📚 Year 10 WJEC Biology Formulas and Theorems Quick Reference | Year 10 WJEC 生物公式定理速查手册
Welcome to your ultimate quick reference handbook for Year 10 WJEC GCSE Biology. This guide compiles every essential formula, equation, and core theorem you will meet in the course, from microscopy and enzyme rates to genetic principles and ecological sampling. Keep it handy for revision, homework, and exam preparation.
欢迎使用这份 Year 10 WJEC GCSE 生物终极速查手册。本手册汇集了课程中你会遇到的每一个重要公式、方程和核心定理，涵盖显微镜、酶反应速率、遗传原理以及生态取样等各个方面。请随身携带，方便复习、作业和备考。
1. Microscopy and Magnification | 显微镜与放大倍数
The magnification formula is the foundation of all microscope work: Magnification = Image size ÷ Actual size, often written as M = I ÷ A. Both I and A must use the same unit (e.g. mm or µm). Convert carefully: 1 mm = 1000 µm.
放大倍数公式是所有显微镜工作的基础：放大倍数 = 图像大小 ÷ 实际大小，常写作 M = I ÷ A。I 和 A 必须使用相同单位（如毫米或微米）。细心换算：1 毫米 = 1000 微米。
The total magnification of a light microscope is the product of the two lenses: Total magnification = Eyepiece lens magnification × Objective lens magnification. For example, a ×10 eyepiece and a ×40 objective give a total magnification of ×400.
光学显微镜的总放大倍数是两个镜头的乘积：总放大倍数 = 目镜放大倍数 × 物镜放大倍数。例如，×10 目镜和 ×40 物镜的总放大倍数为 ×400。
Always rearrange the formula to find actual size when needed: Actual size = Image size ÷ Magnification. This is vital for calculating cell dimensions from scale bars.
当需要求实际大小时，记得将公式变形：实际大小 = 图像大小 ÷ 放大倍数。这对于根据比例尺计算细胞尺寸至关重要。
2. Enzyme Activity and Rate Calculations | 酶活性与速率计算
The rate of an enzyme-controlled reaction can be calculated as: Rate = Change in amount of product (or substrate) ÷ Time taken. For example, measuring the volume of oxygen produced by catalase every 10 seconds.
酶控制反应的速率可计算为：速率 = 产物（或底物）量的变化 ÷ 所用时间。例如，每 10 秒测量过氧化氢酶产生的氧气体积。
If the experiment measures the time taken for a specific change (e.g. starch disappearance), a useful reciprocal rate is: Rate = 1 ÷ Time (s⁻¹). A shorter time indicates a faster rate.
如果实验测量特定变化所需的时间（如淀粉消失），一个常用的倒数速率公式为：速率 = 1 ÷ 时间 (s⁻¹)。时间越短，速率越快。
When plotting a graph, draw a tangent to find the initial rate at a particular substrate concentration, then calculate the gradient.
绘图时，可以通过画切线求出特定底物浓度下的初始速率，然后计算梯度。
3. Osmosis and Percentage Change in Mass | 渗透作用与质量变化百分比
In osmosis investigations, compare mass changes using: Percentage change in mass = (Final mass – Initial mass) ÷ Initial mass × 100%. A positive value means mass has increased (water gained); a negative value means mass has decreased (water lost).
在渗透作用研究中，使用以下公式比较质量变化：质量变化百分比 = (最终质量 – 初始质量) ÷ 初始质量 × 100%。正值表示质量增加（吸水）；负值表示质量减少（失水）。
This calculation eliminates the effect of different starting masses, allowing a fair comparison between tissue samples or potato cylinders placed in different sugar solutions.
该计算消除了不同起始质量的影响，使得在不同糖溶液中放置的组织样品或土豆条之间可以进行公平比较。
4. Photosynthesis Equation | 光合作用方程式
The word equation for photosynthesis must be memorised: Carbon dioxide + Water → Glucose + Oxygen, with light energy and chlorophyll required over the arrow.
光合作用的文字方程式必须牢记：二氧化碳 + 水 → 葡萄糖 + 氧气，箭头上方需标注光能和叶绿素。
The balanced symbol equation for photosynthesis is: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. This shows that six molecules of carbon dioxide and six molecules of water produce one molecule of glucose and six molecules of oxygen.
光合作用的配平化学方程式为：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。这表明六个二氧化碳分子和六个水分子生成一个葡萄糖分子与六个氧分子。
5. Respiration Equations | 呼吸作用方程式
Aerobic respiration requires oxygen and releases a large amount of energy. The word equation is: Glucose + Oxygen → Carbon dioxide + Water (+ energy).
有氧呼吸需要氧气并释放大量能量。文字方程式为：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。
Its symbol equation is: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O. Notice it is the reverse of photosynthesis in terms of reactants and products.
其化学方程式为：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。注意反应物和产物与光合作用恰好相反。
Anaerobic respiration in animals produces lactic acid: Glucose → Lactic acid (+ energy). The symbol equation is: C₆H₁₂O₆ → 2C₃H₆O₃.
动物的无氧呼吸产生乳酸：葡萄糖 → 乳酸（+ 能量）。化学方程式为：C₆H₁₂O₆ → 2C₃H₆O₃。
In yeast and some plants, anaerobic respiration produces ethanol and carbon dioxide: Glucose → Ethanol + Carbon dioxide (+ energy). Symbolically: C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂.
在酵母和某些植物中，无氧呼吸产生乙醇和二氧化碳：葡萄糖 → 乙醇 + 二氧化碳（+ 能量）。化学方程式：C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂。
6. Binary Fission and Bacterial Growth | 二分裂与细菌生长
Bacteria multiply by binary fission, doubling their number each division. The population after n divisions is given by: N = N₀ × 2ⁿ, where N₀ is the starting number and n is the number of division cycles.
细菌通过二分裂繁殖，每次分裂数量加倍。n 次分裂后的种群数量计算公式为：N = N₀ × 2ⁿ，其中 N₀ 为初始数量，n 为分裂周期数。
bacterium divides for 2 hours (120 min), n = 120 ÷ 20 = 6, so final number is 1 × 2⁶ = 64.
你可以通过总时间除以平均分裂时间得到 n（例如每 20 分钟分裂一次）。若一个细菌分裂 2 小时（120 分钟），n = 120 ÷ 20 = 6，最终数量为 1 × 2⁶ = 64。
7. Efficiency of Biomass Transfer | 生物量传递效率
In ecosystems, only a small percentage of biomass is passed from one trophic level to the next. The efficiency is calculated as: Efficiency (% = (Biomass transferred to the next level ÷ Biomass available at the previous level) × 100%.
在生态系统中，只有一小部分生物量从一个营养级传递到下一个。效率的计算公式为：效率 (%) = (传递到下一级的生物量 ÷ 前一级可用的生物量) × 100%。
Energy transfer efficiency can be calculated in the same way using energy values (kJ). Typical efficiency is around 10%, explaining why food chains rarely exceed four or five levels.
能量传递效率也可以用能量值（千焦）以同样的方式计算。典型的效率约为 10%，这解释了为什么食物链很少超过四到五个营养级。
8. Surface Area to Volume Ratio | 表面积与体积之比
The surface area to volume ratio (SA:V) influences how easily substances can enter or leave a cell. For a cube of side length L, Surface area = 6L² and Volume = L³, so SA:V = 6L² ÷ L³ = 6 ÷ L.
表面积与体积之比 (SA:V) 影响物质进入或离开细胞的难易程度。对于边长为 L 的立方体，表面积 = 6L²，体积 = L³，因此 SA:V = 6L² ÷ L³ = 6 ÷ L。
As an organism or structure grows larger, its volume increases much faster than its surface area, so the SA:V ratio decreases. This is why large multicellular organisms require specialised exchange surfaces and transport systems.
随着生物体或结构增大，其体积增长比表面积快得多，因此 SA:V 比减小。这就是为什么大型多细胞生物需要特化的交换表面和运输系统。
9. Fundamental Genetic Theorems | 基本遗传学定理
Mendel's Law of Segregation: Each individual possesses two alleles for each gene, located on homologous chromosomes. During gamete formation, the two alleles segregate so that each gamete receives only one allele.
孟德尔分离定律：每个个体对于每个基因拥有两个等位基因，位于同源染色体上。在配子形成过程中，两个等位基因分离，使每个配子只获得一个等位基因。
Mendel's Law of Independent Assortment: Alleles for different genes are distributed to gametes independently of one another, provided the genes are on different chromosomes. This explains the 9:3:3:1 ratio in a dihybrid cross.
孟德尔自由组合定律：不同基因的等位基因在分配至配子时彼此独立，只要这些基因位于不同的染色体上。这解释了双因子杂交中 9:3:3:1 的比例。
Chargaff's Rule: always equals thymine (T), and the amount of cytosine (C) always equals guanine (G). Thus, %A = %T and %C = %G, and the total purines equal total pyrimidines.
查戈夫法则：在一个双链 DNA 分子中，腺嘌呤 (A) 的数量总是等于胸腺嘧啶 (T)，胞嘧啶 (C) 的数量总是等于鸟嘌呤 (G)。因此，%A = %T 且 %C = %G，并且嘌呤总量等于嘧啶总量。
10. Sampling with Quadrats – Essential Formulas | 样方取样基本公式
When estimating population size using quadrats: (Mean number of individuals per quadrat ÷ Area of one quadrat) × Total area of the habitat.
使用样方估算种群数量时：估算数量 = (每样方的平均个体数 ÷ 单个样方面积) × 生境总面积。
Percentage cover is used for plants or sessile organisms that are hard to count: Percentage cover = (Area covered by the species ÷ Total quadrat area) × 100%.
百分比覆盖度适用于难以计数的植物或固着生物：百分比覆盖度 = (物种覆盖的面积 ÷ 样方面积) × 100%。
Frequency gives a measure of how common a species is across all quadrats: Frequency = (Number of quadrats containing the species ÷ Total number of quadrats) × 100%.
频度衡量一个物种在所有样方中的常见程度：频度 = (含有该物种的样方数 ÷ 样方总数) × 100%。
11. Transpiration Rate | 蒸腾速率
A potometer measures the rate of transpiration by recording water uptake. The rate can be calculated as: Rate of transpiration = Distance moved by air bubble (mm) ÷ Time taken (min), giving a rate in mm/min.
蒸腾仪通过记录吸水情况测量蒸腾速率。计算公式为：蒸腾速率 = 气泡移动的距离 (mm) ÷ 所用时间 (min)，单位为 mm/min。
Alternatively, you can measure the change in volume of water in a measuring cylinder over time: Rate = Volume decrease ÷ Time. Factors such as light, humidity, wind and temperature all affect this rate.
也可以测量量筒中水体积随时间的减少量：速率 = 体积减少量 ÷ 时间。光照、湿度、风和温度等因素都会影响该速率。
12. Inverse Square Law and Light Intensity | 平方反比定律与光强
In the context of photosynthesis, light intensity follows an inverse square relationship: Light intensity (I) ∝ 1 ÷ distance² (d²). If you double the distance from a light source, the intensity falls to one-quarter.
在光合作用背景下，光强遵循平方反比关系：光强 (I) ∝ 1 ÷ 距离² (d²)。如果将距离光源的距离加倍，光强将降至四分之一。
Although not a formula you routinely calculate in WJEC exams, understanding this relationship helps interpret why the rate of photosynthesis plateaus and why light becomes limiting with increasing distance.
尽管在 WJEC 考试中你不常直接计算该公式，但理解这一关系有助于解释为什么光合作用速率会达到平台期，以及为什么随着距离增加光照会成为限制因素。
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