AQA A-Level Biology: Formula Summary Handbook | AQA A-Level 生物：公式汇总手册

📚 AQA A-Level Biology: Formula Summary Handbook | AQA A-Level 生物：公式汇总手册

Being comfortable with quantitative skills and memorised formulae is essential for AQA A-Level Biology. This handbook gathers every key equation you need for Paper 1, Paper 2 and Paper 3 – from magnification and dilution series to statistical tests and population genetics. Use it alongside past papers to build speed and confidence in calculation questions.

掌握定量技能和牢记公式对于 AQA A-Level 生物学至关重要。本手册汇集了试卷一、试卷二和试卷三所需的所有关键方程式——从放大率和稀释系列到统计检验和群体遗传学。配合历年真题使用，帮助你在计算题中提升速度和信心。

1. Magnification Formula | 放大率公式

Magnification (M) is the number of times larger an image is compared to the real object. The relationship links image size, actual size and magnification.

放大率 (M) 是指图像比实际物体放大的倍数。该关系式连接图像大小、实际大小和放大率。

Magnification = Image size ÷ Actual size   |   M = I / A

实际大小 = 图像大小 ÷ 放大率   |   A = I / M

Always convert all measurements to the same unit (usually μm or mm) before substituting into the formula. Remember that 1 mm = 1000 μm.

在代入公式前，所有测量值必须转换为相同单位（通常为 μm 或 mm）。记住 1 mm = 1000 μm。

2. Dilution Series | 稀释系列

When preparing serial dilutions to produce a calibration curve or reduce a bacterial culture’s concentration, the dilution factor and volume relationships are used.

当制备系列稀释液以制作标准曲线或降低细菌培养物浓度时，需使用稀释因子和体积关系式。

C₁V₁ = C₂V₂

Where C₁ and V₁ are the initial concentration and volume, and C₂ and V₂ are the final concentration and volume after dilution. For a 1 in 10 dilution, mix 1 part stock with 9 parts diluent.

其中 C₁ 和 V₁ 是初始浓度和体积，C₂ 和 V₂ 是稀释后的最终浓度和体积。对于 1 比 10 稀释，将 1 份原液与 9 份稀释液混合。

Serial dilutions often produce a logarithmic scale. The dilution factor after n serial steps is (dilution factor)ⁿ.

系列稀释通常产生对数刻度。经过 n 个系列步骤后的稀释因子为（稀释因子）ⁿ。

3. Surface Area to Volume Ratio | 表面积与体积比

As an organism or structure increases in size, its surface area to volume ratio decreases. This affects rates of diffusion, osmosis and heat exchange.

随着生物体或结构尺寸增大，其表面积与体积之比减小。这会影响到扩散速率、渗透作用和热量交换。

Surface Area : Volume = Total surface area (cm²) / Total volume (cm³)

For a cube of side length L, SA = 6L², V = L³, so SA:V = 6/L. For a sphere of radius r, SA = 4πr², V = 4/3 πr³, giving SA:V = 3/r.

对于边长为 L 的立方体，表面积 = 6L²，体积 = L³，因此 SA:V = 6/L。对于半径为 r 的球体，表面积 = 4πr²，体积 = 4/3 πr³，SA:V = 3/r。

Small organisms (e.g. bacteria) have a large SA:V ratio, allowing efficient exchange across their body surface. Larger organisms need specialised exchange surfaces and transport systems.

小型生物（如细菌）具有较大的 SA:V 比值，可通过体表高效交换。较大生物则需要特化的交换表面和运输系统。

4. Cardiac Output | 心输出量

Cardiac output is the volume of blood pumped by the left ventricle per minute. It is determined by heart rate and stroke volume.

心输出量是左心室每分钟泵出的血液体积，由心率和每搏输出量决定。

Cardiac Output (CO) = Heart Rate (HR) × Stroke Volume (SV)

HR is measured in beats per minute (bpm); SV is the volume of blood ejected per beat (ml per beat). Typical resting values: HR ≈ 70 bpm, SV ≈ 70 ml, giving CO ≈ 4900 ml min⁻¹ (4.9 L min⁻¹).

心率以每分钟搏动次数 (bpm) 测量；每搏输出量是每次搏动射出的血液体积（毫升/搏）。典型静息值：HR ≈ 70 bpm，SV ≈ 70 ml，因此 CO ≈ 4900 ml min⁻¹（4.9 L min⁻¹）。

During exercise, both HR and SV increase, so cardiac output rises significantly to supply more oxygen to muscles.

运动时，心率和每搏输出量均增加，因此心输出量显著上升，为肌肉提供更多氧气。

5. Respiratory Quotient (RQ) | 呼吸商

The respiratory quotient indicates which substrate is being metabolised during respiration. It is the ratio of carbon dioxide produced to oxygen consumed.

呼吸商表明在呼吸过程中哪种底物正在被代谢，它是产生的二氧化碳与消耗的氧气的比值。

RQ = CO₂ produced / O₂ consumed

Typical RQ values: carbohydrate ≈ 1.0; lipid ≈ 0.7; protein ≈ 0.9. A value between 0.7 and 1.0 suggests mixed substrate use. Values may exceed 1.0 if anaerobic respiration occurs.

典型 RQ 值：碳水化合物 ≈ 1.0；脂质 ≈ 0.7；蛋白质 ≈ 0.9。值介于 0.7 与 1.0 之间表明混合底物利用。若发生无氧呼吸，RQ 值可能超过 1.0。

To calculate RQ from experimental data, measure the volume of O₂ taken in and CO₂ given out over a set time using a respirometer.

要根据实验数据计算 RQ，使用呼吸计测量一定时间内吸入的 O₂ 体积和释放的 CO₂ 体积。

6. Water Potential | 水势

Water potential (Ψ) determines the direction of water movement by osmosis. Water moves from regions of higher (less negative) water potential to lower (more negative) water potential.

水势 (Ψ) 决定渗透作用中水分移动的方向。水从较高（负值较小）水势区域向较低（负值较大）水势区域移动。

Ψ = Ψₛ + Ψₚ

Ψₛ (solute potential) is always negative or zero; adding solutes makes Ψₛ more negative. Ψₚ (pressure potential) is usually positive inside plant cells due to the cell wall exerting pressure. In a fully turgid cell, Ψₚ = −Ψₛ, so Ψ = 0.

Ψₛ（溶质势）始终为负值或零；添加溶质使 Ψₛ 的负值更大。Ψₚ（压力势）在植物细胞内通常为正值，因为细胞壁施加压力。在完全膨胀的细胞中，Ψₚ = −Ψₛ，因此 Ψ = 0。

In pure water at standard conditions, Ψ = 0 kPa. Units are typically kilopascals (kPa).

在标准条件下的纯水中，Ψ = 0 kPa。单位通常为千帕 (kPa)。

7. Pulmonary Ventilation Rate | 肺通气量

Pulmonary ventilation (minute ventilation) is the volume of air moved into and out of the lungs per minute. It depends on tidal volume and breathing rate.

肺通气量（每分通气量）是每分钟进出肺部的空气体积，取决于潮气量和呼吸频率。

Pulmonary Ventilation Rate = Tidal Volume × Breathing Rate

Tidal volume (TV) is the volume of air inhaled or exhaled per breath (dm³); breathing rate (f) is breaths per minute. At rest, TV ≈ 0.5 dm³, f ≈ 12 min⁻¹, so ventilation rate ≈ 6 dm³ min⁻¹.

潮气量 (TV) 是每次呼吸吸入或呼出的空气体积 (dm³)；呼吸频率 (f) 为每分钟呼吸次数。静息时，TV ≈ 0.5 dm³，f ≈ 12 min⁻¹，因此通气量 ≈ 6 dm³ min⁻¹。

During strenuous exercise, tidal volume and breathing rate both increase, boosting ventilation to >100 dm³ min⁻¹ in trained athletes.

剧烈运动时，潮气量和呼吸频率均增加，通气量在训练有素的运动员中可提升至 >100 dm³ min⁻¹。

8. Population Growth and Estimation | 种群增长与估计

Population dynamics involve birth, death, immigration and emigration. The population growth rate can be calculated for a given time interval.

种群动态涉及出生、死亡、迁入和迁出。可计算特定时间间隔内的种群增长率。

Population Growth Rate = (Births + Immigration) − (Deaths + Emigration)

For exponential growth of cells (e.g. bacteria) when each cell divides into two every generation, the number after n generations is:

当细胞（如细菌）每代一分为二时，n 代后的数量为：

N = N₀ × 2ⁿ

N₀ is the starting number, n is the number of generations. The number of generations can be found from: n = (log N − log N₀) / log 2.

N₀ 是起始数量，n 是世代数。世代数可由 n = (log N − log N₀) / log 2 求出。

For motile organisms, the Lincoln index (mark–release–recapture) estimates population size:

对于移动生物，林肯指数（标志重捕法）估算种群大小：

Estimated population size = (M × C) / R

M = number captured and marked in first sample, C = total number captured in second sample, R = number of marked individuals recaptured.

M = 第一次样本中捕获并标记的个体数，C = 第二次样本中捕获的总数，R = 重捕的标记个体数。该估计假设标记不影响生存且种群混合均匀。

9. Simpson’s Index of Diversity | 辛普森多样性指数

Biodiversity can be quantified using Simpson’s Index of Diversity (d). A high value indicates high diversity. The AQA specification uses the following formula:

生物多样性可用辛普森多样性指数 (d) 量化。高值表示多样性高。AQA 考纲使用以下公式：

d = N(N − 1) / Σ n(n − 1)

N = total number of organisms of all species, n = total number of organisms of each species. Σ means sum of n(n−1) for all species.

N = 所有物种的个体总数，n = 每个物种的个体总数。Σ 表示对所有物种的 n(n−1) 求和。

This reciprocal form means that as diversity increases, d increases. In a community with only one species, n=N, and d=1. The value can range from 1 to potentially large numbers.

这种倒数形式意味着多样性增加时 d 值增大。在只有一个物种的群落中，n=N，d=1。该值可从 1 到大数值变化。

10. Chi-squared Test | 卡方检验

Chi-squared (χ²) test is used to determine whether there is a significant difference between observed and expected frequencies in categorical data.

卡方 (χ²) 检验用于判断分类数据中观察频数与期望频数之间是否存在显著差异。

χ² = Σ (O − E)² / E

O = observed frequency, E = expected frequency. Sum is taken over all categories. Degrees of freedom (df) = number of categories − 1 for a goodness‑of‑fit test.

O = 观察频数，E = 期望频数。对所有分类求和。对于拟合优度检验，自由度 (df) = 分类数 − 1。

Compare the calculated χ² to the critical value at p=0.05 for the appropriate df. If χ² > critical value, reject the null hypothesis; the difference is significant.

将计算出的 χ² 与对应自由度下 p=0.05 的临界值比较。若 χ² > 临界值，则拒绝零假设；差异显著。

11. Standard Deviation and t-test | 标准偏差与 t 检验

Standard deviation measures the spread of data around the mean. It is used in the unpaired t-test to compare the means of two independent samples.

标准偏差衡量数据围绕均值的离散程度。它用于非配对 t 检验中以比较两个独立样本的均值。

Standard deviation: s = √[ Σ(x − x̄)² / (n − 1) ]

x = each individual value, x̄ = sample mean, n = number of observations. The denominator (n−1) gives the sample standard deviation; larger s indicates greater spread.

x = 每个个体值，x̄ = 样本均值，n = 观察值个数。分母 (n−1) 得到样本标准偏差；s 越大表示离散程度越大。

Unpaired t‑test: t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)

Where x̄₁, x̄₂ are means of group 1 and 2, s₁, s₂ are standard deviations, n₁, n₂ are sample sizes. Degrees of freedom = n₁ + n₂ − 2. If calculated t > critical t at p=0.05, the difference is significant.

其中 x̄₁、x̄₂ 为两组均值，s₁、s₂ 为标准偏差，n₁、n₂ 为样本大小。自由度 = n₁ + n₂ – 2。若计算 t > p=0.05 时的临界 t 值，则差异显著。

12. Hardy‑Weinberg Principle | 哈迪-温伯格平衡

The Hardy‑Weinberg principle predicts allele and genotype frequencies in a non‑evolving population. It provides a null model for detecting evolutionary change.

哈迪-温伯格原理预测非进化种群中等位基因和基因型频率，为检测进化变化提供零模型。

Allele frequency: p + q = 1

Genotype frequency: p² + 2pq + q² = 1

p = frequency of the dominant allele, q = frequency of the recessive allele. p² = frequency of homozygous dominant, 2pq = heterozygous, q² = homozygous recessive.

p = 显性等位基因频率，q = 隐性等位基因频率。p² = 显性纯合子频率，2pq = 杂合子频率，q² = 隐性纯合子频率。

If the observed frequencies deviate significantly from those expected under Hardy‑Weinberg, the population may be experiencing evolution, non‑random mating, gene flow or selection. The null hypothesis assumes no change.

若观察频率显著偏离哈迪-温伯格预期值，该种群可能正在经历进化、非随机交配、基因流动或选择。零假设假定无变化。

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