Year 9 Cambridge Biology: Formula & Theorem Quick-Reference Handbook | Year 9 剑桥生物：公式定理速查手册

📚 Year 9 Cambridge Biology: Formula & Theorem Quick-Reference Handbook | Year 9 剑桥生物：公式定理速查手册

This handbook gathers all the essential formulas, word equations, chemical equations and key biological principles required for Year 9 Cambridge Biology. Use it to revise effectively and to check your understanding before assessments.

本手册汇集了 Year 9 剑桥生物所需的所有关键公式、文字方程式、化学方程式和重要生物学原理，可用于高效复习并在评估前检查自己的理解程度。

1. Magnification Formula | 放大率公式

When you observe specimens under a microscope, you often need to calculate the magnification or the real size of an object. The relationship between image size, actual size and magnification is straightforward.

在显微镜下观察标本时，你经常需要计算放大倍数或物体的真实大小。图像尺寸、实际尺寸和放大率之间的关系很简单。

Magnification = Image size ÷ Actual size

放大率 = 图像尺寸 ÷ 实际尺寸

Always check that both measurements use the same unit, and remember common conversions: 1 mm = 1000 µm (micrometres).

一定要确保两个测量值使用相同的单位，并记住常见的换算：1 mm = 1000 µm（微米）。

Image size is the length you measure with a ruler on a diagram or photograph.
图像尺寸是你用尺子在示意图或照片上测得的长度。
Actual size is the true length of the biological specimen.
实际尺寸是生物标本的真实长度。
To find image size, rearrange the formula: Image size = Magnification × Actual size.
要计算图像尺寸，可进行公式变形：图像尺寸 = 放大率 × 实际尺寸。
To find actual size, use: Actual size = Image size ÷ Magnification.
要计算实际尺寸，则使用：实际尺寸 = 图像尺寸 ÷ 放大率。

2. Photosynthesis Equation | 光合作用方程式

Photosynthesis is the process by which plants and some bacteria convert light energy into chemical energy. The overall word equation and balanced chemical equation are must-know fundamentals.

光合作用是植物和某些细菌将光能转化为化学能的过程。其总文字方程式和配平的化学方程式是必须掌握的基础内容。

Word equation:

文字方程式：

Carbon dioxide + Water → Glucose + Oxygen

二氧化碳 + 水 → 葡萄糖 + 氧气

Balanced chemical equation:

配平的化学方程式：

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂

The reaction only takes place in the presence of light and chlorophyll. Light provides the energy, and chlorophyll is the green pigment that absorbs sunlight inside chloroplasts.

该反应只有在光能和叶绿素存在时才能进行。光提供能量，叶绿素是叶绿体内吸收阳光的绿色色素。

Three limiting factors control the rate of photosynthesis: light intensity, carbon dioxide concentration and temperature.

有三个限制因素控制光合作用速率：光照强度、二氧化碳浓度和温度。

3. Aerobic Respiration Equation | 有氧呼吸方程式

Aerobic respiration releases energy from glucose in the presence of oxygen. It occurs continuously in most living cells to power life processes.

有氧呼吸在有氧气存在的条件下从葡萄糖中释放能量。该过程在大多数活细胞中持续不断地进行，为生命活动提供动力。

Word equation:

文字方程式：

Glucose + Oxygen → Carbon dioxide + Water (+ energy)

葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）

Balanced chemical equation:

配平的化学方程式：

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP

The energy is released in the form of ATP (adenosine triphosphate), which is used for muscle contraction, cell division, protein synthesis and maintaining body temperature in mammals.

能量以 ATP（三磷酸腺苷）的形式释放，用于肌肉收缩、细胞分裂、蛋白质合成以及哺乳动物维持体温等过程。

4. Anaerobic Respiration in Yeast (Fermentation) | 酵母菌无氧呼吸（发酵）

When oxygen is absent, yeast can still release energy from glucose through anaerobic respiration, which produces ethanol and carbon dioxide. This process is economically important for baking and brewing.

在无氧的情况下，酵母菌依然可以通过无氧呼吸从葡萄糖中释放能量，并产生乙醇和二氧化碳。这一过程在面包制作和酿酒中具有重要的经济价值。

Word equation:

文字方程式：

Glucose → Ethanol + Carbon dioxide (+ some energy)

葡萄糖 → 乙醇 + 二氧化碳（+ 少量能量）

Balanced chemical equation:

配平的化学方程式：

C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂

The carbon dioxide gas makes dough rise, while the ethanol evaporates during baking. In brewing, ethanol is the desired product.

二氧化碳气体使面团膨胀，而乙醇在烘烤过程中会挥发。在酿酒业中，乙醇则是目标产物。

5. Anaerobic Respiration in Animals | 动物无氧呼吸

During intense exercise, muscle cells may not receive enough oxygen to meet energy demands. They then respire anaerobically, producing lactic acid instead of ethanol.

在剧烈运动期间，肌肉细胞可能无法获得足够氧气满足能量需求，这时它们就进行无氧呼吸，产生乳酸而不是乙醇。

Word equation:

文字方程式：

Glucose → Lactic acid (+ some energy)

葡萄糖 → 乳酸（+ 少量能量）

Chemical equation:

化学方程式：

C₆H₁₂O₆ → 2C₃H₆O₃

Lactic acid builds up in the muscles, causing fatigue and cramps. After exercise, extra oxygen is needed to break down the lactic acid – this is known as the oxygen debt.

乳酸在肌肉中积累，导致疲劳和抽筋。运动后需要额外摄入氧气来分解乳酸，这就是所谓的氧债。

6. Energy Content of Food | 食物能量计算

You can estimate the energy stored in a food sample by burning it and using the heat released to raise the temperature of a known mass of water. The result is often expressed as energy per gram of food.

你可以通过燃烧食物样本并利用释放的热量加热已知质量的水来估算储存的能量，结果通常表示为每克食物所含的能量。

The energy transferred to the water is calculated first:

首先计算传递给水的能量：

Energy (J) = mass of water (g) × 4.2 J/g°C × temperature rise (°C)

能量（J）= 水的质量（g）× 4.2 J/g°C × 温度上升值（°C）

Then, to find the energy per gram of food, use:

然后，要计算每克食物含有的能量，使用以下公式：

Energy per gram (J/g) = Energy (J) ÷ mass of food sample (g)

每克能量（J/g）= 能量（J）÷ 食物样本的质量（g）

The constant 4.2 J/g°C is the specific heat capacity of water: it takes 4.2 joules to raise the temperature of 1 gram of water by 1 °C. In an examination, you may need to comment on experimental errors such as heat loss to the surroundings.

常数 4.2 J/g°C 是水的比热容：使 1 克水温升高 1 °C 需要 4.2 焦耳的能量。在考试中，你可能需要讨论实验误差，例如向周围环境散失的热量。

7. Enzyme Properties and the Lock-and-Key Model | 酶的性质与锁钥模型

Enzymes are biological catalysts that speed up metabolic reactions without being used up. They are globular proteins with an active site that is complementary to a specific substrate.

酶是生物催化剂，能加快代谢反应而自身不被消耗。它们是球状蛋白质，其活性部位与特定底物互补。

The Lock-and-Key theory states that the substrate fits precisely into the enzyme’s active site, just as a key fits a lock. The reaction occurs, and products are released.

锁钥模型指出，底物恰好能嵌入酶的活性部位，就像钥匙开锁一样。反应发生后，产物被释放出来。

Key properties to remember:

需要记住的关键性质：

Enzymes lower the activation energy of a reaction.
酶能降低反应的活化能。
Each enzyme only catalyses one type of reaction (specificity).
每种酶只催化一种类型的反应（专一性）。
Enzyme activity is affected by temperature: activity increases up to an optimum temperature, then the enzyme denatures and activity drops sharply.
酶的活性受温度影响：活性随温度升高而增加，达到最适温度后酶会变性，活性急剧下降。
pH also influences activity; each enzyme has an optimum pH (e.g. pepsin works best at pH 2, amylase at pH 7).
pH 也会影响活性；每种酶都有最适 pH（例如胃蛋白酶的最适 pH 约为 2，淀粉酶约为 7）。

8. Diffusion, Osmosis and Active Transport | 扩散、渗透和主动运输

Cells move substances across membranes using three main processes. It is essential to distinguish among them, especially for Year 9 exams.

细胞通过三种主要过程跨膜运输物质。区分这三者至关重要，尤其是在 Year 9 考试中。

Feature / 特征	Diffusion 扩散	Osmosis 渗透	Active Transport 主动运输
Definition 定义	Net movement of particles from a region of high concentration to low concentration. 粒子从高浓度区域向低浓度区域的净移动。	Net movement of water molecules through a partially permeable membrane from a region of high water potential to low water potential. 水分子通过半透膜从高水势区域向低水势区域的净移动。	Movement of molecules against a concentration gradient, from low to high concentration. 分子逆浓度梯度从低浓度到高浓度的移动。
Energy required? 需要能量？	No – passive process. 否 – 被动过程。	No – passive process. 否 – 被动过程。	Yes – requires ATP. 是 – 需要 ATP。
Protein carriers? 载体蛋白？	Not usually required (simple diffusion). 通常不需要（简单扩散）。	No, uses special channel proteins called aquaporins. 否，但使用称为水通道蛋白的特殊通道蛋白。	Yes, specific carrier proteins are essential. 是，特定的载体蛋白不可或缺。
Example 例子	Oxygen diffusing into red blood cells in the lungs. 氧气在肺部扩散进入红细胞。	Water uptake by root hair cells from the soil. 根毛细胞从土壤中吸收水分。	Absorption of mineral ions by root hairs from dilute soil solutions. 根毛从稀薄的土壤溶液中吸收矿物质离子。

In osmosis, a plant cell placed in pure water becomes turgid; an animal cell may burst. In a concentrated solution, plant cells become plasmolysed and animal cells shrink.

在渗透作用中，置于纯水中的植物细胞会变得饱满（硬挺）；动物细胞则可能破裂。在浓溶液中，植物细胞会发生质壁分离，动物细胞会皱缩。

9. Food Test Identification Table | 食物测试鉴定表

Laboratory tests allow you to identify the presence of specific nutrients in food samples. The following table summarises the standard test methods for starch, reducing sugars, protein and lipids.

通过实验室检测可以确定食物样本中特定营养物质的存在。下表总结了淀粉、还原糖、蛋白质和脂肪的标准测试方法。

Nutrient 营养素	Reagent / Test 试剂 / 测试	Procedure 操作	Positive result 阳性结果
Starch 淀粉	Iodine solution 碘液	Add a few drops to the sample. 向样本滴加几滴。	Blue-black colour 蓝黑色
Reducing sugars (e.g. glucose) 还原糖（如葡萄糖）	Benedict’s solution 本尼迪克特试剂	Add solution, heat in a water bath (80 °C+). 加入试剂，在热水浴中加热（80 °C 以上）。	Green → yellow → brick-red precipitate 绿色 → 黄色 → 砖红色沉淀
Protein 蛋白质	Biuret reagent (sodium hydroxide + copper sulfate) 双缩脲试剂（氢氧化钠 + 硫酸铜）	Add Biuret A then Biuret B, shake gently. 先加双缩脲 A 液，再加 B 液，轻轻摇匀。	Lilac / purple colour 淡紫色 / 紫色
Lipids (fats) 脂类（脂肪）	Ethanol emulsion test 乙醇乳液测试	Mix with ethanol, then add water and shake. 加入乙醇混合，然后加入水并振荡。	Cloudy white emulsion 乳白色浑浊乳液

Always use a fresh sample for each test, and remember that the Benedict’s test is semi-quantitative – the amount of precipitate indicates the concentration of reducing sugar.

每次测试都应使用新鲜的样本，并记住本尼迪克特试验是半定量的——沉淀的量反映了还原糖的浓度高低。

10. Cell Theory and Microscopy | 细胞学说与显微镜使用

Cell theory is a fundamental concept that unites all living organisms. You need to know its main points and how microscopy supports the study of cells.

细胞学说是统一所有生物体的基本概念。你需要了解其主要观点以及显微镜如何支持细胞的研究。

All living things are composed of one or more cells.
所有生物都由一个或多个细胞构成。
The cell is the basic unit of structure and function in organisms.
细胞是生物体结构和功能的基本单位。
All cells arise from pre-existing cells by cell division.
所有细胞都通过细胞分裂来自已有的细胞。

When preparing a specimen for the light microscope, you place a thin sample on a glass slide, add a drop of water or stain, and gently lower a coverslip to avoid air bubbles.

为光学显微镜准备标本时，要把薄的样本放在载玻片上，滴加一滴水或染色剂，然后轻轻放下盖玻片以避免气泡。

Stain such as methylene blue (for animal cells) and iodine solution (for plant cells) help make structures like the nucleus and cell wall visible. Remember that you can use the magnification formula from Section 1 to calculate sizes.

亚甲基蓝（用于动物细胞）和碘液（用于植物细胞）等染色剂有助于看清细胞核和细胞壁等结构。别忘了你可以使用第 1 节中的放大率公式来计算尺寸。

11. The Human Circulatory System | 人体循环系统定理

The human cardiovascular system is a double circulatory system, meaning that blood passes through the heart twice in one complete circuit. This is a key principle for Year 9 biology.

人体心血管系统是一个双循环系统，这意味着血液在一次完整的循环路径中会两次经过心脏。这是 Year 9 生物的一个关键原理。

Sequence of blood flow through the heart (deoxygenated blood):

血液流经心脏的顺序（脱氧血）：

Vena cava → Right atrium → Right ventricle → Pulmonary artery → Lungs

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Year 9 Cambridge Biology: Formula & Theorem Quick-Reference Handbook | Year 9 剑桥生物：公式定理速查手册