📚 GCSE AQA Biology: Formulae Handbook | GCSE AQA 生物：公式汇总手册
This handbook brings together all the essential equations and calculations you need to confidently tackle the maths-based questions in your AQA GCSE Biology exam. Each formula is presented with clear explanations, worked examples and unit guidance to help you apply it correctly.
本手册汇总了你在 AQA GCSE 生物考试中取得成功所需的所有核心公式与计算。每个公式都配有清晰的解释、示例及单位说明，帮助你正确运用。
1. Magnification | 放大倍率
Magnification describes how many times larger an image appears compared to the real object. Both sizes must be in the same unit before calculating.
放大倍率表示图像比实物大了多少倍。计算前必须将两者换算为同一单位。
Magnification = Image size ÷ Actual size
放大倍率 = 图像大小 ÷ 实际大小
s check that you have converted measurements such as millimetres to micrometres if needed.
常用单位换算：1 mm = 1000 µm；1 µm = 1000 nm。务必根据题目要求完成单位转换再代入计算。
- Example: of a cell measures 24 mm. The actual cell is 0.006 mm. Magnification = 24 ÷ 0.006 = ×4000.
- 示例： 一个细胞图像长 24 mm，实际细胞为 0.006 mm。放大倍率 = 24 ÷ 0.006 = ×4000。
2. Rate of Reaction (Enzymes) | 反应速率（酶）
The rate of an enzyme-controlled reaction can be expressed either by the quantity of product formed per unit time or by the reciprocal of the time taken for a specific change to occur.
酶促反应速率既可以用单位时间内生成物的量来表示，也可以用特定变化所需时间的倒数来表示。
Rate = Amount of product formed ÷ Time
速率 = 生成物的量 ÷ 时间
Rate = 1 ÷ Time taken for a change
速率 = 1 ÷ 变化所需时间
When using the endpoint method (e.g. starch– en given as 1/time (s⁻¹). For continuous monitoring, rate = volume of gas produced / time.
采用终点法（如淀粉–碘实验）时，速率通常表示为 1/时间（s⁻¹）。连续监测实验中，速率 = 产生气体的体积 / 时间。
- Example: 5 cm³ of oxygen is produced in 25 seconds. Rate = 5 ÷ 25 = 0.2 cm³/s.
- 示例： 25 秒内产生 5 cm³ 氧气。速率 = 5 ÷ 25 = 0.2 cm³/s。
3. Rate of Photosynthesis | 光合作用速率
Photosynthesis rate is commonly measured by recording the volume of oxygen produced per unit time or by using the inverted-rate method with an indicator.
光合作用速率常通过测量单位时间内产生的氧气体积，或使用指示剂的倒速率法来计算。
Rate of photosynthesis = Volume of O&sub2; produced ÷ Time
光合速率 = 产生的 O&sub2; 体积 ÷ 时间
Rate of photosynthesis = 1 ÷ Time for indicator to change colour (ET&sb5;&sb0;)
光合速率 = 1 ÷ 指示剂变色所需时间（ET&sb5;&sb0;）
The ET₅₀ value represents the time for half the indicator to change colour and is used to estimate the rate. Always state units, e.g. min⁻¹ or s⁻¹.
ET₅₀ 值表示一半指示剂变色所需时间，用于估算速率。必须注明单位，如 min⁻¹ 或 s⁻¹。
4. Rate of Respiration | 呼吸速率
Respiration rate can be assessed by measuring carbon dioxide production or oxygen consumption over time.
呼吸速率可以通过测量二氧化碳的产生或氧气的消耗随时间的变化来评估。
Rate of respiration = Volume of CO&sub2; produced ÷ Time
呼吸速率 = 产生的 CO&sub2; 体积 ÷ 时间
Rate of respiration = 1 ÷ Time for indicator colour change
呼吸速率 = 1 ÷ 指示剂变色时间
In respirometer experiments, the rate is often expressed as distance moved by a liquid per minute, which is proportional to the volume of oxygen consumed.
在呼吸计实验中，速率常表示为液体每分钟移动的距离，该距离与消耗的氧气体积成正比。
5. Efficiency of Energy Transfer | 能量传递效率
Energy transfer between trophic levels is inefficient; only a fraction is converted into new biomass. Efficiency is always expressed as a percentage.
营养级之间的能量传递效率很低，只有一小部分转化为新生物量。效率总是以百分比表示。
Efficiency (% ss at next trophic level ÷ Energy in biomass at previous trophic level) × 100
效率 (%) = (下一营养级生物量中的能量 ÷ 上一营养级生物量中的能量) × 100
This equation can also be applied to the energy transferred from a food source into an organism's growth.
该等式也可用于从食物源转移到生物体生长的那部分能量。
- Example: kJ of energy and stores 500 kJ in its body. Efficiency = (500 ÷ 5000) × 100 = 10%.
- 示例： 一只兔子摄入含 5000 kJ 能量的草，体内储存 500 kJ。效率 = (500 ÷ 5000) × 100 = 10%。
6. Efficiency of Biomass Transfer | 生物量传递效率
Biomass transfer efficiency focuses on the dry mass of organisms rather than energy content. It is calculated similarly to energy efficiency.
生物量传递效率关注的是生物的干重而非能量。其计算方式与能量效率类似。
Efficiency (%) = (Biomass at higher trophic level ÷ Biomass at lower trophic level) × 100
效率 (%) = (较高营养级生物量 ÷ 较低营养级生物量) × 100
Recall that the biomass available is always less at higher trophic levels due to respiration, egestion and excretion.
请记住，由于呼吸作用、排遗和排泄，高营养级的生物量总是更少。
7. Population Density | 种群密度
Population density tells you how many individuals live in a given area or volume. It is a useful measure when sampling habitats.
种群密度表明单位面积或体积内个体的数量，是栖息地采样时的重要指标。
Population density = Number of individuals ÷ Area (or Volume)
种群密度 = 个体数量 ÷ 面积（或体积）
Typical units are individuals per m² for quadrat sampling or individuals per m³ for aquatic environments.
典型单位是样方采样中的 个/m²，或水体环境中的 个/m³。
8. Heart Rate | 心率
Heart rate is the number of times the heart beats per minute. It can be determined from pulse recordings or measured directly.
心率是每分钟心脏跳动的次数，可通过脉搏记录或直接测量得到。
Heart rate (bpm) = Number of beats ÷ Time (min)
心率 (bpm) = 心跳次数 ÷ 时间（分钟）
If you count beats over a fraction of a minute, scale the value appropriately, e.g. beats in 15 seconds × 4.
如果计数时间不足一分钟，需要进行换算，例如 15 秒的心跳数 × 4。
9. Surface Area to Volume Ratio | 表面积与体积比
Organisms exchange substances across their surfaces. The surface area to volume ratio (SA:V) explains why small organisms can rely on diffusion alone.
生物体通过表面进行物质交换。表面积与体积比 (SA:V) 解释了为什么小生物可以仅依靠扩散。
SA:V = Total surface area ÷ Volume
SA:V = 总表面积 ÷ 体积
As an object gets larger, its volume grows faster than its surface area, so the ratio decreases. Diffusion becomes less efficient, necessitating transport systems.
物体越大，体积增长比表面积快，因此比值下降。扩散效率降低，需要专门的运输系统。
10. Concentration of Solutions | 溶液浓度
Concentration measures how much solute is dissolved in a given volume of solvent. This is useful when describing osmosis and diffusion experiments.
浓度衡量在一定体积的溶剂中溶解了多少溶质，这在描述渗透和扩散实验时很有用。
Concentration = Mass of solute (g) ÷ Volume of solution (dm³)
浓度 = 溶质质量 (g) ÷ 溶液体积 (dm³)
typically g/dm³. Remember that 1 dm³ = 1000 cm³. You can convert by dividing cm³ by 1000.
单位通常是 g/dm³。请记住 1 dm³ = 1000 cm³，将 cm³ 除以 1000 即可换算。
11. Mean and Range | 平均值与范围
The mean is used to find a typical value from repeated measurements, while the range describes the spread of the data.
平均值用于从重复测量中找到典型值，而范围描述数据的离散程度。
Mean = Sum of all values ÷ Number of values
平均值 = 所有数值之和 ÷ 数值的个数
Range = Maximum value − Minimum value
范围 = 最大值 − 最小值
Always calculate the mean after removing any anomalous results. The range helps to evaluate the reliability of your data.
计算平均值前应剔除异常值。范围有助于评估数据的可靠性。
12. Percentage Change | 百分比变化
Percentage change is a very common calculation in biology, especially when comparing before-and-after results, such as mass change in osmosis.
百分比变化在生物学中很常见，特别用于比较前后结果，例如渗透作用中的质量变化。
rcentage change = ((New value − Original value) ÷ Original value) × 100
百分比变化 = ((新值 − 原值) ÷ 原值) × 100
A positive percentage indicates an increase, while a negative percentage indicates a decrease. Use this equation when plotting results or drawing conclusions from osmosis experiments.
正值表示增加，负值表示减少。在绘制图表或分析渗透实验结果时经常使用该公式。
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