📚 Formula & Theorem Quick Reference for Year 11 Eduqas Biology | Year 11 Eduqas 生物公式定理速查手册
This handbook distils every formula, mathematical relationship and core principle that appears in the Eduqas GCSE Biology specification. Use it to check calculations, refresh your memory before exams, and ensure you apply the correct equation every time.
本手册浓缩了 Eduqas GCSE 生物大纲中出现的每一个公式、数学关系与核心原理。用它来核对计算、考前温习，并确保每次都能套用正确的等式。
1. Magnification & Cell Size | 放大倍数与细胞尺寸
The relationship between image size, actual size and magnification is fundamental. Always convert all lengths to the same unit before substituting numbers.
图像大小、实际大小与放大倍数之间的关系是基础。代入数字前，务必把所有长度换算成同一单位。
Magnification = Image size ÷ Actual size
放大倍数 = 图像大小 ÷ 实际大小
The rearranged forms are: Image size = Magnification × Actual size and Actual size = Image size ÷ Magnification. For example, if a cell measures 24 mm on a micrograph and the magnification is ×400, the actual size is 24 mm ÷ 400 = 0.06 mm = 60 µm.
变换后的形式为：图像大小 = 放大倍数 × 实际大小 及 实际大小 = 图像大小 ÷ 放大倍数。例如，若显微照片上细胞长 24 mm，放大倍数为 ×400，则实际大小 = 24 mm ÷ 400 = 0.06 mm = 60 µm。
Essential unit conversions:
必备单位换算：
- 1 cm = 10 mm; 1 mm = 1000 µm; 1 µm = 1000 nm
- To convert a larger unit to a smaller one, multiply (e.g. mm → µm: ×1000).
- 较大单位换算为较小单位要乘（如 mm → µm: ×1000）。
| 1 cm | 10 mm |
| 1 mm | 1000 µm |
| 1 µm | 1000 nm |
2. Percentage Change & Rate Calculations | 百分比变化与反应速率
Percentage change quantifies how a variable alters over time, while rate measures how quickly a process occurs.
百分比变化用于量化变量随时间的变化，速率则衡量过程发生的快慢。
Percentage change = (Final value – Initial value) / Initial value × 100
百分比变化 = (最终值 – 初始值) / 初始值 × 100
A positive result indicates an increase; a negative result indicates a decrease. This is often used to compare growth in plants or change in mass during osmosis experiments.
正数表示增加，负数表示减少。此公式常用于比较植物的生长或渗透作用实验中质量的变化。
For rate of reaction, we use:
反应速率使用以下公式：
Rate = Change in quantity ÷ Time taken
速率 = 数量变化 ÷ 所用时间
With enzyme-controlled reactions, rate can be expressed as the volume of product produced per minute (cm³/min) or as 1 ÷ time taken for a standard change to occur.
在酶控制反应中，速率可表示为每分钟产生产物的体积 (cm³/min)，或表示为 1 ÷ 完成某个标准变化所用的时间。
3. Chromatography and Rf Value | 色谱法与 Rf 值
Chromatography separates mixtures and the Rf value helps identify components. It is a ratio and has no units.
色谱法分离混合物，Rf 值用于鉴定组分。它是一个比值，没有单位。
Rf = Distance moved by substance ÷ Distance moved by solvent front
Rf = 物质移动距离 ÷ 溶剂前沿移动距离
The distances are measured from the baseline. An Rf value is always less than 1. Identical Rf values under the same conditions suggest the same substance.
距离从基线量起。Rf 值始终小于 1。相同条件下若 Rf 值相等，则提示为同种物质。
4. Energy & Biomass Transfer Efficiency | 能量与生物量传递效率
At each trophic level, only a fraction of energy or biomass is passed on. Efficiency calculations reveal the productivity of food chains.
在每个营养级，只有一小部分能量或生物量被传递。效率计算可揭示食物链的生产力。
Efficiency (%) = (Biomass transferred to the next level ÷ Biomass available at the previous level) × 100
效率 (%) = (传递至下一级的生物量 ÷ 前一级可利用的生物量) × 100
Alternatively, replace ‘biomass’ with ‘energy’ in kJ. Typical efficiencies range from 5 % to 20 %, with the remainder lost through respiration, undigested material and heat.
也可用“能量 (kJ)”替代“生物量”。典型效率介于 5% 至 20%，其余部分通过呼吸作用、未消化物质及热而损耗。
5. Cardiac Output & Ventilation Rate | 心输出量与呼吸速率
These two formulas link structure to function in the circulatory and respiratory systems.
这两个公式将循环系统与呼吸系统的结构与功能联系起来。
Cardiac output (cm³/min) = Heart rate (beats/min) × Stroke volume (cm³/beat)
心输出量 (cm³/min) = 心率 (次/分) × 每搏输出量 (cm³/次)
Ventilation (breathing) rate is determined simply by counting breaths:
通气（呼吸）速率通过计数呼吸次数得出：
Breathing rate = Number of breaths taken ÷ Time (minutes)
呼吸速率 = 呼吸次数 ÷ 时间 (分钟)
During exercise, both heart rate and breathing rate rise to deliver more oxygen and remove carbon dioxide more rapidly.
运动时，心率和呼吸速率都会上升，以更快地输送氧气和清除二氧化碳。
6. Body Mass Index (BMI) & Waist-to-Hip Ratio | 体重指数与腰臀比
BMI is a screening tool for weight categories. Waist-to-hip ratio indicates the distribution of body fat.
BMI 是一种体重分级的筛查工具。腰臀比反映体脂分布情况。
BMI = Body mass (kg) ÷ (Height in metres)²
BMI = 体重 (kg) ÷ (身高以米计)²
Example: a person weighing 68 kg and 1.72 m tall has BMI = 68 ÷ (1.72)² ≈ 23.0 kg/m².
示例：体重 68 kg、身高 1.72 m 的人，BMI = 68 ÷ (1.72)² ≈ 23.0 kg/m²。
Waist-to-hip ratio = Waist circumference ÷ Hip circumference
腰臀比 = 腰围 ÷ 臀围
A ratio above 0.90 for males or 0.85 for females often suggests a higher risk of obesity-related disease.
男性比值高于 0.90、女性高于 0.85 通常提示肥胖相关疾病风险较高。
7. Population Estimation (Capture-Recapture) | 种群数量估算（标记重捕法）
The Lincoln index estimates the size of a mobile population. Accuracy depends on several assumptions.
林肯指数用以估算活动种群的大小。准确性依赖于若干条件假设。
Estimated population size (N) = (M × C) ÷ R
种群数量估算值 (N) = (M × C) ÷ R
Where M = number captured, marked and released in the first sample; C = total number captured in the second sample; R = number of marked individuals recaptured in the second sample.
其中 M = 首次取样标记并释放的个体数；C = 第二次取样捕获总数；R = 第二次样本中带有标记的个体数。
This method assumes no births, deaths, immigration or emigration between samples, and that marks do not affect survival or detection.
该方法假定两次取样间无出生、死亡、迁入或迁出，且标记不影响生存或被发现的概率。
8. Genetic Ratios & Mendelian Principles | 遗传比率与孟德尔定律
While not equations in the algebraic sense, these proportional patterns and laws underpin inheritance problems.
虽非代数意义上的公式，这些比例模式与定律是解答遗传问题的基础。
Law of Segregation: Each individual has two alleles for a gene; these separate when gametes form, so each gamete carries only one allele.
分离定律： 每个个体每对等位基因有两个，形成配子时彼此分离，每个配子只含一个。
Law of Independent Assortment: Alleles for different genes are distributed to gametes independently of each other (applies to genes on different chromosomes).
自由组合定律： 不同基因的等位基因独立地分配到配子中（适用于不同染色体上的基因）。
A monohybrid cross between two heterozygous parents (Tt × Tt) gives a 3:1 phenotypic ratio when dominance is complete. A dihybrid cross between double heterozygotes yields the classic 9:3:3:1 ratio.
若完全显性，两个杂合亲本 (Tt × Tt) 的单基因杂交产生 3:1 表型比。双基因杂合子杂交产生典型的 9:3:3:1 比。
You can predict probabilities by multiplying independent events: probability of genotype aa = chance of ‘a’ from one parent × chance of ‘a’ from the other.
可通过独立事件相乘预测概率：基因型 aa 的概率 = 来自一方亲本的 ‘a’ 概率 × 来自另一方亲本的 ‘a’ 概率。
9. Surface Area to Volume Ratio | 表面积与体积比
This ratio dictates how efficiently substances are exchanged across cell surfaces. As an organism or cell grows, volume increases faster than surface area, reducing the ratio.
该比值决定物质通过细胞表面交换的效率。随着生物体或细胞长大，体积的增加快于表面积，使比值下降。
For a cube-shaped organism of side length L:
边长为 L 的立方体：
Surface area = 6L²; Volume = L³; SA:V ratio = 6L² / L³ = 6 / L
表面积 = 6L²; 体积 = L³; SA:V 比 = 6L² / L³ = 6 / L
A cube with 1 cm side has an SA:V of 6 : 1; with 3 cm side it drops to 2 : 1. Small organisms rely on diffusion alone; large ones need transport systems.
边长 1 cm 的立方体 SA:V 为 6 : 1；边长 3 cm 时降至 2 : 1。微小生物单靠扩散即可，大型生物需要运输系统。
10. Photosynthesis & Respiration Symbol Equations | 光合作用与呼吸的符号方程
These balanced chemical equations are core ‘theorems’ you must recall and apply in explanations of energy flow.
这些配平的化学方程是必须记忆并用于解释能量流动的核心“定理”。
Photosynthesis (endothermic):
光合作用（吸热）：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Aerobic respiration (exothermic):
有氧呼吸（放热）：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ ATP)
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ ATP)
Anaerobic respiration in animals: Glucose → Lactic acid (+ some ATP). In yeast: Glucose → Ethanol + Carbon dioxide (+ some ATP).
动物无氧呼吸：葡萄糖 → 乳酸 (+ 少量 ATP)。酵母中：葡萄糖 → 乙醇 + 二氧化碳 (+ 少量 ATP)。
These equations show that the products of photosynthesis become the reactants of respiration, driving the carbon cycle.
这些方程表明光合作用的产物变为呼吸作用的反应物，驱动碳循环。
11. Enzyme Theory: Lock-and-Key & Denaturation | 酶理论：锁钥模型与变性
The lock-and-key model is the accepted simplification describing enzyme–substrate interaction. The active site has a complementary shape to the substrate.
锁钥模型是一种公认的简化描述，用以说明酶与底物的相互作用。活性部位的形状与底物互补。
Lock-and-key hypothesis: Substrate fits exactly into the enzyme’s active site, forming an enzyme–substrate complex. This lowers the activation energy and products are released.
锁钥假说： 底物恰好嵌入酶的活性部位，形成酶-底物复合物，从而降低活化能，产物随之释放。
Denaturation is a permanent change to the active site’s shape caused by extreme temperature or pH. The substrate no longer fits, so the enzyme stops working.
变性是指极端温度或 pH 引起活性部位形状的永久改变。底物不再契合，酶的功能随之停止。
At optimum conditions, rate is maximal; beyond optimum, rate falls to zero once the enzyme is fully denatured.
在最适条件下，速率最大；超过最适条件，一旦酶完全变性，速率降至零。
This is not a numeric formula, but a qualitative theorem essential for explaining rate graphs.
这不是数值公式，却是解释速率曲线图不可或缺的定性定理。
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