📚 Year 7 CIE Biology: Formulae & Theorems Quick Reference Handbook | 7年级 CIE 生物：公式定理速查手册
Welcome to your quick reference guide for the essential formulas, equations and core principles you need to master in Year 7 CIE Biology. This handbook summarises the key quantitative relationships and fundamental biological 'theorems' that underpin topics from cells to ecosystems. Use it for rapid revision whenever you encounter a calculation or need to recall a core concept.
欢迎使用这本为 Year 7 CIE 生物课程精心编写的核心公式与定理速查手册。它汇集了从细胞到生态系统各个主题中必须掌握的定量关系和生物学基本原理。当你需要迅速查阅计算方法或回顾核心概念时，这本手册就是你最便捷的复习伙伴。
1. The Cell Theory | 细胞学说
All living organisms are composed of one or more cells. The cell is the basic structural and functional unit of life. All cells arise from pre-existing cells by cell division.
所有生物都由一个或多个细胞组成。细胞是生命体结构与功能的基本单位。所有细胞都来自原有细胞的分裂。
These three statements form the foundation of modern biology. They apply to all organisms, whether unicellular bacteria or multicellular plants and animals.
这三条陈述构成了现代生物学的基础，适用于所有生物，无论是单细胞的细菌还是多细胞的植物和动物。
2. Microscope Magnification Formula | 显微镜放大倍数公式
To find the total magnification of a light microscope, multiply the magnifying power of the eyepiece lens by the magnifying power of the objective lens being used.
要计算光学显微镜的总放大倍数，只需将目镜的放大倍数与所用物镜的放大倍数相乘。
Total magnification = Eyepiece magnification × Objective magnification
总放大倍数 = 目镜放大倍数 × 物镜放大倍数
f the eyepiece is ×10 and the objective is ×40, the total magnification is 10 × 40 = ×400.
例如，如果目镜为 ×10，物镜为 ×40，总放大倍数就是 10 × 40 = ×400。
3. Calculating Actual Size of a Specimen | 标本实际尺寸的计算
When you view a cell or organism under a microscope, the image you see is enlarged. You can work out the real size of the object using the magnification. Remember to convert all lengths to the same unit before calculating.
在显微镜下观察细胞或生物时，看到的图像是放大的。利用放大倍数你可以计算出物体的真实尺寸。计算前务必把所有长度换算为相同单位。
Actual size = Image size ÷ Magnification
实际尺寸 = 图像尺寸 ÷ 放大倍数
nd the magnification is ×400, the actual size is 5 mm ÷ 400 = 0.0125 mm, which equals 12.5 µm. (1 mm = 1000 µm)
如果一个细胞的图像长度为 5 mm，放大倍数为 ×400，则实际尺寸为 5 mm ÷ 400 = 0.0125 mm，即 12.5 µm。（1 mm = 1000 µm）
4. 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 overall reaction can be written as a word equation or a balanced chemical equation.
光合作用是绿色植物及某些其他生物利用光能，将二氧化碳和水转化为葡萄糖和氧气的过程。总反应可以用文字方程式或平衡的化学方程式表示。
Word equation:
文字方程式：
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
Balanced symbol equation:
平衡化学方程式：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This reaction takes place in the chloroplasts and requires light energy captured by chlorophyll.
该反应在叶绿体中进行，并需要叶绿素捕获的光能。
5. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration is the process that releases energy from glucose in the presence of oxygen. It occurs continuously in the mitochondria of most living cells.
有氧呼吸是在有氧气参与的情况下，从葡萄糖中释放能量的过程。它在大多数活细胞的线粒体中持续进行。
Word equation for aerobic respiration:
有氧呼吸的文字方程式：
Glucose + Oxygen → Carbon dioxide + Water + Energy
葡萄糖 + 氧气 → 二氧化碳 + 水 + 能量
Balanced symbol equation:
平衡化学方程式：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + Energy (ATP)
The energy released is used for activities such as muscle contraction, active transport and maintaining body temperature.
释放的能量用于肌肉收缩、主动运输以及维持体温等生命活动。
6. The 10% Energy Transfer Rule | 10% 能量传递定律
In a food chain, energy is passed from one trophic level to the next. However, only about 10% of the energy stored in one level is transferred to the level above. The rest is lost as heat, through movement or in undigested waste.
在食物链中，能量会从一个营养级传递到下一个营养级。然而，大约只有10%的能量会转移到上一营养级，其余的能量以热能形式散失，或在运动和未消化的废物中损失。
Energy transferred to next level ≈ Energy at current level × 0.10
传递到下一级的能量 ≈ 本级能量 × 0.10
This rule explains why food chains rarely have more than five trophic levels and why a large number of producers is always needed to support top predators.
这一定律解释了为什么食物链的长度很少超过五个营养级，以及为什么需要大量的生产者才能支撑顶端的捕食者。
7. Population Density Formula | 种群密度公式
Ecologists often need to estimate how many individuals of a species live in a given area. Population density is a simple measure that helps compare different habitats.
生态学家经常需要估计某个物种在一定区域内的个体数量。种群密度是一种简单的度量方法，便于比较不同的栖息地。
Population density = Number of individuals ÷ Area
种群密度 = 个体数目 ÷ 面积
sies are counted in a field of 2 m², the population density is 80 ÷ 2 = 40 daisies per m².
如果在 2 平方米的田野中数到 80 朵雏菊，则种群密度为 80 ÷ 2 = 40 朵每平方米。
8. Anaerobic Respiration (Fermentation) Equations | 无氧呼吸（发酵）方程式
When oxygen is scarce or absent, cells can release a small amount of energy from glucose through anaerobic respiration. The products differ between animals and yeast.
当氧气不足或缺氧时，细胞可以通过无氧呼吸从葡萄糖中释放少量能量。动物与酵母的产物有所不同。
In animals (lactic acid fermentation):
在动物体内（乳酸发酵）：
Glucose → Lactic acid + Energy
葡萄糖 → 乳酸 + 能量
C₆H₁₂O₆ → 2C₃H₆O₃ + Energy
In yeast and some plants (alcohol fermentation):
在酵母和某些植物中（酒精发酵）：
Glucose → Ethanol + Carbon dioxide + Energy
葡萄糖 → 乙醇 + 二氧化碳 + 能量
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ + Energy
Anaerobic respiration does not require oxygen and produces much less energy than aerobic respiration.
无氧呼吸不需要氧气，并且释放的能量比有氧呼吸少得多。
9. Biomass and Pyramid of Biomass | 生物量与生物量金字塔
Biomass is the total mass of living material present in a particular organism or across a trophic level. It is usually measured as dry mass to exclude water content.
生物量是指一个特定生物体内或一个营养级中全部活物质的总质量。通常以干重测量，以排除水分的影响。
Biomass of one trophic level = Average dry mass of one individual × Number of individuals
某营养级的生物量 = 个体的平均干重 × 个体数目
When you draw a pyramid of biomass, each bar represents the dry mass of all organisms at that trophic level. Because of the 10% energy rule, the pyramid is almost always upright, with the producers forming the widest base.
绘制生物量金字塔时，每个条形代表该营养级全部生物的总干重。由于10%能量定律，金字塔几乎总是正立的，生产者构成最宽的底部。
10. Sampling Techniques: Percentage Cover and Capture-Recapture | 取样技术：百分比覆盖度与标志重捕法
It is often impractical to count every organism in a habitat. Percentage cover, estimated using a quadrat, is a quick way to assess the abundance of plants or stationary organisms.
通常不可能将栖息地中的每种生物都数一遍。使用样方估算的百分比覆盖度，是评估植物或静止生物丰度的一种快速方法。
age cover = (Area covered by the species inside the quadrat ÷ Total area of quadrat) × 100%
百分比覆盖度 = （样方内该物种覆盖的面积 ÷ 样方面积）× 100%
For mobile animals, the capture-mark-recapture method can be used to estimate population size. The basic principle is that the proportion of marked individuals in a second sample reflects the total population.
对于移动的动物，可以用标志重捕法估算种群大小。基本原理是，第二次样本中已标记个体的比例能反映出总种群数量。
Although you do not need the full Lincoln index in Year 7, knowing the principle helps you design fair ecological investigations.
虽然 7 年级不需要完整的林肯指数，但了解这一原理有助你设计公平的生态调查。
11. Rate of Enzyme-Controlled Reactions | 酶促反应速率
Enzymes are biological catalysts that speed up reactions. While there is no single formula at this level, you can compare reaction rates by measuring how fast a product appears or a substrate disappears.
酶是加速反应的生物催化剂。本阶段虽无固定公式，但你可以通过测量产物生成的快慢或者底物消失的快慢来比较反应速率。
Rate of reaction = Amount of product formed ÷ Time taken
反应速率 = 生成的产物量 ÷ 所需时间
or Rate of reaction = 1 ÷ Time taken for a change to occur
或者 反应速率 = 1 ÷ 变化发生所需时间
The rate is highest at the optimum temperature and pH for the enzyme. Beyond these limits, the enzyme denatures and the rate drops dramatically.
在酶的最适温度和最适 pH 下，反应速率最高。超出这些范围，酶会发生变性，反应速率急剧下降。
12. Surface Area to Volume Ratio (SA:V) | 表面积与体积之比
As an object gets larger, its surface area does not increase as quickly as its volume. This principle explains why cells are microscopic and why larger organisms need specialised exchange surfaces.
物体变大时，其表面积的增长速度没有体积快。这一原理解释了为什么细胞必须微小，以及为什么较大的生物体需要特化的交换表面。
Surface area : Volume ratio = Surface area ÷ Volume
表面积与体积之比 = 表面积 ÷ 体积
Small cells have a high SA:V ratio, allowing efficient diffusion of oxygen, nutrients and waste products.
小细胞具有较高的表面积与体积比，这使得氧气、营养物质和废物的扩散非常高效。
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