📚 A-Level Biology: Formula Summary Handbook | A-Level 生物：公式汇总手册
This handbook brings together the key formulas and quantitative skills that appear throughout A-Level Biology specifications. Whether you are calculating the magnification of a micrograph, working out cardiac output, predicting allele frequencies, or assessing biodiversity with Simpson’s Index, being confident with these equations will boost your exam performance. Each section presents the formula with clear definitions, worked examples, and the biological context you need.
本手册汇总了 A-Level 生物课程中反复出现的关键公式与定量技能。从计算显微图像的放大倍数、心输出量，到预测等位基因频率、用辛普森指数评估生物多样性，熟练掌握这些方程将显著提升你的考试成绩。每个部分都提供了公式、清晰的定义、计算实例以及所需的生物学背景。
1. The Magnification Formula | 放大倍数公式
Magnification describes how many times larger an image appears compared to the real object. The equation is fundamental for microscopy work.
放大倍数描述的是图像相较于真实物体被放大的倍数。该方程是显微镜工作的基础。
M = I ÷ A
where M = magnification, I = image size, A = actual size. All values must be expressed in the same unit. The formula can be rearranged using a triangle: I = M × A and A = I ÷ M.
式中 M 为放大倍数，I 为图像尺寸，A 为实际尺寸。所有数值必须使用相同单位。公式可通过三角关系变形：I = M × A 以及 A = I ÷ M。
Example: An image of a mitochondrion measures 30 mm on a micrograph. The magnification used is ×20,000. The actual length = 30 mm ÷ 20,000 = 0.0015 mm = 1.5 µm. Always convert to appropriate units, such as micrometres (µm) for cells.
示例：线粒体的显微图像测量长度为 30 mm，所用放大倍数为 ×20,000。实际长度 = 30 mm ÷ 20,000 = 0.0015 mm = 1.5 µm。为方便表达细胞结构，始终应换算为合适的单位，如微米 (µm)。
2. Calculating Actual Size from a Scale Bar | 用比例尺计算实际尺寸
When an image includes a scale bar, you can determine actual size without knowing magnification. Measure the scale bar in the image with a ruler, note the length it represents, then use the proportion:
当图像中含有比例尺时，无需已知放大倍数即可求出实际尺寸。用直尺量取图像中比例尺的长度，记录其所代表的实际长度，然后利用比例关系：
Actual size of object = (measured length of object ÷ measured length of scale bar) × true length of scale bar
This is essentially a ratio method. Make sure both measured lengths are in the same unit.
这本质上是一种比值法。确保两个测量长度采用相同单位。
Example: A scale bar representing 10 µm measures 16 mm on the drawing. A chloroplast measures 24 mm. Actual length = (24 ÷ 16) × 10 µm = 1.5 × 10 µm = 15 µm.
示例：代表 10 µm 的比例尺在图上长度为 16 mm，叶绿体测量长度为 24 mm。实际长度 = (24 ÷ 16) × 10 µm = 1.5 × 10 µm = 15 µm。
3. Surface Area to Volume Ratio | 表面积与体积比
This ratio is critical for understanding exchange surfaces, rates of diffusion, and heat loss. For a regular shape you calculate surface area and volume separately, then determine SA:V.
该比值对于理解交换表面、扩散速率以及热量散失至关重要。对于规则形状，需分别计算表面积和体积，再求 SA:V 比。
SA:V ratio = surface area ÷ volume
The ratio is often simplified to a unit ratio, e.g. 6:1. As an organism or cell increases in size, its SA:V ratio decreases, reducing the efficiency of exchange unless adaptations are present.
比值通常简化为单位比，例如 6:1。随着生物体或细胞体积增大，SA:V 比值下降，降低交换效率，除非存在相应的适应结构。
For a cube of side length L: surface area = 6L², volume = L³, so SA:V = 6L² / L³ = 6/L. A small cube (L=1 mm) has SA:V = 6:1; a larger cube (L=2 mm) has SA:V = 3:1.
对于边长为 L 的立方体：表面积 = 6L²，体积 = L³，因此 SA:V = 6L² / L³ = 6/L。 一个小立方体 (L=1 mm) 的 SA:V = 6:1；较大的立方体 (L=2 mm) 的 SA:V = 3:1。
4. Water Potential (Ψ) | 水势 (Ψ)
Water potential governs the movement of water by osmosis. The equation combines solute potential and pressure potential.
水势决定渗透作用中水分的移动方向。该方程将溶质势与压力势结合。
Ψ = Ψₛ + Ψₚ
Ψₛ (solute potential) is always negative or zero; the more solute present, the more negative the value. Ψₚ (pressure potential) is usually positive inside a plant cell due to turgor pressure. Water flows from regions of higher water potential to lower water potential. Pure water under standard conditions has Ψ = 0 kPa.
Ψₛ（溶质势）始终为负值或零；溶质越多，数值越负。Ψₚ（压力势）在植物细胞内因膨压通常为正值。水分从水势较高的区域流向水势较低的区域。标准条件下纯水的 Ψ = 0 kPa。
Example: A plant cell has Ψₛ = -700 kPa and Ψₚ = +300 kPa, giving Ψ = -400 kPa. If the surrounding solution has Ψ = -200 kPa, water will enter the cell because -200 is higher than -400.
示例：某植物细胞 Ψₛ = -700 kPa，Ψₚ = +300 kPa，因此 Ψ = -400 kPa。若周围溶液 Ψ = -200 kPa，水分将进入细胞，因为 -200 高于 -400。
5. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle per minute. It depends on heart rate and stroke volume.
心输出量是指一个心室每分钟泵出的血液体积，其大小取决于心率和搏出量。
CO = HR × SV
CO = cardiac output (dm³ min⁻¹ or L min⁻¹), HR = heart rate (beats per minute, bpm), SV = stroke volume (dm³ or L per beat). Typical resting values: HR ~70 bpm, SV ~0.07 L, so CO ≈ 4.9 L min⁻¹. During exercise, both HR and SV can increase, significantly raising CO.
CO = 心输出量 (dm³ min⁻¹ 或 L min⁻¹)，HR = 心率 (次/分，bpm)，SV = 搏出量 (dm³ 或 L/次)。典型静息值：HR ~70 bpm，SV ~0.07 L，因此 CO ≈ 4.9 L min⁻¹。运动时心率和搏出量均可增大，显著提升心输出量。
6. Lung Volumes and Minute Ventilation | 肺容积与每分通气量
Minute ventilation is the total volume of air moved into and out of the lungs per minute. It is the product of tidal volume and breathing rate.
每分通气量是每分钟进出肺部的气体总量，为潮气量与呼吸频率的乘积。
MV = TV × f
MV = minute ventilation (dm³ min⁻¹), TV = tidal volume (dm³ per breath), f = breathing rate (breaths min⁻¹). For a typical person at rest: TV ≈ 0.5 dm³, f ≈ 12 breaths min⁻¹, so MV ≈ 6.0 dm³ min⁻¹.
MV = 每分通气量 (dm³ min⁻¹)，TV = 潮气量 (dm³/次)，f = 呼吸频率 (次/分)。典型静息状态下：TV ≈ 0.5 dm³，f ≈ 12 次/分，因此 MV ≈ 6.0 dm³ min⁻¹。
Alveolar ventilation rate accounts for dead space: Alveolar ventilation = (TV – dead space) × f. Dead space is the volume of air remaining in the conducting zone, approximately 0.15 dm³.
肺泡通气量需扣除无效腔：肺泡通气量 = (TV – 无效腔量) × f。无效腔是停留在传导区的气体，约 0.15 dm³。
7. Respiratory Quotient (RQ) | 呼吸商 (RQ)
RQ reveals which respiratory substrate is being used by cells. It is the ratio of carbon dioxide produced to oxygen consumed.
呼吸商可以揭示细胞正在利用哪种呼吸底物，它是产生的二氧化碳与消耗的氧气的体积比。
RQ = volume of CO₂ released ÷ volume of O₂ consumed
Values typically fall in characteristic ranges: carbohydrate ~1.0, lipid ~0.7, protein ~0.9. An RQ greater than 1.0 can indicate anaerobic respiration or fat synthesis. Measurements rely on a respirometer setup with soda lime to absorb CO₂.
RQ 值通常处于特征范围：碳水化合物 ~1.0，脂质 ~0.7，蛋白质 ~0.9。RQ 大于 1.0 可能提示存在无氧呼吸或脂肪合成。测量需使用呼吸计装置，并用钠石灰吸收 CO₂。
8. Net Primary Productivity (NPP) | 净初级生产力 (NPP)
NPP represents the chemical energy stored in plant biomass after respiratory losses are subtracted from gross primary productivity.
NPP 表示从总初级生产力中扣除呼吸损耗后，储存在植物生物量中的化学能。
NPP = GPP − R
GPP = gross primary productivity (total energy fixed by photosynthesis), R = respiratory losses by the plant. Units are typically kJ m⁻² yr⁻¹ or g m⁻² yr⁻¹. NPP is the energy available to the next trophic level.
GPP = 总初级生产力（光合作用固定的总能量），R = 植物自身的呼吸损耗。单位通常为 kJ m⁻² yr⁻¹ 或 g m⁻² yr⁻¹。NPP 是可供下一营养级利用的能量。
9. Efficiency of Energy Transfer | 能量传递效率
Between trophic levels, only a fraction of consumed energy is converted into new biomass. Efficiency calculations highlight losses through faeces, respiration, and uneaten material.
在营养级之间，只有一部分被摄取的能量转化为新的生物量。效率计算凸显了粪便、呼吸以及未被取食部分导致的能量损失。
Efficiency (%) = (energy incorporated into biomass at the higher level ÷ energy available at the lower level) × 100
Usually this is between 5% and 20%, with a common estimate of 10% used in simple pyramids. For example, if primary consumers ingest 8,000 kJ from plants and pass 800 kJ into their own biomass, the transfer efficiency is (800 ÷ 8,000) × 100 = 10%.
效率通常介于 5% 至 20% 之间，简单金字塔中常用 10% 的估算值。例如，初级消费者从植物中摄取 8,000 kJ 能量，其中 800 kJ 转化为自身生物量，则传递效率 = (800 ÷ 8,000) × 100 = 10%。
10. Mark-Release-Recapture (Lincoln Index) | 标记重捕法（林肯指数）
This method estimates the population size of mobile organisms. The formula assumes random mixing and no migration, births, or deaths between sampling.
该方法用于估算活动性生物种群的大小。公式假设两次采样之间个体随机混合，且无迁移、出生或死亡。
N = (n₁ × n₂) ÷ m
N = estimated total population, n₁ = number caught and marked in the first sample, n₂ = total number caught in the second sample, m = number of marked individuals recaptured in the second sample. All individuals should be marked harmlessly and released promptly.
N = 估算的种群总数，n₁ = 第一次捕获并标记的个体数，n₂ = 第二次捕获的总数，m = 第二次捕获中已标记的个体数。所有个体应以无害方式标记并迅速释放。
Example: 50 woodlice are marked and released. In the second catch, 80 woodlice are captured, of which 10 are marked. N = (50 × 80) ÷ 10 = 400. The population is estimated at 400 individuals.
示例：标记并释放 50 只鼠妇。第二次捕获 80 只，其中有 10 只带有标记。N = (50 × 80) ÷ 10 = 400。估计种群数量为 400 只。
11. Hardy-Weinberg Principle | 哈代-温伯格定律
The Hardy-Weinberg model predicts allele and genotype frequencies in a population that is not evolving. It provides a null hypothesis when investigating genetic change.
哈代-温伯格模型可预测不发生进化的种群中的等位基因与基因型频率，为研究遗传变化提供了零假设。
p + q = 1
p² + 2pq + q² = 1
p = frequency of the dominant allele, q = frequency of the recessive allele. p² = frequency of homozygous dominant genotype, q² = frequency of homozygous recessive genotype, 2pq = frequency of heterozygous genotype. The population must be large, randomly mating, and free from mutation, migration, and natural selection for the equilibrium to hold.
p = 显性等位基因的频率，q = 隐性等位基因的频率。p² = 纯合显性基因型的频率，q² = 纯合隐性基因型的频率，2pq = 杂合基因型的频率。种群必须足够大、随机交配，且无突变、迁移和自然选择，平衡才能成立。
Example: If 16% of a population shows a recessive trait (q² = 0.16), then q = √0.16 = 0.4 and p = 1 – 0.4 = 0.6. The heterozygous frequency = 2pq = 2 × 0.6 × 0.4 = 0.48, or 48%.
示例：若一个种群中有 16% 的个体表现出隐性性状 (q² = 0.16)，则 q = √0.16 = 0.4，p = 1 – 0.4 = 0.6。杂合子频率 = 2pq = 2 × 0.6 × 0.4 = 0.48，即 48%。
12. Statistical Tests: Chi-Squared and Simpson’s Index | 统计检验：卡方与辛普森多样性指数
The chi-squared test is used to compare observed and expected categorical data, such as phenotype ratios in genetics. The formula is:
卡方检验用于比较观测与预期的分类数据，例如遗传学中的表型比例。公式为：
χ² = Σ ( (O − E)² / E )
O = observed frequency, E = expected frequency. The degree of freedom (df) is number of categories minus 1. Compare the calculated χ² value with a critical value at p=0.05; if χ² exceeds the critical value, the null hypothesis is rejected.
O = 观测频数，E = 预期频数。自由度 (df) 为类别数减 1。将计算所得的 χ² 值与 p=0.05 时的临界值比较；若 χ² 大于临界值，则拒绝零假设。
Simpson’s Index of Diversity (D) measures biodiversity, accounting for both species richness and evenness. A higher value indicates greater diversity.
辛普森多样性指数 (D) 用于衡量生物多样性，兼顾物种丰富度与均匀度。数值越高，多样性越大。
D = 1 − Σ (n / N)²
n = number of individuals of a particular species, N = total number of individuals of all species. The sum of (n/N)² is taken across all species. D ranges from 0 (no diversity) to close to 1 (very high diversity). An alternative formula using n(n-1)/N(N-1) is sometimes used for small sample sizes.
n = 某一特定物种的个体数，N = 所有物种的总个体数。对所有物种的 (n/N)² 求和。D 值范围从 0（无多样性）到接近 1（多样性极高）。对于小样本，有时会使用 n(n-1)/N(N-1) 作为替代公式。
Published by TutorHao | Biology Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply