📚 Year 12 AQA Biology: Formula & Key Principles Quick-Reference Handbook | AQA 12年级生物学：公式定理速查手册
This handbook condenses all essential formulae, laws, and key principles required for Year 12 AQA Biology. Each entry is presented with its equation, a worked example where appropriate, and the core concept, supporting quick revision and accurate application in exam questions.
本手册凝练了 AQA 12 年级生物学考试涉及的所有重要公式、定律和关键原理。每个条目均列出方程、示例计算（如适用）以及核心概念，以便快速复习并在考试中准确运用。
1. Magnification | 放大倍数
Magnification is the number of times larger an image appears compared to the actual size of the specimen. It is a ratio and therefore has no units.
放大倍数是图像与实物实际尺寸相比放大的倍数。它是一个比率，因此没有单位。
Magnification = Image size / Actual size
e: Use the formula triangle to rearrange: Image size = Magnification × Actual size, and Actual size = Image size / Magnification.
可利用公式三角进行转换：图像尺寸 = 放大倍数 × 实际尺寸，实际尺寸 = 图像尺寸 / 放大倍数。
Worked example: g 24 mm across. The actual cell diameter is 0.006 mm. Magnification = 24 / 0.006 = 4000 ×.
计算示例： 一张显微照片中细胞直径为 24 mm，实际细胞直径为 0.006 mm。放大倍数 = 24 / 0.006 = 4000 倍。
- Always convert all measurements to the same unit before calculating. Common units: mm, µm (µm = 10⁻³ mm), nm (nm = 10⁻⁶ mm).
- 计算前务必把所有测量值换算为相同单位。常用单位：mm、µm (1 µm = 10⁻³ mm)、nm (1 nm = 10⁻⁶ mm)。
2. 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 surface. A faster rate is achieved by a larger surface area, a greater concentration difference, and a shorter diffusion distance.
菲克定律描述了影响物质跨膜或表面扩散速率的因素。更大的表面积、更大的浓度差和更短的扩散距离均能提高扩散速率。
Rate of diffusion ∝ (Surface area × Concentration difference) / Diffusion distance
Adaptations such as the thin walls of alveoli, extensive capillary networks, and flattened shape of capillaries maximise these variables for efficient gas exchange.
肺泡的薄壁、丰富的毛细血管网以及毛细血管的扁平形态等适应性结构正是为了最大化这些变量，实现高效的气体交换。
- Surface area (SA) is often increased by folding of membranes or villi.
- 表面积 (SA) 通常通过膜折叠或形成绒毛来增加。
- Concentration difference is maintained by continuous blood flow and ventilation.
- 浓度差通过持续的血流和通气来维持。
- Diffusion distance is minimised by single-layered squamous epithelia.
- 单层扁平上皮使扩散距离最小化。
3. Surface Area to Volume Ratio | 表面积与体积比
As an organism or cell increases in size, its surface area to volume ratio (SA:V) decreases. This limits the rate at which substances can enter and leave the cell by diffusion.
随着生物体或细胞体积的增大，其表面积与体积之比 (SA:V) 下降。这会限制物质通过扩散进出细胞的速率。
SA:V ratio = Surface area / Volume
all cube (side = 1 mm) has SA:V = 6:1; a larger cube (side = 3 mm) has SA:V = 54:27 = 2:1.
以立方体为例：表面积 = 6 × 边长²，体积 = 边长³。小立方体 (边长 1 mm) 的 SA:V = 6:1；较大立方体 (边长 3 mm) 的 SA:V = 54:27 = 2:1。
- Smaller organisms have a high SA:V ratio and can rely on diffusion for exchange.
- 体积较小的生物具有高 SA:V 比，可依赖扩散进行物质交换。
- Larger multicellular organisms require specialised exchange surfaces and transport systems.
- 大型多细胞生物需要特化的交换表面和运输系统。
4. Water Potential | 水势
Water potential (Ψ) is the pressure exerted by water molecules as they move. It determines the direction of water movement across a partially permeable membrane—water always moves from a region of higher water potential to a region of lower water potential.
水势 (Ψ) 是水分子移动时产生的压力，决定水分跨过半透膜的净移动方向——水总是从水势较高的区域流向水势较低的区域。
Ψ = Ψs + Ψp
Ψs is the solute potential (always negative or zero), and Ψp ally positive inside a plant cell). Units are kilopascals (kPa). Pure water has Ψ = 0 kPa.
Ψs 为溶质势（总是负值或零），Ψp 为压力势（在植物细胞内通常为正值）。单位为千帕 (kPa)。纯水的水势为 0 kPa。
- Adding solute lowers Ψ, making it more negative.
- 加入溶质会使水势降低，变得更负。
- In a turgid plant cell, Ψp is high, and the cell contents push against the cell wall.
- 在膨胀的植物细胞中，压力势很高，细胞内含物挤压细胞壁。
- If an animal cell is placed in pure water, water enters by osmosis and may cause lysis.
- 若将动物细胞置于纯水中，水通过渗透作用进入细胞，可能导致细胞破裂。
5. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle per minute. It reflects the efficiency of the heart as a pump and changes during exercise.
心输出量是指一个心室每分钟泵出的血液体积，反映了心脏的泵血效率，并在运动时发生变化。
Cardiac output (CO) = Heart rate (HR) × Stroke volume (SV)
er beat (ml or litres). Typical resting values: HR = 70 bpm, SV = 70 ml, CO = 4.9 L min⁻¹.
心率的单位为次/分 (bpm)，每搏输出量为每次搏动射出的血量 (ml 或 L)。静息时的典型值：心率 70 bpm，每搏输出量 70 ml，心输出量约为 4.9 L min⁻¹。
- During exercise, both HR and SV increase, raising cardiac output significantly.
- 运动时，心率和每搏输出量均增加，心输出量显著上升。
- Monitoring CO can indicate fitness levels or cardiac health.
- 监测心输出量可反映健康水平或心脏功能状况。
6. Pulmonary Ventilation | 肺通气量
Pulmonary ventilation is the total volume of air moved into and out of the lungs per minute. It is calculated from tidal volume and breathing rate.
肺通气量是指每分钟进出肺部的气体总体积，由潮气量和呼吸频率计算得出。
Pulmonary ventilation (VE) = Tidal volume (TV) × Breathing frequency (f)
Tidal volume is the volume of air inhaled or exhaled per breath (approx. 0.5 L at rest), and breathing frequency is the number of breaths per minute (approx. 12–16 at rest). Units: L min⁻¹.
潮气量是每次呼吸吸入或呼出的气体体积（静息时约 0.5 L），呼吸频率为每分钟呼吸次数（静息时约 12–16 次）。单位：L min⁻¹。
- A spirometer trace can be used to obtain TV and f, enabling calculation of ventilation.
- 可通过肺活量描记图获得 TV 和 f，进而计算通气量。
- During vigorous exercise, ventilation can increase to over 100 L min⁻¹.
- 剧烈运动时，肺通气量可增至 100 L min⁻¹ 以上。
7. Q10 Temperature Coefficient | 温度系数 Q10
The Q10 coefficient measures the effect of a 10 °C temperature increase on the rate of a reaction. It indicates how sensitive the reaction is to temperature changes.
Q10 系数用于衡量温度升高 10 °C 对反应速率的影响，反映反应对温度变化的敏感程度。
Q₁₀ = (R₂ / R₁)10/(T₂−T₁)
Where R₁ and R₂ are the reaction rates at temperatures T₁ and T₂ (in °C). For many enzyme-controlled reactions, Q10 is around 2, meaning the rate doubles with a 10 °C rise until the enzyme denatures.
R₁ 和 R₂ 分别为温度 T₁ 和 T₂ (°C) 下的反应速率。对多数酶促反应而言，Q10 约为 2，即温度每升高 10 °C，速率翻倍，直至酶变性。
Example: Rate at 25 °C is 0.8 arbitrary units; rate at 35 °C is 1.5. Q₁₀ = (1.5 / 0.8)10/(35−25) = (1.875)¹ = 1.875.
示例： 25 °C 时反应速率为 0.8 任意单位，35 °C 时为 1.5。Q₁₀ = (1.5 / 0.8)10/(35−25) = (1.875)¹ = 1.875。
- Q10 values above 1 indicate rate increases with warming; below 1 implies a decline, often due to denaturation.
- Q10 大于 1 表示升温使速率增加；小于 1 通常由于酶变性导致速率下降。
8. Rate of Reaction | 反应速率
Reaction rate can be defined as the speed at which substrate is converted to product, or product appears over time. For enzyme-driven experiments, the initial rate is most reliable.
反应速率可定义为单位时间内底物转化为产物或产物生成的速率。在酶促实验中，起始速率最为可靠。
Rate = Change in quantity (e.g. product formed) / Time taken
Commonly, the initial rate is calculated as 1 / time for a specific event to occur (e.g. time for starch to be completely digested). Units: s⁻¹ or arbitrary units per minute.
通常，起始速率可用某一特定事件发生所需时间的倒数来计算（如淀粉完全消化所需时间）。单位：s⁻¹ 或任意单位/分钟。
- Plotting product concentration against time gives a curve; initial rate is the gradient of the tangent at time zero.
- 绘制产物浓度-时间曲线，起始速率为时间零点处切线的斜率。
- Temperature, pH, enzyme concentration, and substrate concentration all affect this rate.
- 温度、pH、酶浓度和底物浓度均会影响反应速率。
9. Chi‑Squared (χ²) Test | 卡方检验
The χ² test compares observed results with expected results to determine whether any difference is due to chance or a significant factor. In Year 12, it is used for goodness-of-fit tests, such as Mendelian ratios.
卡方检验用于比较观察值与预期值，以判断差异是由偶然因素还是显著因素导致。在 12 年级，该检验用于拟合优度检测，例如孟德尔比例。
χ² = Σ (O − E)² / E
requency. Σ means sum over all categories. Calculate the difference, square it, divide by expected, and sum for all groups.
O 为观察频数，E 为预期频数。Σ 表示所有类别的总和。先求差值，平方，除以预期值，再把各组结果相加。
- Degrees of freedom (df) = number of categories − 1.
- 自由度 (df) = 类别数 − 1。
- ue at p = 0.05 for the appropriate df. If χ² > critical value, reject the null hypothesis.
- 将计算所得的 χ² 值与相应自由度下 p = 0.05 的临界值比较。若 χ² > 临界值，则拒绝零假设。
- Null hypothesis: There is no significant difference between observed and expected frequencies.
- 零假设：观察频数与预期频数之间无显著差异。
10. Simpson’s Index of Diversity | 辛普森多样性指数
The index of diversity (d) quantifies species biodiversity in a habitat, taking into account both species richness and evenness. A higher value indicates greater diversity.
多样性指数 (d) 用于量化栖息地的物种生物多样性，同时考虑物种丰富度和均匀度。指数值越高，多样性越高。
d = N(N − 1) / Σ n(n − 1)
f a single species. Σ n(n − 1) means you calculate n(n − 1) for each species and then sum these values.
N 为所有物种的个体总数；n 为某一物种的个体总数。Σ n(n − 1) 表示先计算每个物种的 n(n − 1)，再将这些值相加。
Example: n(n − 1) = (10×9) + (4×3) + (2×1) = 90 + 12 + 2 = 104. d = 16×15 / 104 = 240 / 104 = 2.31.
示例： 一个样本包含 10 株雏菊、4 株毛茛和 2 株蒲公英。N = 16。Σ n(n − 1) = (10×9) + (4×3) + (2×1) = 90 + 12 + 2 = 104。d = 16×15 / 104 = 240 / 104 = 2.31。
- Farming and deforestation reduce species diversity, lowering the index.
- 农业开垦和森林砍伐会降低物种多样性，使指数减小。
- A high d suggests a stable ecosystem with less domination by a single species.
- d 值高表明生态系统稳定，单一物种的优势程度低。
11. Percentage Change and Uncertainty | 百分比变化与不确定度
Calculating percentage change is common in osmosis and mass-change experiments. It normalises results when initial values differ.
百分比变化的计算常见于渗透作用和质量变化实验中，可在初始值不同时对结果进行标准化。
Percentage change = (Final value − Initial value) / Initial value × 100%
A positive value indicates an increase; a negative value indicates a decrease. Always quote the direction of change.
正值表示增加，负值表示减少。应始终标明变化的方向。
Uncertainty: For a measurement of 5.2 cm on a ruler with mm markings, uncertainty = ±0.5 mm = ±0.05 cm.
不确定度： 单次读数的测量不确定度通常为仪器最小刻度的一半。用毫米刻度的尺子测得 5.2 cm 时，不确定度 = ±0.5 mm = ±0.05 cm。
- Percentage uncertainty = (Absolute uncertainty / Measured value) × 100%.
- 百分比不确定度 = (绝对不确定度 / 测量值) × 100%。
- When averaging repeated measurements, uncertainty can be reduced to half the range: (max − min)/2.
- 重复测量取平均值时，不确定度可缩小为极差的一半：(最大值 − 最小值) / 2。
12. Key Principles and Models | 重要原理与模型
Lock and key model: The active site of an enzyme has a fixed shape that is exactly complementary to the substrate, like a key fitting a lock. This model explains specificity but does not account for the flexibility of the active site.
锁钥模型： 酶的活性部位具有
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