📚 Year 12 Edexcel Biology: Formula & Theorem Quick Reference Handbook | 年级12 Edexcel 生物：公式定理速查手册
Mastering the quantitative skills in Year 12 Edexcel A Biology is essential for analysing data, interpreting experiments, and solving examination problems. This quick reference handbook brings together all the formulas, theorems, and mathematical relationships you need, from magnification and cardiac output to the Hardy‑Weinberg principle and statistical tests. Each entry is explained in clear steps and paired with practical examples, so you can revise efficiently and tackle calculation questions with confidence.
掌握Edexcel A Level 生物 Year 12 的定量技能是分析数据、解读实验和解决考试问题的关键。本速查手册汇总了所有必备的公式、定理和数学关系，从放大倍率、心输出量到哈代‑温伯格原理和统计检验，每个条目都附有清晰的步骤说明和实例，助你高效复习、从容应对计算题。
1. Microscopy Calculations | 显微镜计算
The core formula linking image size, actual size, and magnification is Magnification = Image size ÷ Actual size and divide by the true length it represents to find the magnification. When converting units, remember: 1 mm = 1000 µm, so to convert mm to µm multiply by 1000.
核心公式是：放大倍率 = 图像尺寸 ÷ 实际尺寸。务必使所有测量值单位统一（通常为毫米或微米）。若图中有比例尺，可在图像上测量比例尺的长度，除以它所代表的真实长度即得放大倍率。单位换算时牢记：1 mm = 1000 µm，将 mm 转换为 µm 需乘以 1000。
Magnification = I / A
I = image size, A = actual size
2. Cardiac Output and Body Mass Index | 心输出量与身体质量指数
Cardiac output is the volume of blood pumped by the heart per minute. It is calculated as cardiac output (CO) = stroke volume (SV) × heart rate (HR). Stroke volume is the volume of blood ejected by each ventricle per beat, and heart rate is beats per minute. CO is typically expressed in L min⁻¹ or mL min⁻¹. To maintain health, cardiac output adjusts through changes in stroke volume or heart rate during exercise.
心输出量是心脏每分钟泵出的血量，公式为 心输出量 (CO) = 每搏输出量 (SV) × 心率 (HR)。每搏输出量是每次心跳一侧心室射出的血量，心率是每分钟心跳次数。心输出量通常以 L min⁻¹ 或 mL min⁻¹ 表示。为维持健康，运动时心输出量会通过每搏输出量或心率的变化来调节。
Body mass index (BMI) estimates whether a person has a healthy body weight for their height: BMI = mass (kg) ÷ [height (m)]². A related ratio, waist‑to‑hip ratio (WHR), helps assess fat distribution: WHR = waist circumference ÷ hip circumference. Both are used as risk indicators for cardiovascular disease.
身体质量指数 (BMI) 用于估算体重是否在健康范围内：BMI = 体重 (kg) ÷ [身高 (m)]²。另一个相关比值腰臀比 (WHR) 用于评估脂肪分布：腰臀比 = 腰围 ÷ 臀围。两者均作为心血管疾病的风险指标。
CO = SV × HR
BMI = mass / (height)²
3. Surface Area to Volume Ratio | 表面积与体积比
The surface area to volume ratio (SA:V) is decisive for transport of heat, gases, and nutrients. For a cube of side length L, surface area = 6L² and volume = L³ ease in size, SA:V decreases, making passive diffusion insufficient. Adaptations such as flattened bodies, extensive capillary networks, and specialised exchange surfaces compensate for a low SA:V.
表面积与体积比 (SA:V) 对热量、气体和养分的运输至关重要。边长为 L 的立方体，表面积 = 6L²，体积 = L³，故 SA:V = 6/L。生物体越大，SA:V 越小，被动扩散便无法满足需求。扁平的身体、丰富的毛细血管网和特化的交换表面等适应特征可弥补低 SA:V。
Cube: SA = 6L², V = L³ → SA:V = 6/L
Sphere: SA = 4πr², V = (4/3)πr³ → SA:V = 3/r
4. Dilution Series and Haemocytometer Counting | 稀释系列与血球计数板计数
When making a dilution series, the dilution factor (DF) equals the total volume divided by the volume of stock solution. For serial dilutions, the overall DF is the product of individual dilution factors. Cell concentration using a haemocytometer is given by: cells per mL = average cell count per square × dilution factor × 10⁴ 10⁴ arises because the counting chamber volume over one small square is 0.1 mm³ = 10⁻⁴ mL.
配制稀释系列时，稀释因子 (DF) 等于总体积除以原液体积。连续稀释的总稀释因子为每一步稀释因子的乘积。用血球计数板计算细胞浓度时，公式为：每毫升细胞数 = 每方格平均细胞数 × 稀释因子 × 10⁴。因子 10⁴ 是因为每个小方格的计数池体积为 0.1 mm³ = 10⁻⁴ mL。
Cell concentration (cells mL⁻¹) = N × DF × 10⁴
N = average count per small square
5. Probability Rules in Genetics | 遗传学中的概率规则
The product rule applies when two independent events both occur: P(A and B) = P(A) × P(B) m heterozygous parents is ½ × ½ = ¼. The sum rule is used for mutually exclusive outcomes: P(A or B) = P(A) + P(B) fspring showing the dominant phenotype (homozygous dominant OR heterozygous) is ¼ + ½ = ¾.
两个独立事件同时发生时用乘法法则：P(A 且 B) = P(A) × P(B)。在单基因杂交中，杂合亲本产生的子代同时获得两个隐性等位基因的概率为 ½ × ½ = ¼。对于互斥事件，用加法法则：P(A 或 B) = P(A) + P(B)。例如子代表现为显性表型（纯合显性或杂合）的概率为 ¼ + ½ = ¾。
6. Hardy‑Weinberg Principle | 哈代‑温伯格原理
The Hardy‑Weinberg equations describe allele and genotype frequencies in a population that is not evolving. For a gene with two alleles, the frequency of the dominant allele is p and the recessive allele is q. The two fundamental equations are: p + q = 1 and p² + 2pq + q² = 1 s recessive. These equations can be used to estimate the proportion of carriers when the frequency of a recessive disorder is known.
哈代‑温伯格方程描述非进化群体中的等位基因频率和基因型频率。对于两个等位基因的基因，设显性等位基因频率为 p，隐性为 q。两个基本方程为：p + q = 1 及 p² + 2pq + q² = 1。其中 p² 为纯合显性频率，2pq 为杂合子频率，q² 为纯合隐性频率。当已知隐性遗传病的发病率时，可用这些公式估算携带者比例。
p + q = 1
p² + 2pq + q² = 1
7. Simpson's Index of Diversity | 辛普森多样性指数
Biodiversity can be quantified using Simpson's Index of Diversity (D): D = 1 – Σ(n/N)², where n is the number of individuals of a particular species and N is the total number of individuals of all species. The value of D ranges from 0 (low diversity) to 1 (infinite diversity). A higher index indicates greater species richness and evenness. This index is used to compare habitats and monitor the effects of environmental changes.
辛普森多样性指数 (D) 是量化生物多样性的指标：D = 1 – Σ(n/N)²，其中 n 为某一物种的个体数，N 为所有物种的总个体数。D 值范围为 0（低多样性）到 1（极高多样性），数值越高表示物种丰富度和均匀度越高。该指数常用于比较不同栖息地和监测环境变化的影响。
D = 1 – Σ (n/N)²
8. Spearman's Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman's rank correlation (rₛ) measures the strength and direction of a monotonic relationship between two ranked variables. The formula is: rₛ = 1 – [6 Σ d² / (n(n² – 1))], where d is the difference between the ranks of each pair, and n is the number of paired observations. The value of rₛ lies between –1 (perfect negative correlation) and +1 (perfect positive correlation). The statistical significance of rₛ must be checked against a critical value table for the appropriate degrees of freedom (n – 2).
斯皮尔曼等级相关系数 (rₛ) 衡量两个排序变量之间单调关系的强度和方向。公式为：rₛ = 1 – [6 Σ d² / (n(n² – 1))]，其中 d 为每对数据等级之差，n 为配对观察值数量。rₛ 值介于 –1（完全负相关）和 +1（完全正相关）之间。rₛ 的统计显著性需与相应自由度 (n – 2) 的临界值表进行比较。
rₛ = 1 – (6 Σ d²) / [n(n² – 1)]
9. Student's t‑test | 学生 t 检验
Student's t‑test is used to determine whether there is a significant difference between the means of two independent samples. The unpaired t‑test formula is: t = (x̄₁ – x̄₂) / √s₁²/n₁ + s₂²/n₂, where x̄₁ and x̄ ans, s₁² and s₂² are the sample variances, and n₁, n₂ are the sample sizes. A calculated t‑value greater than the critical t‑ allows rejection of the null hypothesis and conclusion that the difference is significant.
学生 t 检验用于判断两个独立样本的平均值是否存在显著差异。非配对 t 检验的公式为：t = (x̄₁ – x̄₂) / √s₁²/n₁ + s₂²/n₂，其中 x̄₁ 和 x̄₂ 为样本均值，s₁² 和 s₂² 为样本方差，n₁ 和 n₂ 为样本量。当计算出的 t 值大于所选显著性水平（通常 p = 0.05）的临界 t 值时，可拒绝零假设，得出差异显著的结论。
t = (x̄₁ – x̄₂) / √s₁²/n₁ + s₂²/n₂
10. Q₁₀ Temperature Coefficient and Percentage Change | Q₁₀ 温度系数与百分比变化
The Q₁₀ coefficient measures the rate of change of a biological process when the temperature is increased by 10°C. For experiments where the temperature interval is exactly 10°C, Q₁₀ = rate at (T+10)°C ÷ rate at T°C. When the gap is not exactly 10°C, the general formula is applied: Q₁₀ = (R₂ / R₁)^(10 / (T₂ – T₁)), where R₁ and R₂ are the rates at temperatures T₁ and T₂. A Q₁₀ of around 2 indicates that the reaction rate doubles for a 10°C rise, typical for many enzyme‑controlled reactions.
Q₁₀ 温度系数用于衡量温度每升高 10°C 时生物过程的速率变化。当温度间隔恰好为 10°C 时，Q₁₀ = (T+10)°C 下的速率 ÷ T°C 下的速率。若间隔不为 10°C，可使用通式：Q₁₀ = (R₂ / R₁)^(10 / (T₂ – T₁))，其中 R₁ 和 R₂ 为温度 T₁ 和 T₂ 下的速率。Q₁₀ 约为 2 时表示温度每升高 10°C 反应速率翻倍，许多酶促反应符合这一规律。
Percentage change is heavily tested in AS Biology: percentage change = [(final value – original value) / original value] × 100%. A negative result indicates a decrease. This calculation appears in data analysis for osmosis, enzyme activity, and cardiac output, so always remember to divide by the original value, not the final one.
百分比变化在 AS 生物中考查频繁：百分比变化 = [(最终值 – 原始值) ÷ 原始值] × 100%。负值表示降低。该计算常见于渗透作用、酶活性和心输出量的数据分析，请始终牢记除以原始值而非最终值。
Q₁₀ = R(T+10) / R(T) or Q₁₀ = (R₂ / R₁)^(10/(T₂ – T₁))
% change = (final – original) / original × 100%
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