📚 Year 10 Edexcel Biology: Formula & Theorem Quick Reference | 爱德思Year 10生物公式定理速查手册
This quick reference guide brings together all the essential formulas, equations and key theorems you need to master Edexcel Year 10 Biology. From magnification calculations to genetic ratios, each entry is paired with a clear explanation to support your revision and exam success.
这份速查手册汇总了攻克爱德思Year 10生物学所需的全部核心公式、方程式和关键定理。从显微镜放大计算到遗传比例，每一条目都配有清晰的解释，助力复习和考试成功。
1. Magnification and Microscope Formulas | 放大与显微镜公式
Magnification = Image size ÷ Actual size
When working with microscope images or drawings, this formula allows you to calculate any one of the three quantities provided the other two are known. Always convert measurements to the same unit (e.g. millimetres or micrometres) before applying the formula.
在处理显微镜图像或绘图时，利用该公式你可以在已知其他两个量的前提下计算出任意一个量。使用前务必将所有测量值转换为相同单位（如毫米或微米）。
Total Magnification = Eyepiece lens magnification × Objective lens magnification
This relationship gives the overall magnifying power of a light microscope. For example, a ×10 eyepiece with a ×40 objective lens yields a total magnification of ×400.
这个关系式给出了光学显微镜的总放大能力。例如，10倍目镜搭配40倍物镜所得总放大倍数为400倍。
2. Rate of Reaction and Enzyme Activity | 反应速率与酶活性
Rate of reaction = Quantity of product formed ÷ Time taken
Enzyme-controlled reactions and other metabolic processes can be monitored by measuring how much product appears per unit time. The rate can also be expressed as 1 ÷ time if using the end-point of a substrate disappearing.
可以通过测量单位时间内产物的生成量来监测酶控反应及其他代谢过程。如果以底物消失为终点，反应速率也可以表示为 1 ÷ 时间。
Rate = 1 ÷ Time (for a fixed end-point)
This simpler form is useful when comparing enzyme activity under different conditions (e.g. pH, temperature). A shorter time indicates a faster rate.
在比较不同条件下（如pH、温度）的酶活性时，这种简化形式十分实用。时间越短，速率越快。
3. Key Equations: Photosynthesis & Respiration | 关键方程式：光合作用与呼吸作用
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
The word summary for photosynthesis is: carbon dioxide + water → glucose + oxygen, in the presence of light energy and chlorophyll. This balanced symbol equation shows the conversion of inorganic molecules into organic food.
光合作用的文字概括为：二氧化碳 + 水 → 葡萄糖 + 氧气，需要光能和叶绿素的参与。这个配平的符号方程式表示无机物转化为有机养料的过程。
Aerobic respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ energy)
Aerobic respiration releases a relatively large amount of energy by completely breaking down glucose using oxygen. The products are carbon dioxide and water.
有氧呼吸利用氧气将葡萄糖彻底分解，释放大量能量。产物是二氧化碳和水。
Anaerobic respiration in animals: Glucose → Lactic acid (+ energy)
Anaerobic respiration in yeast: Glucose → Ethanol + Carbon dioxide (+ energy)
In the absence of oxygen, cells can still release some energy through anaerobic pathways. Animals produce lactic acid, while yeast and plants produce ethanol and carbon dioxide.
即使在缺氧条件下，细胞仍能通过无氧途径释放少量能量。动物产生乳酸，而酵母和植物则生成乙醇和二氧化碳。
4. Energy Transfer and Efficiency | 能量传递与效率
Efficiency (%) = (Energy transferred to next level ÷ Energy available at previous level) × 100
In food chains and ecological pyramids, energy is lost between trophic levels due to respiration, movement and excretion. This formula calculates the percentage of energy that is successfully passed on.
在食物链和生态金字塔中，能量会因呼吸作用、运动和排泄在营养级之间散失。该公式计算成功传递的能量百分比。
Typically, only around 10% of energy is transferred to the biomass of the next trophic level; the remainder is lost as heat and waste.
通常只有大约10%的能量传递到下一营养级的生物量中，其余能量以热量和废物的形式散失。
5. Body Mass Index (BMI) | 身体质量指数
BMI = Mass (kg) ÷ (Height (m))²
BMI is a screening tool used to classify individuals as underweight, normal, overweight or obese. It is calculated by dividing body mass in kilograms by the square of height in metres.
BMI是一种用于将个体划分为偏瘦、正常、超重或肥胖的筛查工具。其计算方法为体重（千克）除以身高（米）的平方。
For an adult, a BMI below 18.5 is considered underweight, 18.5–24.9 is healthy, 25–29.9 is overweight, and 30 or above is obese.
对于成人，BMI低于18.5视为体重过轻，18.5–24.9为健康范围，25–29.9为超重，30及以上则为肥胖。
6. Surface Area to Volume Ratio | 表面积与体积比
Surface area : Volume ratio = Surface area ÷ Volume
This ratio is crucial for understanding exchange of substances in organisms. As a cell or organism increases in size, its volume grows faster than its surface area, making the SA:V ratio smaller and diffusion less efficient.
这一比值对于理解生物体内的物质交换至关重要。当细胞或生物体体积增大时，其体积增长快于表面积，导致表面积与体积比减小，扩散效率降低。
For a cube of side length L, SA:V = 6L² / L³ = 6 / L. Small organisms have a large SA:V ratio, allowing them to rely mostly on diffusion for transport.
对于边长为L的立方体，SA:V = 6L² / L³ = 6 / L。小生物具有较大的表面积体积比，因此它们主要依靠扩散完成运输。
7. Cardiac Output and Heart Rate | 心输出量与心率
Cardiac Output (CO) = Heart Rate (HR) × Stroke Volume (SV)
Cardiac output is the volume of blood pumped by one ventricle per minute. Stroke volume is the volume ejected per beat. Typical resting values are around 70 beats/min for heart rate and 70 cm³/beat for stroke volume.
心输出量指的是一个心室每分钟泵出的血液体积。每搏输出量是每次心跳泵出的体积。静息时典型心率为约70次/分钟，每搏输出量约70立方厘米/次。
During exercise, both heart rate and stroke volume increase, leading to a higher cardiac output to supply muscles with more oxygen and glucose.
运动时，心率和每搏输出量均增加，心输出量随之升高，从而为肌肉提供更多的氧气和葡萄糖。
8. Transpiration Rate and Water Uptake | 蒸腾速率与吸水
Rate of transpiration = Distance moved by air bubble ÷ Time taken
Using a potometer, the movement of an air bubble along a capillary tube indicates water uptake by the shoot. The faster the transpiration rate, the quicker the bubble travels.
借助蒸腾计，毛细管内气泡的移动可以指示枝条的吸水速率。蒸腾速率越快，气泡移动就越快。
Typical units are mm/min or cm³/min if the cross-sectional area is known. Environmental factors such as light, temperature, humidity and wind alter the rate.
典型单位为毫米/分钟，或已知横截面积时用立方厘米/分钟。光照、温度、湿度和风速等环境因素都会改变蒸腾速率。
9. Bacterial Growth Calculations | 细菌生长计算
Number of bacteria = Initial number × 2ⁿ (where n = number of binary fission divisions)
Bacteria reproduce by binary fission, doubling their population after each division. If you know the starting population and the number of divisions, you can predict the final count using this exponential formula.
细菌通过二分裂繁殖，每次分裂后种群数量翻倍。如果已知起始数量和分裂次数，就可以用这个指数公式预测最终数量。
For example, after 5 divisions a single bacterium gives 1 × 2⁵ = 32 cells. Always ensure the time interval matches the division frequency.
例如，经过5次分裂，单个细菌可产生1 × 2⁵ = 32个细胞。请始终确保时间间隔与分裂频率相匹配。
10. Sampling and Population Estimates | 抽样与种群估计
Population density = Total number of individuals ÷ Area sampled
When using quadrats to sample a habitat, population density tells you how many organisms exist per unit area (e.g. per m²). This is estimated by counting organisms in randomly placed quadrats and scaling up.
使用样方对栖息地进行抽样时，种群密度能够反映单位面积（如每平方米）内的生物数量。通过随机放置样方并计数，再将结果放大即可估算。
Estimated population size (capture–recapture) = (M × C) ÷ R
M = number of individuals captured, marked and released in the first sample; C = total number captured in the second sample; R = number of marked individuals recaptured in the second sample. This Lincoln index assumes a closed population and random mixing.
M = 第一次捕获、标记并释放的个体数；C = 第二次捕获的总个体数；R = 第二次捕获中带有标记的个体数。此林肯指数假设种群封闭且标记个体均匀混合。
11. Genetic Ratios and Probability | 遗传比例与概率
Monohybrid cross phenotype ratio (heterozygous parents): 3 dominant : 1 recessive
When both parents are heterozygous for a single trait (e.g. Bb × Bb), the expected offspring phenotype ratio is 3 showing the dominant trait to 1 showing the recessive trait. The genotype ratio is 1 BB : 2 Bb : 1 bb.
对于单性状杂交，若双亲均为杂合子（如 Bb × Bb），预期后代表型比为3个显性性状 : 1个隐性性状。基因型比例为1 BB : 2 Bb : 1 bb。
Probability of a specific genotype = Number of favourable outcomes ÷ Total number of possible outcomes
Use a Punnett square to list all possible allele combinations. The probability can be expressed as a fraction, decimal or percentage. This allows prediction of inheritance patterns.
使用旁氏表列出所有可能的等位基因组合。概率可以用分数、小数或百分比表示，从而预测遗传模式。
12. Percentage Change and Rate Calculations | 百分比变化与速率计算
Percentage change = (Final value − Initial value) ÷ Initial value × 100%
This formula is widely used in osmosis experiments to describe changes in mass or length of plant tissue. A positive value indicates an increase, while a negative value indicates a decrease.
该公式广泛用于渗透实验，以描述植物组织质量或长度的变化。正值表示增加，负值表示减少。
Average rate = Total quantity ÷ Total time
Rates can be applied to many biological processes — heart rate, breathing rate, gas production or substrate consumption. Always state the units, such as beats/min or cm³/min.
速率可应用于众多生物学过程——心率、呼吸频率、气体产生或底物消耗。务必注明单位，如次/分钟或立方厘米/分钟。
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