📚 Year 7 CIE Biology: Formula & Theorem Quick Reference Handbook | Year 7 CIE 生物：公式定理速查手册
This quick reference handbook compiles the essential formulas, word equations, and key biological principles (often referred to as 'theorems' in a broader sense) that every Year 7 student following the CIE Lower Secondary Science curriculum needs to master. From the word equations for life processes to the rules governing energy transfer in ecosystems, having these at your fingertips will sharpen your exam responses and deepen your understanding of practical work. Treat this as your go-to revision tool for building confidence in biology.
这本速查手册汇编了 Year 7 学生在 CIE 初中科学课程中必须掌握的基本公式、文字方程和关键生物学原理（广义上常被视为“定理”）。从生命过程的文字方程到生态系统能量传递的法则，随时查阅这些内容将使你的考试作答更精准，同时加深对实验操作的理解。把它当作你的首选复习工具，帮你在生物学中建立信心。
1. The Word Equation for Photosynthesis | 光合作用文字方程
Photosynthesis is the process by which green plants, algae, and some bacteria use light energy to convert carbon dioxide and water into glucose (a sugar) and oxygen. It takes place in chloroplasts, which contain the green pigment chlorophyll. The overall word equation summarises the reactants and products.
光合作用是绿色植物、藻类和一些细菌利用光能将二氧化碳和水转化成葡萄糖（一种糖）和氧气的过程。它发生在含有绿色色素叶绿素的叶绿体中。总的文字方程式概括了反应物和生成物。
carbon dioxide + water → glucose + oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
Light energy and chlorophyll are required but do not appear in the word equation as substances. Remember that the arrow indicates the direction of the reaction, and glucose is used by the plant for energy and growth, while oxygen is released as a waste product or used in respiration.
光能和叶绿素是必需的，但不出现在文字方程式中作为物质。记住箭头表示反应的方向，葡萄糖被植物用于能量和生长，而氧气作为废弃物释放，或用于呼吸作用。
2. The Word Equation for Aerobic Respiration | 有氧呼吸文字方程
Aerobic respiration is the process by which living cells release energy from glucose in the presence of oxygen. It occurs continuously in the mitochondria of plant and animal cells. The word equation shows the breakdown of glucose to release energy for life processes such as movement, growth, and repair.
有氧呼吸是活细胞在氧气存在下从葡萄糖中释放能量的过程。它持续发生在植物和动物细胞的线粒体中。文字方程显示了葡萄糖的分解，以释放用于运动、生长和修复等生命过程的能量。
glucose + oxygen → carbon dioxide + water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
Note that carbon dioxide and water are the waste products, while energy is released and stored in a molecule called ATP for cellular work. Some textbooks write 'energy released' next to the products. This equation is essentially the reverse of photosynthesis, but the energy involved comes from chemical bonds, not light.
请注意二氧化碳和水是废弃物，而能量被释放并储存在称为ATP的分子中，供细胞工作使用。有些教科书在产物旁写“释放能量”。这个方程本质上是光合作用的逆向过程，但涉及的能量来自化学键而非光。
3. Magnification Formula (Microscopy) | 放大倍数公式（显微镜）
When using a light microscope, the total magnification of the image you see is calculated by multiplying the magnification of the eyepiece lens by the magnification of the objective lens. This formula allows you to determine how many times larger the specimen appears compared to its actual size.
使用光学显微镜时，你所见图像的总放大倍数是用目镜放大倍数乘以物镜放大倍数来计算的。这个公式能帮助你确定标本比实际尺寸放大了多少倍。
total magnification = eyepiece lens magnification × objective lens magnification
总放大倍数 = 目镜放大倍数 × 物镜放大倍数
the total magnification is 10 × 40 = 400×. This multiplication principle is a fundamental 'theorem' for all microscopy work and appears frequently in practical assessments.
例如，如果目镜放大10×，物镜放大40×，总放大倍数为 10 × 40 = 400×。这一乘法原理是所有显微镜工作的一项基本“定理”，在实验考核中频繁出现。
4. Calculating Breathing Rate and Pulse Rate | 呼吸率和脉搏率的计算
Breathing rate (ventilation rate) is the number of breaths taken per minute. Pulse rate (heart rate) is the number of heartbeats per minute. These are vital measures of how the body responds to exercise and maintains homeostasis. Both follow a simple ratio formula.
呼吸率（通气率）是每分钟呼吸的次数。脉搏率（心率）是每分钟心跳的次数。它们是衡量身体如何应对运动并维持稳态的重要指标。两者都遵循简单的比率公式。
breathing rate (breaths/min) = number of breaths ÷ time (minutes)
呼吸率（次/分钟） = 呼吸次数 ÷ 时间（分钟）
pulse rate (beats/min) = number of beats ÷ time (minutes)
脉搏率（次/分钟） = 心跳次数 ÷ 时间（分钟）
When recording results, always ensure the time unit is consistent; for example, count for 30 seconds and multiply by 2 to obtain a rate per minute. An increased breathing and pulse rate during exercise reflects the higher demand for oxygen and the need to remove carbon dioxide faster.
记录结果时，务必确保时间单位一致；例如，数30秒然后乘以2得到每分钟的速率。运动时呼吸和脉搏率升高，反映了对氧气需求的增加以及更快移除二氧化碳的需要。
5. Energy Transfer in Food Chains (The 10% Rule) | 食物链中的能量传递（10%法则）
Energy flows through an ecosystem from producers to consumers. A consistent ecological 'theorem' states that only about 10% of the energy at one trophic level is transferred to the next level. The remaining 90% is lost mainly through heat from respiration, movement, and waste materials.
能量通过生态系统从生产者流向消费者。一条恒定的生态学“定理”指出，某一营养级的能量只有大约10%传递到下一级。剩下的90%主要通过呼吸产热、运动和排泄物散失。
energy available at next level ≈ 10% of energy at current level
下一营养级可用能量 ≈ 当前营养级能量的10%
This rule explains why food chains rarely have more than four or five trophic levels — there simply is not enough energy to support another layer of consumers. You can apply this principle when interpreting pyramids of energy or biomass, although exact percentages may vary slightly.
这条法则解释了为什么食物链很少有超过四到五个营养级——根本没有足够的能量来支撑再多一层的消费者。你在解读能量锥体或生物量锥体时可以应用这一原理，尽管精确百分比可能略有变化。
6. Surface Area to Volume Ratio (SA:V) | 表面积与体积比（SA:V）
For any cell or organism, the surface area to volume ratio is a critical factor affecting how substances move in and out. As an object gets larger, its volume increases much faster than its surface area, causing the SA:V ratio to decrease. This is often expressed as a simple division.
对于任何细胞或生物体，表面积与体积比是影响物质进出方式的关键因素。当物体变大时，其体积增长远比表面积增长快，导致SA:V比降低。这通常表示为一个简单的除法。
surface area : volume = surface area ÷ volume
表面积 : 体积 = 表面积 ÷ 体积
Single-celled organisms like amoeba have a very large SA:V ratio, allowing efficient diffusion of oxygen and nutrients directly across their cell membrane. Larger multicellular organisms need specialised exchange surfaces (e.g., lungs, gills) and transport systems because their SA:V ratio is too small to rely on diffusion alone.
像变形虫这样的单细胞生物具有非常大的SA:V比，使氧气和营养物质能直接通过细胞膜高效扩散。较大的多细胞生物则需要特化的交换表面（如肺、鳃）和运输系统，因为它们的SA:V比太小，无法仅依赖扩散。
7. Diffusion and Concentration Gradient | 扩散与浓度梯度
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration, down a concentration gradient. While not a strict mathematical formula at Year 7, the relationship can be expressed as a proportionality: the rate of diffusion increases when the concentration gradient is steeper, the surface area is larger, or the distance is shorter.
扩散是粒子从高浓度区域向低浓度区域的净移动，沿着浓度梯度进行。虽然在 Year 7 阶段还不是严格的数学公式，但这种关系可以表示为一个比例关系：浓度梯度越陡峭、表面积越大或距离越短，扩散速率就越快。
rate of diffusion ∝ (surface area × concentration difference) ÷ distance
扩散速率 ∝ （表面积 × 浓度差） ÷ 距离
This 'theorem' underpins many biological processes, from gas exchange in leaves and lungs to the absorption of digested food. Students should remember that diffusion is a passive process requiring no energy from the cell.
这条“定理”支撑了许多生物学过程，从叶片和肺的气体交换到消化后食物的吸收。学生应记住，扩散是一种被动过程，不需要细胞提供能量。
8. Energy Values of Nutrients (kJ per gram) | 营养素能量值（千焦每克）
Different food groups provide different amounts of energy when respired. In human nutrition, an important set of conversion factors allows you to estimate the energy content of a meal based on its mass of carbohydrates, proteins, and fats. These values are treated as standard constants.
不同的食物组在呼吸作用时提供不同量的能量。在人体营养学中，一组重要的转换因子可让你根据碳水化合物、蛋白质和脂肪的质量来估算一餐的能量含量。这些数值被视为标准常数。
| Nutrient (营养素) | Energy (能量) |
|---|---|
| Carbohydrate (碳水化合物) | 17 kJ/g |
| Protein (蛋白质) | 17 kJ/g |
| Fat (脂肪) | 38 kJ/g |
al energy (kJ) = (mass of carbohydrate × 17) + (mass of protein × 17) + (mass of fat × 38)
总能量（千焦） = （碳水化合物质量 × 17） + （蛋白质质量 × 17） + （脂肪质量 × 38）
you to compare the energy density of different foods and understand why fats are so energy-rich.
例如，一份含有10克碳水化合物、5克蛋白质和2克脂肪的零食提供 (10×17)+(5×17)+(2×38) = 170 + 85 + 76 = 331 千焦能量。这个公式让你能够比较不同食物的能量密度，并理解为何脂肪含能如此之高。
9. The Pyramid of Numbers and the Pyramid of Biomass | 数量锥体与生物量锥体
Ecologists represent feeding relationships not only with food chains but also with pyramids of numbers and pyramids of biomass. The shape of these pyramids can be predicted using a simple theorem: typically, the biomass of producers is greater than that of primary consumers, and so on, due to the 10% energy transfer rule, though pyramids of numbers can sometimes be inverted.
生态学家不仅用食物链，还用数量锥体和生物量锥体来表示摄食关系。这些锥体的形状可以用一个简单的定理来预测：由于10%的能量传递法则，生产者的生物量通常大于初级消费者，以此类推，尽管数量锥体有时可能是倒置的。
biomass at level n+1 < biomass at level n (normally)
第n+1营养级的生物量 < 第n营养级的生物量（通常情况）
In drawing a pyramid of biomass, each bar is proportional to the total mass of living organisms at that trophic level. When accurate data is unavailable, this inequality theorem helps you predict the correct relative sizes of the bars. Remember that a single large tree can be a producer, yet many insects feeding on it may result in an odd-looking pyramid of numbers, but the pyramid of biomass will almost always be pyramid-shaped.
绘制生物量锥体时，每个条形图都与该营养级生物的总质量成比例。当没有精确数据时，这条不等式定理可以帮助你预测条形图的正确相对大小。记住，一棵大树可以是生产者，但许多以它为食的昆虫可能导致奇怪的数量锥体形状，不过生物量锥体几乎总是呈金字塔形。
10. Key Principles of Cells (Cell Theory Summary) | 细胞关键原理（细胞学说概要）
The cell theory, a cornerstone biological 'theorem', consists of three statements that apply to all living organisms. It provides the framework for understanding structure and function at microscopic level and is referenced throughout Year 7 topics such as specialised cells, tissues, and unicellular life.
细胞学说，作为一项基石性的生物“定理”，由三条适用于所有生物的陈述组成。它为从微观层面理解结构和功能提供了框架，并在 Year 7 的专题（如特化细胞、组织和单细胞生命）中反复被引用。
First, all living things are made up of one or more cells. | 首先，所有生物都由一个或多个细胞组成。
Second, the cell is the basic structural and functional unit of all organisms. | 第二，细胞是所有生物体结构和功能的基本单位。
Third, all cells arise from pre-existing cells through cell division. | 第三，所有细胞均来自已存在的细胞，通过细胞分裂产生。
These statements are not mathematical formulas, but they function as fundamental biological laws. When you study the life processes summarised by 'MRS GREN' (Movement, Respiration, Sensitivity, Growth, Reproduction, Excretion, Nutrition), you are applying cell theory to understand how cells carry out these functions.
这些陈述虽不是数学公式，但它们如同基本的生物学定律。当你学习用“MRS GREN”（运动、呼吸、感应、生长、繁殖、排泄、营养）概括的生命过程时，你就是在应用细胞学说来理解细胞如何执行这些功能。
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