📚 Year 10 CAIE Biology: Quick Reference Handbook of Formulas and Theorems | CAIE Year 10 生物：公式定理速查手册
This quick reference handbook brings together the essential mathematical relationships, laws and core principles you need to master for Year 10 CAIE Biology. From magnification and surface area to volume ratios to genetic probability and energy transfer efficiency, each concept is presented in a clear, bilingual format to support both learning and revision.
这本速查手册汇总了 Year 10 CAIE 生物课程必须掌握的数学关系、定律和核心原理。从放大倍数计算、表面积与体积比到遗传概率和能量传递效率，每个概念都以清晰的双语形式呈现，方便学习和复习。
1. Magnification Formula | 放大倍数公式
Magnification is the number of times larger an image is compared to the real size of the object. It is calculated using the equation: Magnification = Image size ÷ Actual size. You must ensure both measurements are in the same unit before dividing. This formula is fundamental for microscope drawings and biological diagrams.
放大倍数是图像比实物实际尺寸放大的倍数。计算公式为：放大倍数 = 图像大小 ÷ 实际大小。计算前必须确保两个测量值单位一致。该公式是显微镜绘图和生物图绘的基础。
Remember: if you are given the magnification and the image size, you can rearrange the formula to find the actual size: Actual size = Image size ÷ Magnification. Similarly, Image size = Magnification × Actual size.
请记住：如果已知放大倍数和图像大小，可以转换公式求实际大小：实际大小 = 图像大小 ÷ 放大倍数。同样，图像大小 = 放大倍数 × 实际大小。
M = I / A
M = I / A
2. Surface Area to Volume Ratio | 表面积与体积比
The surface area to volume ratio (SA:V) is a critical concept explaining why cells are microscopic and why organisms need specialised exchange surfaces. As an object increases in size, its volume grows faster than its surface area, causing the SA:V to decrease. A high SA:V allows efficient diffusion of substances into and out of the cell.
表面积与体积比 (SA:V) 是解释细胞为何微小以及生物体为何需要特化交换表面的关键概念。物体增大时，体积的增长快于表面积，导致 SA:V 下降。高表面积体积比有助于物质高效地进出细胞。
with a low SA:V, such as large animals, rely on transport systems like the circulatory system and specialised gas exchange organs.
对立方体而言，表面积 = 6 × 边长²，体积 = 边长³。球体的表面积 = 4πr²，体积 = 4/3 πr³。低 SA:V 的生物（如大型动物）依赖循环系统等运输系统以及特化的气体交换器官。
3. Fick's Law of Diffusion | 菲克扩散定律
Fick's Law describes the rate of diffusion across a membrane. It states that the rate of diffusion is directly proportional to the surface area and the concentration difference, and inversely proportional to the thickness of the membrane. The relationship can be written as:
菲克定律描述了物质跨膜扩散的速率。定律指出扩散速率与表面积和浓度差成正比，与膜的厚度成反比。该关系可写作：
Rate of diffusion ∝ (Surface area × Concentration difference) / Thickness of membrane
扩散速率 ∝ (表面积 × 浓度差) / 膜厚度
The alveoli in the lungs, villi in the small intestine and gills in fish all show adaptations that maximise Fick's Law: large surface area, thin exchange surface and a steep concentration gradient maintained by blood flow or ventilation.
肺部的肺泡、小肠绒毛和鱼类的鳃都表现出最大化菲克定律的适应特征：表面积大、交换面薄、通过血流或通气维持陡峭的浓度梯度。
4. Rate of Enzyme-Catalysed Reactions | 酶促反应速率
The rate of an enzyme-controlled reaction can be measured by recording the time taken for a substrate to be used up or a product to appear. A simple formula to compare rates is:
酶控反应速率可通过记录底物耗尽或产物出现所需的时间来测量。比较反应速率的简单公式是：
Rate = 1 / Time
速率 = 1 / 时间
ationship is useful for plotting graphs of enzyme activity against temperature or pH, showing how the rate increases to an optimum and then declines as the enzyme denatures.
例如，在碘液测试中若淀粉消失需 20 秒，则速率为 1/20 = 0.05 s⁻¹。该关系有助于绘制酶活性随温度或 pH 变化的曲线，显示速率上升至最适值后因酶变性而下降。
5. Genetic Probability and Ratios | 遗传概率与比例
Monohybrid inheritance follows Mendel' ngle gene with complete dominance produces a phenotypic ratio of 3:1 (dominant : recessive) and a genotypic ratio of 1:2:1 (homozygous dominant : heterozygous : homozygous recessive).
单基因杂交遵循孟德尔定律。两个杂合子（如 Tt × Tt）在完全显性下的杂交，表现型比例为 3:1（显性 : 隐性），基因型比例为 1:2:1（纯合显性 : 杂合 : 纯合隐性）。
y of each gamete combination. A test cross (heterozygote × homozygous recessive) gives a 1:1 ratio, which helps determine an unknown genotype.
可利用庞纳特方格计算概率。特定基因型的遗传概率由每种配子组合的概率相乘得出。测交（杂合子 × 隐性纯合子）产生 1:1 的比例，有助于确定未知基因型。
| T | t | |
| T | TT | Tt |
| t | Tt | tt |
| T | t | |
| T | TT | Tt |
| t | Tt | tt |
6. Energy Transfer and Trophic Levels | 能量传递与营养级
In a food chain, only about 10% of the energy is transferred from one trophic level to the next. The rest is lost through respiration, heat, movement, uneaten parts and waste. The efficiency of energy transfer can be calculated using:
在食物链中，大约只有 10% 的能量从一个营养级传递到下一个营养级。其余能量通过呼吸作用、热量、运动、未被取食的部分以及排泄物散失。能量传递效率可通过以下公式计算：
Efficiency (%) = (Energy available to the next level / Energy available to the previous level) × 100
效率 (%) = (传递给下一级的能量 / 上一级可用的能量) × 100
Pyramids of energy are always upright because energy decreases at each successive trophic level. This low transfer efficiency explains why food chains rarely exceed four or five trophic levels and why vegetarian diets require less land and resources.
能量金字塔总是呈正塔形，因为能量在每一级递减。低传递效率解释了食物链很少超过四或五个营养级的原因，也解释了素食饮食为何需要更少的土地和资源。
7. Estimation of Osmosis: Percentage Change in Mass | 渗透估算：质量变化百分比
Osmosis experiments with potato cylinders or dialysis tubing often use the percentage change in mass to compare the movement of water in different solutions. The formula is:
使用土豆条或透析袋进行渗透实验时，常通过质量变化百分比来比较不同溶液中水分的运动。公式为：
Percentage change in mass = ((Final mass − Initial mass) / Initial mass) × 100
质量变化百分比 = ((最终质量 − 初始质量) / 初始质量) × 100
A positive value indicates water gain (hypotonic solution), a negative value indicates water loss (hypertonic solution), and no change suggests the solution is isotonic. Plotting percentage change against solute concentration helps identify the concentration of cell sap when the curve crosses zero.
正值表示吸水（低渗溶液），负值表示失水（高渗溶液），无变化则表明溶液等渗。以质量变化百分比对溶质浓度作图，曲线与零线交点即为细胞液浓度。
8. Limiting Factors in Photosynthesis | 光合作用的限制因子
The rate of photosynthesis is determined by the factor in shortest supply: light intensity, carbon dioxide concentration or temperature. At low light intensities, light is the limiting factor; as light increases, the rate rises until another factor becomes limiting. The concept is embodied in the law of limiting factors, which can be investigated using aquatic plants counting oxygen bubbles.
光合作用速率由供应最短缺的因子决定：光照强度、二氧化碳浓度或温度。低光照下，光是限制因子；光照增强时速率上升，直至另一因子成为限制。限制因子定律可通过用水生植物数气泡的方法进行研究。
The balanced summary equations for photosynthesis and aerobic respiration are also essential:
光合作用和有氧呼吸的总结性方程也必不可少：
Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
光合作用：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Aerobic respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ energy)
有氧呼吸：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ 能量)
udes glycolysis, the Krebs cycle and the electron transport chain. Anaerobic respiration in yeast produces ethanol and carbon dioxide: C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂; in muscle cells, glucose is converted to lactic acid.
请记住这些只是总体总结；光合作用包括两个阶段（光反应和暗反应），呼吸作用包括糖酵解、克雷布斯循环和电子传递链。酵母的无氧呼吸产生乙醇和二氧化碳：C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂；在肌肉细胞中，葡萄糖则转化为乳酸。
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