📚 AS AQA Biology: Quick Formula & Theorem Reference Manual | AS AQA 生物：公式定理速查手册
This concise reference manual gathers all essential formulae, mathematical relationships, and key biological theorems required for the AS AQA Biology specification. From magnification and Fick’s Law to cardiac output and Simpson’s diversity index, each entry is presented with clear definitions and worked examples to support quick revision and accurate application in exam questions.
本速查手册汇集了 AS AQA 生物课程要求掌握的全部核心公式、数量关系和重要生物学定理。从放大倍率、菲克定律到心输出量和辛普森多样性指数，每项均配有清晰定义和计算示例，方便快速复习并在考试中精准使用。
1. Units and Conversions | 单位与换算
In AS Biology, measurements often need to be converted between millimetres (mm), micrometres (µm) and nanometres (nm). Accurate unit conversion underpins calculations of magnification and scale.
在 AS 生物中，测量值常常需要在毫米（mm）、微米（µm）和纳米（nm）之间转换。准确地进行单位换算是放大倍率和比例尺计算的基础。
The relationships are: 1 cm = 10 mm, 1 mm = 1000 µm, 1 µ 1000 nm. Always ensure both measurements are in the same unit before applying any formula.
换算关系为：1 cm = 10 mm，1 mm = 1000 µm，1 µm = 1000 nm。在代入任何公式之前，务必确认两个测量值的单位一致。
- Example: Convert 0.025 mm to µm. 0.025 × 1000 = 25 µm.
- 示例：将 0.025 mm 转换为 µm。0.025 × 1000 = 25 µm。
1 mm = 1000 µm | 1 µm = 1000 nm
2. Magnification Formula | 放大倍率公式
Magnification is the ratio of the size of an image to the actual size of the specimen. This formula is used extensively in microscope work and biological drawings.
放大倍率是指图像大小与标本实际大小之间的比值。该公式广泛应用于显微镜观察和生物绘图。
Magnification = Image size ÷ Actual size
The three quantities are linked: rearrange to find any unknown. Use a consistent unit, typically µm or mm. If given a scale bar, measure its image length, then divide by the true length stated on the bar.
三个变量彼此关联，可重新排列求解。使用统一单位，通常为 µm 或 mm。若给出比例尺，先测量其在图像中的长度，再除以比例尺标注的真实长度。
- Measurement tip: I = M × A and A = I ÷ M.
- 测量技巧：I = M × A，A = I ÷ M。
3. Surface Area to Volume Ratio | 表面积与体积比
The surface area to volume ratio (SA:V) is a key concept that explains the limits of cell size and the efficiency of exchange. A higher SA:V permits faster diffusion of substances across the membrane.
表面积与体积比（SA:V）是解释细胞大小限制和交换效率的核心概念。较高的 SA:V 能让物质更快地跨膜扩散。
For a cube-shaped cell of side length l io decreases, making diffusion inadequate for large organisms, which therefore need specialised exchange surfaces.
对于边长为 l 的立方体细胞，表面积 = 6l²，体积 = l³，因此 SA:V = 6/l。随着尺寸增大，比值下降，大体积生物无法仅靠扩散维持生命，因此需要特化的交换表面。
- Small organisms: high SA:V → rely on simple diffusion.
- 小生物：高 SA:V → 依赖简单扩散。
- Large organisms: low SA:V → require transport systems and specialised exchange organs.
- 大型生物：低 SA:V → 需要运输系统和特化交换器官。
4. 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. It is an excellent framework for understanding adaptations of gas exchange systems.
菲克定律描述了影响跨膜或交换表面扩散速率的因素。它是理解气体交换系统适应性的极佳框架。
Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Diffusion distance
To maximise diffusion, an exchange surface should have a large surface area, a steep concentration gradient (maintained by a rich blood supply or ventilation), and a thin barrier (minimum diffusion distance). Examples include alveolar epithelium, gill lamellae, and root hair cells.
为使扩散最大化，交换表面应具备大的表面积、陡峭的浓度梯度（通过充足的血流或通气维持）以及薄的屏障（最短扩散距离）。例如肺泡上皮、鳃薄片和根毛细胞。
| Factor | Adaptation example |
|---|---|
| Surface area | Many alveoli / gill filaments |
| Concentration difference | Constant blood flow & ventilation |
| Diffusion distance | Squamous epithelial cells, one-cell-thick walls |
菲克定律影响因素表：表面积 → 众多肺泡/鳃丝；浓度差 → 持续血流与通气；扩散距离 → 扁平上皮细胞，单细胞厚度的壁。
5. Cardiac Output and Heart Rate | 心输出量与心率
Cardiac output is the volume of blood pumped by one ventricle per minute. Its components are stroke volume (volume per beat) and heart rate (beats per minute).
心输出量是指一个心室每分钟泵出的血液量，由每搏输出量（每次搏动泵血量）和心率（每分钟搏动次数）共同决定。
Cardiac output (cm³ min⁻¹) = Stroke volume (cm³) × Heart rate (bpm)
cardiac output during exercise. Typical values: resting CO ≈ 5 dm³ min⁻¹, SV ≈ 70 cm³, HR ≈ 70 bpm.
训练有素的运动员通常每搏输出量较高、静息心率较低，静息时心输出量不变，但运动时心输出量可大幅增加。典型数值：静息心输出量约 5 dm³ min⁻¹，每搏输出量约 70 cm³，心率约 70 bpm。
- Rearrange: SV = CO ÷ HR and HR = CO ÷ SV.
- 可按需变换：SV = CO ÷ HR，HR = CO ÷ SV。
6. Lung Volumes and Pulmonary Ventilation | 肺容量与肺通气量
Breathing measurements can be interpreted from a spirometer trace. The key volumes are tidal volume (TV), vital capacity (VC), inspiratory and expiratory reserve volumes, and residual volume.
呼吸测量可通过肺量计图谱解读。关键指标包括潮气量（TV）、肺活量（VC）、补吸气量、补呼气量和残气量。
Vital capacity = TV + IRV + ERV
Total lung capacity = Vital capacity + Residual volume
Pulmonary ventilation (minute volume) tells us how much air moves in and out per minute.
肺通气量（每分钟气流量）表示每分钟进出肺部的空气量。
Pulmonary ventilation (dm³ min⁻¹) = Tidal volume (dm³) × Breathing rate (min⁻¹)
A typical tidal volume at rest is around 0.5 dm³, breathing rate 12–16 min⁻¹ giving a pulmonary ventilation of 6–8 dm³ min⁻¹. These values increase sharply during exercise.
静息时典型潮气量约为 0.5 dm³，呼吸频率 12–16 min⁻¹，肺通气量约 6–8 dm³ min⁻¹。运动时这些数值急剧上升。
7. Mitotic Index | 有丝分裂指数
The mitotic index is used to quantify the proportion of cells undergoing mitosis in a tissue. It is of diagnostic value in cancer biology, where high mitotic indices indicate rapid cell division.
有丝分裂指数用于量化组织中正在进行有丝分裂的细胞比例，在癌症生物学中具有诊断价值，高有丝分裂指数意味着细胞快速分裂。
dex = (Number of cells with visible chromosomes) ÷ (Total number of cells observed)
Only cells in which chromosomes are visibly condensed (prophase, metaphase, anaphase, telophase) are counted. Interphase cells are not included in the numerator. The result is often multiplied by 100 to give a percentage.
只计数可见染色体的细胞（前期、中期、后期、末期），间期细胞不计入分子。结果通常乘以 100 以百分比表示。
- Practice: A root tip squash shows 18 mitotic cells out of 200. Mitotic index = 18/200 = 0.09 or 9%.
- 练习：一个根尖压片显示 200 个细胞中有 18 个有丝分裂细胞，有丝分裂指数 = 18/200 = 0.09 或 9%。
8. Simpson’s Diversity Index | 辛普森多样性指数
Simpson’s Diversity Index (D) is a measure of species diversity that accounts for both species richness (number of species) and evenness (relative abundance). A high value indicates high biodiversity.
辛普森多样性指数（D）是一个物种多样性度量，综合考虑了物种丰富度（物种数量）和均匀度（相对丰度）。数值越高表示生物多样性越高。
D = 1 − Σ(n/N)²
where n = total number of organisms of a particular species, and N species. Calculate (n/N)² for each species, sum these values, and subtract the sum from 1.
其中 n = 某一特定物种的个体总数，N = 所有物种的个体总数。分别计算每个物种的 (n/N)²，求和，再用 1 减去该总和。
- Example: N=100). Sum of (n/N)² = (0.5)²+(0.3)²+(0.2)² = 0.25+0.09+0.04 = 0.38; D = 1 - 0.38 = 0.62.
- 示例：3 个物种：50、30、20（N=100）。(n/N)² 之和 = (0.5)²+(0.3)²+(0.2)² = 0.25+0.09+0.04 = 0.38；D = 1 - 0.38 = 0.62。
9. Proportion of Polymorphic Gene Loci | 多态性基因座比例
Genetic diversity can also be assessed by the proportion of polymorphic gene loci in a population. This value indicates the genetic variability available for natural selection.
遗传多样性也可通过种群中多态性基因座的比例来评估。该值反映了可供自然选择利用的遗传变异程度。
on of polymorphic loci = Number of polymorphic loci ÷ Total number of loci examined
A locus is considered polymorphic if it has two or more alleles occurring at frequencies higher than a rare mutation, typically above 1%. Populations with high genetic diversity are more resilient to environmental changes.
若某基因座拥有两个或两个以上等位基因且等位基因频率高于罕见突变率（通常 > 1%），则认为该座是多态性的。高遗传多样性的种群对环境变化的适应力更强。
- rcentage. If 15 out of 50 investigated loci are polymorphic, proportion = 15/50 = 0.30 (30%).
- 用小数或百分数表示。若检查的 50 个基因座中有 15 个为多态性，比例 = 15/50 = 0.30（30%）。
10. Rate of Enzyme-Controlled Reactions | 酶控反应速率
Enzyme reaction rates can be calculated using the reciprocal of the time taken for a measurable change, such as the disappearance of substrate or appearance of product.
酶促反应速率可通过可测量变化所需时间的倒数来计算，例如底物消失或产物出现的时间。
Rate = 1 ÷ time (s⁻¹)
While not a universal law, this expression is used throughout AS biology to plot progress curves and investigate the effect of temperature, pH, substrate concentration, and inhibitors. A shorter time to endpoint, or a steeper initial gradient, indicates a faster rate.
尽管不是普适定律，但该表达式在 AS 生物中贯穿使用，用于绘制反应进程曲线，研究温度、pH、底物浓度和抑制剂的影响。达到终点的时间越短，或初始梯度越陡，速率越快。
- asurements, rate = change in product concentration ÷ change in time (initial rate).
- 对于连续测量，速率 = 产物浓度变化量 ÷ 时间变化量（初始速率）。
11. DNA Base Pairing Rules (Chargaff’s Rule) | DNA 碱基配对规则（查加夫法则）
anine bases equals cytosine (G = C). This is the foundation of complementary base pairing.
查加夫法则指出，在双链 DNA 分子中，腺嘌呤（A）与胸腺嘧啶（T）数量相等，鸟嘌呤（G）与胞嘧啶（C）数量相等。这是互补碱基配对的基础。
A = T and G ≡ C
redicting base composition in unknown DNA strands and underpins semiconservative replication.
因此，总嘌呤含量等于总嘧啶含量：(A+G) = (T+C)。该法则有助于预测未知 DNA 链的碱基组成，也是半保留复制的理论基础。
- If a DNA sample contains 22% thymine, it must contain 22% adenine, and the remaining 56% is split equally between guanine and cytosine (28% each).
- 若某 DNA 样本含 22% 胸腺嘧啶，则必定含 22% 腺嘌呤，剩余 56% 均分给鸟嘌呤和胞嘧啶（各 28%）。
12. The Central Dogma of Molecular Biology | 分子生物学的中心法则
The Central Dogma summarises the flow of genetic information in cells: DNA stores the code, transcription copies it into mRNA, and translation synthesises a polypeptide chain. The sequence is unidirectional under normal cellular conditions.
中心法则概括了细胞中遗传信息的流动：DNA 储存编码，转录将其复制为 mRNA，翻译合成多肽链。在正常细胞条件下，信息传递是单向的。
DNA → RNA → Protein
The triplet code on DNA is transcribed into a complementary mRNA codon, which is then read by tRNA anticodons during translation. This theorem underpins our understanding of gene expression, mutation effects, and genetic engineering.
DNA 上的三联体密码被转录成互补的 mRNA 密码子，翻译时由 tRNA 反密码子识别。这条定理是我们理解基因表达、突变影响和基因工程的基础。
- Retroviruses can reverse transcribe RNA to DNA, but this does not invalidate the general direction of the central dogma.
- 逆转录病毒能将 RNA 逆转录为 DNA，但这并不推翻中心法则的一般方向。
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