📚 WJEC A-Level Biology Calculation Drill | A-Level WJEC 生物：计算题专项训练
Calculations form a vital part of WJEC A-Level Biology, appearing across topics from microscopy to population ecology. This drill consolidates the key numerical skills required, with step-by-step methods and worked examples to build confidence for exam questions. Mastering these techniques will help you secure marks quickly and accurately.
计算是 WJEC A-Level 生物学的重要组成部分，涉及从显微镜使用到种群生态的多个主题。本次专项训练整合了所需的关键计算技能，通过分步方法和例题练习来增强应对考试题目的信心。掌握这些技巧将帮助你快速、准确地拿下分数。
1. Microscope Measurements and Magnification | 显微镜测量与放大倍数
The relationship between magnification, image size and actual specimen size is fundamental. Use the formula and always check that units match. If you measure an image in millimetres, convert to the same unit as the actual size (often micrometres).
放大倍数、图像大小与实际样本大小之间的关系是基础。使用公式时务必确保单位一致。如果以毫米为单位测量图像，需将其转换为与实际尺寸相同的单位（通常为微米）。
Magnification = Image size ÷ Actual size
Example: A student draws a cell 50 mm long. The actual cell is 0.2 mm. Magnification = 50 ÷ 0.2 = ×250. To find actual size: Actual size = Image size ÷ Magnification. In an exam, you might convert mm to µm (1 mm = 1000 µm).
示例：一名学生画了一个长 50 mm 的细胞。该细胞实际长度为 0.2 mm。放大倍数 = 50 ÷ 0.2 = ×250。若要计算实际大小：实际大小 = 图像大小 ÷ 放大倍数。考试中可能需要将毫米转换为微米（1 mm = 1000 µm）。
2. Haemocytometer Cell Counting | 血球计数板细胞计数
A haemocytometer is used to estimate cell concentration. After staining, count cells in a known volume of the central grid. The depth of the chamber (usually 0.1 mm) and the area of the counted squares are used to calculate cells per cm³ or per cm³ of original suspension if dilution was applied.
血球计数板用于估算细胞浓度。染色后，在中央网格的已知体积内计数细胞。使用计数室的深度（通常为 0.1 mm）和计数的方格面积来计算每立方厘米的细胞数，如果进行了稀释，还要换算回原始悬液中的浓度。
Key formula: Cells per cm³ = (Average count per square × Dilution factor) ÷ (Area of square counted (mm²) × Depth (mm)). With a standard haemocytometer, the volume over one small square is 0.1 mm × 0.0025 mm² = 0.00025 mm³ = 2.5 × 10⁻⁴ mm³. Convert mm³ to cm³ (1 cm³ = 1000 mm³). Multiply by dilution factor if needed.
关键公式：每立方厘米的细胞数 = （每个方格的平均计数 × 稀释因子） ÷ （所计方格的面积（mm²） × 深度（mm））。对于标准血球计数板，一个小方格上方的体积为 0.1 mm × 0.0025 mm² = 0.00025 mm³ = 2.5 × 10⁻⁴ mm³。将 mm³ 转换为 cm³（1 cm³ = 1000 mm³）。必要时乘以稀释因子。
3. Serial Dilutions | 连续稀释
Serial dilutions are used to reduce the concentration of a solution in a stepwise manner, typically by a factor of 10. Each step adds a fixed volume of the previous solution to a known volume of diluent. The final concentration is calculated as the original concentration multiplied by the dilution factor raised to the power of the number of dilution steps.
连续稀释用于逐步降低溶液浓度，通常每次稀释 10 倍。每一步取固定体积的上一步溶液加入到已知体积的稀释液中。最终浓度计算为原始浓度乘以稀释因子的稀释次数次方。
If you dilute 1 cm³ of stock into 9 cm³ of water, the dilution factor is 1/10 (1 part in 10). After two such dilutions, the concentration is original × (1/10)² = original × 0.01. Always express the factor as a ratio or fraction.
如果取 1 cm³ 原液加入到 9 cm³ 水中，稀释因子为 1/10（十分之一）。经过两次这样的稀释后，浓度为原浓度 × (1/10)² = 原浓度 × 0.01。始终用比例或分数表示该因子。
4. Enzyme Rate Calculations | 酶反应速率计算
Reaction rate is often calculated as the amount of product formed (or substrate used) per unit time. From a progress curve, take the initial linear portion to determine initial rate. Units could be cm³ min⁻¹, arbitrary units s⁻¹, or absorbance change per minute.
反应速率通常计算为单位时间内产物的生成量（或底物的消耗量）。从反应进程曲线中取初始线性部分来确定初始速率。单位可以是 cm³ min⁻¹、任意单位 s⁻¹ 或每分钟吸光度变化。
Rate = Change in product / Time. For example, if 4.5 cm³ of O₂ is produced in 3 minutes, rate = 4.5 ÷ 3 = 1.5 cm³ min⁻¹. When substrate concentration is varied, you can calculate the rate at each concentration and plot rate against concentration to investigate kinetics.
速率 = 产物的变化量 / 时间。例如，如果在 3 分钟内产生 4.5 cm³ 的 O₂，速率 = 4.5 ÷ 3 = 1.5 cm³ min⁻¹。当改变底物浓度时，可以计算每个浓度下的速率，并绘制速率-浓度曲线来研究动力学。
5. Percentage Change and Increase | 百分比变化与增长
Percentage change is frequently examined in WJEC Biology, for example when comparing final and initial masses in osmosis experiments, or bacterial population growth. The formula works whether values increase or decrease.
百分比变化在 WJEC 生物学考试中经常出现，例如比较渗透实验中的最终质量和初始质量，或细菌种群增长。无论数值增加还是减少，该公式均适用。
Percentage change = (Final value – Initial value) ÷ Initial value × 100%
A negative result indicates a percentage decrease. If a potato chip’s mass goes from 2.5 g to 2.3 g, the change is (2.3 – 2.5) / 2.5 × 100% = –8%, an 8% loss in mass. Always show the sign or state ‘decrease’.
负值表示百分比减少。如果马铃薯条的质量从 2.5 g 变为 2.3 g，变化为 (2.3 – 2.5) / 2.5 × 100% = –8%，即质量损失了 8%。始终标明符号或注明“减少”。
6. Population Growth: Exponential | 种群指数增长
Bacterial populations can grow exponentially when resources are unlimited. The basic model is Nt = N0 × 2n, where Nt is the population after t hours, N0 the starting population, and n the number of generations (divisions) that have occurred.
在资源无限的情况下，细菌种群可呈指数增长。基本模型为 Nₜ = N₀ × 2ⁿ，其中 Nₜ 代表 t 小时后的种群数量，N₀ 为初始种群数量，n 为已发生的代数（分裂次数）。
Example: Starting with 500 bacteria, with a doubling time of 30 minutes, how many after 3 hours? n = 3 hours × (2 divisions per hour) = 6 generations. N = 500 × 2⁶ = 500 × 64 = 32 000 cells. Sometimes questions ask for log values or to estimate generation time from a graph.
示例：初始有 500 个细菌，倍增时间为 30 分钟，3 小时后有多少？n = 3 小时 ×（每小时 2 次分裂）= 6 代。N = 500 × 2⁶ = 500 × 64 = 32 000 个细胞。有时题目要求对数值或从曲线图中估算代时。
7. Mark-Release-Recapture (Lincoln Index) | 标记重捕法估计种群
For motile organisms, the Lincoln Index estimates population size (N) using a simple proportion. The method assumes random mixing of marked and unmarked individuals, no births or deaths between samples, and no mark loss.
对于活动性强的生物，林肯指数通过简单的比例估算种群大小（N）。该方法假设标记个体与未标记个体随机混合，两次取样之间没有出生或死亡，且标记不丢失。
N = (M × C) ÷ R
where M = number initially captured and marked, C = total number captured in second sample, R = number of marked individuals recaptured in second sample. Example: 40 woodlice marked, later 50 captured, of which 10 were marked. N = (40 × 50) ÷ 10 = 200. Calculate the population estimate and discuss assumptions.
其中 M = 最初被捕获并标记的个体数，C = 第二次取样中捕获的总个体数，R = 第二次取样中重捕的标记个体数。示例：标记了 40 只潮虫，之后捕获 50 只，其中 10 只带有标记。N = (40 × 50) ÷ 10 = 200。计算种群估计值并讨论假设条件。
8. Chi-Squared (χ²) Test Calculations | 卡方检验计算
The chi-squared test is used in genetics and ecology to compare observed and expected frequencies. You need to calculate χ², determine degrees of freedom, and compare to a critical value table at p = 0.05.
卡方检验用于遗传学和生态学中比较观察频数和期望频数。你需要计算 χ²，确定自由度，并将其与 p = 0.05 时的临界值表进行比较。
χ² = Σ (O – E)² ÷ E
O = observed value, E = expected value. Work through a genetic cross: a dihybrid cross with 9:3:3:1 expected ratio. Observed counts: 90, 30, 28, 12. Calculate respective expected numbers based on total 160. For category 1, expected = 9/16 × 160 = 90, O = 90, (O – E)² / E = 0. Summing yields χ², then compare with critical value for df = 3. If χ² < critical value, accept null hypothesis of no significant difference.
O = 观察值，E = 期望值。以双杂合子杂交的 9:3:3:1 比例为例。观察值：90, 30, 28, 12。根据总数 160 计算各自的期望值。对于类别 1，期望值 = 9/16 × 160 = 90，O = 90，(O – E)² / E = 0。求和得到 χ²，然后与自由度 3 的临界值比较。若 χ² < 临界值，则接受无显著差异的零假设。
9. Genetic Probability and Ratios | 遗传概率与比例
Genetic calculations often involve Punnett squares and the product rule. For single-gene crosses, determine the genotypic and phenotypic ratios. In dihybrid crosses, expected phenotypes are 9:3:3:1 when both parents are heterozygous for two unlinked genes.
遗传学计算常涉及旁氏表和乘法法则。对于单基因杂交，确定基因型比和表型比。在双杂合子杂交中，当亲本在两个非连锁基因上均为杂合时，期望的表型比为 9:3:3:1。
To find the probability of a particular genotype, multiply the probabilities of getting each allele. For example, AaBb × AaBb, probability of aabb = ¼ × ¼ = 1/16. For sex-linked inheritance, take parental genotypes and track the X and Y chromosomes. Pedigree analysis may require calculating risk of an individual being a carrier.
要找出特定基因型的概率，将获得每个等位基因的概率相乘。例如，AaBb × AaBb，得到 aabb 的概率 = ¼ × ¼ = 1/16。对于伴性遗传，根据亲代基因型追踪 X 和 Y 染色体。系谱分析可能需要计算个体成为携带者的风险。
10. 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 affects rates of diffusion, heat exchange, and material transport. Calculations are required for cubes and spheres.
随着生物体或细胞体积增大，其表面积与体积之比（SA:V）减小。这会影响扩散速率、热量交换和物质运输。考试中需要计算立方体和球体的相关数值。
Cube: SA = 6 × (side length)², V = (side length)³. For side 2 cm, SA = 24 cm², V = 8 cm³, ratio = 24:8 = 3:1. If side becomes 4 cm, SA = 96 cm², V = 64 cm³, ratio = 96:64 = 1.5:1. Calculate and explain why large organisms need specialised exchange surfaces.
立方体：SA = 6 ×（边长）²，V =（边长）³。若边长为 2 cm，SA = 24 cm²，V = 8 cm³，比值为 24:8 = 3:1。若边长变为 4 cm，SA = 96 cm²，V = 64 cm³，比值为 96:64 = 1.5:1。计算并解释为什么大型生物需要特化的交换表面。
11. Respiration Rate and Oxygen Uptake | 呼吸速率与氧气消耗量计算
Using a respirometer, you can measure the change in gas volume as oxygen is consumed (CO₂ absorbed by KOH). Rate of oxygen uptake is calculated as volume change per unit time per mass of organism. Often expressed as mm³ O₂ g⁻¹ min⁻¹.
使用呼吸计，你可以测量由于氧气消耗（CO₂ 被 KOH 吸收）引起的气体体积变化。氧气消耗速率计算为单位时间内单位生物体质量的体积变化。通常表示为 mm³ O₂ g⁻¹ min⁻¹。
Calculation: Liquid column moves 8 mm in 5 min; capillary tube has diameter 1 mm (radius 0.5 mm). Volume = π r² × distance moved. V = π × (0.5)² × 8 = π × 0.25 × 8 = 2π ≈ 6.28 mm³. Rate = 6.28 mm³ / 5 min = 1.256 mm³ min⁻¹. Then divide by mass of organism (e.g. 0.2 g) = 6.28 mm³ min⁻¹ g⁻¹.
计算：液柱在 5 分钟内移动了 8 mm；毛细管直径为 1 mm（半径为 0.5 mm）。体积 = π r² × 移动距离。V = π × (0.5)² × 8 = π × 0.25 × 8 = 2π ≈ 6.28 mm³。速率 = 6.28 mm³ / 5 min = 1.256 mm³ min⁻¹。然后除以生物体质量（如 0.2 g）= 6.28 mm³ min⁻¹ g⁻¹。
12. Dilution Factors in Colorimetry | 比色法中的稀释因子
In colorimetry, a standard curve of absorbance vs. concentration is used to find an unknown concentration. If the unknown sample was diluted before measurement, multiply the result by the dilution factor to get the original concentration.
在比色法中，利用吸光度-浓度标准曲线来求未知浓度。如果待测样本在测量前进行了稀释，则需将结果乘以稀释因子以获得原始浓度。
For example, a glucose solution of unknown concentration is diluted 1 in 5 (1 cm³ + 4 cm³ water) and gives an absorbance corresponding to 0.12 mg cm⁻³. Original concentration = 0.12 mg cm⁻³ × 5 = 0.6 mg cm⁻³. Always check the dilution factor by calculating the ratio of final volume to sample volume.
例如，将未知浓度的葡萄糖溶液进行 1:5 稀释（1 cm³ + 4 cm³ 水），测得的吸光度对应 0.12 mg cm⁻³。原始浓度 = 0.12 mg cm⁻³ × 5 = 0.6 mg cm⁻³。通过计算最终体积与样本体积的比率来确认稀释因子。
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