IGCSE Edexcel Biology Formula Handbook | IGCSE Edexcel 生物：公式汇总手册

📚 IGCSE Edexcel Biology Formula Handbook | IGCSE Edexcel 生物：公式汇总手册

Welcome to the ultimate formula handbook for IGCSE Edexcel Biology. This guide brings together every essential equation you need — from magnification and microscopy to respiration, photosynthesis, osmosis, and ecology. Each formula is presented clearly with definitions of symbols, worked examples, common pitfalls, and tips for exam success. Whether you are revising for Paper 1 or Paper 2, mastering these formulas will sharpen your calculation skills and boost your confidence.

欢迎使用 IGCSE Edexcel 生物终极公式手册。本指南汇集了你需要的所有关键方程式——从放大倍率和显微镜到呼吸作用、光合作用、渗透以及生态学。每个公式都清晰地呈现了符号定义、解题示例、常见陷阱和应试技巧。无论你是在复习试卷一还是试卷二，掌握这些公式都将提升你的计算能力，增强你的信心。

1. Magnification Formula | 放大倍率公式

Magnification is calculated by dividing the size of the image by the actual size of the specimen. The formula is Magnification = Image size / Actual size. All three quantities must be expressed in the same unit — usually millimetres (mm) or micrometres (µm). Remember: 1 mm = 1000 µm. If you are given a scale bar, measure its length on the image and use the real size it represents.

放大倍率的计算方法是图像尺寸除以样本实际尺寸。公式为 放大倍率 = 图像尺寸 / 实际尺寸。这三个量必须用同一单位表示——通常是毫米 (mm) 或微米 (µm)。请记住：1 mm = 1000 µm。如果题目中给出了比例尺，则需要测量它在图像上的长度，并使用它所代表的真实尺寸。

M = I / A, where M = magnification (no units), I = image size, A = actual size.
M = I / A，其中 M = 放大倍率（无单位），I = 图像尺寸，A = 实际尺寸。
Convert all measurements to the same unit before calculating.
计算前将所有测量值转换为相同单位。
Rearranged forms: I = M × A and A = I / M.
变形公式：I = M × A 和 A = I / M。

Symbol	Meaning	Common Unit
M	Magnification	(times, ×)
I	Image size	mm or µm
A	Actual size	mm or µm

Example: A cell image measures 20 mm across. Its real diameter is 0.5 mm. Magnification = 20 / 0.5 = ×40.

示例：一张细胞图像的直径为 20 mm。其真实直径为 0.5 mm。放大倍率 = 20 / 0.5 = ×40。

2. Estimating Cell Size Using Field of View | 利用视野估算细胞大小

When using a microscope, you can estimate the size of a cell if you know the diameter of the field of view. Count how many cells fit across the diameter, then use Cell size = Field of view diameter / Number of cells. This method works best for roughly uniform cells like cheek cells or onion epidermis.

使用显微镜时，如果你知道视野直径，就可以估算细胞的大小。数出有多少个细胞横跨该直径，然后使用 细胞大小 = 视野直径 / 细胞数量。这种方法对大致均匀的细胞（如口腔上皮细胞或洋葱表皮细胞）效果最好。

At low power (×40 total magnification), the field of view is about 4.5 mm. At medium power (×100), it is about 1.8 mm. At high power (×400), it drops to 0.45 mm. Always confirm the scale with your specific microscope if required.

在低倍镜下（总放大倍率 ×40），视野直径约为 4.5 mm。中倍镜下（×100）约为 1.8 mm。高倍镜下（×400）降至 0.45 mm。如果题目有要求，务必根据你所使用的特定显微镜确认比例尺。

3. Food Test Quantitative Equations | 食物测试定量方程

For the Benedict’s test, a semi-quantitative relationship exists between the concentration of reducing sugar and the colour change. The mass of precipitate formed can be used with the formula Concentration = Mass of reducing sugar / Volume of solution. In colorimetry, the absorbance of the Benedict’s solution after reaction is proportional to sugar concentration.

在本尼迪克特测试中，还原糖的浓度与颜色变化之间存在半定量关系。形成的沉淀质量可用公式 浓度 = 还原糖质量 / 溶液体积 来表示。在比色法中，反应后本尼迪克特溶液的吸光度与糖浓度成正比。

For vitamin C titration with DCPIP, use Vitamin C content = Volume of DCPIP used × Concentration factor. A standard curve using known vitamin C concentrations is often required to convert volume of DCPIP into actual vitamin C concentration.

在用 DCPIP 滴定维生素 C 时，使用 维生素 C 含量 = 所用 DCPIP 体积 × 浓度系数。通常需要用已知浓度的维生素 C 制作标准曲线，将所用 DCPIP 的体积换算成实际的维生素 C 浓度。

4. Rate of Enzyme-Controlled Reactions | 酶促反应速率

The rate of an enzyme-catalysed reaction can be measured as the amount of product formed per unit time, or the amount of substrate used per unit time. The formula is Rate = Change in quantity / Time taken. Common practical contexts include measuring the volume of oxygen produced from catalase breaking down hydrogen peroxide, or recording the time for starch to disappear with amylase.

酶促反应的速率可以用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 = 量的变化 / 所用时间。常见的实验场景包括测量过氧化氢酶分解过氧化氢产生的氧气体积，或记录淀粉酶使淀粉消失所需的时间。

Rate = ΔQ / Δt, where ΔQ = change in quantity (volume, mass, or concentration), Δt = time interval.
速率 = ΔQ / Δt，其中 ΔQ = 量的变化（体积、质量或浓度），Δt = 时间间隔。
Initial rate is often the fastest part of the reaction — measure over the first 30-60 seconds.
初始速率通常是反应最快的部分——在最初 30-60 秒内进行测量。
Units: cm³/s, g/min, mol/dm³/s, depending on the variable measured.
单位：cm³/s、g/min、mol/dm³/s，取决于测量的变量。

Example: 15 cm³ of oxygen is produced in 120 seconds. Rate = 15 / 120 = 0.125 cm³/s.

示例：在 120 秒内生成了 15 cm³ 的氧气。速率 = 15 / 120 = 0.125 cm³/s。

5. Rate of Photosynthesis | 光合作用速率

The rate of photosynthesis is commonly measured using pondweed (Elodea) by counting the number of oxygen bubbles released per minute, or by measuring the volume of oxygen collected in a gas syringe. The formula is Rate = Number of bubbles / Time or Rate = Volume of O₂ / Time.

光合作用的速率通常使用水草（如伊乐藻）来测量，方法有两种：一是计数每分钟释放的氧气气泡数量，二是测量集气注射器中收集的氧气体积。公式为 速率 = 气泡数量 / 时间 或 速率 = O₂ 体积 / 时间。

When investigating the effect of light intensity, an inverse square relationship Light intensity ∝ 1/d² is used, where d is the distance between the lamp and the plant. Combine this with the photosynthesis rate to plot rate against 1/d².

在研究光强度的影响时，使用平方反比关系 光强度 ∝ 1/d²，其中 d 是光源到植物的距离。将其与光合作用速率结合起来，可以绘制速率与 1/d² 的关系图。

Light intensity = 1 / d² (arbitrary units)

光强度 = 1 / d²（任意单位）

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

The respiratory quotient indicates which substrate is being respired. It is calculated as RQ = Volume of CO₂ released / Volume of O₂ consumed. An RQ of 1.0 suggests carbohydrate respiration. An RQ of about 0.7 to 0.8 suggests lipid respiration. An RQ greater than 1.0 suggests anaerobic respiration in some organisms.

呼吸商表明哪种底物正在被呼吸。计算公式为 RQ = 释放的 CO₂ 体积 / 消耗的 O₂ 体积。RQ 为 1.0 表明是碳水化合物呼吸。RQ 约为 0.7 到 0.8 表明是脂质呼吸。RQ 大于 1.0 表明某些生物体正在进行无氧呼吸。

Substrate	RQ
Carbohydrate / 碳水化合物	1.0
Lipid / 脂质	~0.7
Protein / 蛋白质	~0.9

RQ values are measured using a respirometer. A typical respirometer setup uses soda lime to absorb CO₂, so the decrease in gas volume directly indicates O₂ consumption. The CO₂ volume is measured in a parallel experiment without soda lime.

RQ 值可使用呼吸计测量。典型的呼吸计装置使用碱石灰来吸收 CO₂，因此气体体积的减少直接反映了 O₂ 的消耗量。而 CO₂ 的体积则在一个不放碱石灰的平行实验中进行测量。

7. Osmosis and Percentage Change in Mass | 渗透与质量百分比变化

When plant tissue is placed in sucrose or salt solutions, water moves by osmosis. The effect is measured by calculating the percentage change in mass using Change = (Final mass – Initial mass) / Initial mass × 100%. A positive value indicates water uptake (the solution is hypotonic). A negative value indicates water loss (the solution is hypertonic).

当植物组织被放入蔗糖或盐溶液中时，水通过渗透作用移动。这种效应通过计算质量百分比变化来衡量，使用 变化 = (最终质量 – 初始质量) / 初始质量 × 100%。正值表示吸水（溶液为低渗溶液）。负值表示失水（溶液为高渗溶液）。

The water potential of a solution that causes zero net change in mass is equal to the water potential of the plant tissue. This can be estimated from a graph of percentage change against concentration by finding the x-intercept (where the line crosses 0%).

引起质量净变化为零的溶液，其水势等于植物组织的水势。可以从质量百分比变化与浓度的关系图中，通过找到 x 轴截距（直线与 0% 轴相交处）来估算该点。

8. Population Growth Rate | 种群增长率

Population change in a habitat is determined by births, deaths, immigration, and emigration. The formula is Population growth rate = (Births + Immigration) – (Deaths + Emigration). This can be applied over a given time period to calculate the net change.

栖息地中种群的变化由出生、死亡、迁入和迁出决定。公式为 种群增长率 = (出生 + 迁入) – (死亡 + 迁出)。这可应用于特定时间段，以计算净变化。

For bacterial growth, when conditions are favourable, bacteria reproduce by binary fission. The number of bacteria after n divisions is N = N₀ × 2ⁿ, where N₀ is the starting population. The mean division time can be calculated if you know the total time and number of divisions.

对于细菌生长而言，在条件适宜时，细菌通过二分裂方式繁殖。n 次分裂后的细菌数量为 N = N₀ × 2ⁿ，其中 N₀ 是初始种群数量。如果你知道总时间和分裂次数，就可以计算平均分裂时间。

N = N₀ × 2ⁿ

Example: starting with 1 bacterium, after 6 hours (with a division time of 30 minutes), n = 12 divisions. N = 1 × 2¹² = 4096 bacteria.

示例：起始为 1 个细菌，6 小时后（分裂时间为 30 分钟），n = 12 次分裂。N = 1 × 2¹² = 4096 个细菌。

9. Efficiency of Biomass Transfer | 生物质传递效率

In ecosystems, energy is transferred between trophic levels. The efficiency of biomass transfer is calculated as Efficiency = (Biomass at higher trophic level / Biomass at lower trophic level) × 100%. This usually ranges between 5% and 20%, with most energy lost as heat through respiration, undigested materials, and movement.

在生态系统中，能量在营养级之间传递。生物质传递效率的计算公式为 效率 = (较高营养级的生物质 / 较低营养级的生物质) × 100%。这个数值通常在 5% 到 20% 之间，因为大部分能量通过呼吸作用、未消化的物质和运动以热的形式散失了。

When constructing pyramids of biomass, values are usually given in g/m² (mass per unit area) or kg/m². Efficiency calculations help explain why food chains rarely have more than four or five trophic levels.

在构建生物质金字塔时，数值通常以 g/m²（每单位面积质量）或 kg/m² 表示。效率计算有助于解释为什么食物链很少超过四或五个营养级。

10. Surface Area to Volume Ratio | 表面积与体积之比

For cubes and spheres, the surface area to volume ratio (SA:V) determines how efficiently substances can be exchanged by diffusion. As an organism or cell gets larger, its volume increases faster than its surface area, causing the SA:V to decrease. The formula for a cube is SA:V = 6s² / s³ = 6 / s, where s is side length.

对于立方体和球体而言，表面积与体积之比 (SA:V) 决定了物质通过扩散进行交换的效率。随着生物体或细胞变大，其体积的增长速度快于表面积，导致 SA:V 下降。立方体的公式为 SA:V = 6s² / s³ = 6 / s，其中 s 是边长。

Small organisms like bacteria have a large SA:V and can rely solely on diffusion for gas exchange. Larger multicellular organisms need specialised exchange surfaces (lungs, gills) and transport systems (blood, xylem, phloem) to overcome the limitations of a small SA:V.

像细菌这样的小型生物拥有较大的 SA:V，可以完全依靠扩散进行气体交换。较大的多细胞生物则需要特化的交换表面（肺、鳃）和运输系统（血液、木质部、韧皮部）来克服 SA:V 小带来的限制。

11. Fick’s Law for Gas Exchange | 气体交换的菲克定律

Fick’s Law describes the rate of diffusion across an exchange surface. It is not a strict numeric equation at IGCSE but a proportional relationship: Rate of diffusion ∝ (Surface area × Concentration difference) / Thickness of membrane. This explains why alveoli are covered in a dense capillary network — to maximise surface area and minimise diffusion distance.

菲克定律描述了物质穿过交换表面的扩散速率。在 IGCSE 阶段，它不是一个严格的数值方程，而是一个比例关系：扩散速率 ∝ (表面积 × 浓度差) / 膜的厚度。这解释了为什么肺泡上覆盖着密集的毛细血管网——为了最大化表面积并最小化扩散距离。

Alveoli: thin walls (one cell thick), large total surface area, steep concentration gradient maintained by ventilation and blood flow.
肺泡：薄壁（一个细胞厚），总表面积大，通过通气和血流维持陡峭的浓度梯度。
Villi: microvilli increase surface area; thin epithelium and rich blood supply maintain a steep gradient.
绒毛：微绒毛增加了表面积；薄的上皮细胞和丰富的血液供应维持了陡峭的梯度。

12. Beer-Lambert Law in Colorimetry | 比色法中的比尔-朗伯定律

In quantitative food tests and enzyme experiments, colorimeters measure the absorbance or transmission of light through a coloured solution. The relationship is Absorbance ∝ Concentration of the coloured compound. The formula used is A = εcl, where A = absorbance, ε = molar absorptivity constant, c = concentration, l = path length. At IGCSE, you simply use the proportional relationship to plot a standard curve.

在定量食物测试和酶实验中，比色计测量穿过有色溶液的光的吸光度或透射率。关系为 吸光度 ∝ 有色化合物的浓度。所用公式为 A = εcl，其中 A = 吸光度，ε = 摩尔吸光系数，c = 浓度，l = 光程长度。在 IGCSE 阶段，你只需利用比例关系绘制标准曲线即可。

Transmission and absorbance are inversely related. A 0% transmission means all light is absorbed (very concentrated). Use the formula Absorbance = log(1 / Transmission) if data is given as percentage transmission. Always plot absorbance against known concentrations, then use the graph to read off unknown values.

透射率和吸光度呈反比关系。透射率为 0% 表示所有光都被吸收（浓度很高）。如果数据以百分比透射率给出，使用公式 吸光度 = log(1 / 透射率) 。总是用吸光度对已知浓度作图，然后利用图表读出未知值。

13. Percentile Charts for Growth | 生长的百分位数图

Growth in infants and children is monitored using percentile charts. While there is no explicit formula to memorise, understanding that a baby’s mass centile is determined by plotting mass against age is essential. Consistent tracking along the same centile indicates healthy growth. A sharp drop across two or more centiles may signal a health problem.

婴儿和儿童的生长通过百分位数图来监测。虽然不需要记忆显式的公式，但理解 婴儿体重百分位是通过对照年龄绘制体重来确定的 这一点至关重要。沿着同一条百分位曲线稳定增长表明生长健康。如果体重急剧下降超过两条百分位线，可能提示健康问题。

Conversion between mass and weight may appear: Weight (N) = Mass (kg) × Gravitational field strength (g, N/kg). Though more physics-based, this occasionally appears in a biological context (e.g., interpreting hospital data).

可能会出现质量和重量之间的换算：重量 (N) = 质量 (kg) × 重力场强度 (g, N/kg)。虽然这更偏物理，但偶尔会在生物学背景下出现（例如，解读医院数据）。

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IGCSE Edexcel Biology Formula Handbook | IGCSE Edexcel 生物：公式汇总手册