📚 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 compiles the essential formulae, equations and key quantitative relationships required for the Year 11 CCEA Biology course. Use it as a rapid revision aid to reinforce your understanding of calculations across topics such as microscopy, enzymes, respiration, genetics and physiological measurements. Each entry presents the core principle alongside a practical explanation in both English and Chinese.
本手册汇编了 Year 11 CCEA 生物课程所需的核心公式、方程式和关键定量关系。可将其作为快速复习工具，巩固对显微测量、酶、呼吸作用、遗传学和生理测量等专题中计算方法的理解。每一条目均以英中双语呈现核心原理并配以实用说明。
1. Microscopy Calculations | 显微测量计算
When using a light microscope, the actual size of a specimen can be determined from its image size. The key formula is: Magnification = Image size ÷ Actual size, which can be rearranged to Actual size = Image size ÷ Magnification is . Image size is often measured with a ruler in millimetres (mm) and must be converted to micrometres (µm) using the conversion 1 mm = 1000 µ size and actual size are expressed in the same units before substituting into the formula.
使用光学显微镜时，标本的实际大小可通过图像尺寸求出。关键公式为：放大倍数 = 图像尺寸 ÷ 实际尺寸，可变形为 实际尺寸 = 图像尺寸 ÷ 放大倍数。图像尺寸通常用尺子以毫米 (mm) 为单位测量，并必须转换为微米 (µm)，换算关系为 1 mm = 1000 µm。代入公式前务必确保图像尺寸与实际尺寸使用相同单位。
2. Enzyme Q₁₀ Temperature Coefficient | 酶 Q₁₀ 温度系数
The Q₁₀ coefficient quantifies how reaction rate changes with a 10°C temperature rise. It is calculated as Q₁₀ = Rate at (T + 10°C) ÷ Rate at T. For most enzyme-controlled reactions, Q₁₀ is close to 2, indicating that the rate roughly doubles per 10°C increase within the enzyme’s optimum range. Beyond the optimum temperature, the enzyme denatures and Q₁₀ becomes meaningless as the rate drops sharply.
Q₁₀ 系数用于量化反应速率随温度每升高 10°C 的变化情况。计算公式为 Q₁₀ = (T+10°C 时的速率) ÷ (T 时的速率)。对于大多数酶促反应，Q₁₀ 接近 2，表明在酶的最适温度范围内温度每升高 10°C，反应速率约翻一番。一旦超过最适温度，酶变性失活，速率骤降，Q₁₀ 便失去意义。
3. Photosynthesis Equations | 光合作用方程式
Photosynthesis is summarised by the word equation: Carbon dioxide + Water → Glucose + Oxygen, with light energy and chlorophyll required. The balanced symbol equation is 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. This endothermic reaction converts light energy into chemical energy stored in glucose, and oxygen is released as a by-product. Remember that light intensity, carbon dioxide concentration and temperature all influence the rate of photosynthesis.
光合作用可概括为文字方程式：二氧化碳 + 水 → 葡萄糖 + 氧气，需要光能和叶绿素。配平的符号方程式为 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。该吸热反应将光能转化为储存在葡萄糖中的化学能，氧气作为副产物释放。请记住，光照强度、二氧化碳浓度和温度都会影响光合作用速率。
4. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration releases energy from glucose in the presence of oxygen. The word equation is: Glucose + Oxygen → Carbon dioxide + Water (+ Energy). The balanced symbol equation is C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O. This process occurs mostly in mitochondria and provides the majority of ATP required for cellular activities in animals, plants and many microorganisms.
有氧呼吸在氧气参与下从葡萄糖中释放能量。文字方程式为：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。配平的符号方程式为 C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。该过程主要在线粒体中进行，为动物、植物和许多微生物的细胞活动提供大部分所需的 ATP。
5. Anaerobic Respiration Equations | 无氧呼吸方程式
When oxygen is limited, cells may undergo anaerobic respiration. In yeast and some plants, the word equation is Glucose → Ethanol + Carbon dioxide (+ Little energy), symbolised as C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂. In animal muscles during strenuous exercise, the equation becomes Glucose → Lactic acid (+ Little energy), or C₆H₁₂O₆ → 2C₃H₆O₃. Anaerobic respiration yields far less ATP than the aerobic pathway and results in an oxygen debt that must be repaid.
当氧气不足时，细胞可能进行无氧呼吸。在酵母和某些植物中，文字方程式为 葡萄糖 → 乙醇 + 二氧化碳（+ 少量能量），符号表示为 C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂。在剧烈运动的动物肌肉中，方程式为 葡萄糖 → 乳酸（+ 少量能量），即 C₆H₁₂O₆ → 2C₃H₆O₃。无氧呼吸产生的 ATP 远少于有氧途径，并会导致氧债，需在运动后偿还。
6. Surface Area to Volume Ratio | 表面积与体积比
The surface area to volume ratio (SA:V) is calculated as Surface area ÷ Volume. As an organism or cell increases in size, its volume grows faster than its surface area, causing the SA:V ratio to decrease. This limits the efficiency of diffusion for the exchange of gases, nutrients and wastes. Small organisms and flattened structures have a large SA:V ratio, which facilitates rapid diffusion across their surfaces.
表面积与体积比 (SA:V) 的计算公式为 表面积 ÷ 体积。随着生物体或细胞体积增大，其体积增长快于表面积增长，导致 SA:V 比值下降。这会限制气体、营养物质和废物通过扩散进行交换的效率。小型生物及扁平的结构具有较大的 SA:V 比值，有利于物质在其表面快速扩散。
7. Fick’s Law (Simplified) | 菲克定律（简化）
The rate of diffusion across a membrane is described by a simplified Fick’s law: Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Diffusion distance. This relationship shows that diffusion is faster when the available surface area is larger, the concentration gradient is steeper, and the diffusion pathway is shorter. Adaptations such as the thin alveolar walls and extensive capillary networks in the lungs maximise these factors for efficient gas exchange.
物质跨膜扩散的速率可用简化的菲克定律描述：扩散速率 ∝ (表面积 × 浓度差) ÷ 扩散距离。该关系表明，当有效表面积更大、浓度梯度更陡、扩散路径更短时，扩散速率更快。肺部的薄肺泡壁和丰富的毛细血管网等适应性特征正是为了最大化这些因素，以实现高效的气体交换。
8. Osmosis and Water Potential | 渗透与水势
Osmosis is the net movement of water molecules through a partially permeable membrane from a region of higher water potential to a region of lower water potential. Pure water has the highest water potential, and the addition of solutes lowers it. While there is no single numerical formula, the underlying principle is that water moves down a water potential gradient until equilibrium is reached. In plant cells, turgor pressure results from water entering the cell by osmosis and pushing the cytoplasm against the cell wall.
渗透是指水分子通过半透膜从水势较高区域向水势较低区域的净移动。纯水的水势最高，溶质的加入会降低水势。尽管没有单一的数值公式，但其基本原理是水沿着水势梯度移动直至达到平衡。在植物细胞中，水分通过渗透进入细胞并将细胞质推向细胞壁，由此产生膨压。
9. Genetics Ratios from Monohybrid Crosses | 单基因杂交的遗传比例
ous (Aa) and show the dominant phenotype. Crossing two F₁ heterozygotes (Aa × Aa) yields a phenotypic ratio of 3:1 (dominant : recessive) and a genotypic ratio of 1:2:1 (AA : Aa : aa). These ratios assume complete dominance and that the genes are not linked on sex chromosomes. A Punnett square can be used to visualise the possible allele combinations and calculate the probability of each genotype.
当纯合显性个体 (AA) 与纯合隐性个体 (aa) 杂交时，所有子一代均为杂合子 (Aa) 并表现显性性状。将两个 F₁ 杂合子杂交 (Aa × Aa) 则得到 表现型比例为 3:1（显性 : 隐性），基因型比例为 1:2:1（AA : Aa : aa）。这些比例建立在完全显性且基因不位于性染色体上的假设之上。庞纳特方格可用于直观呈现等位基因的可能组合并计算每种基因型的概率。
10. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI provides a measure of body fat based on height and mass. The formula is BMI = Mass (kg) ÷ (Height (m))² tween 18.5 and 24.9 is generally considered healthy, while values below 18.5 suggest underweight and values above 24.9 indicate overweight. BMI does not distinguish between muscle and fat mass, so it must be interpreted cautiously.
BMI 是根据身高和体重衡量体脂程度的一项指标。公式为 BMI = 体重 (kg) ÷ (身高 (m))²。例如，体重 70 kg、身高 1.75 m 的人，BMI = 70 ÷ (1.75 × 1.75) ≈ 22.9。在成年人中，BMI 介于 18.5 至 24.9 之间通常被视为健康，低于 18.5 提示偏瘦，高于 24.9 则提示超重。BMI 无法区分肌肉与脂肪，因此解读时需谨慎。
11. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by the heart in one minute. It is calculated as Cardiac output (L/min) = Heart rate (beats/min) × Stroke volume (L/beat). Stroke volume is the amount of blood ejected by a ventricle during one contraction. During exercise, both heart rate and stroke volume increase, resulting in a significantly higher cardiac output to deliver more oxygen to working muscles.
心输出量是指心脏每分钟泵出的血液量。计算公式为 心输出量 (L/min) = 心率 (次/分) × 每搏输出量 (L/次)。每搏输出量是一个心室在一次收缩时射出的血量。运动时，心率和每搏输出量均增加，使心输出量显著提高，从而向工作肌肉输送更多氧气。
12. Energy Transfer Efficiency in Food Chains | 食物链中的能量传递效率
In an ecosystem, energy is transferred from one trophic level to the next, but much is lost through respiration, egestion and uneaten parts. The efficiency of energy transfer is given by Efficiency (%) = (Energy in the higher trophic level ÷ Energy in the lower trophic level) × 100. Transfer efficiencies are typically around 10%, which explains why food chains rarely exceed four or five trophic levels and why the biomass pyramid narrows sharply towards the top.
在生态系统中，能量沿营养级逐级传递，但大部分能量通过呼吸、排泄和未被取食的部分而散失。能量传递效率的计算公式为 效率 (%) = (较高营养级的能量 ÷ 较低营养级的能量) × 100。传递效率通常约为 10%，这解释了为何食物链很少超过四到五个营养级，以及生物量金字塔为何向顶端急剧收窄。
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