📚 IGCSE Biology Formula & Theorem Quick Reference Handbook | IGCSE生物公式定理速查手册
This quick reference handbook distils the essential formulas, equations, ratios and key principles you need for Cambridge IGCSE Biology (0610/0970). Master these tools to solve calculation questions, predict genetic outcomes, interpret experimental data and explain biological processes with confidence.
本速查手册提炼了剑桥 IGCSE 生物 (0610/0970) 所需的核心公式、方程式、比率和关键原理。掌握这些工具，你就能自信地解决计算题、预测遗传结果、解读实验数据并解释生物学过程。
1. Magnification Formula | 放大倍数公式
Magnification is how much larger an image appears compared with the real specimen. Always use the same unit for image size and actual size.
放大倍数是指图像比真实标本放大了多少。计算时务必保持图像大小和实际大小的单位一致。
Magnification = Image size ÷ Actual size
To find actual size: Actual size = Image size ÷ Magnification. For example, if a cell image measures 30 mm at ×600, actual size = 30 ÷ 600 = 0.05 mm = 50 µm.
求实际大小：实际大小 = 图像大小 ÷ 放大倍数。例如，细胞图像长 30 mm，放大倍数 ×600，实际大小 = 30 ÷ 600 = 0.05 mm = 50 µm。
Remember that 1 mm = 1000 µm, so always convert to the same unit before dividing.
记住 1 mm = 1000 µm，计算前务必统一单位。
2. Rate of Reaction (Enzyme Activity) | 反应速率（酶活性）
Enzyme activity is often measured as the rate at which a substrate disappears or a product appears. Rate is calculated as the change in quantity divided by time.
酶活性通常通过底物消失或产物出现的速率来测量。速率等于变化量除以时间。
Rate = Quantity of product formed ÷ Time
Alternatively, when tracking a change like colour disappearance: Rate = 1 ÷ time taken for the change to occur (e.g. 1/t). This gives a relative rate suitable for plotting graphs.
若追踪某个变化（如颜色消失），可用速率 = 1 ÷ 变化所需时间（1/t）。这给出适合绘图的相对速率。
Units depend on what is measured: cm³ of O₂ per minute (cm³ min⁻¹) or absorbance change per second (s⁻¹).
单位取决于测量对象：每分钟产生的氧气体积（cm³ min⁻¹）或每秒吸光度变化（s⁻¹）。
3. Photosynthesis Equation | 光合作用方程式
The overall balanced chemical equation for photosynthesis shows how light energy converts carbon dioxide and water into glucose and oxygen.
光合作用总平衡化学方程式展示了光能如何将二氧化碳和水转化为葡萄糖和氧气。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This process requires light energy and chlorophyll. The glucose may be used for respiration, stored as starch, or converted into cellulose, proteins and other organic molecules.
该过程需要光能和叶绿素。生成的葡萄糖可用于呼吸作用、以淀粉形式储存，或转化成纤维素、蛋白质等有机物。
Rate of photosynthesis can be measured as O₂ volume produced per unit time or as 1/time for a leaf disc to rise.
光合速率可通过单位时间内产生的氧气体积或叶片上浮所需的 1/时间 来测量。
4. Respiration Equations | 呼吸作用方程式
Aerobic respiration releases a large amount of energy by fully oxidising glucose. The summary equation is the reverse of photosynthesis but occurs in all living cells.
有氧呼吸通过完全氧化葡萄糖释放大量能量。其总方程式与光合作用相反，但发生在所有活细胞中。
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ ATP)
Anaerobic respiration in yeast (fermentation) produces ethanol and carbon dioxide.
酵母的无氧呼吸（发酵）产生乙醇和二氧化碳。
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
Anaerobic respiration in animal cells and some bacteria yields lactic acid, which can cause muscle fatigue.
动物细胞和某些细菌的无氧呼吸产生乳酸，可导致肌肉疲劳。
C₆H₁₂O₆ → 2C₃H₆O₃
Aerobic respiration yields far more ATP (approximately 36-38 ATP) than anaerobic (2 ATP per glucose).
有氧呼吸产生的 ATP（约 36-38 个）远多于无氧呼吸（每分子葡萄糖产 2 个 ATP）。
5. Net Gas Exchange & Compensation Point | 净气体交换与补偿点
In plants, photosynthesis produces O₂ and uses CO₂, while respiration does the opposite. Net gas exchange depends on the balance between these two processes.
在植物中，光合作用产 O₂ 耗 CO₂，呼吸作用则相反。净气体交换取决于这两个过程的平衡。
Net photosynthesis = Gross photosynthesis − Respiration
At the compensation point (for light intensity or CO₂ concentration), the rates of photosynthesis and respiration are equal, so net gas exchange is zero.
在补偿点（光照强度或 CO₂ 浓度），光合作用与呼吸作用速率相等，净气体交换为零。
Above the compensation point, photosynthesis exceeds respiration, meaning the plant releases more oxygen and takes up more carbon dioxide.
在补偿点以上，光合作用超过呼吸作用，植物释放更多氧气并吸收更多二氧化碳。
6. Heart Rate & Pulse Rate | 心率和脉搏率
Heart rate is the number of heartbeats per minute. It can be measured by feeling the pulse at the wrist or neck.
心率是每分钟心跳的次数，可通过手腕或颈部脉搏测得。
Heart rate (bpm) = Number of beats ÷ Time (min)
Pulse rate equals heart rate in a healthy individual. You may investigate the effect of exercise by measuring pulse rate before and after activity.
健康人的脉搏率等于心率。可通过测量运动前后脉搏率来探究运动的影响。
Remember to count beats for a fixed time (e.g. 15 seconds) then multiply to obtain beats per minute.
记住固定时间计数（如数 15 秒）然后乘以相应倍数得到每分钟心跳数。
7. Genetic Ratios & Punnett Square Rules | 遗传比率与庞纳特方格规则
A monohybrid cross between two heterozygous individuals (Tt × Tt) produces a phenotypic ratio of 3 dominant : 1 recessive.
两个杂合个体（Tt × Tt）的单杂交产生 3 显性 : 1 隐性的表现型比。
Phenotypic ratio = 3 : 1
The genotypic ratio for the same cross is 1 homozygous dominant : 2 heterozygous : 1 homozygous recessive (1 TT : 2 Tt : 1 tt).
相同杂交的基因型比为 1 显性纯合 : 2 杂合 : 1 隐性纯合 (1 TT : 2 Tt : 1 tt)。
A dihybrid cross of two heterozygous parents for two genes (RrYy × RrYy) yields the classic 9 : 3 : 3 : 1 phenotypic ratio when genes are unlinked.
两个基因均为杂合的双杂交 (RrYy × RrYy) 在不连锁时产生经典的 9 : 3 : 3 : 1 表现型比。
A test cross of heterozygous × homozygous recessive gives a 1 : 1 phenotypic ratio, revealing the genotype of the unknown parent.
测交（杂合 × 隐性纯合）产生 1 : 1 表现型比，可揭示未知亲本的基因型。
8. Diffusion & Fick’s Law Relationship | 扩散与菲克定律关系
The rate of diffusion across an exchange surface is influenced by three key factors, which can be summarised in a proportionality statement resembling Fick’s law.
交换表面上的扩散速率受三个关键因素影响，可概括为一个类似菲克定律的比例关系式。
Rate of diffusion ∝ (Surface area × Concentration gradient) ÷ Diffusion distance
-
A larger surface area (e.g. alveoli, villi) increases diffusion rate.
更大的表面积（如肺泡、小肠绒毛）提高扩散速率。
-
A steeper concentration gradient (greater difference) drives faster diffusion.
更陡的浓度梯度（更大的浓度差）使扩散更快。
-
A thinner exchange surface (shorter diffusion distance) speeds up diffusion.
更薄的交换表面（更短的扩散距离）加快扩散。
9. Population Size Estimation | 种群数量估算
The capture-mark-recapture method estimates the total population size (N) using the Lincoln index.
标志重捕法使用林肯指数估算总种群数量 (N)。
N = (M × C) ÷ R
M = number of individuals captured in the first sample and marked. C = total number captured in the second sample. R = number of marked individuals recaptured in the second sample.
M = 首次捕获并标记的个体数；C = 第二次捕获的总个体数；R = 第二次捕获中已被标记的个体数。
This method assumes no migration, no births or deaths, and that marked individuals mix evenly with the population.
该方法假设没有迁移、出生或死亡，且标记个体与种群均匀混合。
For stationary organisms, population density can be estimated using quadrats: calculate the mean number per quadrat and multiply by the ratio (total area / quadrat area).
对于固着生物，可使用样方估算种群密度：计算每个样方的平均个体数，再乘以（总面积 ÷ 样方面积）。
10. Respiration Quotient (RQ) | 呼吸商
The respiration quotient (RQ) indicates which respiratory substrate is being used. It is the ratio of carbon dioxide produced to oxygen consumed.
呼吸商 (RQ) 显示细胞正在使用哪种呼吸底物，它是产生的二氧化碳与消耗的氧气体积之比。
RQ = CO₂ produced ÷ O₂ consumed
| Substrate | RQ value |
|---|---|
| Carbohydrate | 1.0 |
| Lipid | ~0.7 |
| Protein | ~0.9 |
The RQ value can be determined experimentally using a respirometer. A value close to 1.0 implies carbohydrate respiration.
实验可用呼吸计测定 RQ 值。若 RQ 接近 1.0，表明主要利用碳水化合物进行呼吸。
11. Energy Flow & the 10% Rule | 能量流动与10%规则
In an ecosystem, energy is transferred along food chains. On average, only about 10% of the energy in one trophic level is passed on to the next level.
在生态系统中，能量沿食物链传递。平均而言，一个营养级中只有约 10% 的能量传递到下一营养级。
Energy transferred ≈ 10% of energy consumed
The remaining 90% is lost mainly through respiration, movement, excretion and uneaten parts. This explains why food chains rarely exceed 4-5 trophic levels.
其余约90%的能量主要通过呼吸、运动、排泄和未食部分而散失。这解释了食物链很少超过4-5个营养级的原因。
You can calculate energy efficiency between trophic levels as: Efficiency (%) = (Energy in higher level ÷ Energy in lower level) × 100.
可计算营养级之间的能量效率：效率 (%) = (较高营养级能量 ÷ 较低营养级能量) × 100。
12. Osmosis & Water Potential | 渗透与水势
Osmosis is the net movement of water molecules from a region of higher water potential to a region of lower water potential through a partially permeable membrane.
渗透是水分子通过半透膜从较高水势区域向较低水势区域的净移动。
Water potential (Ψ) is measured in kilopascals (kPa). Pure water has a water potential of 0 kPa; solutions have negative water potentials.
水势 (Ψ) 以千帕 (kPa) 为单位。纯水的水势为 0 kPa，溶液的水势为负值。
The more concentrated the solute, the more negative the water potential. Water moves down the water potential gradient until equilibrium is reached.
溶质浓度越高，水势越负。水沿着水势梯度移动，直至达到平衡。
In plant cells, osmosis creates turgor pressure that keeps cells rigid. Plasmolysis occurs when cells lose water in a hypertonic solution.
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