📚 Year 11 CCEA Biology: Formula and Theorem Quick Reference Handbook | Year 11 CCEA 生物：公式定理速查手册
This handbook brings together all the essential formulas, equations, and key principles you need for the Year 11 CCEA Biology course. Each entry is presented with a clear explanation in English and a matching Chinese translation, so you can rapidly revise and truly understand the core quantitative and theoretical backbone of the subject. Use it to check your recall, to practise calculations, and to build confidence ahead of your examinations.
本手册汇集了 Year 11 CCEA 生物学课程中所有必要的公式、方程式和关键原理。每个条目均配有明确的英文解释和对应的中文翻译，帮助你快速复习并真正理解这门学科的核心定量与理论支柱。你可以用它来检查记忆、练习计算，并在考试前树立信心。
1. Magnification Formula | 放大倍率公式
When using a microscope, the magnification tells you how many times larger the image appears compared to the actual specimen. The formula relates image size, actual size, and magnification. Both image size and actual size must be in the same unit before you calculate.
使用显微镜时，放大倍率表示图像比实际标本大多少倍。该公式将图像尺寸、实际尺寸和放大倍率关联起来。计算前，图像尺寸和实际尺寸必须采用相同的单位。
Magnification = Image size ÷ Actual size
放大倍率 = 图像尺寸 ÷ 实际尺寸
size = Image size ÷ Magnification. This is essential for measuring cells from micrographs.
你可以将公式变形来求实际尺寸：实际尺寸 = 图像尺寸 ÷ 放大倍率。这对于根据显微照片测量细胞至关重要。
2. Photosynthesis Word and Symbol Equations | 光合作用文字和符号方程式
Photosynthesis is the process by which green plants, algae, and some bacteria convert light energy into chemical energy stored in glucose. The overall reaction shows that carbon dioxide and water are used to produce glucose and oxygen, with light energy being absorbed by chlorophyll.
光合作用是绿色植物、藻类和一些细菌将光能转化为储存在葡萄糖中的化学能的过程。总反应表明，二氧化碳和水在叶绿素吸收光能的条件下生成葡萄糖和氧气。
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
The balanced symbol equation for photosynthesis is:
光合作用的配平符号方程式为：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Remember that light energy is not written as a reactant but is a condition written above the arrow. Chlorophyll is the catalyst.
请注意，光能并非作为反应物书写，而是写在箭头之上的条件。叶绿素是催化剂。
3. Aerobic Respiration Equation | 需氧呼吸方程式
Aerobic respiration is the complete breakdown of glucose in the presence of oxygen to release a relatively large amount of energy. It occurs continuously in the mitochondria of most cells and produces carbon dioxide and water as waste products.
需氧呼吸是在有氧条件下葡萄糖的完全分解，释放出相对大量的能量。该过程在大多数细胞的线粒体中持续进行，并产生二氧化碳和水作为废物。
Glucose + Oxygen → Carbon dioxide + Water (+ energy released)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 释放的能量）
The balanced symbol equation is the reverse of photosynthesis because respiration uses the products of photosynthesis.
配平的符号方程式与光合作用互为逆反应，因为呼吸作用使用光合作用的产物。
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Energy is released in the form of ATP, which powers cellular activities such as muscle contraction, active transport, and maintaining body temperature in mammals.
能量以 ATP 的形式释放，为肌肉收缩、主动运输以及哺乳动物维持体温等细胞活动提供动力。
4. Anaerobic Respiration Equations | 厌氧呼吸方程式
When oxygen is limited, cells can respire without it, but this is much less efficient at transferring energy. In animals, anaerobic respiration produces lactic acid, which can lead to muscle fatigue and cramp. The lactic acid must later be oxidised to carbon dioxide and water during recovery.
当氧气有限时，细胞可以进行无氧呼吸，但这种方式传递能量的效率要低得多。在动物体内，厌氧呼吸产生乳酸，这可能导致肌肉疲劳和痉挛。乳酸随后必须在恢复期间被氧化为二氧化碳和水。
Glucose → Lactic acid (+ energy)
葡萄糖 → 乳酸（+ 能量）
C₆H₁₂O₆ → 2C₃H₆O₃
In plant cells and microorganisms such as yeast, anaerobic respiration produces ethanol and carbon dioxide. This process is known as fermentation and is exploited in baking and brewing.
在植物细胞和酵母等微生物中，厌氧呼吸产生乙醇和二氧化碳。该过程称为发酵，被用于烘焙和酿造。
Glucose → Ethanol + Carbon dioxide (+ energy)
葡萄糖 → 乙醇 + 二氧化碳（+ 能量）
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
5. Enzyme Activity and the Lock-and-Key Theorem | 酶活性与锁钥定理
Enzymes are biological catalysts that speed up metabolic reactions without being used up. The lock-and-key theorem states that each enzyme has an active site with a specific shape that is complementary to a single type of substrate. Once the substrate binds, an enzyme–substrate complex forms, and products are released, leaving the enzyme unchanged.
酶是生物催化剂，能加速代谢反应而自身不被消耗。锁钥定理指出，每种酶都有一个特定形状的活性位点，该形状与单一类型的底物互补。底物结合后形成酶-底物复合物，随后产物被释放，酶恢复原状。
Enzyme activity is affected by temperature and pH. As temperature increases, kinetic energy rises, so collisions between enzyme and substrate become more frequent, increasing the rate of reaction up to an optimum. Beyond the optimum temperature, the enzyme denatures: the active site loses its shape permanently, and the substrate can no longer fit.
酶活性受温度和 pH 影响。温度升高时，动能增加，酶与底物之间的碰撞更频繁，反应速率上升直至最适温度。超过最适温度后，酶会变性：活性位点永久性地失去形状，底物不再能契合。
Similarly, each enzyme works best at a specific optimum pH. Straying too far from this pH disrupts the bonds holding the enzyme’s tertiary structure, causing denaturation. The induced-fit model is a refinement of the lock-and-key theorem, suggesting the active site changes shape slightly to accommodate the substrate.
同样，每种酶在其特定的最适 pH 下活性最高。偏离此 pH 过远会破坏维持酶三级结构的键，导致变性。诱导契合模型是对锁钥定理的细化，认为活性位点会发生轻微形变以容纳底物。
6. Diffusion and Surface Area : Volume Ratio (Fick's Principle) | 扩散与表面积体积比（菲克原理）
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration down a concentration gradient. The rate of diffusion across a membrane is influenced by surface area, concentration difference, membrane thickness, and temperature. Fick's principle summarises this relationship.
扩散是粒子沿浓度梯度从较高浓度区域向较低浓度区域的净移动。跨膜扩散的速率受表面积、浓度差、膜厚度和温度影响。菲克原理概括了这一关系。
Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Membrane thickness
扩散速率 ∝（表面积 × 浓度差）÷ 膜厚度
As organisms increase in size, their surface area to volume ratio (SA:V) decreases. This means that larger organisms cannot rely on diffusion alone to supply all their cells with oxygen and nutrients and to remove waste; they need specialised transport systems such as the circulatory system.
随着生物体体积增大，其表面积与体积之比（SA:V）减小。这意味着较大的生物不能仅仅依靠扩散来为所有细胞提供氧气和营养并清除废物；它们需要像循环系统这样的专门运输系统。
In gas exchange, structures like alveoli, gill filaments, and root hairs have large surface areas, thin membranes, and steep concentration gradients to maximise diffusion rate.
在气体交换中，肺泡、鳃丝和根毛等结构具有很大的表面积、很薄的膜和陡峭的浓度梯度，以最大化扩散速率。
7. Monohybrid Inheritance and Mendel's Law of Segregation | 单因子杂交与孟德尔分离定律
Mendel’s first law, the Law of Segregation, states that each individual possesses a pair of alleles for any particular characteristic, and these alleles segregate during gamete formation so that each gamete carries only one allele. When gametes fuse at fertilisation, the offspring inherits one allele from each parent, restoring the pair.
孟德尔第一定律，即分离定律，指出每个个体对于任何特定性状都拥有一对等位基因，而在配子形成过程中，这些等位基因会分离，使得每个配子只携带一个等位基因。配子在受精时融合，子代从每个亲本各继承一个等位基因，从而恢复成对状态。
t square, you can predict the probability of offspring genotypes and phenotypes. If the dominant allele is represented by 'A' and the recessive by 'a' genotypic ratio of 1 AA : 2 Aa : 1 aa and a phenotypic ratio of 3 dominant : 1 recessive.
单因子杂交追踪单个基因的遗传。利用庞纳特方格，你可以预测子代基因型和表型的概率。如果显性等位基因用‘A’表示，隐性用‘a’表示，则两个杂合亲本杂交（Aa × Aa）产生的基因型比例为 1 AA : 2 Aa : 1 aa，表型比例为 3 显性 : 1 隐性。
Genetic diagrams should always show the parental phenotypes and genotypes, the gametes produced, and then the possible offspring combinations. This theorem is fundamental to understanding patterns of inheritance and genetic disorders.
遗传图解应始终显示亲本的表型和基因型、产生的配子，以及可能的子代组合。该定理是理解遗传模式和遗传病的基础。
8. Natural Selection and the Theory of Evolution | 自然选择与进化论
Natural selection is the mechanism by which evolution occurs. The theorem, proposed by Charles Darwin, can be summarised in four key points: within any population, there is genetic variation; organisms produce more offspring than can survive; individuals with advantageous alleles are better adapted to their environment and more likely to survive and reproduce; these favourable alleles are passed on to the next generation, increasing their frequency in the gene pool over many generations.
自然选择是进化发生的机制。由查尔斯·达尔文提出的这一理论可概括为四个要点：任何种群内都存在遗传变异；生物体产生的后代数量超过能够存活的数量；具有优势等位基因的个体更适应环境，更有可能存活和繁殖；这些有利的等位基因被传递给下一代，经过许多代后在基因库中的频率增加。
This leads to gradual changes in species and can eventually result in the formation of new species (speciation) when populations become reproductively isolated. Antibiotic resistance in bacteria and the industrial melanism of peppered moths are classic examples of natural selection in action.
这导致物种逐渐变化，当种群形成生殖隔离时，最终可能导致新物种的形成（物种形成）。细菌的抗生素抗性和桦尺蛾的工业黑化是自然选择作用的经典例子。
It is important to note that natural selection acts on the phenotype of an organism but, because the phenotype reflects the genotype, the underlying allele frequencies change. This theorem stands alongside Mendel’s laws to form the foundation of modern genetics.
需要注意的是，自然选择作用于生物体的表型，但由于表型反映基因型，其背后的等位基因频率会发生改变。该理论与孟德尔定律一起构成了现代遗传学的基础。
9. Cardiac Output Formula | 心输出量公式
Cardiac output is the volume of blood pumped by the heart per minute. It is a product of heart rate (the number of beats per minute) and stroke volume (the volume of blood pumped out of the left ventricle per beat). Monitoring cardiac output provides insight into the efficiency of the cardiovascular system.
心输出量是心脏每分钟泵出的血液量。它是心率（每分钟心跳次数）与每搏输出量（左心室每次搏动泵出的血液量）的乘积。监测心输出量可以了解心血管系统的效率。
Cardiac output = Heart rate × Stroke volume
心输出量 = 心率 × 每搏输出量
During exercise, both heart rate and stroke volume increase, so cardiac output rises to deliver more oxygen and glucose to respiring muscles and to remove waste products such as heat and carbon dioxide more quickly.
运动时，心率和每搏输出量均增加，因此心输出量上升，以便向正在呼吸的肌肉输送更多的氧气和葡萄糖，并更快地清除热量和二氧化碳等废物。
Calculations often require you to convert heart rate from beats per 15 seconds to beats per minute, or to find stroke volume given cardiac output and heart rate.
计算时常需要你将心率从每15秒心跳次数转换为每分钟心跳次数，或根据心输出量和心率求出每搏输出量。
10. Osmosis and Water Potential Principle | 渗透作用和水势原理
Osmosis is the net movement of water molecules from a region of higher water potential (dilute solution) to a region of lower water potential (concentrated solution) through a partially permeable membrane. Water potential is measured in kilopascals (kPa); pure water has a water potential of zero, and solutes lower water potential, making it more negative.
渗透作用是水分子通过半透膜从较高水势区域（稀溶液）向较低水势区域（浓溶液）的净移动。水势以千帕（kPa）为单位；纯水的水势为零，溶质使水势降低并变得更负。
The principle states that water will always move down the water potential gradient. In plant cells, the rigid cell wall prevents bursting when water enters by osmosis; instead, the cell becomes turgid, which supports the plant. In animal cells, a lack of a cell wall can lead to lysis (bursting) in hypotonic solutions or crenation (shrinking) in hypertonic solutions.
该原理指出，水总是沿水势梯度向下移动。在植物细胞中，当水分通过渗透作用进入时，坚硬的细胞壁可防止细胞破裂；相反，细胞变得硬挺（膨胀），从而支撑植物。动物细胞没有细胞壁，在低渗溶液中可能发生裂解（破裂），在高渗溶液中则可能发生皱缩。
Calculating percentage change in mass or size is a common way to analyse osmosis experiments.
计算质量或尺寸的百分比变化是分析渗透作用实验的常用方法。
Percentage change = ((Final value − Initial value) ÷ Initial value) × 100%
百分比变化 = （（最终值 − 初始值）÷ 初始值）× 100%
11. Energy Transfer in Food Chains | 食物链中的能量传递
Energy flows through ecosystems in food chains from producers to various consumers. The principle of ecological efficiency states that only about 10% of the energy stored in one trophic level is transferred to the next level. The rest is lost through respiration, movement, heat, and undigested material.
能量通过食物链从生产者流向各级消费者。生态效率原理指出，在一个营养级中储存的能量只有大约 10% 传递到下一营养级。其余能量通过呼吸作用、运动、热量以及未消化的物质散失。
You can calculate the efficiency of energy transfer using the formula:
你可以使用以下公式计算能量传递效率：
Efficiency (% Energy available at next trophic level ÷ Energy available at previous trophic level) × 100
效率（%）= （下一营养级可利用的能量 ÷ 上一营养级可利用的能量）× 100
This low efficiency explains why food chains rarely have more than four or five trophic levels and why there is less biomass at higher trophic levels. Pyramids of energy, biomass, and numbers visually represent these losses.
如此低的效率解释了为什么食物链很少超过四到五个营养级，以及为什么较高营养级的生物量较少。能量金字塔、生物量金字塔和数量金字塔直观地反映了这些损耗。
12. Digestive Enzymes and Breakdown Reactions | 消化酶与分解反应
Digestion involves the breakdown of large, insoluble molecules into small, soluble ones that can be absorbed into the blood. This process depends on specific enzymes that catalyse hydrolysis reactions. The key theorem for digestion is that each type of nutrient is broken down by a specific enzyme at an optimal pH.
消化过程涉及将大分子不溶性物质分解为可被血液吸收的小分子可溶性物质。该过程依赖于催化水解反应的特异性酶。消化的关键定理是，每种营养素都由一种特定的酶在最适 pH 下分解。
Carbohydrases, such as amylase, break down starch into maltose and other sugars. Proteases digest proteins into amino acids. Lipases break down lipids into fatty acids and glycerol. Bile, produced by the liver, emulsifies fats to increase surface area for lipase action and neutralises stomach acid to provide an alkaline pH for enzymes in the small intestine.
淀粉酶等糖酶将淀粉分解为麦芽糖和其他糖类。蛋白酶将蛋白质消化为氨基酸。脂肪酶将脂质分解为脂肪酸和甘油。肝脏产生的胆汁可乳化脂肪以增加脂肪酶作用的表面积，并中和胃酸，为小肠中的酶提供碱性 pH 环境。
The overall simplified word equations for these breakdown reactions are:
这些分解反应的简化文字方程式如下：
Starch → Maltose (by amylase)
淀粉 → 麦芽糖（通过淀粉酶）
Proteins → Amino acids (by protease)
蛋白质 → 氨基酸（通过蛋白酶）
Lipids → Fatty acids + Glycerol (by lipase)
脂质 → 脂肪酸 + 甘油（通过脂肪酶）
These reactions are essential to understand alongside the lock-and-key theorem, as the specificity of the active site ensures that each enzyme acts on only one substrate.
这些反应需要与锁钥定理结合理解，因为活性位点的特异性确保每种酶只作用于一种底物。
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