📚 Year 11 Edexcel Biology: Quick-Reference Handbook of Formulas and Theorems | Year 11 Edexcel 生物：公式定理速查手册
This handbook provides a concise summary of the essential formulas and theorems you need to master for the Year 11 Edexcel Biology course. From magnification to energy transfer, these equations underpin both paper 1 and paper 2 examinations. Keep this guide handy for last-minute revision and practice.
本手册简要总结了 Year 11 Edexcel 生物学课程中必须掌握的关键公式与定理。从放大倍数计算到能量传递效率，这些公式贯穿试卷一和试卷二。将此指南放在手边，方便考前冲刺与练习。
1. Magnification Formula | 放大倍数公式
must ensure that both measurements are in the same unit before substituting into the formula. Common unit conversions include 1 mm = 1000 µm and 1 µ r or the actual size of a cell and asked to calculate the magnification or the image size.
放大倍数公式将图像大小与实际标本大小联系起来。这是显微镜相关考题的基础。代入公式前，必须确保两个测量值使用相同单位。常见单位转换有：1 毫米 = 1000 微米，1 微米 = 1000 纳米。在许多试题中，你会拿到一个比例尺或细胞的实际大小，并被要求计算放大倍数或图像大小。
ratio to find the actual size. When calculating the size of a subcellular structure from a drawing, use the formula rearranged as Actual size = Image size ÷ Magnification.
始终将测量值转换为相同单位后再代入公式。如果给出了比例尺，可测量其毫米长度，并用比例计算实际大小。当从绘图计算亚细胞结构的大小时，可使用公式变形：实际大小 = 图像大小 ÷ 放大倍数。
| Symbol | Meaning | Units |
|---|---|---|
| M | Magnification | times (×) |
| I | Image size | mm or µm |
| A | Actual size | mm or µm |
Magnification = Image size ÷ Actual size ; M = I / A
2. Rate of Enzyme-Controlled Reactions | 酶促反应速率
time. This is often expressed as Rate = Change in quantity ÷ Time taken. In the Edexcel IGCSE core practicals, you may investigate the effect of pH or temperature on amylase by recording the time taken for starch to break down (using iodine solution). The rate can then be calculated as 1 ÷ time for the end-point to be reached.
酶促反应速率可通过测量单位时间内产物的生成量或底物的消耗量来确定。通常表示为：速率 = 变化量 ÷ 所用时间。在 Edexcel IGCSE 的核心实验中，你可能通过记录淀粉分解所需时间（使用碘液）来研究 pH 或温度对淀粉酶的影响。速率可计算为 1 ÷ 到达终点所用时间。
When plotting graphs, the initial rate is often the steepest part of the curve, indicating the fastest rate before substrate depletion or denaturation occurs. Always quote the unit, such as cm³/min for gas production or g/min for mass change.
绘制曲线图时，初始速率通常是曲线最陡峭的部分，代表底物耗尽或酶变性前的最快速率。务必标注单位，例如气体产生用 cm³/min，质量变化用 g/min。
Rate of reaction = Δ Quantity (product or substrate) / Time
3. Fick's Law of Diffusion | 菲克扩散定律
Fick's Law describes the factors affecting the rate of diffusion across a membrane or exchange surface. The rate of diffusion is directly proportional to the surface area available for exchange and the concentration gradient (difference in concentration between two regions). It is inversely proportional to the thickness (distance) of the exchange surface. This law explains many biological adaptations, such as the flattened alveolar epithelium in lungs, the extensive network of root hairs in plants, and the biconcave shape of red blood cells.
菲克定律描述了影响跨膜或跨交换表面扩散速率的因素。扩散速率与可用于交换的表面积和浓度梯度（两区域间的浓度差）成正比，与交换表面的厚度（扩散距离）成反比。该定律解释了许多生物适应性结构，如肺泡的扁平上皮、植物庞大的根毛网络以及红细胞的凹盘状形态。
In exam answers, you should link structural features to Fick's Law: a large surface area shortens diffusion time, a steep concentration gradient is maintained by ventilation or blood flow, and a thin membrane shortens the diffusion distance.
在答题时，你应当将结构特点与菲克定律相联系：大的表面积缩短扩散时间；通过通气或血流维持陡峭的浓度梯度；薄的膜缩短扩散距离。
| Rate of diffusion | ∝ (Surface area × Concentration gradient) / Thickness of exchange surface |
4. Respiration Equations | 呼吸作用方程式
Respiration is an exothermic process that releases energy in the form of ATP from glucose. You must know the word equations and balanced symbol equations for aerobic respiration in plants and animals, as well as anaerobic respiration in animals and in yeast. Aerobic respiration requires oxygen and produces a high yield of ATP. Anaerobic respiration occurs when oxygen is scarce and yields much less ATP per glucose molecule.
呼吸作用是一个放能过程，以 ATP 的形式从葡萄糖中释放能量。你必须掌握动植物有氧呼吸，以及动物和酵母无氧呼吸的文字方程式和配平的符号方程式。有氧呼吸需要氧气，并产生大量的 ATP。无氧呼吸在氧气不足时发生，每分子葡萄糖产生的 ATP 少得多。
| Aerobic | Glucose + Oxygen → Carbon dioxide + Water (+ ATP) |
| C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O | |
| Anaerobic (animals) | Glucose → Lactic acid (+ ATP) |
| C₆H₁₂O₆ → 2C₃H₆O₃ | |
| Anaerobic (yeast) | Glucose → Ethanol + Carbon dioxide (+ ATP) |
| C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ |
Note that the symbol equations must be balanced, and the energy released is not written in the symbol equation. The lactic acid produced in muscles causes fatigue and an oxygen debt, which is repaid by deep breathing after exercise. Yeast fermentation is exploited in baking and brewing.
注意符号方程式必须配平，且释放的能量不写入符号方程式中。肌肉中产生的乳酸会导致疲劳和氧债，运动后通过深呼吸偿还。酵母发酵被用于烘焙和酿酒。
5. Photosynthesis Equation | 光合作用方程式
Photosynthesis is an endothermic reaction in which green plants and algae use light energy to synthesise glucose from carbon dioxide and water. The process takes place in chloroplasts containing chlorophyll. The overall word equation and balanced symbol equation are required for the Edexcel specification. Oxygen is released as a by-product. The rate of photosynthesis can be limited by light intensity, carbon dioxide concentration, and temperature.
光合作用是一个吸热反应，绿色植物和藻类利用光能将二氧化碳和水合成葡萄糖。该过程在含有叶绿素的叶绿体中进行。Edexcel 大纲要求掌握总文字方程式和配平的符号方程式。氧气作为副产物释放。光合作用速率受光照强度、二氧化碳浓度和温度的限制。
| Word equation | Carbon dioxide + Water → Glucose + Oxygen |
| Symbol equation | 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ |
Remember to mention that light energy and chlorophyll are required (they appear above the arrow). The glucose produced is used for respiration, converted to starch for storage, or used to synthesise cellulose, lipids, and amino acids. In aquatic plants, oxygen production (bubbles) can be used to measure the rate.
记得注明该反应需要光能和叶绿素（写在箭头上方）。产生的葡萄糖用于呼吸作用，转化为淀粉储存，或用于合成纤维素、脂质和氨基酸。在水生植物中，可用氧气产生量（气泡数）来测量速率。
6. Cardiac Output, Stroke Volume and Heart Rate | 心输出量、每搏输出量与心率
e) and the stroke volume (SV, the volume of blood pumped per beat). This relationship is described by the equation: Cardiac Output = Stroke Volume × Heart Rate. Athletes typically have a lower resting heart rate and a higher stroke volume compared to sedentary individuals, allowing the same cardiac output with greater efficiency.
心输出量 (CO) 是左心室每分钟泵出的血液容积，由心率 (HR，每分钟搏动次数) 和每搏输出量 (SV，每次搏动泵出的血量) 决定。这一关系通过公式表达：心输出量 = 每搏输出量 × 心率。与久坐者相比，运动员通常静息心率较低而每搏输出量较高，从而以更高效率维持同等心输出量。
Cardiac Output (cm³/min or dm³/min) = Stroke Volume (cm³/beat) × Heart Rate (beats/min)
You may be asked to calculate any of the three variables if the other two are provided. Remember that during exercise, both heart rate and stroke volume can increase, markedly raising cardiac output to deliver more oxygen to the muscles.
若给定其中两个变量，可能会要求计算第三个。记住，运动期间心率和每搏输出量均可增加，显著提高心输出量以向肌肉输送更多氧气。
7. Body Mass Index (BMI) | 身体质量指数
Body Mass Index (BMI) is a simple screening tool that classifies adults into categories of underweight, normal weight, overweight, and obese. It is calculated as body mass in kilograms divided by the square of height in metres. Although BMI does not directly measure body fat and may misclassify muscular individuals, it is widely used in epidemiological studies. The formula is straightforward and may appear in data analysis or health-related questions.
身体质量指数 (BMI) 是一项简单的筛查工具，将成人分为体重不足、正常、超重和肥胖等类别。其计算方式为体重（千克）除以身高（米）的平方。虽然 BMI 不能直接测量体脂且可能错误分类肌肉发达者，但仍广泛用于流行病学研究。公式简单，可能出现在数据分析或健康相关试题中。
| BMI | = body mass (kg) / [height (m)]² |
ealthy range. A BMI below 18.5 is considered underweight, and above 30 is obese. Always remember to square the height first before division.
例如，一个体重 70 千克、身高 1.75 米的人，BMI 为 70 / (1.75)² ≈ 22.9，属于健康范围。BMI 低于 18.5 为体重不足，高于 30 为肥胖。始终注意先对身高取平方，再做除法。
8. Respiratory Quotient (RQ) | 呼吸商
The respiratory quotient (RQ) is the ratio of the volume of carbon dioxide produced to the volume of oxygen consumed during respiration. It provides information about the substrate being respired. Carbohydrate respiration gives an RQ close to 1.0, lipid respiration yields an RQ around 0.7, and protein typically gives values between 0.8 and 0.9. RQ values are commonly determined using a respirometer. If a respiring organism produces more CO₂ than the O₂ it consumes, the RQ will be greater than 1, which can occur during anaerobic respiration.
呼吸商 (RQ) 是呼吸过程中释放的二氧化碳体积与消耗的氧气体积之比，可用于推断正在被呼吸的底物。碳水化合物的呼吸商接近 1.0，脂肪呼吸商约为 0.7，蛋白质通常在 0.8 至 0.9 之间。RQ 值通常用呼吸计测定。若呼吸生物产生的 CO₂ 多于消耗的 O₂，RQ 将大于 1，这在无氧呼吸时可能发生。
| RQ | = Volume of CO₂ produced / Volume of O₂ consumed |
In practical work, a U-tube respirometer with soda lime absorbs CO₂, allowing the measurement of O₂ uptake. A separate setup without soda lime measures the net change in volume; the difference gives CO₂ production. These measurements are then used to calculate RQ.
在实验中，装有碱石灰的 U 形管呼吸计可吸收 CO₂，用于测量 O₂ 的消耗量。另一套无碱石灰的装置测量体积净变化，差值即为 CO₂ 产生量。这些测量值随后用于计算 RQ。
9. Genetic Probability and Monohybrid Ratios | 遗传概率与单基因杂交比
als (e.g., Tt × Tt) are crossed and complete dominance applies, the expected genotypic ratio is 1 TT : 2 Tt : 1 tt. The corresponding phenotypic ratio is 3 : 1 (dominant phenotype : recessive phenotype). The probability of an offspring inheriting a particular genotype can be expressed as a fraction (e.g., 1/4), a ratio (1:3), or a percentage (25%).
在涉及一对等位基因的单基因杂交中，可用庞纳特方格预测后代结果。当两个杂合个体（如 Tt × Tt）杂交且为完全显性时，预期的基因型比为 1 TT : 2 Tt : 1 tt，相应的表型比为 3
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