📚 Year 9 CCEA Biology: Formula & Theorem Quick Reference Guide | Year 9 CCEA 生物：公式定理速查手册
This quick reference handbook brings together the key formulas, word equations and numerical relationships you need to master in Year 9 CCEA Biology. Each entry explains what the formula does, how to use it and includes a worked example or context, helping you build confidence before assessments.
这本速查手册整理了 Year 9 CCEA 生物学中必须掌握的关键公式、文字方程式和数量关系。每个条目都解释了公式的含义、使用方法，并提供了计算示例或情境背景，帮助你在评估前树立信心。
1. Magnification Formula | 放大倍数公式
When observing specimens under a microscope, you often need to calculate how much larger the image appears compared to the object's real size. The magnification formula links image size, actual size and magnification.
Magnification = Image size ÷ Actual size
The same relationship can be rearranged to find the actual size if you know the image size and magnification:
Actual size = Image size ÷ Magnification
All measurements must be in the same units, usually millimetres (mm) or micrometres (µm). Remember that 1 mm = 1000 µm.
Example: A cheek cell is drawn with a diameter of 40 mm. The drawing' gnification is ×400. The actual diameter of the cell is 40 mm ÷ 400 = 0.1 mm, which is 100 µm.
用显微镜观察标本时，常常需要计算图像比实物放大了多少。放大倍数公式将图像大小、实际大小和放大倍数联系起来。
放大倍数 = 图像大小 ÷ 实际大小
如果已知图像大小和放大倍数，也可以重新排列公式来求实际大小：
实际大小 = 图像大小 ÷ 放大倍数
所有测量必须使用相同的单位，通常为毫米（mm）或微米（µm）。请牢记 1 mm = 1000 µm。
示例：一个口腔上皮细胞绘图直径为 40 mm，绘图放大倍率为 ×400。细胞的实际直径为 40 mm ÷ 400 = 0.1 mm，即 100 µm。
2. Word Equation for Photosynthesis | 光合作用文字方程
Photosynthesis is the process by which green plants and some other organisms use light energy to synthesise glucose from carbon dioxide and water. The word equation summarises the reactants and products.
carbon dioxide + water → glucose + oxygen
This reaction takes place in chloroplasts and requires light energy absorbed by chlorophyll. The oxygen produced is released into the atmosphere as a by-product.
To remember the requirements, note that light and chlorophyll are essential conditions, not reactants, so they are often written above the arrow.
光合作用是绿色植物及某些其他生物利用光能，将二氧化碳和水合成葡萄糖的过程。文字方程总结了反应物和产物。
二氧化碳 + 水 → 葡萄糖 + 氧气
该反应发生在叶绿体中，需要叶绿素吸收的光能。产生的氧气作为副产品释放到大气中。
请注意，光和叶绿素是必要条件而非反应物，因此通常标注在箭头上下方。
3. Balanced Chemical Equation for Photosynthesis | 光合作用化学平衡方程
The word equation is useful, but the balanced symbol equation shows the exact number of molecules involved and confirms that mass is conserved during photosynthesis.
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Six molecules of carbon dioxide combine with six molecules of water, using light energy, to produce one molecule of glucose and six molecules of oxygen. The equation is balanced because the same number of each type of atom appears on both sides.
This equation helps you calculate the ratio of gas exchange: for every six CO₂ taken in, six O₂ are released.
文字方程很实用，而配平的符号方程则精确显示出所涉及分子的数量，并证实了光合作用中物质守恒。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
六个二氧化碳分子与六个水分子在光能作用下反应，生成一个葡萄糖分子和六个氧气分子。由于两边各种原子的数目相等，因此该方程式是配平的。
利用该方程式可推算气体交换的比例：每吸收六个 CO₂，就会释放出六个 O₂。
4. Word Equation for Aerobic Respiration | 有氧呼吸文字方程
Aerobic respiration is the process that releases energy from glucose in the presence of oxygen. It occurs continuously in the mitochondria of most cells.
glucose + oxygen → carbon dioxide + water (+ energy)
The energy released is used to form ATP, which powers cellular activities such as muscle contraction, active transport and keeping a constant body temperature in mammals.
Notice that aerobic respiration is essentially the reverse of photosynthesis in terms of chemical change, although the processes occur in different organelles and serve different purposes.
有氧呼吸是在有氧气参与下从葡萄糖中释放能量的过程，它持续发生在大多数细胞的线粒体中。
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
释放的能量用于合成 ATP，从而驱动肌肉收缩、主动运输以及哺乳动物维持恒定体温等细胞活动。
注意，就化学变化而言，有氧呼吸基本上是光合作用的逆过程，但两者发生在不同的细胞器中，功能也截然不同。
5. Anaerobic Respiration Equations | 无氧呼吸方程
When oxygen is scarce, cells can still release a small amount of energy through anaerobic respiration. The products differ between animals and plants or yeast.
In animals: glucose → lactic acid (+ energy)
In plants and yeast: glucose → ethanol + carbon dioxide (+ energy)
Anaerobic respiration generates much less ATP per glucose molecule than aerobic respiration. The build-up of lactic acid in muscles causes fatigue and pain, which is why we breathe heavily after intense exercise to repay the 'oxygen debt'.
In yeast, anaerobic respiration is exploited in brewing and baking, where ethanol and carbon dioxide are desired products.
缺氧时，细胞仍可通过无氧呼吸释放少量能量。动物与植物（或酵母）的产物有所不同。
动物：葡萄糖 → 乳酸（+ 能量）
植物和酵母：葡萄糖 → 乙醇 + 二氧化碳（+ 能量）
与有氧呼吸相比，无氧呼吸每个葡萄糖分子产生的 ATP 要少得多。肌肉中乳酸积累会引起疲劳和酸痛，因此剧烈运动后我们会大口呼吸，以偿还“氧债”。
对酵母而言，无氧呼吸被用于酿酒和烘焙，其中乙醇和二氧化碳正是所需产物。
6. Energy Transfer in Food Chains (10% Rule) | 食物链中的能量传递（10%定律）
As energy moves up the trophic levels of a food chain, only a fraction is transferred to the next level. The 10% rule is a useful approximation for understanding energy loss.
Energy transfer efficiency ≈ (Energy at trophic level ÷ Energy at previous level) × 100% ≈ 10%
Most energy is lost through respiration, movement, heat and uneaten parts. This explains why food chains rarely have more than four or five trophic levels and why shorter food chains are more efficient for food production.
Example: If the producer level contains 20,000 kJ of energy, the primary consumer might store only about 2,000 kJ.
能量沿食物链的营养级向上流动时，只有一小部分传递到下一级。10% 定律是帮助理解能量损耗的实用近似。
能量传递效率 ≈（本级能量 ÷ 上一级能量）× 100% ≈ 10%
绝大部分能量通过呼吸、运动、散热以及未被取食的部分而散失。这解释了为什么食物链通常不超过四到五个营养级，也说明了为何较短的食物链在食品生产中效率更高。
示例：若生产者层级含有 20,000 kJ 的能量，初级消费者约只能储存 2,000 kJ。
7. Surface Area to Volume Ratio and Diffusion | 表面积体积比与扩散
The surface area to volume ratio (SA:V) is a crucial concept for understanding how organisms exchange substances with their environment. It is calculated by comparing an object's outer surface area with its internal volume.
SA:V = Surface area ÷ Volume
As an organism or cell gets larger, its volume increases more rapidly than its surface area, causing the SA:V to decrease. A low SA:V makes diffusion of gases, nutrients and wastes too slow to sustain life, which is why large multicellular organisms need specialised exchange surfaces and transport systems.
Small organisms such as Amoeba rely solely on diffusion across their body surface because they have a very high SA:V.
表面积与体积比（SA:V）是理解生物体如何与环境进行物质交换的关键概念。计算时，用物体的外表面面积与其内部体积做比较。
SA:V = 表面积 ÷ 体积
当生物体或细胞变大时，体积的增长比表面积更快，导致 SA:V 下降。过低的 SA:V 会使气体、养分和废物的扩散过于缓慢，无法维持生命，因此大型多细胞生物需要特化的交换表面和运输系统。
像变形虫这样的小生物具有极高的 SA:V，仅靠体表扩散就能满足生命需求。
8. Enzyme Reaction Rate Calculation | 酶反应速率计算
Enzymes are biological catalysts that speed up reactions. You can measure their activity by monitoring how quickly substrate is broken down or product is formed over a given time.
Rate of reaction = Quantity of substrate used (or product formed) ÷ Time
Common practical contexts include the breakdown of hydrogen peroxide by catalase (measuring oxygen produced) or the digestion of starch by amylase (measuring the time for iodine to stop turning blue-black).
Example: If 20 cm³ of oxygen is produced in 100 seconds, the rate is 20 ÷ 100 = 0.2 cm³/s.
Faster rates are observed at the enzyme's optimum temperature and pH; extremes cause denaturation and a sharp drop in rate.
酶是能加速反应的生物催化剂。通过监测一定时间内底物的减少量或产物的生成量，可以衡量酶的活性。
反应速率 = 底物消耗量（或产物生成量）÷ 时间
常见的实验情境包括：用过氧化氢酶分解过氧化氢（测量产生的氧气），或用淀粉酶消化淀粉（记录碘液不再变蓝黑所需的时间）。
示例：若 100 秒内产生 20 cm³ 氧气，反应速率为 20 ÷ 100 = 0.2 cm³/s。
在酶的最适温度和最适 pH 下速率最快；极端条件会导致酶变性，反应速率急剧下降。
9. Heart Rate, Stroke Volume and Cardiac Output | 心率、每搏输出量与心输出量
Cardiac output is the volume of blood pumped by the heart per minute and shows how effectively the circulatory system delivers oxygen and nutrients to tissues.
Cardiac output (cm³/min) = Heart rate (beats/min) × Stroke volume (cm³/beat)
During exercise, both heart rate and stroke volume increase, nearly doubling cardiac output to meet the higher demand for oxygen. A typical resting cardiac output for a teenager is around 5,000 cm³/min.
eart rate of 70 bpm and stroke volume of 70 cm³, cardiac output = 70 × 70 = 4,900 cm³/min.
心输出量是心脏每分钟泵出的血液体积，体现循环系统向组织输送氧气和营养物质的效率。
心输出量 (cm³/min) = 心率 (次/分) × 每搏输出量 (cm³/次)
运动时，心率和每搏输出量均上升，心输出量几乎加倍，以满足机体对氧气的高需求。青少年静息时典型的心输出量约为 5,000 cm³/min。
示例：静息心率 70 bpm，每搏输出量 70 cm³，则心输出量 = 70 × 70 = 4,900 cm³/min。
10. DNA Base Pairing Rules | DNA碱基配对规则
DNA is a double-stranded molecule made of nucleotides. The two strands are held together by complementary base pairing, which follows a strict rule essential for replication and protein synthesis.
Adenine (A) pairs with Thymine (T) via two hydrogen bonds.
Cytosine (C) pairs with Guanine (G) via three hydrogen bonds.
This means the amount of adenine always equals thymine, and cytosine always equals guanine in a DNA molecule. This pattern is known as Chargaff's rule, which helped Watson and Crick determine the double helix structure.
When a cell divides, the DNA unzips and each strand serves as a template for building a new complementary strand, ensuring genetic information is copied faithfully.
DNA 是由核苷酸组成的双链分子。两条链通过互补碱基配对连接，严格的规则对 DNA 复制和蛋白质合成至关重要。
腺嘌呤 (A) 与胸腺嘧啶 (T) 通过两个氢键配对。
胞嘧啶 (C) 与鸟嘌呤 (G) 通过三个氢键配对。
因此，DNA 分子中腺嘌呤的含量总是等于胸腺嘧啶，胞嘧啶等于鸟嘌呤。这一规律被称为查戈夫法则，帮助沃森和克里克确定了双螺旋结构。
细胞分裂时，DNA 解旋，每条单链作为模板合成新的互补链，从而保证遗传信息被精确复制。
Published by TutorHao | Biology Revision Series | aleveler.com
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