📚 GCSE OCR Biology: Formula Summary Handbook | GCSE OCR 生物：公式汇总手册
This revision handbook brings together all the essential mathematical formulas required for GCSE OCR Biology, from microscopy and unit conversions to rates of reaction and ecological sampling. Each formula is explained with key units and tips to help you apply it confidently in exams.
这本复习手册汇集了 GCSE OCR 生物学所需的所有核心数学公式，涵盖显微镜计算、单位换算、反应速率以及生态采样等。每个公式都配有关键单位和应用建议，帮助你在考试中自信运用。
1. Magnification Formula | 放大倍率公式
Magnification describes how many times larger an image appears compared to the real specimen. The formula is Magnification = Image size ÷ Actual size. You can rearrange this as a triangle with image size at the top, and actual size and magnification sharing the bottom. Always convert all measurements to the same unit before calculating.
放大倍率表示图像比真实标本大多少倍。公式为 放大倍率 = 图像尺寸 ÷ 实际尺寸。你可以将其排成三角形，图像尺寸在上，实际尺寸和放大倍率在下。计算前务必把所有测量值换算成相同单位。
2. Actual Size Calculation | 实际尺寸计算
To find the real size of a specimen from a micrograph or drawing, rearrange the magnification formula: Actual size = Image size ÷ Magnification. The image size is usually measured in millimetres using a ruler, while actual size is often expressed in micrometres (µm). Convert mm to µm by multiplying by 1000.
若要根据显微照片或绘图计算标本的真实尺寸，可将放大倍率公式变形：实际尺寸 = 图像尺寸 ÷ 放大倍率。图像尺寸通常用直尺以毫米（mm）测量，而实际尺寸常以微米（µm）表示。将 mm 转换为 µm 时需乘以 1000。
3. Unit Conversions in Biology | 生物单位转换
Many calculations require moving between centimetres (cm), millimetres (mm), micrometres (µm) and nanometres (nm). The key conversion factors are: 1 cm = 10 mm, 1 mm = 1000 µm, and 1 µm = 1000 nm. To convert from a larger unit to a smaller one, multiply; to go from smaller to larger, divide. For example, 5 mm = 5 × 1000 = 5000 µm.
很多计算需要在厘米（cm）、毫米（mm）、微米（µm）和纳米（nm）之间转换。关键换算关系为：1 cm = 10 mm，1 mm = 1000 µm，1 µm = 1000 nm。从大单位换算到小单位用乘法，反之用除法。例如，5 mm = 5 × 1000 = 5000 µm。
4. Microscope Calibration | 显微镜校准
An eyepiece graticule must be calibrated using a stage micrometer. The formula for one eyepiece unit is: One eyepiece unit (µm) = (Number of stage divisions × Length of one stage division) ÷ Number of eyepiece divisions matched. Usually one stage division is 10 µm. Once calibrated, the real length of an object can be found by Actual size = Number of eyepiece units × Calibration factor. Never forget that the calibration factor changes with each objective lens.
目镜测微尺必须用镜台测微尺进行校准。一个目镜刻度单位的计算公式为：一个目镜单位（µm）=（镜台格数 × 每格长度）÷ 对齐的目镜格数。通常镜台测微尺每格为 10 µm。校准后，物体的实际长度可用 实际尺寸 = 目镜格数 × 校准因子 求出。校准因子会随物镜放大倍数而改变，切勿忘记重新校准。
5. Rate of Reaction | 反应速率
Rate of reaction measures how quickly a substrate is used up or a product is formed. In enzyme experiments, rate can be expressed as Rate = Amount of product formed ÷ Time or Rate = 1 ÷ Time taken for a measured change (e.g. time for starch to disappear). If a reaction produces 20 cm³ of oxygen in 10 seconds, the rate is 2 cm³/s. Ensure you use the correct units.
反应速率用于衡量底物消耗或产物生成的速度。在酶实验中，速率可用 速率 = 产物生成量 ÷ 时间 或 速率 = 1 ÷ 出现可测变化所用时间（如淀粉完全消失的时间）来表示。若某反应在 10 秒内产生 20 cm³ 氧气，则速率为 2 cm³/s。注意使用正确单位。
6. Percentage Change in Mass (Osmosis) | 质量百分比变化（渗透作用）
Percentage change in mass is a standard way to compare osmosis results. The formula is: Percentage change = ((Final mass – Initial mass) ÷ Initial mass) × 100. A positive value means water has been taken up (gain in mass), while a negative value indicates water loss. Using percentage change allows fair comparison between samples with different starting masses.
质量百分比变化是衡量渗透作用的常用方法。公式为：百分比变化 =（（最终质量 – 初始质量）÷ 初始质量）× 100。正值表示吸水增重，负值表示失水减重。采用百分比变化可以在初始质量不同的样品之间进行公平比较。
7. Surface Area to Volume Ratio | 表面积与体积比
Surface area to volume ratio (SA:V) is crucial for understanding transport in organisms. For a cube, Surface area = 6 × side² and Volume = side³. The ratio can be simplified to SA:V = 6 ÷ side. As an object gets larger, its SA:V decreases. This ratio explains why small organisms can rely on diffusion alone, while larger organisms need specialised exchange surfaces and transport systems.
表面积与体积比（SA:V）对理解生物体内物质运输至关重要。对于一个立方体，表面积 = 6 × 边长²，体积 = 边长³。比值可简化为 SA:V = 6 ÷ 边长。物体越大，其 SA:V 越小。这一比值解释了为什么小生物仅靠扩散即可满足需求，而大型生物则需要特化的交换表面和运输系统。
8. Body Mass Index (BMI) | 身体质量指数
BMI is a screening tool used to classify underweight, healthy weight, overweight and obesity. The formula is: BMI = Body mass (kg) ÷ (Height (m))². A BMI below 18.5 is considered underweight, 18.5–24.9 healthy, 25–29.9 overweight, and 30 or above obese. Remember that BMI does not account for muscle mass, so it is a general guide only.
BMI 是用于划分偏瘦、健康体重、超重和肥胖的评估工具。公式为：BMI = 体重（kg）÷（身高（m））²。BMI 低于 18.5 为偏瘦，18.5–24.9 为健康，25–29.9 为超重，30 及以上为肥胖。注意 BMI 不区分肌肉和脂肪，因此只作为一般性参考。
9. Calculating Mean Values | 计算平均值
The mean is used to summarise repeated measurements. The formula is: Mean = Sum of all values ÷ Number of values. Before calculating, identify any anomalous results that do not fit the pattern and exclude them from the calculation. Stating the mean without outliers increases the reliability of your conclusion. Always use the correct units and round appropriately.
平均值用于汇总多次测量的数据。公式为：平均值 = 所有数值之和 ÷ 数值个数。计算前应识别并剔除不符合整体规律的异常值。排除异常值后得出的平均值能提高结论的可靠性。记得保留正确单位并合理取整。
10. Capture-Mark-Recapture (Lincoln Index) | 标志重捕法（林肯指数）
This method estimates the population size of mobile organisms. The formula is: Estimated population size (N) = (Number in first sample (n₁) × Number in second sample (n₂)) ÷ Number of marked individuals recaptured (m). Important assumptions include: no migration, no births or deaths during the study, and that the marks do not affect survival or make individuals more visible. The method is handy for sampling species such as woodlice or pond snails.
该方法用于估算移动生物的种群大小。公式为：种群估算值（N）=（第一次标记数（n₁）× 第二次捕捉总数（n₂））÷ 第二次捕捉中带标记的个体数（m）。重要假设包括：研究期间无迁移、无出生或死亡，标记不影响生存概率也不使个体更显眼。此法常用于估算潮虫或椎实螺等物种的数量。
11. Rate of Photosynthesis | 光合作用速率
Photosynthesis rate can be measured by collecting oxygen bubbles from an aquatic plant. The simplest formula is: Rate = Volume of oxygen produced ÷ Time. If using a floating leaf disc assay, the rate can be expressed using the time for 50% of discs to float (ET₅₀): Rate = 1 ÷ ET₅₀. Factors such as light intensity, carbon dioxide concentration and temperature affect the rate, and the formula helps compare the effect of changing one variable while keeping others constant.
光合作用速率可通过收集水生植物产生的氧气泡来测定。最简单的公式是：速率 = 产生的氧气体积 ÷ 时间。若采用叶圆片上浮法，则可用 50% 叶圆片上浮所需时间（ET₅₀）来计算：速率 = 1 ÷ ET₅₀。光照强度、二氧化碳浓度和温度等因素会影响速率，利用该公式可在控制其他变量的条件下比较单一变量的影响。
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