📚 Year 12 WJEC Biology: Formula and Theorem Quick Reference Handbook | 12年级 WJEC 生物：公式定理速查手册
This revision handbook provides a concise collection of essential formulas, equations and fundamental theorems that every Year 12 WJEC Biology student must master. From magnification to Hardy–Weinberg, each entry is designed to reinforce quantitative skills and key concepts for AS-level success.
这本复习手册汇集了12年级 WJEC 生物学中必须掌握的核心公式、方程和基本定理。从放大率到哈迪–温伯格原理，每一条都在强化你的量化分析能力和关键概念，为 AS 阶段的成功打下基础。
1. Magnification Formula | 放大率公式
The magnification formula links image size to actual object size and is essential when working with microscope drawings and photomicrographs. Always convert measurements to the same unit (usually micrometres) before substituting values.
放大率公式关联图像尺寸与实物尺寸，是处理显微镜图和照片时必须掌握的工具。代入数值前务必把所有测量值换算成同一单位（通常为微米）。
Magnification = Image size ÷ Actual size or M = I ÷ A
放大率 = 图像尺寸 ÷ 实际尺寸 或 M = I ÷ A
Remember: 1 mm = 1000 µm. If a cell image measures 10 mm on a photograph and its actual size is 2 µm, first convert 10 mm = 10 000 µm, then Magnification = 10 000 ÷ 2 = ×5000.
记住：1 mm = 1000 µm。若照片上细胞图像长 10 mm，实际大小为 2 µm，先转换 10 mm = 10 000 µm，则放大率 = 10 000 ÷ 2 = ×5000。
2. Surface Area to Volume Ratio | 表面积与体积比
The surface area : volume (SA:V) ratio determines how efficiently a cell can exchange materials with its environment. As a cell or organism grows larger, its volume increases more rapidly than its surface area, so the SA:V ratio falls.
表面积与体积比 (SA:V) 决定了细胞与环境物质交换的效率。细胞或生物体越大，体积的增长快于表面积，因此 SA:V 比值下降。
SA : V ratio = Surface area ÷ Volume
表面积 : 体积比 = 表面积 ÷ 体积
For a simple cube of side length L, surface area = 6L², volume = L³, so SA:V = 6/L. Small cells have a large SA:V ratio, which favours rapid diffusion. This explains why active cells, such as root hair cells or erythrocytes, are tiny.
以边长为 L 的立方体为例，表面积 = 6L²，体积 = L³，则 SA:V = 6/L。小细胞的 SA:V 比值大，有利于快速扩散，这就解释了为什么根毛细胞、红细胞等活跃细胞体积微小。
3. Fick’s Law of Diffusion | 菲克扩散定律
Fick’s law describes the rate of diffusion across a membrane and highlights three key factors that maximise transport efficiency. It is especially relevant when evaluating adaptations of gas exchange surfaces.
菲克定律描述了跨膜扩散速率，指出影响运输效率的三个关键因素。在评估气体交换表面的适应性时，这一定律尤为重要。
Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Membrane thickness
扩散速率 ∝ (表面积 × 浓度差) ÷ 膜厚度
A large surface area, a steep concentration gradient and a thin exchange surface all increase the rate of diffusion. Mammalian alveoli, fish gills and plant leaves all exhibit these features.
大表面积、陡峭的浓度梯度以及薄的交换面都能提高扩散速率。哺乳动物的肺泡、鱼鳃和植物叶片都体现了这些特征。
4. Water Potential Equation | 水势方程
Water potential (ψ) is the measure of free energy of water and predicts the direction of water movement by osmosis. Water always moves from a region of higher (less negative) water potential to a region of lower (more negative) water potential.
水势 (ψ) 是水自由能的度量，用于预测渗透作用中水的运动方向。水总是从水势较高（负值小）的区域流向水势较低（负值大）的区域。
ψ = ψs + ψp
水势 = 溶质势 + 压力势
ψs (solute potential) is added to ψp (pressure potential). In an open container at atmospheric pressure, ψp = 0. Pure water has ψ = 0 MPa; adding solutes makes ψs negative, reducing ψ.
ψs（溶质势）与 ψp（压力势）相加。在敞口容器中大气压下 ψp = 0。纯水水势为 0 MPa；加入溶质会使 ψs 变为负值，从而降低水势。
5. Cardiac Output Calculation | 心输出量计算
Cardiac output quantifies the volume of blood pumped by each ventricle per minute and reflects how the circulatory system meets metabolic demands.
心输出量衡量每个心室每分钟泵出的血量，反映循环系统满足代谢需求的能力。
Cardiac output (CO) = Stroke volume (SV) × Heart rate (HR)
心输出量 (CO) = 每搏输出量 (SV) × 心率 (HR)
Cardiac output is expressed in litres per minute (L min⁻¹). In a resting adult, typical values are SV ≈ 70 mL, HR ≈ 72 bpm, giving CO ≈ 5.0 L min⁻¹. During exercise, both SV and HR increase, raising CO significantly.
心输出量单位为升每分钟（L min⁻¹）。静息成年人典型值为 SV ≈ 70 mL，HR ≈ 72 bpm，CO ≈ 5.0 L min⁻¹。运动时 SV 与 HR 均升高，心输出量显著增加。
6. Respiratory Quotient (RQ) | 呼吸商
The respiratory quotient indicates the type of substrate being respired and can be calculated from the ratio of carbon dioxide produced to oxygen consumed.
呼吸商显示正在被呼吸的底物类型，可通过二氧化碳产生量与氧气消耗量的比值计算。
RQ = CO₂ produced ÷ O₂ consumed
RQ = 产生的 CO₂ ÷ 消耗的 O₂
- Carbohydrate (glucose): C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O → RQ = 6/6 = 1.0
- Carbohydrate (葡萄糖): C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O → RQ = 6/6 = 1.0
- Lipid: RQ ≈ 0.7 (e.g. tripalmitin RQ = 0.71)
- 脂质: RQ ≈ 0.7（如三棕榈酸甘油酯 RQ = 0.71）
- Protein: RQ ≈ 0.9
- 蛋白质: RQ ≈ 0.9
7. Hardy–Weinberg Principle | 哈迪–温伯格原理
The Hardy–Weinberg principle provides a mathematical model for predicting allele and genotype frequencies in a non-evolving population. It serves as a null hypothesis for detecting evolutionary change.
哈迪–温伯格原理为预测非进化群体中等位基因与基因型频率提供了数学模型，是检测进化变化的零假设。
p + q = 1 and p² + 2pq + q² = 1
p + q = 1 且 p² + 2pq + q² = 1
p = frequency of the dominant allele, q = frequency of the recessive allele. p² = frequency of homozygous dominant, 2pq = frequency of heterozygotes, q² = frequency of homozygous recessive. The population must be large, randomly mating, and free of mutation, migration and natural selection.
p = 显性等位基因频率，q = 隐性等位基因频率。p² = 纯合显性基因型频率，2pq = 杂合子频率，q² = 纯合隐性频率。群体需满足大群体、随机交配、无突变、无迁移和自然选择等条件。
8. Simpson’s Diversity Index | 辛普森多样性指数
Simpson’s index quantifies biodiversity by considering both species richness and species evenness. A higher value indicates greater diversity.
辛普森指数从物种丰富度和均匀度两方面量化生物多样性。数值越高，多样性越大。
D = 1 – Σ (n / N)²
D = 1 – Σ (n / N)²
where n = number of individuals of a particular species, N = total number of individuals of all species. The sum is taken over all species present. D ranges from 0 (low diversity) to almost 1 (high diversity).
其中 n = 某一物种的个体数，N = 所有物种的个体总数。对所有现存物种求和。D 值范围为 0（低多样性）至接近 1（高多样性）。
9. Chi-squared (χ²) Test | 卡方(χ²)检验
The chi-squared test is used to determine if there is a significant difference between observed and expected frequencies. In WJEC Biology, it is commonly applied to genetic crosses and ecological data.
卡方检验用于判断观察频数与期望频数之间是否存在显著差异。在 WJEC 生物学中，通常应用于遗传杂交和生态学数据。
χ² = Σ (O – E)² / E
χ² = Σ (观察值 O – 期望值 E)² / E
O = observed value, E = expected value. Calculate χ², determine degrees of freedom (usually number of categories – 1), then compare against a critical value from the χ² distribution table at p = 0.05. If the calculated χ² > critical value, the null hypothesis is rejected.
O = 观察值，E = 期望值。计算 χ²，确定自由度（通常为类别数 – 1），然后与 χ² 分布表中 p = 0.05 的临界值比较。若计算 χ² > 临界值，则拒绝零假设。
10. Student’s t-test | 学生t检验
Student’s t-test is used to compare the means of two sets of data and assess whether any difference is statistically significant. The unpaired (independent) t-test is a standard tool on the WJEC specification.
学生t检验用于比较两组数据的平均值，判断其差异是否具有统计学意义。非配对（独立样本）t检验是 WJEC 课纲中的标准工具。
t = (x̄₁ – x̄₂) / √(s₁²/n₁ + s₂²/n₂)
t = (均值₁ – 均值₂) / √(方差₁/n₁ + 方差₂/n₂)
x̄₁ and x̄₂ are sample means, s₁² and s₂² are sample variances, and n₁, n₂ are sample sizes. Compare the calculated t value against a critical value at p = 0.05 and appropriate degrees of freedom (n₁ + n₂ – 2). If t > critical value, the means are significantly different.
x̄₁、x̄₂ 为样本均值，s₁²、s₂² 为样本方差，n₁、n₂ 为样本大小。将算出的 t 值与 p=0.05 及相应自由度 (n₁ + n₂ – 2) 的临界值比较。若 t > 临界值，则均值存在显著差异。
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