📚 GCSE Biology Formula Summary Handbook | GCSE 生物公式汇总手册
Biology is not just about learning facts; you also need to be confident in handling essential formulas and calculations. This handbook compiles all the key equations, ratios and quantitative methods that appear in GCSE biology, from microscopy to bioenergetics and ecology. Mastering these will boost your performance in both practical-based and data-analysis questions.
生物学不仅仅是记忆事实，你还需要熟练掌握必要的公式和计算。本手册汇集了GCSE生物中出现的关键方程式、比率以及定量方法，涵盖从显微镜观察到生物能量学、生态学等领域。掌握这些内容将提升你在实验类试题和数据分析题中的表现。
1. Magnification Formula | 放大倍数公式
Magnification tells you how many times larger an image is compared to the actual object. This is fundamental to microscopy and any scaled diagram.
放大倍数告诉你图像比实际物体大多少倍，这是显微镜操作和带比例图示的基础。
Magnification = Image size ÷ Actual size
放大倍数 = 图像大小 ÷ 实际大小
Both image size and actual size must be in the same unit before you divide them. Common units are millimetres (mm), micrometres (µm) and nanometres (nm). Always check your unit conversions carefully.
进行除法计算前，图像大小和实际大小必须用相同单位。常用单位是毫米（mm）、微米（µm）和纳米（nm），要仔细检查单位换算。
2. Rearranging the Magnification Formula | 放大倍数公式的变形
Exam questions often ask you to find the actual size of a cell or the image size. You simply rearrange the basic formula.
考试中常要求计算细胞的实际大小或图像大小，只需对基本公式进行简单变形即可。
Actual size = Image size ÷ Magnification
实际大小 = 图像大小 ÷ 放大倍数
Image size = Magnification × Actual size
图像大小 = 放大倍数 × 实际大小
d 1 µm = 1000 nm. Converting everything to µm is a safe way to avoid mistakes.
记住 1 mm = 1000 µm，1 µm = 1000 nm。将所有数值统一换算为微米（µm）是避免错误的好方法。
3. Surface Area to Volume Ratio | 表面积与体积比
This ratio is crucial for understanding how the size of an organism affects diffusion, heat loss and the need for exchange surfaces. As an object gets bigger, its surface area to volume ratio decreases.
这个比率对于理解生物体大小如何影响扩散、热散失以及对交换表面的需求至关重要。物体越大，其表面积与体积之比就越小。
For a cube with side length s e area = 6s²;, Volume = s³;, so SA:V = 6/s. For a sphere, similar principles apply – volume increases faster than surface area.
对于边长为s的立方体：表面积 = 6s²;，体积 = s³;，因此 SA:V = 6/s。对于球体也是如此——体积的增长速度比表面积快得多。
Single-celled organisms have a large SA:V, allowing rapid diffusion. Multicellular organisms need specialised exchange surfaces like alveoli or villi to compensate for their small SA:V.
单细胞生物拥有很大的表面积与体积比，可以进行快速扩散。多细胞生物则需要像肺泡或绒毛那样的特化交换表面来弥补较小的 SA:V。
4. Rate of Photosynthesis | 光合作用速率
The rate of photosynthesis can be measured by monitoring the production of oxygen, the consumption of carbon dioxide, or the increase in biomass over a given time.
光合作用速率可以通过测量一定时间内氧气的生成量、二氧化碳的消耗量或生物量的增加来确定。
Rate = Change in measured quantity ÷ Time taken
速率 = 所测量的变化量 ÷ 所用时间
In the pondweed (Elodea) experiment, you often count the number of oxygen bubbles produced per minute. Alternatively, you can collect the gas and measure its volume in cm³/min.
在水蕴草（伊乐藻）实验中，通常数每分钟产生的氧气气泡数。也可以收集气体并测量其体积，单位为 cm³/min。
If you use an indicator that changes colour when CO&sub2; is consumed, the rate can also be expressed as 1 ÷ time taken for the colour change.
如果使用随着 CO&sub2; 消耗而变色的指示剂，速率也可表示为 1 ÷ 颜色变化所需的时间。
5. Rate of Respiration | 呼吸速率
Respiration rate is determined in a similar way, usually by measuring the volume of carbon dioxide produced or oxygen consumed per unit time.
呼吸速率的测定方式与此类似，通常测量单位时间内产生的二氧化碳或消耗的氧气的体积。
Rate of respiration = Volume of CO&sub2; produced ÷ Time
呼吸速率 = 产生的 CO&sub2; 体积 ÷ 时间
Experiments using respirometers often involve coloured liquid moving along a capillary tube. The distance moved per minute can be converted into volume of oxygen taken up.
使用呼吸计的实验常包含着色液体在毛细管中移动的情况。每分钟移动的距离可以换算为摄取氧气的体积。
Always control temperature carefully, because a rise in temperature can expand the gas and give a misleading result.
必须仔细控制温度，因为温度升高会使气体膨胀，导致误导性的结果。
6. Energy Content of Food (Calorimetry) | 食物能量测定（量热法）
You can estimate the energy stored in a food sample by burning it and using the heat released to raise the temperature of a known mass of water.
通过燃烧食物样品，并用释放的热量升高已知质量水的温度，就可以估算食物中储存的能量。
Energy (J) = mass of water (g) × 4.2 J/g°C × temperature rise (°C)
能量（焦耳）= 水的质量（克）× 4.2 J/g°C × 温度升高值（°C）
Energy per gram (J/g) = Energy (J) ÷ mass of food burned (g)
每克能量（J/g）= 能量（焦耳）÷ 燃烧的食物质量（克）
| Variable | 变量 |
|---|---|
| Mass of water (g) | 水的质量（克） |
| Initial water temperature (°C) | 水初始温度（°C） |
| Final water temperature (°C) | 水最终温度（°C） |
| Temperature rise (°C) | 温度升高值（°C） |
| Mass of food sample (g) | 食物样品质量（克） |
The value 4.2 J/g°C is the specific heat capacity of water. Inaccuracies arise because not all heat is transferred to the water, so the result is usually an underestimate.
4.2 J/g°C 是水的比热容。由于并非所有热量都被传递给水，实验结果往往比真实值偏低。
7. Efficiency of Biomass Transfer | 生物量传递效率
In a food chain, only a small percentage of the biomass or energy from one trophic level is passed on to the next level. This efficiency can be calculated as follows.
在食物链中，一个营养级的生物量或能量只有一小部分能传递给下一个营养级，其效率可按如下方式计算。
Efficiency (% iomass transferred to next level ÷ Biomass available at previous level) × 100
效率（%）=（传递给下一级的生物量 ÷ 前一级可用的生物量）× 100
only 200 g becomes rabbit biomass, the efficiency is (200 ÷ 2000) × 100 = 10%. Losses occur through respiration, egestion, excretion and uneaten parts.
例如，草产生了 2000 g 生物量，而只有 200 g 转化为兔的生物量，效率为（200 ÷ 2000）× 100 = 10%。损失主要来自呼吸作用、排遗、排泄和未被取食的部分。
In energy terms, you can use the same formula with kilojoules (kJ) instead of biomass mass.
以能量表达时，可用千焦（kJ）代替生物量质量，套用相同的公式。
8. Cardiac Output | 心输出量
Cardiac output is the volume of blood the heart pumps out in one minute. It links heart rate and stroke volume, two commonly measured values.
心输出量是心脏每分钟泵出的血液体积，它将心率与每搏输出量这两个常测指标联系起来。
Cardiac output (cm³/min) = Heart rate (beats/min) × Stroke volume (cm³)
心输出量（cm³/min）= 心率（次/分）× 每搏输出量（cm³）
Stroke volume is the amount of blood pushed out by the left ventricle with each beat. During exercise, both heart rate and stroke volume increase, raising cardiac output significantly.
每搏输出量是左心室每次搏动挤压出的血液量。运动时，心率和每搏输出量均增加，从而显著提升心输出量。
Typical resting values are about 70 beats/min and 70 cm³, giving a cardiac output around 4900 cm³/min (4.9 L/min).
典型的静息值约为 70 次/分和 70 cm³，心输出量约为 4900 cm³/min（4.9 L/min）。
9. Population Estimation Using Quadrats | 用样方估算种群数量
For slow-moving or stationary organisms, you can estimate the total population in a large area by taking samples with quadrats.
针对移动缓慢或不动的生物，可以通过样方抽样来估算较大区域内的种群总量。
tion = (Mean count per quadrat ÷ Area of one quadrat) × Total area of habitat
估算种群数量 =（每样方的平均计数 ÷ 一个样方的面积）× 栖息地的总面积
m², the estimate is (12 ÷ 0.25) × 500 = 48 × 500 = 24,000 daisies.
例如，一个 0.25 m² 的样方中平均有 12 株雏菊，草地面积为 500 m²，则估算为（12 ÷ 0.25）× 500 = 48 × 500 = 24,000 株雏菊。
You must place quadrats randomly to avoid bias. Often greater number of quadrats gives a more reliable mean.
必须随机放置样方以避免偏差，通常样方数量越多，平均值越可靠。
10. Rate of Enzyme-Controlled Reactions | 酶控制反应速率
Enzyme activity can be measured by recording how fast a substrate disappears or a product appears. A common GCSE approach uses the reciprocal of time taken for a standard change to occur.
酶活性可通过记录底物消失或产物出现的快慢来测定。GCSE中常用标准变化发生所需时间的倒数来表示速率。
Rate = 1 ÷ Time (s) for the reaction to reach a set endpoint
速率 = 1 ÷ 达到设定终点所需的时间（秒）
For example, when amylase breaks down starch, you can time how long it takes for the iodine test to stop turning blue-black. A shorter time means a faster rate.
例如，当淀粉酶分解淀粉时，可以记录碘液不再变蓝黑色的时长。时间越短，速率越快。
of product formed (e.g. mg) ÷ Time (min). Both approaches are valid, just be consistent.
如果测量随时间变化的产物量，则使用：速率 = 形成的产物量（如 mg）÷ 时间（min）。两种方法均有效，但要前后一致。
11. Percentage Change Calculation | 百分比变化计算
This formula is widely used to compare before-and-after data, e.g. change in mass during osmosis experiments or growth measurements.
这个公式广泛用于比较前后数据，例如渗透实验中质量的变化或生长测量。 Published by TutorHao | GCSE Biology Revision Series | aleveler.com
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