📚 Year 8 CIE Biology: Formula & Theorem Quick Reference Handbook | Year 8 CIE 生物：公式定理速查手册
This quick reference handbook brings together the key formulas, equations and essential rules that you will meet in Year 8 CIE Biology. Use it to check magnification calculations, write balanced symbol equations for photosynthesis and respiration, apply the cardiac output formula, explore inheritance ratios and recall the conditions that affect diffusion and enzyme action. Each entry is presented with a clear statement of the formula or relationship, followed by a worked example or a short explanation.
这本速查手册汇集了 Year 8 CIE 生物课程中最核心的公式、方程式和重要规律。你可以用它来核对显微镜放大率和细胞尺寸的计算，写出光合作用与呼吸作用的配平符号方程式，应用心输出量公式，推演单基因杂交的遗传比例，以及回顾影响扩散和酶活性的因素。每一个条目都给出了清晰的公式或关系式，并配有示例或简洁说明。
1. Microscope Magnification Formula | 显微镜放大率公式
The total magnification of a light microscope is found by multiplying the magnifying power of the eyepiece lens by the magnifying power of the objective lens.
普通光学显微镜的总放大倍率等于目镜放大倍数乘以物镜放大倍数。
Total magnification = Eyepiece magnification × Objective lens magnification
总放大率 = 目镜放大倍数 × 物镜放大倍数
0. This tells you how many times larger the image appears compared with the real specimen.
例如，若目镜为×10、物镜为×40，则总放大倍率为 10 × 40 = ×400。这表示图像比实际标本放大了400倍。
2. Calculating Actual Cell Size | 计算细胞实际大小
Once you have measured the size of a cell in a drawing or micrograph, you can find its real size by rearranging the magnification formula. Remember to convert units so that the image size and actual size use the same length unit before comparing.
当你测量出绘图或显微照片中细胞的大小之后，可以通过变换放大率公式求出细胞的实际尺寸。计算时要注意统一单位，把图像尺寸和实际尺寸换算成相同的长度单位。
Actual size = Image size ÷ Total magnification
实际尺寸 = 图像尺寸 ÷ 总放大率
ification of ×400, the actual size is 20 ÷ 400 = 0.05 mm. To express this in micrometres (µm), multiply by 1000: 0.05 mm × 1000 = 50 µm. Always check that the final answer has a sensible unit for cells.
若细胞图像在×400 放大下测得长度为 20 mm，则实际尺寸为 20 ÷ 400 = 0.05 mm。化为微米 (µm) 需乘以1000：0.05 mm × 1000 = 50 µm。最后一定要检查单位是否适合细胞尺度。
3. Photosynthesis Equation | 光合作用方程式
Photosynthesis is the process by which green plants use light energy to convert carbon dioxide and water into glucose and oxygen. The reaction takes place in chloroplasts and requires chlorophyll.
光合作用是绿色植物利用光能，将二氧化碳和水转化为葡萄糖和氧气的过程。该反应在叶绿体中进行，需要叶绿素参与。
Carbon dioxide + water → glucose + oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
The balanced chemical equation is:
配平的化学方程式为：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Light and chlorophyll are essential conditions; they are often written above the arrow. Glucose produced may be used immediately for respiration, stored as starch or used to build other organic molecules.
光和叶绿素是必需条件，常被写在箭头之上。生成的葡萄糖可当即用于呼吸作用，或转化为淀粉储存，也可用于合成其他有机物。
4. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration releases energy from glucose by using oxygen. It occurs continuously in the mitochondria of most living cells and is the most efficient way to produce ATP.
有氧呼吸利用氧气将葡萄糖中的能量释放出来。它在大多数活细胞的线粒体中持续进行，是生成 ATP 最高效的方式。
Glucose + oxygen → carbon dioxide + water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
The balanced chemical equation is:
配平的化学方程式为：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
The energy released is used for processes such as muscle contraction, cell division, active transport and maintaining a constant body temperature. Carbon dioxide and water are waste products that are removed from the body.
释放的能量用于肌肉收缩、细胞分裂、主动运输和维持恒定体温等生命活动。二氧化碳和水是代谢废物，会被排出体外。
5. Anaerobic Respiration in Yeast | 酵母无氧呼吸方程式
When yeast cells are deprived of oxygen, they carry out anaerobic respiration (fermentation). This produces ethanol and carbon dioxide, and releases a small amount of energy.
酵母细胞在缺氧时进行无氧呼吸（发酵），产物是乙醇和二氧化碳，并释放少量能量。
Glucose → ethanol + carbon dioxide (+ energy)
葡萄糖 → 乙醇 + 二氧化碳（+ 能量）
The balanced symbol equation is:
配平的符号方程式为：
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
This reaction is exploited in baking and brewing. The carbon dioxide makes bread rise, and ethanol is the alcohol in beer and wine. Note that glucose is only partially broken down, so much less energy is released than in aerobic respiration.
这一反应被用于烘焙和酿酒。二氧化碳使面包膨胀，乙醇则是啤酒和葡萄酒中的酒精。注意，葡萄糖只被部分分解，因此释放的能量远比有氧呼吸少。
6. Anaerobic Respiration in Humans | 人体无氧呼吸方程式
During vigorous exercise, muscle cells may not receive enough oxygen to meet the energy demand. They then switch to anaerobic respiration, producing lactic acid instead of ethanol.
剧烈运动时，肌肉细胞可能无法获得足够氧气来满足能量需求，此时便转而进行无氧呼吸，产物是乳酸而非乙醇。
Glucose → lactic acid (+ energy)
葡萄糖 → 乳酸（+ 能量）
The balanced equation is:
配平方程式为：
C₆H₁₂O₆ → 2C₃H₆O₃
C₆H₁₂O₆ → 2C₃H₆O₃
Lactic acid builds up in muscles and causes the burning sensation and cramp associated with fatigue. After exercise, extra oxygen is needed to break down the lactic acid – this is called the 'oxygen debt'. Strenuous activity can only be sustained for a short time under anaerobic conditions.
乳酸在肌肉中积累会引起灼烧感和疲劳性抽筋。运动后需要额外吸入氧气来分解乳酸，这被称为“氧债”。在无氧条件下，高强度活动只能维持很短时间。
7. Cardiac Output Formula | 心输出量公式
Cardiac output is the volume of blood pumped by the heart per minute. It depends on how often the heart beats and how much blood is ejected with each beat.
心输出量是指心脏每分钟泵出的血液体积，它取决于心率和每搏输出量。
Cardiac output (CO) = Heart rate (HR) × Stroke volume (SV)
心输出量 (CO) = 心率 (HR) × 每搏输出量 (SV)
If a person' 4900 mL/min, or 4.9 L/min. Athletes often have a higher stroke volume, so their resting heart rate can be lower while still maintaining a normal cardiac output.
例如，某人安静时心率为 70 次/分、每搏输出量为 70 mL，则心输出量 = 70 × 70 = 4900 mL/min，即 4.9 L/min。运动员通常每搏输出量较大，因此安静心率可以较低，但仍能维持正常的心输出量。
8. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI is a simple measure used to estimate whether a person has a healthy body weight for their height. It is useful for identifying categories such as underweight, normal, overweight and obese in populations.
BMI 是一个简单指标，用于评估体重与身高是否相称。在人群中，它可用于识别偏瘦、正常、超重和肥胖等类别。
BMI = body mass (kg) ÷ [height (m)]²
BMI = 体重（kg） ÷ [身高（m）]²
nt who weighs 45 kg and is 1.50 m tall, BMI = 45 ÷ (1.50 × 1.50) = 45 ÷ 2.25 = 20.0 kg/m².
一位体重 45 kg、身高 1.50 m 的学生，BMI = 45 ÷ (1.50 × 1.50) = 45 ÷ 2.25 = 20.0 kg/m²。
| BMI range (kg/m²) | Weight status |
|---|---|
| Below 18.5 | Underweight |
| 18.5 – 24.9 | Normal weight |
| 25.0 – 29.9 | Overweight |
| 30.0 and above | Obese |
Although BMI is widely used, it does not distinguish between muscle and fat. Therefore, very muscular individuals may have a high BMI without excess body fat.
虽然 BMI 被广泛使用，但它不能区分肌肉和脂肪。因此，肌肉发达的人可能 BMI 较高，但体脂并未超标。
9. Monohybrid Inheritance Ratio | 单基因杂交遗传比率
Monohybrid inheritance involves a single characteristic controlled by one gene with two alleles. When two heterozygous individuals are crossed, the characteristic appears in offspring in a predictable phenotype ratio.
单基因杂交关注由一对等位基因控制的性状。当两个杂合个体交配时，子代性状出现的表型比例是可以预测的。
ross between two heterozygous tall plants (Tt × Tt) produces the following Punnett square:
以豌豆植株的高茎（T，显性）和矮茎（t，隐性）为例，两株杂合高茎豌豆异交（Tt × Tt）可得如下庞纳特方格：
| T | t | |
|---|---|---|
| T | TT | Tt |
| t | Tt | tt |
The genotype ratio is 1 TT : 2 Tt : 1 tt, and the phenotype ratio is 3 tall : 1 dwarf. This classic 3:1 ratio appears whenever two heterozygotes are crossed for a trait showing complete dominance.
基因型比例为 1 TT : 2 Tt : 1 tt，表型比例为 3 高 : 1 矮。在任何显性完全的单基因性状中，两个杂合子杂交均会出现这个经典 3:1 比例。
10. Factors Affecting Diffusion Rate | 影响扩散速率的因素
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration. The rate at which diffusion occurs depends on several physical conditions.
扩散是粒子从高浓度区域向低浓度区域的净移动，其速率受若干物理条件影响。
- Concentration gradient – a steeper gradient gives faster diffusion.
- Temperature – higher temperature increases kinetic energy, so particles move and diffuse more quickly.
- Surface area – a larger surface area allows more particles to cross at the same time, increasing the rate.
- Diffusion distance – a shorter distance means less time for particles to travel, so diffusion is faster.
These relationships can be remembered qualitatively: diffusion is fast when the gradient is steep, the system is warm, the membrane area is large and the barrier is thin.
- 浓度梯度 – 梯度越陡，扩散越快。
- 温度 – 温度升高使粒子动能增加，移动和扩散都加快。
- 表面积 – 较大的表面积能让更多粒子同时通过，从而提高速率。
- 扩散距离 – 距离越短，粒子移动耗时越少，扩散越快。
这些关系可定性记忆：浓度梯度大、温度高、膜面积大、屏障薄时，扩散速率就高。
11. Optimum Conditions for Enzyme Activity | 酶活性的最适条件
Enzymes are biological catalysts that speed up reactions without being used up. Each enzyme has an optimum temperature and pH at which its activity is highest.
酶是生物催化剂，能在不消耗自身的情况下加速反应。每种酶都有其活性最高的最适温度和最适 pH。
For most human enzymes
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