📚 Year 13 OCR Biology: Formula & Theorem Quick Reference | A Level OCR 生物：公式定理速查手册
Mastering the quantitative aspects of A Level Biology is essential for success in OCR exams. This quick reference guide compiles all the key formulas, equations, and theorems you will encounter in Year 13, from energy transfer to population genetics and statistics. Use it alongside your revision to ensure you can apply them accurately under timed conditions.
掌握 A Level 生物学的定量分析是 OCR 考试成功的关键。本速查手册汇总了 Year 13 中所有重要的公式、方程和定理，涵盖能量传递、群体遗传学与统计等内容。配合复习使用，确保您在限时条件下能准确应用。
1. Photosynthesis & Productivity | 光合作用与生产力
Net photosynthesis or net primary productivity (NPP) is determined by subtracting respiratory losses (R) from gross primary productivity (GPP). The core formula is NPP = GPP – R. The efficiency of energy conversion can be expressed as (NPP / GPP) × 100%.
净光合作用或净初级生产力（NPP）由总初级生产力（GPP）减去呼吸消耗（R）得出。核心公式为 NPP = GPP – R。能量转化效率可表示为 (NPP / GPP) × 100%。
GPP represents the total energy fixed by photosynthesis; R accounts for energy lost through respiration by the plant itself. NPP is the energy available for growth and reproduction, or to primary consumers.
GPP 代表光合作用固定的总能量；R 表示植物自身通过呼吸损失的能量。NPP 是可供生长繁殖或传递给初级消费者的能量。
2. Respiration & Respiratory Quotient (RQ) | 呼吸作用与呼吸商
The respiratory quotient (RQ) is the ratio of carbon dioxide produced to oxygen consumed during respiration, measured under the same time and conditions: RQ = CO₂ produced / O₂ consumed.
呼吸商（RQ）是指在相同时间和条件下，呼吸作用中释放的二氧化碳与消耗的氧气的体积比：RQ = CO₂ 产生量 / O₂ 消耗量。
RQ values indicate the respiratory substrate being used: carbohydrate 1.0, lipid ~0.7, protein ~0.9. A value above 1.0 suggests anaerobic respiration is also taking place, as extra CO₂ is released without O₂ uptake.
RQ 值可以指示呼吸底物类型：碳水化合物 1.0，脂质约 0.7，蛋白质约 0.9。RQ 大于 1.0 表明存在无氧呼吸，因为在额外释放 CO₂ 时没有相应的 O₂ 消耗。
3. Water Potential (ψ) | 水势
Water potential (ψ, measured in kPa or MPa) determines the direction of water movement. It is the sum of solute potential (ψₛ) and pressure potential (ψₚ): ψ = ψₛ + ψₚ.
水势（ψ，单位为 kPa 或 MPa）决定水的运动方向，它是溶质势（ψₛ）与压力势（ψₚ）之和：ψ = ψₛ + ψₚ。
Solute potential (ψₛ) is always negative or zero and decreases as solute concentration increases. Pressure potential (ψₚ) is usually positive inside living cells due to turgor pressure pushing against the cell wall; it can be zero or negative in xylem under tension. Pure water at atmospheric pressure has a water potential of zero.
溶质势（ψₛ）始终为负值或零，并随溶质浓度升高而降低。压力势（ψₚ）在活细胞内通常为正值，由膨压推挤细胞壁产生；在木质部导管中受张力作用时可为零或负值。大气压下纯水的水势为零。
4. Hardy-Weinberg Principle | 哈迪-温伯格定律
For a gene with two alleles, the allele frequencies in a population are given by p + q = 1, where p is the frequency of the dominant allele and q is the frequency of the recessive allele.
对于一对等位基因，种群中的等位基因频率满足 p + q = 1，其中 p 为显性等位基因频率，q 为隐性等位基因频率。
The expected genotype frequencies are described by the expansion: p² + 2pq + q² = 1. Here, p² = homozygous dominant, 2pq = heterozygous, and q² = homozygous recessive. This equilibrium is only maintained under specific conditions: large population size, random mating, no mutations, no migration (gene flow), and no natural selection acting on the alleles.
预期的基因型频率可由二项展开式给出：p² + 2pq + q² = 1，其中 p² = 显性纯合体，2pq = 杂合体，q² = 隐性纯合体。该平衡仅在下述条件下维持：群体足够大、随机交配、无突变、无迁移（无基因流）以及该基因不受自然选择影响。
5. Simpson’s Index of Diversity (D) | 辛普森多样性指数
Simpson’s Index of Diversity is used to measure biodiversity, taking into account both species richness and evenness. The OCR formula is: D = 1 – ( Σ n(n – 1) ) / ( N(N – 1) ), where n = number of individuals of a particular species, and N = total number of individuals of all species.
辛普森多样性指数用于衡量生物多样性，兼顾物种丰富度和均匀度。OCR 公式为：D = 1 – ( Σ n(n – 1) ) / ( N(N – 1) )，其中 n 为某一物种的个体数，N 为所有物种的总个体数。
D always lies between 0 and 1. A value closer to 1 indicates high diversity (many species present in relatively equal numbers), while a value near 0 suggests low diversity, often dominated by one or a few species. The index is particularly useful for comparing the biodiversity of different habitats.
D 值介于 0 到 1 之间。越接近 1 表示多样性越高（物种丰富且数量分布均匀），越接近 0 表示多样性越低，常由少数物种占绝对优势。该指数尤其适用于比较不同栖息地的生物多样性。
6. Mark-Recapture (Lincoln Index) | 标记重捕法（林肯指数）
The Lincoln index estimates population size for motile organisms. The formula is: N = (M × C) / R, where N = population estimate, M = number of individuals initially captured, marked, and released, C = total number of individuals captured in the second sample, and R = number of marked individuals recaptured in that second sample.
林肯指数用于估算活动生物种群的大小。公式为：N = (M × C) / R，其中 N = 种群数量估计值，M = 首次捕获并标记释放的个体数，C = 第二次捕获的总个体数，R = 第二次捕获中带标记的个体数。
This method relies on assumptions: marked and unmarked individuals mix randomly, no significant immigration, emigration, births, or deaths occur between sampling, marking does not affect survival or catchability, and marks are not lost. If assumptions are violated, the estimate becomes less reliable.
该方法依赖于以下假设：标记与未标记个体随机混合，两次取样之间无明显迁入、迁出、出生或死亡，标记不影响生存或被捕获的概率，且标记不会脱落。若假设不成立，估计值可靠性下降。
7. Chi-squared Test (χ²) | 卡方检验
The chi-squared test determines whether there is a significant difference between observed and expected frequencies. The test statistic is: χ² = Σ ((O – E)² / E), where O = observed value and E = expected value. Summation is over all categories.
卡方检验用于判断观察频数与期望频数是否存在显著差异。检验统计量为：χ² = Σ ((O – E)² / E)，其中 O 为观察值，E 为期望值，对所有类别求和。
Degrees of freedom (df) for a goodness-of-fit test equals the number of categories minus one. For contingency tables, df = (rows – 1) × (columns – 1). Calculate χ², then compare it with a critical value at a set probability level (usually p = 0.05). If χ² exceeds the critical value, the null hypothesis is rejected, indicating a significant difference or association.
拟合优度检验的自由度 (df) 等于类别数减一。对于列联表，df = (行数 – 1) × (列数 – 1)。计算 χ² 后，与设定概率水平（通常 p = 0.05）下的临界值比较。若 χ² 大于临界值，则拒绝零假设，表明存在显著差异或关联。
8. Student’s t-test & Standard Deviation | 学生t检验与标准差
Standard deviation measures the spread of data around the mean. It is calculated as: s = √( Σ(x – x̄)² / (n – 1) ), where x = each data point, x̄ = sample mean, and n = sample size. The standard error of the mean (SE) is SE = s / √n.
标准差衡量数据在均值周围的离散程度，计算公式为：s = √( Σ(x – x̄)² / (n – 1) )，其中 x 为各数据点，x̄ 为样本均值，n 为样本量。均值的标准误 (SE) 为 SE = s / √n。
The unpaired (independent) t-test compares the means of two independent samples: t = |x̄₁ – x̄₂| / √(s₁²/n₁ + s₂²/n₂). The calculated t-value is compared with a critical value for the appropriate degrees of freedom. If t is greater than the
Published by TutorHao | Year 13 Biology Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导