IB & CIE Biology: Formula Summary Handbook | IB CIE 生物：公式汇总手册

📚 IB & CIE Biology: Formula Summary Handbook | IB CIE 生物：公式汇总手册

This article provides a comprehensive compilation of the most important formulas found in IB and CIE A-Level Biology. Quantitative skills are assessed in both theory papers and practical examinations, requiring you to calculate magnification, cardiac output, diversity indices, and statistical tests. Understanding when and how to apply these formulas will enhance your data-analysis abilities and boost your exam performance.

本文全面整理了IB和CIE A-Level生物考试中最重要的公式。定量技能在理论试卷和实验考试中都会考查，要求你能够计算放大倍率、心输出量、多样性指数和统计检验。理解何时以及如何应用这些公式，将提升你的数据分析能力，并提高考试成绩。

1. Microscope Magnification | 显微镜放大倍率

In microscopy, magnification describes how many times larger an image appears compared to the actual specimen. It is a fundamental calculation for both light and electron micrographs, as well as biological drawings.

在显微镜学中，放大倍率描述了图像相较于实际标本放大了多少倍。这是光学和电子显微照片以及生物绘图中的基本计算。

Magnification = Image size / Actual size

The image size is measured with a ruler, and the actual size is the real dimension of the object. Always convert both values to the same units (e.g., mm to µm by multiplying by 1000) before dividing. You can rearrange the formula to find actual size: Actual size = Image size / Magnification.

图像大小用直尺测量，实际大小是物体的真实尺寸。在相除之前，务必先将两个值转换为相同的单位（例如，毫米转换为微米，乘以1000）。你可以重新排列公式计算实际大小：实际大小 = 图像大小 / 放大倍率。

Be careful with scale bars: if a scale bar represents 10 µm and measures 20 mm on the image, the magnification is 20 000 µm / 10 µm = ×2000.

注意比例尺：如果一个比例尺代表10µm，在图像上测得20 mm，那么放大倍率为20 000 µm / 10 µm = ×2000。

2. Cardiac Output & Heart Rate | 心输出量与心率

Cardiac output is the volume of blood pumped by one ventricle per minute. It reflects the efficiency of the circulatory system and is regulated according to the body’s demands.

心输出量是一个心室每分钟泵出的血液体积。它反映了循环系统的效率，并根据身体的需求进行调节。

Cardiac output (CO) = Heart rate (HR) × Stroke volume (SV)

Heart rate is the number of beats per minute (bpm). Stroke volume is the volume of blood ejected per beat (ml). A typical resting cardiac output is around 5 L/min. During exercise, both HR and SV increase, raising CO.

心率是每分钟心跳次数（bpm）。每搏量是每次搏动射出的血液体积（ml）。典型的静息心输出量约为5 L/min。运动时，心率和每搏量均增加，从而提高心输出量。

3. Respiratory Quotient (RQ) | 呼吸商

The respiratory quotient indicates which type of respiratory substrate is being metabolised. It is calculated from the volumes of gases exchanged during respiration.

呼吸商反映了正在代谢的呼吸底物类型。它通过呼吸过程中交换的气体体积计算得出。

RQ = Volume of CO₂ produced / Volume of O₂ consumed

For carbohydrates, RQ = 1.0 (equal volumes of CO₂ and O₂). For lipids, RQ is about 0.7 because more O₂ is needed to oxidise fatty acids. For proteins, RQ is roughly 0.8–0.9. An RQ value can help determine metabolic fuel use in organisms or tissues.

碳水化合物的RQ为1.0（CO₂和O₂体积相等）。脂类的RQ约为0.7，因为氧化脂肪酸需要更多氧气。蛋白质的RQ约为0.8–0.9。RQ值有助于确定生物体或组织所使用的代谢燃料。

4. Lincoln Index (Capture-Mark-Recapture) | 林肯指数（捉放法）

The Lincoln Index estimates population size for mobile organisms. It involves capturing, marking,

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