Formula Summary Handbook for IGCSE WJEC Biology | IGCSE WJEC 生物：公式汇总手册

📚 Formula Summary Handbook for IGCSE WJEC Biology | IGCSE WJEC 生物：公式汇总手册

Mastering the key formulas in IGCSE WJEC Biology is essential for success in data analysis, practical questions, and core theory. This handbook compiles all the important equations you need, from magnification and rates of reaction to energy transfer efficiency and population estimates. Use it as a quick revision guide, ensuring you understand each formula’s components, units, and how it is applied in a biological context.

掌握 IGCSE WJEC 生物学中的关键公式，对于在数据分析、实验题和核心理论上取得成功至关重要。本手册汇集了所有你需要的重要方程式，从放大倍数、反应速率到能量传递效率和种群估计。请将其用作快速复习指南，确保你理解每个公式的组成部分、单位以及如何在生物学情景中应用它们。

1. Magnification Calculation | 放大倍数计算

Magnification tells you how many times larger an image appears compared to the real specimen. The basic formula is: Magnification = Image size ÷ Actual size. You can rearrange this to find image size (Image size = Magnification × Actual size) or actual size (Actual size = Image size ÷ Magnification). Always check that both sizes are in the same unit before calculating.

放大倍数表示图像比实际标本大多少倍。基本公式是：放大倍数 = 图像大小 ÷ 实际大小。你可以将其变形为求图像大小（图像大小 = 放大倍数 × 实际大小）或实际大小（实际大小 = 图像大小 ÷ 放大倍数）。计算前务必确保两个大小使用相同的单位。

M = I ÷ A

2. Actual Size and Unit Conversions | 实际尺寸与单位转换

When working with microscopes, you often need to convert between millimetres (mm) and micrometres (µm). Remember that 1 mm = 1000 µm. To calculate the real size of a cell, use Actual size = Image size ÷ Magnification. For example, if a cell image is 20 mm wide at ×400, the actual width is 20 mm ÷ 400 = 0.05 mm, which is 50 µm.

在使用显微镜时，你经常需要在毫米（mm）和微米（µm）之间进行转换。记住 1 mm = 1000 µm。要计算细胞的真实大小，使用实际大小 = 图像大小 ÷ 放大倍数。例如，如果一个细胞图像在 ×400 下宽度为 20 mm，则实际宽度为 20 mm ÷ 400 = 0.05 mm，即 50 µm。

Actual Size = Image Size ÷ Magnification; 1 mm = 1000 µm

3. Rate of Reaction (Enzyme Activity) | 反应速率（酶活性）

The rate of an enzyme‑controlled reaction can be measured by the amount of product formed or substrate used per unit time. The formula is: Rate = Quantity of product (or substrate used) ÷ Time. In many practicals, the rate is expressed as Rate = 1 ÷ Time if the endpoint is a clear colour change (e.g. starch disappearing with amylase). Units could be cm³/min for gas, g/min for mass, or simply s⁻¹.

酶控反应的速率可以通过单位时间内产物的生成量或底物的消耗量来衡量。公式为：速率 = 产物量（或消耗的底物量）÷ 时间。在许多实验中，如果终点是明显的颜色变化（例如淀粉被淀粉酶分解消失），速率常表示为速率 = 1 ÷ 时间。单位可以是 cm³/min（气体）、g/min（质量），或简单的 s⁻¹。

Rate = Amount ÷ Time; Rate = 1 ÷ Time

4. Photosynthesis Rate | 光合作用速率

The rate of photosynthesis can be estimated by measuring oxygen production, carbon dioxide uptake, or increase in biomass (dry mass) over time. A common formula is: Photosynthesis rate = Volume of O₂ produced ÷ Time. Using water plants like Elodea, you count bubbles per minute or use a gas syringe. Always consider limiting factors such as light intensity, CO₂ concentration, and temperature.

光合作用速率可以通过测量氧气产生量、二氧化碳吸收量或生物量（干重）随时间的变化来估算。一个常见的公式是：光合作用速率 = 产生 O₂ 的体积 ÷ 时间。使用如伊乐藻等水生植物时，你可以计数每分钟的气泡数或使用气体注射器。始终要考虑光照强度、CO₂ 浓度和温度等限制因素。

Rate of Photosynthesis = Volume of O₂ ÷ Time (min)

5. Transpiration Rate | 蒸腾作用速率

Transpiration rate indicates how quickly a plant loses water vapour. It can be measured using a potometer (distance travelled by an air bubble per unit time) or by mass loss. The formula: Transpiration rate = Water loss (g or cm³) ÷ Time. Alternatively, Rate = Distance moved by bubble ÷ Time. Environmental factors like light, humidity, and wind speed alter this rate.

蒸腾速率表示植物散失水蒸气的快慢。可以使用蒸腾计（气泡在单位时间内移动的距离）或通过质量损失来测量。公式为：蒸腾速率 = 失水量（g 或 cm³）÷ 时间。或者，速率 = 气泡移动的距离 ÷ 时间。光照、湿度和风速等环境因素会改变这一速率。

Rate = Water Loss ÷ Time; Rate = Bubble Distance ÷ Time

6. Respiratory Quotient (RQ) | 呼吸商（RQ）

The respiratory quotient tells you what type of respiratory substrate an organism is using. It is calculated as: RQ = Volume of CO₂ produced ÷ Volume of O₂ used. For carbohydrates, RQ = 1.0; for lipids, RQ ≈ 0.7; and for proteins, RQ ≈ 0.9. This formula is applied in simple respirometer experiments.

呼吸商告诉你生物体正在使用哪种呼吸底物。计算公式为：RQ = 产生 CO₂ 的体积 ÷ 消耗 O₂ 的体积。对于碳水化合物，RQ = 1.0；对于脂类，RQ ≈ 0.7；对于蛋白质，RQ ≈ 0.9。这个公式应用于简单的呼吸计实验中。

RQ = V(CO₂ produced) ÷ V(O₂ used)

7. Cardiac Output | 心输出量

Cardiac output is the volume of blood pumped by the heart per minute. It connects heart rate and stroke volume: Cardiac Output = Heart Rate × Stroke Volume. Heart rate is measured in beats per minute (bpm), stroke volume in cm³ or mL per beat, so cardiac output is usually given in cm³/min or L/min. This equation appears in circulatory system topics and exercise physiology questions.

心输出量是心脏每分钟泵出的血液体积。它连接了心率和每搏输出量：心输出量 = 心率 × 每搏输出量。心率以每分钟心跳次数（bpm）计，每搏输出量以每次搏动的 cm³ 或 mL 计，因此心输出量通常以 cm³/min 或 L/min 表示。该方程出现在循环系统专题和运动生理学问题中。

CO = HR × SV

8. Energy Transfer Efficiency | 能量传递效率

In a food chain, only a fraction of energy stored in one trophic level is transferred to the next. Efficiency is calculated as: Efficiency (%) = (Energy in biomass of higher trophic level ÷ Energy in biomass of lower trophic level) × 100. Energy is typically measured in kJ per m² per year. This principle explains why food chains rarely exceed 4–5 trophic levels.

在食物链中，储存在一个营养级中的能量只有一小部分会传递到下一个营养级。能量传递效率的计算公式为：效率（%）= (较高营养级生物量中的能量 ÷ 较低营养级生物量中的能量) × 100。能量通常以 kJ/m²/年 表示。这一原理解释了为什么食物链很少超过 4–5 个营养级。

Efficiency (%) = (En+1 ÷ En) × 100

9. Population Estimate (Lincoln Index) | 种群估计（林肯指数）

The Lincoln Index estimates the total population size of motile animals using capture‑mark‑recapture. The formula is: N = (M × C) ÷ R, where N = estimated total population, M = number caught and marked in the first sample, C = total number caught in the second sample, and R = number of marked individuals recaptured. Key assumptions include no migration, equal catchability, and marks not being lost.

林肯指数利用标记重捕法来估计活动性动物的种群总数。公式为：N = (M × C) ÷ R，其中 N = 估计的种群总数，M = 首次样本中捕获并标记的数量，C = 第二次样本中捕获的总数，R = 重捕到的已标记个体数。关键假设包括无迁入迁出、捕获机会均等、标记不脱落等。

N = (M × C) ÷ R

10. Body Mass Index (BMI) | 身体质量指数（BMI）

BMI is a simple index used to classify weight status in humans. It is defined as: BMI = Mass (kg) ÷ Height² (m²). For example, a person of 70 kg and 1.75 m tall has a BMI of 70 ÷ (1.75)² ≈ 22.9. While BMI does not directly measure body fat, it is a useful screening tool in discussions of diet and health.

BMI 是一种用于对人类体重状况进行分类的简单指数。其定义为：BMI = 体重（kg）÷ 身高²（m²）。例如，一个体重 70 kg、身高 1.75 m 的人，BMI 为 70 ÷ (1.75)² ≈ 22.9。虽然 BMI 不直接测量体脂，但在讨论饮食与健康时是一个有用的筛查工具。

BMI = Weight (kg) ÷ Height² (m²)

11. Percentage Change | 百分比变化

Percentage change is used to compare the change in a variable such as mass, length, or rate. The formula is: Percentage Change = ((Final value − Initial value) ÷ Initial value) × 100%. A positive value indicates an increase, while a negative value shows a decrease. This is essential for osmosis experiments where you calculate the percentage change in mass of potato cylinders.

百分比变化用于比较某个变量（如质量、长度或速率）的变化情况。公式为：百分比变化 = ((终值 − 初值) ÷ 初值) × 100%。正值表示增加，负值表示减少。这对于渗透实验中计算土豆条质量变化的百分比至关重要。

% Change = ((Final − Initial) ÷ Initial) × 100

12. Temperature Coefficient (Q₁₀) | 温度系数 (Q₁₀)

The Q₁₀ value indicates how much the rate of a reaction increases when the temperature is raised by 10 °C. It is calculated as: Q₁₀ = Rate at (T + 10) °C ÷ Rate at T °C. For many enzyme‑controlled reactions within their optimum range, Q₁₀ is around 2, meaning the rate doubles. Above the optimum temperature, the rate falls sharply as enzymes denature.

Q₁₀ 值表示温度每升高 10 °C 时反应速率增加的倍数。计算公式为：Q₁₀ = (T + 10) °C 下的速率 ÷ T °C 下的速率。对于许多处于最适温度范围内的酶控反应，Q₁₀ 大约为 2，意味着速率加倍。当温度超过最适点后，酶开始变性，速率急剧下降。

Q₁₀ = Rate(T+10) ÷ RateT

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