📚 Year 9 WJEC Biology: Quick Reference Handbook of Formulas and Theorems | Year 9 WJEC 生物：公式定理速查手册
This quick-reference guide brings together the key formulae, equations, and theorems you will use throughout Year 9 WJEC Biology. Mastering these will help you solve numerical problems, predict experimental outcomes, and interpret data confidently in both coursework and examinations.
本速查指南汇集了 Year 9 WJEC 生物课程中使用的关键公式、方程和定理。掌握它们将帮助你解决数值问题、预测实验结果，并在课程作业和考试中自信地解读数据。
1. Microscopy and Magnification | 显微镜与放大率
Magnification = Image size / Actual size
放大率 = 图像大小 / 实际大小
Image size is the size of the specimen measured on the micrograph or drawing; actual size is its real-life size. Both must be in the same unit, usually millimetres (mm) or micrometres (µm).
图像大小是在显微照片或绘图上测得的标本尺寸；实际大小是它的真实尺寸。两者必须使用相同单位，通常为毫米（mm）或微米（µm）。
To rearrange the formula: Image size = Magnification × Actual size and Actual size = Image size / Magnification.
公式变形：图像大小 = 放大率 × 实际大小；实际大小 = 图像大小 / 放大率。
Common unit conversions essential for microscopy:
显微镜常用的单位换算：
| Unit (单位) | Equivalent (等值) |
|---|---|
| 1 metre (m) / 1 米 | 1000 millimetres (mm) / 1000 毫米 |
| 1 millimetre (mm) / 1 毫米 | 1000 micrometres (µm) / 1000 微米 |
| 1 micrometre (µm) / 1 微米 | 1000 nanometres (nm) / 1000 纳米 |
res 50 mm on a drawing and its actual size is 0.02 mm. Magnification = 50 / 0.02 = 2500 ×.
计算示例：一张图上细胞的长度为 50 mm，其实际大小为 0.02 mm。放大率 = 50 / 0.02 = 2500 倍。
2. Surface Area to Volume Ratio | 表面积与体积比
For a cube of side length L: Surface area = 6L² and Volume = L³.
对于边长为 L 的立方体：表面积 = 6L²，体积 = L³。
The surface area to volume ratio (SA:V) is 6L² / L³ = 6 / L. As an organism or cell grows larger, its SA:V decreases.
表面积与体积比 (SA:V) 为 6L² / L³ = 6 / L。随着生物体或细胞增大，其 SA:V 比值下降。
For a sphere: Surface area = 4πr², Volume = (4/3)πr³, so SA:V = 3/r.
对于球体：表面积 = 4πr²，体积 = (4/3)πr³，因此 SA:V = 3/r。
A high SA:V allows efficient diffusion of substances into and out of cells. This is why actively dividing cells are small and why larger organisms need specialised exchange surfaces (e.g., lungs, gills).
高 SA:V 有利于物质高效地进出细胞。这就是为什么活跃分裂的细胞体积都很小，以及为什么较大的生物体需要专门的交换表面（如肺、鳃）。
3. Rate of Reaction in Enzyme Experiments | 酶实验中的反应速率
The rate of an enzyme-catalysed reaction can be calculated as:
酶催化反应的速率可以通过以下方式计算：
Rate = Change in amount of product or substrate / Time taken
速率 = 产物或底物的变化量 / 所用时间
In many school experiments (e.g., amylase breaking down starch), the rate is measured as the reciprocal of the time taken for a visible change: Rate = 1 / time (s⁻¹). A shorter time indicates a faster rate.
在许多学校实验中（如淀粉酶分解淀粉），速率通过可视变化所需时间的倒数来衡量：速率 = 1 / 时间 (s⁻¹)。时间越短，表示速率越快。
Units depend on what is measured: if gas volume is collected, rate might be in cm³/s; if mass change is measured, rate could be g/min.
单位取决于测量对象：如果收集气体体积，速率单位可以是 cm³/s；如果测量质量变化，速率单位可以是 g/min。
Typical expected results: the rate increases with temperature up to an optimum, then falls rapidly as the enzyme denatures. A similar bell-shaped curve is seen for pH.
典型的预期结果：速率随温度升高而增加，直至最适温度，然后因酶变性而急剧下降。pH 的影响也呈现类似的钟形曲线。
4. Percentage Change in Mass | 质量百分比变化
In osmosis experiments (e.g., placing potato cylinders in different sugar concentrations), the percentage change in mass quantifies water gain or loss:
在渗透实验中（例如将土豆条置于不同浓度的糖溶液中），质量百分比变化用于量化水分的得失：
Percentage change = (Final mass – Initial mass) / Initial mass × 100%
百分比变化 = (最终质量 – 初始质量) / 初始质量 × 100%
A positive value means mass was gained (water moved into the cells by osmosis). A negative value means mass was lost (water moved out). Plotting this against solute concentration helps identify the isotonic point where no net change occurs.
正值表示质量增加（水通过渗透进入细胞）。负值表示质量减少（水向外流出）。将该值对溶液浓度作图，有助于确定没有净变化的等渗点。
5. Photosynthesis Equations | 光合作用方程式
The overall word equation for photosynthesis:
光合作用的总文字方程式：
carbon dioxide + water → glucose + oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
The balanced symbol equation, showing that the reaction requires light energy and chlorophyll:
配平的符号方程式，表明该反应需要光能和叶绿素：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Photosynthesis is an endothermic reaction; it takes in energy from sunlight. The rate can be limited by light intensity, carbon dioxide concentration, and temperature.
光合作用是吸热反应；它吸收来自阳光的能量。其速率可能受光照强度、二氧化碳浓度和温度的限制。
6. Respiration Equations | 呼吸作用方程式
Aerobic respiration requires oxygen and releases a large amount of energy:
有氧呼吸需要氧气，并释放大量能量：
glucose + oxygen → carbon dioxide + water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水 (+ 能量)
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Anaerobic respiration in animals produces lactic acid and relatively little energy:
动物的无氧呼吸产生乳酸和相对较少的能量：
glucose → lactic acid (+ energy)
葡萄糖 → 乳酸 (+ 能量)
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