surface area × concentration difference) ÷ diffusion distance
扩散速率 ∝ (表面积 × 浓度差) ÷ 扩散距离
An increase in surface area (e.g. folded membranes, alveoli) speeds up diffusion. A larger concentration gradient (greater difference) also increases the rate. A shorter diffusion distance (thin exchange surfaces) makes diffusion faster. Raising the temperature adds kinetic energy, accelerating particle movement.
增大表面积（如折叠膜、肺泡）会加快扩散。较大的浓度梯度（更大的浓度差）也会提高速率。较短的扩散距离（薄交换面）使扩散更快。升温增加动能，也加速粒子运动。
In living organisms, adaptations such as the flattened shape of leaves, the numerous alveoli in lungs, and the villi in the small intestine all maximise the surface‑area‑to‑volume ratio for efficient diffusion.
在生物体中，扁平的叶片、大量肺泡和小肠绒毛等适应性结构都最大限度地提高了表面积与体积之比，以利于高效扩散。
7. Osmosis: The Water Movement Rule | 渗透：水分移动法则
Osmosis is a special type of diffusion: the net movement of water molecules through a partially permeable membrane from a region of higher water potential (lower solute concentration) to a region of lower water potential (higher solute concentration).
渗透是一种特殊的扩散：水分子通过选择性透过膜的净移动，从水势较高（溶质浓度较低）的区域向水势较低（溶质浓度较高）的区域移动。
The rule can be stated as: Water moves from a dilute solution to a more concentrated solution across a partially permeable membrane. In plant cells, the cell wall prevents bursting; the cell becomes turgid when filled with water and plasmolysed when water leaves. In animal cells, excessive water entry may cause lysis (bursting), and water loss leads to crenation.
该法则可以表述为：水穿过部分透膜，从稀溶液向浓溶液移动。在植物细胞中，细胞壁可防止胀破；细胞吸水充足时变得硬挺（质壁分离复原），失水时发生质壁分离。在动物细胞中，过多水分进入会导致细胞胀破，失水则导致皱缩。
8. Monohybrid Inheritance and Probability Ratios | 单基因遗传与概率比例
Mendel’s law of segregation states that each individual has two alleles for a characteristic, which separate during gamete formation so each gamete carries only one allele. When a dominant allele is present, it masks the recessive allele in the phenotype.
孟德尔分离定律指出，每个个体对某一性状拥有两个等位基因，它们在配子形成时分离，每个配子只携带一个等位基因。当显性等位基因存在时，会在表现型中掩盖隐性等位基因。
us parents (e.g. Tt × Tt, where T = tall, t = dwarf) yields these ratios in the offspring:
对两个杂合亲本（如Tt × Tt，T = 高茎，t = 矮茎）采用庞纳特方格，后代比例如下：
Genotype ratio: 1 TT : 2 Tt : 1 tt
基因型比例：1 TT : 2 Tt : 1 tt
Phenotype ratio: 3 tall : 1 dwarf
表现型比例：3 高茎 : 1 矮茎
If one parent is homozygous dominant (TT) and the other homozygous recessive (tt), all offspring will be heterozygous (Tt) and show the dominant trait — a 100% tall progeny. Understanding these ratios helps predict inheritance of genetic disorders and traits in CIE problems.
如果一方为纯合显性（TT），另一方为纯合隐性（tt），所有后代均为杂
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