📚 Year 9 CAIE Biology: Formula and Theorem Quick Reference Handbook | Year 9 CAIE 生物：公式定理速查手册
This handbook condenses all essential formulas, equations, and key principles you need for Year 9 CAIE Biology. From magnification to respiration, every calculation and core theorem is explained clearly with examples.
这本手册浓缩了 Year 9 CAIE 生物所需的所有基本公式、方程和关键原理。从放大倍数到呼吸作用，每一个计算和核心定理都配有清晰解释和实例。
1. Magnification Formula | 放大倍数公式
The most frequently used formula in microscopy links image size, actual size, and magnification. Remember to keep units consistent – convert all measurements to the same unit before calculating.
显微镜中最常用的公式将图像大小、实际大小和放大倍数联系起来。计算前务必将所有测量值转换为相同单位，保持单位一致。
Magnification = Image size ÷ Actual size
放大倍数 = 图像大小 ÷ 实际大小
Alternatively, you can rearrange it: Actual size = Image size ÷ Magnification, and Image size = Magnification × Actual size a microscope with magnification ×400, the actual size is 25 mm ÷ 400 = 0.0625 mm (or 62.5 µm).
或者可以变形：实际大小 = 图像大小 ÷ 放大倍数，图像大小 = 放大倍数 × 实际大小。如果一个细胞图像在放大 400 倍的显微镜下测量为 25 mm，实际大小为 25 mm ÷ 400 = 0.0625 mm（即 62.5 µm）。
| Quantity 量 | Common units 常用单位 |
|---|---|
| Image size | mm, µm |
| Actual size | µm, nm |
| Magnification | × (no unit 无单位) |
2. Surface Area to Volume Ratio | 表面积与体积之比
As an object becomes larger, its surface area to volume ratio decreases. This principle explains why cells are microscopic and why organisms need specialised exchange surfaces.
随着物体变大，其表面积与体积之比减小。这一原理解释了为什么细胞如此微小，以及生物体为何需要特化的交换表面。
SA:V ratio = Surface Area ÷ Volume
表面积与体积比 = 表面积 ÷ 体积
For a cube with side length l, SA = 6l² and V = l³, so SA:V = 6/l. This shows that as l increases, the ratio falls. Small cells have a high SA:V, which supports efficient diffusion of oxygen, nutrients, and waste.
对于边长为 l 的立方体，表面积 = 6l²，体积 = l³，因此表面积与体积比 = 6/l。这表明随着 l 增大，比值下降。小细胞拥有高表面积与体积比，有利于氧气、营养物质和废物的高效扩散。
- A small cube with l = 1 cm: SA:V = 6 ÷ 1 = 6
- A large cube with l = 3 cm: SA:V = 54 ÷ 27 = 2
- 边长为 1 cm 的小立方体：表面积与体积比 = 6 ÷ 1 = 6
- 边长为 3 cm 的大立方体：表面积与体积比 = 54 ÷ 27 = 2
3. Rate of Diffusion | 扩散速率
Diffusion rate is influenced by concentration gradient, temperature, surface area, and distance. The relationship can be summarised by Fick's law (simplified version).
扩散速率受浓度梯度、温度、表面积和扩散距离的影响。这些关系可以用菲克定律的简化形式来概括。
Rate of diffusion ∝ (Surface Area × Concentration difference) ÷ Diffusion distance
扩散速率 ∝ (表面积 × 浓度差) ÷ 扩散距离
e. Adaptations like the flattened shape of leaves and the folded inner membranes of mitochondria maximise diffusion efficiency.
表面积加倍 → 速率加倍。浓度差加倍 → 速率加倍。膜厚度加倍 → 速率减半。例如叶片扁平形态和线粒体内膜折叠等适应性结构，都能最大限度地提高扩散效率。
4. Osmosis and Water Potential | 渗透作用与水势
Osmosis is the net movement of water molecules from a region of higher water potential (less concentrated solution) to a region of lower water potential (more concentrated solution) through a partially permeable membrane.
渗透作用是水分子通过部分透膜，从水势较高（浓度较低）的区域向水势较低（浓度较高）的区域净移动。
Water moves: High water potential → Low water potential
水移动方向：高水势 → 低水势
Pure water has the highest water potential (0 kPa by convention). Adding solutes lowers the water potential (makes it more negative). Plant cells in dilute solution become turgid; in concentrated solution they become plasmolysed. Animal cells may burst (lysis) in dilute solution or shrink (crenation) in concentrated solution.
纯水的水势最高（约定为 0 kPa）。加入溶质会降低水势（使其更负）。植物细胞在稀溶液中变得饱满（质壁分离复原）；在浓溶液中发生质壁分离。动物细胞在稀溶液中可能破裂（溶血），在浓溶液中皱缩。
5. Enzyme Activity and Reaction Rate | 酶活性与反应速率
The rate of an enzyme-controlled reaction can be measured by the amount of product formed per unit time or the amount of substrate used per unit time. The rate often follows the formula below.
酶控反应的速率可以用单位时间内产物的生成量或底物的消耗量来衡量。速率通常遵循以下公式。
Rate of reaction = Change in concentration / Time
反应速率 = 浓度变化 / 时间
For practical work, you might measure volume of oxygen produced in catalase experiments or time taken for starch to disappear with amylase. Always calculate as 1 ÷ time taken for a fixed change, or use the gradient of a concentration–time graph.
在实验中，你可以测量过氧化氢酶产生氧气的体积，或淀粉酶分解淀粉所需的时间。通常取固定变化所需时间的倒数，或使用浓度-时间图的斜率来计算速率。
- Optimum temperature for most human enzymes: around 37 °C.
- Optimum pH varies: pepsin (pH 2), amylase (pH 7).
- 大多数人体酶的最适温度：约 37 °C。
- 最适 pH 值各异：胃蛋白酶 (pH 2)，淀粉酶 (pH 7)。
6. Word and Chemical Equations for Photosynthesis | 光合作用的文字与化学方程
Photosynthesis is the process by which plants produce glucose and oxygen from carbon dioxide and water using light energy. The overall word and balanced chemical equations must be memorised.
光合作用是植物利用光能，将二氧化碳和水转化为葡萄糖和氧气的过程。必须记住总体的文字方程式和平衡化学方程式。
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Chlorophyll absorbs light energy to drive this reaction. Glucose is stored as starch or used in respiration. Limiting factors include light intensity, carbon dioxide concentration, and temperature – each can be investigated by measuring the rate of oxygen production (e.g., counting bubbles from pondweed).
叶绿素吸收光能驱动该反应。葡萄糖以淀粉形式储存或用于呼吸作用。限制因素包括光照强度、二氧化碳浓度和温度——可以通过测量氧气产生速率（如计数水草气泡）来研究每一个因素。
7. Equations for Aerobic and Anaerobic Respiration | 有氧呼吸与无氧呼吸的方程
Respiration releases energy from glucose to power cellular activities. The equations differ depending on oxygen availability.
呼吸作用从葡萄糖中释放能量，驱动细胞活动。根据氧气供应情况，方程式会有所不同。
Aerobic: Glucose + Oxygen → Carbon dioxide + Water (+ lots of energy)
有氧呼吸：葡萄糖 + 氧气 → 二氧化碳 + 水 (+ 大量能量)
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Anaerobic in animals: Glucose → Lactic acid (+ some energy)
动物无氧呼吸：葡萄糖 → 乳酸 (+ 少量能量)
Anaerobic in yeast: Glucose → Ethanol + Carbon dioxide (+ some energy)
酵母无氧呼吸：葡萄糖 → 乙醇 + 二氧化碳 (+ 少量能量)
Aerobic respiration releases about 32 kJ per gram of glucose, while anaerobic respiration releases much less. The oxygen debt is the amount of oxygen needed to oxidise lactic acid back to carbon dioxide and water.
有氧呼吸每克葡萄糖大约释放 32 kJ 能量，而无氧呼吸释放的能量少得多。氧债是将乳酸氧化回二氧化碳和水所需的氧气量。
8. Energy Content in Food | 食物中的能量含量
The energy released when food is burned can be calculated using calorimetry. A known mass of food is burned to heat a known volume of water, and the temperature rise is measured.
食物燃烧时释放的能量可以通过量热法计算。燃烧已知质量的食物，加热已知体积的水，测量水温升高的度数。
Energy (J) = mass of water (g) × 4.2 × temperature rise (°C)
能量 (焦耳) = 水的质量 (克) × 4.2 × 温度升高值 (°C)
mass of food burned. The constant 4.2 is the specific heat capacity of water (J/g/°C). This experiment helps compare the energy stores in different food types, although it underestimates total energy because heat is lost to the surroundings.
然后，每克能量 = 总能量 ÷ 燃烧的食物质量。常数 4.2 是水的比热容 (J/g/°C)。这个实验有助于比较不同食物的能量储存，但由于热量散失到周围环境中，测得的能量值会偏低。
| Nutrient 营养素 | Energy per gram (kJ) |
|---|---|
| Carbohydrate 碳水化合物 | ~17 |
| Protein 蛋白质 | ~17 |
| Fat 脂肪 | ~39 |
9. Body Mass Index (BMI) | 身体质量指数
BMI is a simple index used to classify underweight, healthy weight, overweight, and obesity. It uses mass and height to estimate body fat.
身体质量指数 (BMI) 是一个用于划分体重过轻、健康体重、超重和肥胖的简单指标。它利用体重和身高来估算体脂。
BMI = Mass (kg) ÷ Height² (m²)
身体质量指数 = 体重 (公斤) ÷ 身高² (米²)
of 1.75 m has a BMI = 70 ÷ (1.75²) = 22.9 kg/m². This falls within the healthy range (18.5– obesity, which increases the risk of heart disease, type 2 diabetes, and other conditions.
例如，一个体重 70 公斤、身高 1.75 米的人，BMI = 70 ÷ (1.75²) = 22.9 kg/m²，落入健康范围 (18.5–24.9) 内。BMI 超过 30 表示肥胖，会增加心脏病、2 型糖尿病等疾病的风险。
10. Punnett Squares and Genetic Ratios | 旁氏表与遗传比例
Monohybrid crosses predict the probability of offspring inheriting certain alleles. The expected phenotypic and genotypic ratios follow Mendelian principles.
单性状杂交可预测子代继承特定等位基因的概率。预期的表现型和基因型比例遵循孟德尔原理。
For heterozygous × heterozygous (e.g., Tt × Tt): Phenotypic ratio = 3 : 1
杂合子 × 杂合子 (例如 Tt × Tt)：表现型比例 = 3 : 1
Genotypic ratio = 1 TT : 2 Tt : 1 tt
基因型比例 = 1 TT : 2 Tt : 1 tt
zygous recessive), the expected offspring ratio is 1 : 1. Use a Punnett grid to combine gametes: each parent contributes one allele, and the grid shows all possible combinations. Always write dominant allele first (e.g., Tt, not tT).
在测交（杂合子 × 纯合隐性）中，预期子代比为 1 : 1。使用旁氏方格组合配子：每个亲本贡献一个等位基因，方格显示所有可能的组合。始终将显性等位基因写在前面（如 Tt 而非 tT）。
11. Biological Sampling: Quadrat Formula | 生物取样：样方公式
To estimate population size or species distribution in a field study, we use quadrats. Mean density and total population can be calculated from sample counts.
在野外研究中，为估算种群数量或物种分布，我们使用样方。通过样本计数可计算平均密度和总种群数量。
Estimated population = Mean count per quadrat × (Total area ÷ Quadrat area)
估算种群数量 = 每样方平均计数 × (总面积 ÷ 样方面积)
For percentage cover (used for plants or slow-moving organisms), place a frame quadrat and estimate the percentage of the quadrat covered by the species. These data can then be used to compare different habitats, such as trampled versus untrampled zones, or to map zonation on a rocky shore.
百分比覆盖度（用于植物或移动缓慢的生物）：放置样方框，估算目标物种覆盖样方面积的百分比。这些数据可用于比较不同栖息地，比如被踩踏区域与未被踩踏区域，或绘制岩岸生态带状分布图。
12. Key Food Tests and Reagent Color Changes | 主要食物测试与试剂颜色变化
Identifying biological molecules is a core skill. The main reagents and expected positive results form a simple table of qualitative analysis.
鉴定生物分子是一项核心技能。主要试剂和预期阳性结果构成一张简单的定性分析表。
| Nutrient 营养素 | Reagent 试剂 | Positive result 阳性结果 |
|---|---|---|
| Starch 淀粉 | Iodine solution 碘液 | Blue-black 蓝黑色 |
| Reducing sugar 还原糖 | Benedict's solution + heat 班氏试剂 + 加热 | Brick-red precipitate 砖红色沉淀 |
| Protein 蛋白质 | Biuret reagent 双缩脲试剂 | Purple/violet 紫色 |
| Lipid (fats/oils) 脂质 | Ethanol emulsion test 乙醇乳浊液测试 | Cloudy white emulsion 乳白色浑浊 |
| Vitamin C 维生素 C | DCPIP solution DCPIP 溶液 | Blue to colourless 蓝色变无色 |
No formula calculation is needed here, but the principle is based on chemical reactions that produce a visible change. A semi-quantitative version for vitamin C uses the volume required to decolourise a fixed volume of DCPIP, establishing a concentration–volume relationship.
这里不需要公式计算，但原理基于产生可见变化的化学反应。维生素 C 的半定量分析使用使固定体积 DCPIP 脱色所需的溶液体积，建立浓度-体积关系。
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