📚 IGCSE Biology: Calculations Practice | IGCSE 生物：计算题专项训练
Calculations are an essential part of IGCSE Biology, appearing in multiple topics including microscopy, ecology, genetics, respiration, and photosynthesis. To score full marks, you need to master key formulas, unit conversions, and logical data interpretation. This guide breaks down every type of calculation you may face, with worked examples and tips to avoid common mistakes.
计算是 IGCSE 生物的重要部分，出现在显微镜、生态、遗传、呼吸作用和光合作用等多个主题中。要拿到满分，你必须掌握关键公式、单位换算和合理的数据分析。本指南将拆解你可能遇到的每一类计算，提供示例和避开常见错误的技巧。
1. Magnification Formula | 放大倍率公式
The core equation in microscopy is: Magnification = Image size ÷ Actual size. You must be able to rearrange it to find actual size: Actual size = Image size ÷ Magnification, or image size: Image size = Magnification × Actual size. The image size is usually measured with a ruler, and actual size is the real object length.
显微镜中的核心公式是：放大倍率 = 图像大小 ÷ 实际大小。你必须会变形，求实际大小：实际大小 = 图像大小 ÷ 放大倍率，或求图像大小：图像大小 = 放大倍率 × 实际大小。图像大小通常用尺子测量，实际大小则是物体的真实长度。
2. Unit Conversions: mm, µm, nm | 单位换算：毫米、微米、纳米
IGCSE questions routinely require conversions. Remember: 1 mm = 1000 µm; 1 µm = 1000 nm. To go from mm to µm, multiply by 1000. To go from µm to mm, divide by 1000. For nm to µm, divide by 1000. Always express your final answer in the unit requested.
IGCSE 题目经常需要单位换算。记住：1 mm = 1000 µm；1 µm = 1000 nm。从 mm 到 µm 乘以 1000；从 µm 到 mm 除以 1000。nm 转 µm 除以 1000。最终答案务必使用题目要求的单位。
3. Measuring Cell Size from Micrographs | 从显微照片测量细胞大小
When given a photomicrograph, use a ruler to measure the length of the cell or organelle in mm, then convert to µm. Apply Actual size = Measured length (µm) ÷ Magnification. If a scale bar is provided, measure the bar in mm, convert to µm, and calculate the actual size represented per mm, then apply to the object.
当提供显微照片时，用尺子测量细胞或细胞器的长度（mm），然后换算为 µm。使用 实际大小 = 测量长度（µm）÷ 放大倍率。如果给出比例尺，测量比例尺的毫米长度，转换为 µm，计算出每毫米代表的实际长度，再应用于待测物。
4. Estimating Population Size Using Quadrats | 使用样方估算种群数量
For slow-moving or stationary organisms, use the formula: Estimated total population = (Mean number per quadrat × Total area) ÷ Quadrat area. Work out the mean from several randomly placed quadrats. Remember to convert all areas to the same unit (e.g., m²).
对于缓慢移动或不动的生物，使用公式：估计总种群数量 = （每样方平均个体数 × 总面积）÷ 样方面积。从多个随机放置的样方中算出平均值。记得将所有面积换算为相同单位（如 m²）。
5. Capture-Mark-Release-Recapture Method | 标记重捕法
For mobile animals, apply the Lincoln Index: Population size = (Number in 1st sample × Number in 2nd sample) ÷ Number of marked individuals in 2nd sample. Assumptions: no death, immigration, or emigration; marks are not lost and do not affect survival. Calculations often ask you to evaluate reliability.
对于可移动的动物，使用林肯指数：种群数量 = （第一次捕捉数 × 第二次捕捉数）÷ 第二次捕捉中标记个体数。假定：没有死亡、迁入或迁出；标记不丢失且不影响生存。计算题常要求评估可靠性。
6. Genetic Ratios and Probability | 遗传比率与概率
Monohybrid crosses give phenotypic ratios of 3:1 or 1:1. Express the probability of a specific genotype or phenotype as a fraction, percentage, or ratio. For example, a heterozygous cross (Tt × Tt) gives a 75% chance of the dominant phenotype. Always clearly state what the ratio refers to (dominant:recessive).
单基因杂交会产生 3:1 或 1:1 的表型比。用分数、百分比或比率表示特定基因型或表型的概率。例如，杂合子杂交（Tt × Tt）产生显性表型的概率为 75%。务必清楚说明比率所指的类别（显性:隐性）。
7. Calculating Rates of Enzyme Activity or Reaction | 酶活性或反应速率计算
Rate is often calculated as Rate = Change in quantity ÷ Time. This could be volume of oxygen produced per minute (cm³/min), mass loss per second (g/s), or change in absorbance per unit time. For enzyme experiments, draw a tangent at the steepest part of the graph to find initial rate if the curve is non-linear.
速率通常计算为 速率 = 量的变化 ÷ 时间。这可以是每分钟产生氧气的体积（cm³/min）、每秒质量减少（g/s），或单位时间内吸光度的变化。对于酶实验，若曲线非线性，可在最陡段画切线求初始速率。
8. Respiration and Gas Volume Measurements | 呼吸作用与气体体积测量
In respirometer experiments, movement of a manometer fluid indicates oxygen consumption. Calculate Oxygen consumption rate = Distance moved × cross-sectional area of capillary ÷ Time. Remember to account for control (non-living) to correct for temperature or pressure changes. Also calculate respiratory quotient (RQ) = CO₂ produced ÷ O₂ consumed, using volumes.
在呼吸计实验中，压力计液体的移动表示氧气的消耗。计算 耗氧速率 = 液柱移动距离 × 毛细管横截面积 ÷ 时间。记得用对照组（非生物）校正温度或气压变化。还要计算呼吸商（RQ）= 产生 CO₂ 体积 ÷ 消耗 O₂ 体积。
9. Photosynthesis Rate and Limiting Factors | 光合作用速率与限制因素
Use the floating disc assay or oxygen production to measure rate. Rate of photosynthesis = Number of bubbles per minute or Volume of O₂ ÷ Time. When interpreting graphs of rate vs. light intensity, CO₂, or temperature, calculate the exact increase in rate when a factor is changed, and identify the limiting factor mathematically.
通过叶盘上浮法或氧气产量来测量速率。光合作用速率 = 每分钟气泡数 或 氧气体积 ÷ 时间。在解释速率与光强、CO₂ 或温度的关系图时，计算因素改变后速率的确切增量，并用数学方法确定限制因素。
10. Percentage Change and Benedict’s / Biuret Calculations | 百分比变化与本尼迪克特/双缩脲计算
Use Percentage change = [(Final value – Initial value) ÷ Initial value] × 100%. This applies to mass change in osmosis experiments, or colorimeter readings. A negative value indicates a decrease. For food tests, you might compare reducing sugar concentration using a calibration curve – find unknown concentration by reading off the graph.
使用 百分比变化 = [(最终值 – 初始值) ÷ 初始值] × 100%。适用于渗透实验中的质量变化，或比色计读数。负值表示减少。对于食物检测，可能使用校准曲线比较还原糖浓度——从图中读出未知物的浓度。
11. Data Analysis: Mean, Median, Range | 数据分析：平均值、中位数、极差
Calculate Mean = Sum of values ÷ Number of values. Identify Range = Largest value – Smallest value. When anomalies are present, you may be asked to omit them and recalculate. Understand that Median is the middle value when data are ordered; useful when data are skewed.
计算 平均数 = 值的总和 ÷ 值的个数。确定 极差 = 最大值 – 最小值。存在异常值时，可能要求剔除后再计算。了解 中位数 是数据排序后的中间值；当数据偏斜时很有用。
12. Interpreting Graphs and Gradient | 解读图表与斜率
Many calculation questions present a graph. Learn to find the gradient: Gradient = Change in y ÷ Change in x. This represents the rate. For curved lines, draw a tangent at a specific point. Be precise with units on both axes. Extrapolation can predict further values but carries uncertainty.
许多计算题给出图表。学会求斜率：斜率 = y 的变化量 ÷ x 的变化量。这代表速率。对曲线，在指定点画切线。注意两轴的单位精确度。外推可预测未来值，但带有不确定性。
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