📚 Year 9 Cambridge Biology: Formula & Theorem Quick Reference Handbook | 九年级剑桥生物：公式定理速查手册
In Year 9 Cambridge Biology, mastering key formulas and quantitative relationships is just as important as understanding concepts. This quick reference handbook pulls together essential equations, ratios, and rules that you are likely to need for calculations, data analysis, and exam questions. From microscope work and energy flow in ecosystems to genetics and human physiology, these tools will help you strengthen your scientific reasoning and secure marks on numerical problems.
在九年级剑桥生物课程中，掌握关键公式和定量关系与理解概念同样重要。这本速查手册汇总了你在计算题、数据分析以及考试中可能会用到的核心方程式、比例和定律。从显微镜操作、生态系统能量流动到遗传学与人体生理学，这些工具将帮助你强化科学推理能力，并在数值类题目中稳稳拿分。
1. Magnification | 放大倍数
Magnification is how much larger an image appears compared to the real object. The formula links image size, actual size, and magnification in a simple triangle relationship.
放大倍数指的是图像相比实物放大了多少。该公式将图像尺寸、实际尺寸和放大倍数联系成一个简单的三角关系。
Always use the same units for image size and actual size (usually millimetres or micrometres). Convert units before calculating.
图像尺寸和实际尺寸务必使用相同单位（通常为毫米或微米）。计算前需先统一单位。
Magnification = Image size ÷ Actual size
放大倍数 = 图像尺寸 ÷ 实际尺寸
- Image size = size of the specimen in a drawing or photograph
- Actual size = real size of the specimen
- 图像尺寸 = 图或照片中标本的尺寸
- 实际尺寸 = 标本的真实尺寸
cation, you can find actual size by rearranging: Actual size = Image size ÷ Magnification.
若已知放大倍数，可变形为：实际尺寸 = 图像尺寸 ÷ 放大倍数。
2. Scale Bar Conversion | 比例尺换算
A scale bar on a micrograph or diagram represents a known actual length. Measuring the scale bar length in the image allows you to calculate how many micrometres per millimetre the drawing represents.
显微照片或示意图上的比例尺代表已知的实际长度。测量图像中比例尺的长度，便可计算出该图每毫米代表多少微米。
Measure the scale bar in mm, note its real length in µm, then find the conversion factor. This factor can then be applied to any structure in the same image.
先以毫米为单位测量比例尺的长度，记录其真实长度（微米），再求出换算系数。此系数可用于同一图像中的任何结构。
Scale factor (µm/mm) = Real length of scale bar (µm) ÷ Measured length of scale bar (mm)
换算系数（微米/毫米） = 比例尺真实长度（微米） ÷ 测得的比例尺长度（毫米）
Then, actual length of specimen (µm) = Measured length of specimen in image (mm) × Scale factor (µm/mm).
随后，标本实际长度（微米）= 图像中标本测量长度（毫米）× 换算系数（微米/毫米）。
3. Photosynthesis Equation | 光合作用方程式
Photosynthesis is the process by which green plants and some other organisms use light energy to convert carbon dioxide and water into glucose and oxygen. The balanced word and chemical equations summarise the inputs and outputs.
光合作用是绿色植物及某些生物利用光能将二氧化碳和水转化为葡萄糖和氧气的过程。以下文字方程和化学方程式概括了反应物和生成物。
Word equation:
Carbon dioxide + Water → Glucose + Oxygen
文字方程式：
二氧化碳 + 水 → 葡萄糖 + 氧气
Balanced chemical equation:
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
化学方程式：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
The reaction requires light energy and chlorophyll. Glucose is often stored as starch or used in respiration.
该反应需要光能和叶绿素。葡萄糖通常以淀粉形式储存，或用于呼吸作用。
4. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration takes place in mitochondria, using oxygen to release energy from glucose. The overall reaction is effectively the reverse of photosynthesis, but it releases energy for cellular activities.
有氧呼吸发生在线粒体中，利用氧气从葡萄糖释放能量。其总反应实质上是光合作用的逆过程，但会为细胞活动释放能量。
Word equation:
Glucose + Oxygen → Carbon dioxide + Water (+ energy)
文字方程式：
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
Balanced chemical equation:
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
化学方程式：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Energy released is used to form ATP, which powers processes such as muscle contraction, active transport, and growth.
释放的能量用于合成ATP，为肌肉收缩、主动运输和生长等过程供能。
5. Energy Transfer in Food Chains (10% Rule) | 食物链能量传递（10%定律）
As energy flows from one trophic level to the next, only a small proportion is transferred to the consumer level. The rest is lost through respiration, waste, and uneaten parts. A useful rule of thumb is that approximately 10% of the energy is passed on.
能量沿营养级流动时，只有一小部分能被传递至消费级。其余能量通过呼吸、排泄物和未被取食的部分散失。一个有用的经验法则是：约10%的能量会被传递给下一级。
If the producer level contains 10,000 kJ, the primary consumer might receive 1,000 kJ, the secondary consumer 100 kJ, and so on. This explains why food chains rarely exceed four or five trophic levels.
若生产者营养级含有10,000 kJ能量，初级消费者可能获得1,000 kJ，次级消费者100 kJ，以此类推。这解释了为何食物链很少超过四到五个营养级。
Energy transfer efficiency (%) = (Energy available to next level ÷ Energy available to current level) × 100
能量传递效率（%）=（传递给下一级的能量 ÷ 本级的可用能量）× 100
6. Mark-Release-Recapture (Lincoln Index) | 标记重捕法（林肯指数）
This method estimates the population size of mobile organisms. A sample is caught, marked, and released. Later, a second sample is captured, and the number of marked individuals is counted.
此方法用于估算移动生物的种群大小。先捕捉一批个体，标记后释放；随后再捕捉第二批样本，统计其中已标记的个体数。
The Lincoln Index formula assumes the proportion of marked animals in the second sample equals the proportion of marked animals in the whole population.
林肯指数公式假设：二次样本中已标记动物的比例，等于整个种群中已标记动物的比例。
N = (M × C) ÷ R
种群数量 N = （M × C） ÷ R
- N = estimated total population size | 估计的种群总数量
- M = number of individuals originally marked and released | 首次标记并释放的个体数
- C = total number captured in the second sample | 第二次捕获的总个体数
- R = number of recaptured (marked) individuals in the second sample | 第二次捕获中带标记的个体数
For accuracy, assumptions must be met: the population is closed, marks are not lost, marking does not affect survival, and mixing is random.
为确保准确性，需满足以下假设：种群封闭、标记不会脱落、标记不影响存活，且个体随机混合。
7. Mendelian Genetics Ratios | 孟德尔遗传比例
Gregor Mendel' cross between two heterozygous parents (Tt × Tt) yields a characteristic phenotype ratio.
孟德尔在豌豆实验中揭示了显隐性单基因性状的遗传规律。两个杂合亲本（Tt × Tt）的单基因杂交会呈现特征性的表现型比例。
Monohybrid cross F2 phenotype ratio:
Dominant : Recessive = 3 : 1
单基因杂交F2表现型比例：
显性性状 : 隐性性状 = 3 : 1
RrYy × RrYy) and the genes are unlinked, the expected phenotype ratio in the offspring is:
若同时观察两个性状（双基因杂交，如RrYy × RrYy），且基因位于不同染色体上，则子代表现型比例为：
9 : 3 : 3 : 1
These ratios assume complete dominance, no gene interaction, independent assortment, and large sample sizes.
这些比例基于完全显性、无基因互作、自由组合以及较大的样本量。
8. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle of the heart per minute. It links heart rate and stroke volume, and it is a fundamental parameter in understanding how the circulatory system responds to exercise.
心输出量是指一个心室每分钟泵出的血液体积。它将心率与每搏输出量联系在一起，是理解循环系统如何应对运动的基本参数。
Cardiac output (ml/min) = Heart rate (beats/min) × Stroke volume (ml/beat)
心输出量（毫升/分钟） = 心率（次/分钟） × 每搏输出量（毫升/次）
- Heart rate: number of heartbeats per minute
- Stroke volume: volume of blood ejected per beat
- 心率：每分钟心跳次数
- 每搏输出量：每次心跳泵出的血液体积
During exercise, both heart rate and stroke volume can increase, significantly raising cardiac output to meet oxygen demand.
运动时，心率和每搏输出量均可增加，从而大幅提升心输出量以满足氧气需求。
9. Body Mass Index (BMI) | 身体质量指数
BMI is a simple measure used to classify whether a person has a healthy body weight for a given height. It is calculated using mass and height and is widely used in studies of nutrition and health.
身体质量指数（BMI）是一项简单指标，用于评估体重相对于身高是否在健康范围内。它通过体重和身高计算得出，广泛应用于营养与健康研究。
BMI = Body mass (kg) ÷ Height² (m²)
BMI = 体重（千克） ÷ 身高²（米²）
Metric interpretation for adults: underweight (below 18.5), normal weight (18.5–24.9), overweight (25–29.9), obese (30 and above). For children, percentiles are used to account for age and sex.
成年人的数值解读：偏瘦（低于18.5）、正常（18.5–24.9）、超重（25–29.9）、肥胖（30及以上）。儿童则需按年龄和性别使用百分位数曲线来判断。
10. Enzyme Activity & Q10 Temperature Coefficient | 酶活性与Q10温度系数
Enzyme-catalysed reactions are sensitive to temperature. The Q10 temperature coefficient quantifies the change in reaction rate when the temperature is increased by 10°C. It is a useful way to compare the effect of temperature on biological reactions.
酶促反应对温度敏感。Q10温度系数量化了温度每升高10°C时反应速率的变化。这是比较温度对生物化学反应影响的有效方式。
For many enzyme reactions, Q10 is close to 2 (i.e., rate doubles) between 0°C and the optimum temperature. Beyond the optimum, denaturation causes reaction rates to drop sharply.
对许多酶促反应来说，在0°C至最适温度之间，Q10接近2（即速率翻倍）。一旦超过最适温度，酶变性会导致反应速率急剧下降。
Q10 = Rate at (T + 10)°C ÷ Rate at T°C
Q10 = (T + 10)°C下的反应速率 ÷ T°C下的反应速率
This equation is only meaningful in the temperature range where the enzyme is still functional. It applies to any temperature-controlled biological process, such as respiration or photosynthesis rate measurements.
该方程仅适用于酶仍具活性的温度范围。它也可以用于受温度调控的生物学过程，如呼吸作用或光合作用速率的测量。
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