📚 Year 9 AQA Biology: Formula & Theorem Quick Reference Handbook | Year 9 AQA 生物：公式定理速查手册
This handbook brings together the essential formulas, equations and key principles you will meet in Year 9 AQA Biology. Use it to revise calculations for microscopy, respiration, photosynthesis, genetics, energy transfer and more. Each rule is explained with a worked example or a simple word equation, followed by the same explanation in Chinese, so you can study confidently in both languages.
这本手册汇总了 Year 9 AQA 生物课程中你必须掌握的核心公式、方程式和重要原理，涵盖显微镜计算、呼吸作用、光合作用、遗传学、能量传递等内容。每条规则都配有实例或文字方程，并附有中文解释，帮助你用双语自信巩固知识。
1. Magnification Formula for Microscopes | 显微镜放大倍数公式
In a light microscope, total magnification is the product of the eyepiece lens magnification and the objective lens magnification. This relationship helps you work out how many times an image is enlarged compared with the real object.
在光学显微镜中，总放大倍数是目镜放大倍数与物镜放大倍数的乘积。这个关系能让你计算出图像比实物放大了多少倍。
Total Magnification = Eyepiece Magnification × Objective Magnification
总放大倍数 = 目镜放大倍数 × 物镜放大倍数
For example, if the eyepiece lens is ×10 and the objective lens is ×40, the total magnification is 10 × 40 = ×400.
例如，若目镜为 ×10，物镜为 ×40，则总放大倍数为 10 × 40 = ×400。
2. Calculating the Real Size of a Specimen | 计算标本的实际大小
When you measure an image under the microscope, the actual size of the object can be found by dividing the measured size by the total magnification. This is often used when drawing scale bars or estimating cell dimensions.
当你在显微镜下测量图像大小时，可以通过将测量值除以总放大倍数求出物体的实际尺寸。这一计算常用于绘制比例尺或估算细胞大小。
Actual Size = Image Size ÷ Magnification
实际大小 = 图像大小 ÷ 放大倍数
If the image of a cell measures 2 mm and the magnification is ×400, the real length is 2 ÷ 400 = 0.005 mm, which is equivalent to 5 μm.
若一个细胞的图像长度为 2 mm，放大倍数为 ×400，则真实长度为 2 ÷ 400 = 0.005 mm，即 5 μm。
3. Surface Area to Volume Ratio | 表面积与体积比
As an organism or a cell increases in size, its surface area to volume ratio decreases. A large ratio allows efficient diffusion of substances, which is why single-celled organisms can rely on diffusion alone, while multicellular organisms need specialised exchange surfaces and transport systems.
生物体或细胞体积增大时，表面积与体积比会减小。较大的比值有利于物质的高效扩散，因此单细胞生物可仅靠扩散生存，而多细胞生物则需要专门的交换表面和运输系统。
Surface Area : Volume = SA ÷ V
表面积 : 体积 = SA ÷ V
For a cube with side 1 cm, SA = 6 cm², V = 1 cm³, so SA:V = 6. For a cube with side 2 cm, SA = 24 cm², V = 8 cm³, so SA:V = 3. The ratio halves when the side length doubles.
边长为 1 cm 的立方体，表面积 6 cm²，体积 1 cm³，SA:V = 6；边长为 2 cm 时，表面积 24 cm²，体积 8 cm³，SA:V = 3。边长加倍，比值减半。
4. Photosynthesis Word and Symbol Equations | 光合作用文字方程与化学方程式
Photosynthesis is the process by which green plants (and some algae) use light energy to convert carbon dioxide and water into glucose and oxygen. Chlorophyll in chloroplasts absorbs the light energy needed to drive the reaction.
光合作用是绿色植物（和部分藻类）利用光能，将二氧化碳和水转化为葡萄糖和氧气的过程。叶绿体中的叶绿素吸收驱动反应所需的光能。
Carbon dioxide + water → glucose + oxygen (light, chlorophyll)
二氧化碳 + 水 → 葡萄糖 + 氧气（光、叶绿素）
The balanced symbol equation is:
配平的化学方程式为：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This shows that six molecules of carbon dioxide react with six molecules of water to produce one molecule of glucose and six molecules of oxygen.
这表明六个二氧化碳分子与六个水分子反应，生成一个葡萄糖分子和六个氧气分子。
5. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration releases energy from glucose in the presence of oxygen. It takes place in the mitochondria of cells and is the most efficient way of producing ATP, the energy currency of the cell.
有氧呼吸在氧气存在下从葡萄糖中释放能量，发生在细胞的线粒体中，是产生 ATP（细胞的能量通货）最有效的方式。
Glucose + oxygen → carbon dioxide + water (+ energy/ATP)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量/ATP）
The symbol equation shows how glucose is completely oxidised:
化学方程式体现了葡萄糖被完全氧化的过程：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Aerobic respiration is summarised as the reverse of photosynthesis in terms of reactants and products, although the biochemical pathways are entirely different.
从反应物和生成物的角度看，有氧呼吸常被概括为光合作用的逆过程，但两者的生化途径完全不同。
6. Anaerobic Respiration (Animals and Yeast) | 无氧呼吸（动物与酵母）
When oxygen is insufficient or absent, cells can still release a small amount of energy through anaerobic respiration. In animals, glucose is converted into lactic acid. In yeast and some plants, glucose is broken down into ethanol and carbon dioxide.
当氧气不足或缺失时，细胞仍可通过无氧呼吸释放少量能量。在动物体内，葡萄糖转化为乳酸；而在酵母和某些植物中，葡萄糖则分解为乙醇和二氧化碳。
In animals:
在动物中：
Glucose → Lactic acid (+ energy)
葡萄糖 → 乳酸（+ 能量）
C₆H₁₂O₆ → 2C₃H₆O₃
In yeast (fermentation):
在酵母中（发酵）：
Glucose → Ethanol + Carbon dioxide (+ energy)
葡萄糖 → 乙醇 + 二氧化碳（+ 能量）
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
Anaerobic respiration produces much less ATP per glucose molecule than aerobic respiration and leads to an oxygen debt in muscles.
与有氧呼吸相比，每分子葡萄糖通过无氧呼吸产生的 ATP 要少得多，并且会导致肌肉中形成氧债。
7. Enzyme Activity and the Lock and Key Model | 酶活性与锁钥模型
Enzymes are biological catalysts that speed up chemical reactions. The ‘lock and key’ theorem states that each enzyme has an active site with a specific shape that fits only a particular substrate, like a key fitting a lock. Once the enzyme-substrate complex forms, the reaction occurs and products are released.
酶是加速化学反应的生物催化剂。“锁钥”定理指出，每种酶都有一个具有特定形状的活性位点，只能与特定的底物契合，就像钥匙插入锁孔一样。酶-底物复合物形成后，反应发生，产物被释放。
Two physical factors denature enzymes by changing the shape of the active site:
两个物理因素会通过改变活性位点的形状使酶变性：
- Temperature: Enzymes work fastest at their optimum temperature (around 37 °C for human enzymes). Above the optimum, the enzyme denatures and activity drops sharply.
- 温度：酶在其最适温度（人体酶约为 37 °C）下反应最快。超过最适温度，酶变性，活性急剧下降。
- pH: Every enzyme has an optimum pH. Stomach protease (pepsin) works best at pH 2, while pancreatic amylase prefers a slightly alkaline pH. Extreme pH values denature the enzyme irreversibly.
- pH 值：每种酶都有最适 pH。胃蛋白酶在 pH 2 时活性最强，而胰淀粉酶偏爱弱碱性环境。极端的 pH 值会使酶不可逆变性。
Although not expressed as a formula, the relationship can be summarised as: enzyme activity increases with temperature up to an optimum, then rapidly drops to zero after denaturation.
虽然无法用公式表达，但可总结为：在一定范围内酶活性随温度升高而增强，达到最适温度后因变性而迅速降为零。
8. Diffusion and Fick’s Law (Simplified) | 扩散与菲克定律（简化版）
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration. The rate of diffusion is crucial for gas exchange in lungs, leaves and cell membranes. A simplified version of Fick’s law helps us remember the three factors that speed up diffusion.
扩散是粒子从高浓度区域向低浓度区域的净移动。扩散速率对肺部、叶片和细胞膜的气体交换至关重要。菲克定律的简化版可以帮助我们记住加速扩散的三个因素。
Rate of Diffusion ∝ (Surface Area × Concentration Difference) ÷ Diffusion Distance
扩散速率 ∝（表面积 × 浓度差）÷ 扩散距离
Increasing the surface area or maintaining a steep concentration gradient raises the rate. A thicker membrane (longer diffusion distance) slows it down. Temperature also increases kinetic energy of particles, so higher temperature → faster diffusion.
增大表面积或保持较大的浓度梯度都可提高扩散速率；膜越厚（扩散距离越长）则速率越慢。温度升高使粒子动能增大，因此高温 → 更快的扩散。
9. Genetic Cross Ratios (Monohybrid Inheritance) | 单基因杂交的遗传比例
Mendel’s laws of inheritance can be represented using Punnett squares. In a monohybrid cross between two heterozygous parents (Tt × Tt) for a trait with complete dominance, the offspring genotype and phenotype ratios follow predictable patterns.
孟德尔遗传定律可使用庞纳特方格表示。在一个显性完全控制的性状中，两个杂合亲本（Tt × Tt）的单基因杂交会产生可预测的基因型和表现型比例。
Genotype ratio: 1 TT : 2 Tt : 1 tt
基因型比： 1 TT : 2 Tt : 1 tt
Phenotype ratio: 3 dominant : 1 recessive
表现型比： 3 显性 : 1 隐性
If a homozygous dominant parent is crossed with a homozygous recessive parent (TT × tt), all F1 offspring are heterozygous (Tt) and show the dominant trait. The recessive trait reappears in the F2 generation only when two recessive alleles come together.
若纯合显性亲本与纯合隐性亲本杂交（TT × tt），所有 F1 后代都是杂合子（Tt）并表现显性性状。隐性性状只有在两个隐性等位基因相遇时才会在 F2 代重新出现。
Family pedigree charts and Punnett squares help you calculate the probability of a child inheriting a particular genotype, with each fertilisation event being independent.
家族系谱图和庞纳特方格有助于计算孩子遗传特定基因型的概率，每次受精事件都是独立的。
10. Heart Rate and Breathing Rate Calculations | 心率与呼吸率的计算
Heart rate is the number of times the heart beats per minute (bpm). You can measure it by counting the pulse for 15 seconds and multiplying by 4, or by using a heart rate monitor. The simple formula is:
心率是心脏每分钟跳动的次数（bpm）。你可以测量 15 秒的脉搏再乘以 4，或使用心率监测器。简单的计算公式为：
Heart Rate (bpm) = Number of heartbeats ÷ Time (minutes)
心率（次/分）= 心跳次数 ÷ 时间（分钟）
Similarly, breathing rate is the number of breaths taken per minute. During exercise, both heart rate and breathing rate increase to supply more oxygen and glucose to muscles and to remove extra carbon dioxide.
同样，呼吸率是每分钟呼吸的次数。运动时，心率和呼吸率都会升高，为肌肉输送更多氧气和葡萄糖并排出多余的二氧化碳。
A typical resting heart rate for a teenager is between 60 and 100 bpm. Athletes often have lower resting heart rates because their heart muscle is stronger and pumps more blood per beat.
青少年典型的静息心率在 60 到 100 次/分之间。运动员通常静息心率较低，因为他们的心肌更强壮，每次搏动泵出的血量更多。
11. Energy Transfer in Food Chains (10% Rule) | 食物链中的能量传递（10% 定律）
In an ecosystem, only a fraction of the energy stored in one trophic level is transferred to the next level. Most energy is lost through respiration, movement, heat and uneaten parts. The rough approximation used in many AQA Key Stage 3 and GCSE contexts is the 10% rule.
在生态系统中，只有一小部分储存在一个营养级中的能量会传递到下一个营养级。大部分能量通过呼吸作用、运动、散热和未被取食的部分而流失。AQA KS3 和 GCSE 阶段常用的粗略估算是 10% 定律。
Efficiency of Energy Transfer ≈ (Energy in next level ÷ Energy in previous level) × 100%
能量传递效率 ≈（下一营养级的能量 ÷ 上一营养级的能量）× 100%
Typically, around 10% of the biomass energy is passed on. If a grassland has 10 000 kJ of energy in the producer level, only about 1 000 kJ reach the primary consumers, and about 100 kJ reach the secondary consumers.
通常约有 10% 的生物质能被向后传递。如果草原的生产者层有 10 000 kJ 能量，那么初级消费者大约只能获得 1 000 kJ，次级消费者大约获得 100 kJ。
This explains why food chains rarely have more than four or five trophic levels and why less meat-intensive diets can be more energy-efficient for the planet.
这就解释了为什么食物链很少超过四到五个营养级，以及减少肉类消耗的饮食对地球来说往往能量效率更高。
12. Quick-Look Table of Common Symbols and Equations | 常用符号与方程式速查表
Use this table as a one-page summary of the chemical symbols and reaction equations that appear throughout Year 9 AQA Biology. Learning these will help you move confidently between word equations and balanced symbol equations.
将本表作为 Year 9 AQA 生物中出现的化学符号和反应方程式的一页式总结。掌握这些内容能让你在文字方程与配平化学方程式之间自如切换。
| Substance / 物质 | Chemical formula / 化学式 | Eqn type / 方程类型 | Example word equation / 示例文字方程 |
| Carbon dioxide / 二氧化碳 | CO₂ | Photosynthesis, Respiration | glucose + O₂ → CO₂ + H₂O |
| Water / 水 | H₂O | Photosynthesis, Respiration | 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ |
| Glucose / 葡萄糖 | C₆H₁₂O₆ | Photosynthesis, Respiration | C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O |
| Oxygen / 氧气 | O₂ | Photosynthesis, Respiration | O₂ produced in photosynthesis |
| Lactic acid / 乳酸 | C₃H₆O₃ | Anaerobic resp. (animals) | glucose → lactic acid |
| Ethanol / 乙醇 | C₂H₅OH | Anaerobic resp. (yeast) | glucose → ethanol + CO₂ |
Memorising these formulas will support your understanding of metabolism, gas exchange and the energy cycles that keep cells alive.
熟记这些化学式将帮助你深入理解新陈代谢、气体交换以及维持细胞生命的能量循环。
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