📚 Cambridge Year 10 Biology: Formula & Theorem Quick Reference Guide | 剑桥 Year 10 生物：公式定理速查手册
Welcome to your essential quick-reference handbook for the key formulas, equations and biological theorems covered in the Cambridge Year 10 Biology course. Whether you are revising for a topic test or preparing for your end-of-year examination, this guide will help you memorise and apply the mathematical relationships and core principles that underpin a wide range of biological processes. Each section presents the theory in clear terms, followed by its direct application in IGCSE-style contexts. Keep this summary close to hand as you work through past papers and concept checkers.
欢迎来到 Year 10 剑桥生物关键公式、方程式与生物学定理的速查手册。无论你是在为阶段性测验复习，还是为大考做准备，这份指南都能帮助你记忆和运用支撑众多生命过程的数学关系与核心原理。每个小节以清晰的方式呈现理论，并紧接其在实际考题中的应用方式。在你刷题和自查概念时，请将这份摘要放在手边随时查阅。
1. Magnification Formula | 放大率公式
Magnification describes how much larger an image appears compared with the object's real size. The relationship is given by the equation:
Magnification = Image size ÷ Actual size
放大率描述了图像相比物体真实尺寸被放大了多少倍。其关系式如下：
放大率 = 图像尺寸 ÷ 实际尺寸
en be required to convert between mm and μm: 1 mm = 1000 μm. Problems commonly involve drawing a cell from a micrograph and asking you to calculate the actual length of the cell or the magnification used.
三个量必须使用相同单位（通常是毫米或微米）。放大率没有单位，因为它是一个比值。你经常需要进行 mm 与 μm 的单位换算：1 mm = 1000 μm。考题常给出显微图像并要求计算细胞的实际长度或所用放大倍数。
• Formula triangle: cover the quantity you need; Image size = Magnification × Actual size.
• 公式三角形：遮盖所需量；图像尺寸 = 放大率 × 实际尺寸。
2. Actual Size Calculation from a Diagram | 从图像计算实际尺寸
When a diagram includes a scale bar or a stated magnification, you can determine the real size of a structure. Measure the length of the object in the diagram with a ruler (in mm), then convert to the appropriate unit.
如果图像带有比例尺或给出放大率，就能确定某个结构的真实尺寸。用直尺测量图中对象的长度（以 mm 为单位），再转换至适宜的单位。
If a scale bar is present, use the formula:
ze = (Measured length of object ÷ Measured length of scale bar) × Value shown on scale bar
如果存在比例尺，则使用公式：
实际尺寸 = (物体的测量长度 ÷ 比例尺的测量长度) × 比例尺标注数值
This is simply a ratio problem. Always state the actual size in μm or mm and check that your answer is biologically plausible (e.g. a mitochondrion is about 1–10 μm long). Practice with diagrams of plant cells and bacterial cells to build confidence.
这本质上是一个比值问题。实际尺寸通常以 μm 或 mm 表示，并需检查答案在生物学上是否合理（例如线粒体长约 1–10 μm）。多练习植物细胞和细菌细胞图能帮助建立信心。
3. Surface Area to Volume Ratio | 表面积与体积比
The surface area to volume ratio (SA:V) determines how efficiently substances can move in and out of a cell or an organism. Smaller objects have a larger SA:V ratio, which favours rapid diffusion. As a cube or a sphere increases in size, its volume grows faster than its surface area, so the SA:V ratio falls.
表面积与体积比 (SA:V) 决定了物质进出细胞或生物体的效率。物体越小，SA:V 比值越大，有利于快速扩散。随着立方体或球体尺寸增大，体积增长速度快于表面积，因此 SA:V 比值下降。
For a cube of side length L, the ratio is calculated as:
SA:V = 6L² ÷ L³ = 6/L
对于边长为 L 的立方体，比值为：
SA:V = 6L² ÷ L³ = 6/L
This principle explains why cells are microscopic, why plants have flattened leaves and why large organisms need transport systems such as the circulatory system. When comparing two cells, the one with the higher SA:V ratio will exchange materials more rapidly.
这一原理解释了为什么细胞很小、为什么植物具有扁平的叶片，以及为什么大型生物需要循环系统等运输系统。比较两个细胞时，SA:V 比值高的那个物质交换更快。
4. Calculating Rate of Reaction in Enzyme Studies | 酶研究中的反应速率计算
When investigating enzyme activity, you often measure how fast a product appears or a substrate disappears. The general formula for rate is:
Rate = Quantity of product formed ÷ Time taken
在研究酶活性时，常测量产物生成或底物消失的快慢。反应速率的通用公式为：
速率 = 生成的产物量 ÷ 所用时间
For example, if catalase breaks down hydrogen peroxide, you can measure the volume of oxygen gas produced per minute (cm³/min). If starch is broken down by amylase, you might record the time taken for the iodine test to stop turning blue‑black. Rate can also be expressed as 1 ÷ time taken to reach a defined endpoint.
例如，过氧化氢酶分解过氧化氢时，可以测量每分钟产生的氧气体积 (cm³/min)。假如淀粉被淀粉酶分解，可以记录碘液不再变蓝黑所需的时间。速率还可以表示为 1 ÷ 达到特定终点所需的时间。
Remember to plot the independent variable on the x‑axis and the rate on the y‑axis when drawing graphs. Controlling temperature and pH is essential for valid comparisons.
绘制图表时记得将自变量放在 x 轴、速率放在 y 轴。控制温度和 pH 对获得有效比较至关重要。
5. Photosynthesis Equation | 光合作用方程式
Photosynthesis is the process by which green plants convert light energy into chemical energy stored in glucose. The word equation and the balanced chemical equation must be memorised:
光合作用是绿色植物将光能转化为化学能并储存在葡萄糖中的过程。必须牢记文字方程式与配平的化学方程式：
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Chlorophyll absorbs light energy, and the reaction requires light and suitable temperature. The glucose produced can be used in respiration, converted to starch for storage, or used to build cellulose and amino acids. In exam questions, you may be given the formula for a variable such as the number of oxygen bubbles, and asked to relate this to the rate of photosynthesis.
叶绿素吸收光能，反应需要光与适宜温度。产生的葡萄糖可用于呼吸作用、转化为淀粉储存，或用于构建纤维素与氨基酸。考题可能会给出气泡数量等变量，并要求将其与光合作用速率联系起来。
6. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration releases energy from glucose in the presence of oxygen. It takes place continuously in the mitochondria of most cells. The summary equations are:
有氧呼吸在氧气存在下从葡萄糖中释放能量，在大多数细胞的线粒体中持续进行。其概括方程式为：
Glucose + Oxygen → Carbon dioxide + Water (+ energy released)
葡萄糖 + 氧气 → 二氧化碳 + 水 (+ 释放的能量)
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Energy is released in the form of ATP, which fuels processes such as muscle contraction, active transport and cell division. You should be able to compare this equation with that of photosynthesis and recognise them as reciprocal reactions.
能量以 ATP 形式释放，为肌肉收缩、主动运输和细胞分裂等过程供能。你应能够将此方程式与光合作用方程式进行比较，并认识到它们互为逆反应。
7. Anaerobic Respiration Equations | 无氧呼吸方程式
When oxygen is insufficient, cells can respire anaerobically. In yeast, this produces ethanol and carbon dioxide (fermentation), whereas in animal muscles, it produces lactic acid. Both processes yield much less ATP than aerobic respiration.
当氧气不足时，细胞可进行无氧呼吸。酵母的无氧呼吸产生乙醇和二氧化碳（发酵），而动物肌肉的无氧呼吸产生乳酸。两者产生的 ATP 远少于有氧呼吸。
- In yeast: Glucose → Ethanol + Carbon dioxide (+ some energy)
- 在酵母中：葡萄糖 → 乙醇 + 二氧化碳 (+ 少量能量)
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
- In muscles: Glucose → Lactic acid (+ some energy)
- 在肌肉中：葡萄糖 → 乳酸 (+ 少量能量)
C₆H₁₂O₆ → 2C₃H₆O₃
Lactic acid build‑up causes muscle fatigue and must be removed by oxidation or converted back to glucose in the liver after exercise. Understanding these equations helps you interpret experiments on gas production and pH changes.
乳酸的积累会导致肌肉疲劳，运动后需通过氧化或在肝脏中重新转化为葡萄糖来清除。理解这些方程式有助于解释气体生成和 pH 变化的实验。
8. Cardiac Output Formula | 心输出量公式
Cardiac output is the volume of blood pumped by one ventricle in one minute. It depends on how fast the heart beats and how much blood is ejected with each beat. The formula is:
心输出量是指一个心室每分钟泵出的血液体积。它取决于心跳的快慢以及每搏输出的血量。公式为：
Cardiac output (CO) = Heart rate (HR) × Stroke volume (SV)
心输出量 (CO) = 心率 (HR) × 每搏输出量 (SV)
Typical resting values for an adult are heart rate 70 beats/min and stroke volume 70 mL, giving a cardiac output of about 4.9 litres/min. During exercise, both heart rate and stroke volume increase, raising cardiac output to meet the muscles' demand for oxygen. Make sure you can rearrange the formula to find any one variable when the other two are given.
成年人静息时的典型数值为心率 70 次/分、每搏输出量 70 mL，心输出量约为 4.9 L/min。运动时心率和每搏输出量均升高，使心输出量增加以满足肌肉的需氧量。务必能熟练变形公式，已知两个量求出第三个量。
9. Minute Ventilation and Lung Volumes | 每分钟通气量与肺容量
The amount of air moved into and out of the lungs each minute is described by the minute ventilation. It is calculated from the tidal volume and breathing rate:
每分钟进出肺部的空气量用每分钟通气量来描述，它由潮气量和呼吸频率计算得来：
Minute ventilation = Tidal volume × Breathing rate
每分钟通气量 = 潮气量 × 呼吸频率
Tidal volume is the amount of air breathed in (or out) during one normal breath, typically around 0.5 litres. Breathing rate is the number of breaths taken per minute. Changes in minute ventilation reflect the body's response to exercise, and you may be asked to interpret spirometer traces or calculate these values from data.
潮气量是一次正常呼吸中吸入（或呼出）的空气量，通常约为 0.5 L。呼吸频率是每分钟呼吸的次数。每分钟通气量的变化反映身体对运动的响应，考题可能要求解读肺活量计图线或根据数据计算这些数值。
Other important terms: vital capacity (maximum volume exhaled after maximal inhalation) and residual volume (air remaining in lungs after forced expiration).
其他重要术语：肺活量（最大吸气后呼出的最大体积）和余气量（用力呼气后仍留在肺中的空气）。
10. Mendelian Genetics and Punnett Squares | 孟德尔遗传与庞纳特方格
Gregor Mendel's experiments with pea plants established two fundamental laws of inheritance. The Law of Segregation states that each individual possesses two alleles for each characteristic, and these alleles separate during gamete formation so each gamete carries only one allele. The Law of Independent Assortment declares that alleles for different characteristics are distributed to gametes independently of one another.
格里哥·孟德尔的豌豆实验确立了两条基本遗传定律。分离定律指出，每个个体针对某一性状具有两个等位基因，这些等位基因在配子形成时分离，因此每个配子只携带一个等位基因。自由组合定律说明，不同性状的等位基因彼此独立地分配到配子中。
ygous (e.g. Aa × Aa), the offspring genotype ratio is 1 AA : 2 Aa : 1 aa. A monohybrid cross for a dominant‑ ct squares, deduce probabilities and explain how the laws account for the observed ratios.
庞纳特方格是预测杂交后代基因型与表现型比例的视觉工具。当双亲均为杂合子（如 Aa × Aa）时，后代基因型比为 1 AA : 2 Aa : 1 aa。单因子杂交的显隐性性状出现 3:1 的表现型比。你需要会构建方格、推导概率，并解释这些定律如何导致观察到的比例。
11. Energy Transfer Efficiency in Food Chains | 食物链中的能量传递效率
Energy is transferred along food chains, but much is lost at each trophic level through respiration, heat, excretion and uneaten parts. The efficiency of energy transfer between two levels can be calculated as:
能量沿食物链传递，但在每一个营养级都有大量能量通过呼吸、散热、排泄和未被取食的部分而流失。两个营养级之间的能量传递效率可用下式计算：
Efficiency (% ed into the higher trophic level ÷ Energy available from the previous trophic level) × 100
效率 (%) = (进入上一营养级的能量 ÷ 来自下一营养级的可用能量) × 100
Typically, only about 10% of the energy is passed on to the next level, which limits the length of food chains. You may be presented with a pyramid of energy or a table of energy values (in kJ per m² per year) and asked to calculate efficiency. Always show your working and express the answer as a percentage.
通常只有约 10% 的能量传递到下一营养级，这限制了食物链的长度。考题可能给出能量金字塔或能量数据表 (kJ/m²/年)，要求计算效率。务必展示计算步骤，并以百分比表示结果。
12. Population Growth Rate Calculation | 种群增长率计算
The change in a population's size over time can be described by the growth rate. A simple formula for the natural population growth rate is:
种群大小随时间的变化可用增长率来描述。自然种群增长率的简单公式为：
Growth rate (%) = [(Number of births − Number of deaths) ÷ Total population] × 100
增长率 (%) = [(出生数 − 死亡数) ÷ 总人口] × 100
on − Emigration) ÷ Initial population. A positive growth rate indicates an increasing population, while a negative rate signals decline. Understanding this formula helps explain the exponential growth of bacteria in a closed nutrient environment and the logistic growth of a population approaching carrying capacity.
在生态学中，你可能需要加入迁入和迁出以获得更全面的视角：增长率 = (出生数 − 死亡数 + 迁入 − 迁出) ÷ 初始种群。正增长率表明种群在增长，负增长率则表示下降。理解该公式有助于解释封闭营养环境中细菌的指数增长，以及种群趋于环境容纳量时的逻辑斯蒂增长。
Practice problems often provide raw counts and ask you to calculate the rate, or to predict the population size after a given time interval assuming constant growth.
练习题目常给出原始数据，要求计算增长率，或假设恒定增长预测某一时段后的种群大小。
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