📚 Year 8 SQA Biology: Formula & Theorem Quick Reference Handbook | Year 8 SQA 生物：公式定理速查手册
This quick reference handbook brings together the essential formulas, equations and core theorems covered in the Year 8 SQA Biology course. From microscope calculations to energy flow in ecosystems, these principles form the foundation for understanding living systems. Use this guide to revise key relationships and apply them confidently in assessments and practical investigations.
本速查手册汇集了 Year 8 SQA 生物课程中的基本公式、方程式和核心定理。从显微镜计算到生态系统的能量流动，这些原理是理解生命系统的基础。利用本手册复习关键关系，并在评估和实验探究中自信地应用它们。
1. Microscope Magnification Formula | 显微镜放大倍数公式
y the magnification of the objective lens. The formula is: Total Magnification = Eyepiece Magnification × Objective Magnification. For example, using a 10× eyepiece and a 40× objective gives a total magnification of 400×.
通过光学显微镜观察标本时，总放大倍数由目镜放大倍数乘以物镜放大倍数计算得出。公式为：总放大倍数 = 目镜倍数 × 物镜倍数。例如，使用 10× 目镜和 40× 物镜时，总放大倍数为 400×。
e size is the length of the specimen in the picture, measured with a ruler. Actual size is the real length of the specimen.
计算显微照片或绘图放大倍数时，使用公式：放大倍数 = 图像大小 ÷ 实际大小。图像大小是用尺子在图片中测量得到的标本长度。实际大小则是标本的真实长度。
M = I ÷ A or Magnification = Image size / Actual size
2. Actual Size Calculation | 实际大小计算
agnification. Remember to convert all measurements to the same unit, usually micrometres (µm) for cells. 1 mm = 1 000 µm.
将放大倍数公式变形后，可以求出细胞或微生物的真实大小：实际大小 = 图像大小 ÷ 放大倍数。记住将所有测量值转换为同一单位，细胞通常以微米（µm）表示。1 mm = 1 000 µm。
agram drawn at a magnification of 60×. The actual length is 24 ÷ 60 = 0.4 mm, which is 400 µm. This conversion is crucial when interpreting biological drawings.
示例：在一幅 60× 放大的示意图中，一条昆虫腿长度为 24 mm。实际长度是 24 ÷ 60 = 0.4 mm，即 400 µm。这种转换在解读生物绘图时至关重要。
3. Cell Theory | 细胞学说
Cell theory is a fundamental theorem of biology, stating that all living organisms are composed of one or more cells, that the cell is the basic unit of structure and function, and that all cells arise from pre-existing cells. This theorem underpins all studies of life at the microscopic level.
细胞学说是生物学的基本定理，指出所有生物体均由一个或多个细胞组成，细胞是结构与功能的基本单位，并且所有细胞都来自已存在的细胞。这一学说是所有微观生命研究的基础。
Whether examining a bacterial colony or a human tissue sample, these three statements remain true. Cell theory was developed in the 19th century through the work of scientists such as Schleiden, Schwann and Virchow.
无论是观察细菌菌落还是人体组织样本，这三条陈述始终成立。细胞学说于 19 世纪由施莱登、施旺和魏尔肖等科学家共同发展形成。
4. Surface Area to Volume Ratio | 表面积与体积比
: SA:V = Surface Area ÷ Volume. For a cube-shaped cell with side length s, surface area = 6s² and volume = s³, so SA:V = 6/s.
随着细胞或生物体变大，其体积的增长速度比表面积更快。表面积与体积比（SA:V）的公式为：SA:V = 表面积 ÷ 体积。对于一个边长为 s 的立方体细胞，表面积 = 6s²，体积 = s³，因此 SA:V = 6/s。
A high SA:V allows efficient movement of oxygen, nutrients and waste products across the cell membrane. This is why large organisms need specialised exchange surfaces such as lungs, gills or leaf mesophyll layers.
较高的 SA:V 有利于氧气、营养物质和代谢废物高效地跨膜运输。这也是大型生物需要特化交换表面（如肺、鳃或叶片叶肉层）的原因。
5. Photosynthesis Equation | 光合作用方程式
Photosynthesis is the process by which green plants, algae and some bacteria convert light energy into chemical energy, using carbon dioxide and water to produce glucose and oxygen. The word equation is:
光合作用是绿色植物、藻类和一些细菌将光能转化为化学能的过程，利用二氧化碳和水生成葡萄糖和氧气。文字方程式为：
carbon dioxide + water → glucose + oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
The balanced chemical equation, using light energy absorbed by chlorophyll, is:
在叶绿素吸收光能的条件下，平衡的化学方程式为：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
This reaction takes place in the chloroplasts of plant cells. The glucose produced is either used immediately for respiration, stored as starch, or converted into cellulose for cell walls.
该反应发生在植物细胞的叶绿体中。产生的葡萄糖要么立即用于呼吸作用，要么以淀粉形式储存，或转化为构成细胞壁的纤维素。
6. Aerobic Respiration Equation | 有氧呼吸方程式
Aerobic respiration releases energy for cell activities by breaking down glucose in the presence of oxygen. The word equation is:
有氧呼吸通过在氧气存在下分解葡萄糖来释放能量，供细胞活动使用。文字方程式为：
glucose + oxygen → carbon dioxide + water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
The balanced chemical equation is the reverse of photosynthesis and occurs in the mitochondria of plant and animal cells:
平衡化学方程式与光合作用互为逆过程，反应发生在植物和动物细胞的线粒体中：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Energy released is stored in ATP molecules, which power processes like muscle contraction, active transport and maintaining body temperature.
释放的能量储存在 ATP 分子中，为肌肉收缩、主动运输和维持体温等过程提供动力。
7. Energy Transfer and the 10% Rule | 能量传递与 10% 规则
In a food chain, only a small fraction of the energy taken in at one trophic level is transferred to the next level. As a rule of thumb, approximately 10% of the chemical energy in food is converted into new biomass. The rest is lost through respiration, movement, heat and undigested materials.
在食物链中，从一个营养级摄入的能量只有一小部分传递到下一营养级。根据经验法则，食物中大约 10% 的化学能转化为新的生物量。其余能量通过呼吸作用、运动、产热和未消化物质而损失。
This 10% Rule explains why food chains are rarely longer than four or five trophic levels and why there are far fewer top predators than producers. It can be expressed as:
这一定律解释了为什么食物链很少超过四到五个营养级，以及为什么顶级捕食者数量远少于生产者。可以用公式表示为：
Energy available at next level ≈ 0.10 × Energy in previous level
8. Population Growth Equation | 种群增长公式
The change in population size over time can be modelled using the formula:
种群大小随时间的变化可以用以下公式建模：
Population change = (Births + Immigration) − (Deaths + Emigration)
种群变化 =（出生数 + 迁入数）−（死亡数 + 迁出数）
If births and immigration exceed deaths and emigration, the population grows. When the four factors balance, the population remains stable. Limiting factors such as food availability, predators and disease often prevent unlimited growth.
如果出生加迁入超过死亡加迁出，种群就会增长；当这四个因素平衡时，种群保持稳定。食物供应、捕食者和疾病等限制因素通常会阻止种群无限增长。
Ecologists use this equation to study endangered species, pest control and the impact of habitat change on wildlife numbers.
生态学家利用该公式研究濒危物种、害虫防治以及栖息地变化对野生生物数量的影响。
9. Genetic Probability – Punnett Square | 遗传概率 – 庞纳特方格
rozygous parents (Aa × Aa), the gametes each carry one allele. The square shows the possible combinations:
庞纳特方格是一种用于预测杂交后代基因型和表型的图表。对于两个杂合亲本（Aa × Aa）的单基因杂交，配子各携带一个等位基因。方格显示了可能的组合：
| A | a | |
| A | AA | Aa |
| a | Aa | aa |
pic ratio becomes 3 dominant : 1 recessive. Probability of a dominant phenotype = 3/4 = 75%.
基因型比例为 1 AA : 2 Aa : 1 aa。如果等位基因 A 为显性、a 为隐性，则表型比例为 3 显性 : 1 隐性。显性表型的概率为 3/4 = 75%。
10. Enzyme Activity – Optimum Conditions Theorem | 酶活性 – 最适条件定理
Enzymes are biological catalysts that speed up reactions without being used up. Each enzyme has an optimum temperature and pH at which its activity is highest. The 'lock and key' model states that the substrate fits precisely into the enzyme's active site, forming an enzyme-substrate complex.
酶是生物催化剂，能在不被消耗的情况下加快反应速率。每种酶都有一个使其活性最高的最适温度和酸碱度。“锁钥模型”提出，底物精确地嵌入酶的活性位点，形成酶-底物复合物。
If the temperature exceeds the optimum, the enzyme denatures: its active site changes shape permanently, and the substrate can no longer bind. At very low temperatures, enzyme activity slows down but the enzyme is not denatured. pH extremes also disrupt the shape of the active site.
如果温度超过最适值，酶会发生变性：其活性位点永久改变形状，底物无法再结合。在极低温度下，酶活性减慢但并未变性。极端的 pH 同样会破坏活性位点的形状。
The effect of temperature on reaction rate follows a bell-shaped curve, rising to a maximum at the optimum temperature and then falling sharply as denaturation occurs.
温度对反应速率的影响呈钟形曲线，在最适温度时升至最高，随后因变性而急剧下降。
11. Principles of Diffusion | 扩散原理
Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration, down a concentration gradient, until equilibrium is reached. No external energy is required — it is a passive process.
扩散是指粒子从高浓度区域沿浓度梯度向低浓度区域的净移动，直至达到平衡。这一过程不需要外部能量，是一种被动运输。
The rate of diffusion is influenced by several factors, which can be summarised as:
扩散速率受多个因素影响，可概括为：
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 temperature gives particles more kinetic energy, further raising the diffusion rate. In the lungs, the alveoli provide a huge surface area, a short diffusion distance and a steep concentration gradient to maximise oxygen uptake.
升高温度使粒子动能增加，从而进一步提高扩散速率。在肺中，肺泡提供了巨大的表面积、极短的扩散距离和陡峭的浓度梯度，以最大限度地摄取氧气。
12. Light Intensity and Photosynthesis Rate | 光照强度与光合作用速率
For aquatic plants such as pondweed, the rate of photosynthesis can be measured by counting oxygen bubbles produced per minute. Light intensity decreases with distance from the light source according to the inverse square law:
对于如水草等水生植物，光合作用的速率可以通过计数每分钟产生的氧气泡来测量。根据平方反比定律，光照强度随距光源的距离增加而减弱：
Light intensity ∝ 1 / d²
光照强度 ∝ 1 / d²
Doubling the distance reduces the light intensity to one quarter. Consequently, the rate of photosynthesis also decreases, provided light is the limiting factor. At very high light intensities, other factors such as CO₂ concentration or temperature may become limiting.
距离加倍会使光照强度降至原来的四分之一。因此，在光照为限制因素的前提下，光合作用速率也会下降。当光照强度非常高时，CO₂ 浓度或温度等其他因素可能会成为新的限制因素。
This relationship helps design experiments and understand why plants grow more slowly in shaded environments.
这种关系有助于设计实验，并解释为什么植物在遮阴环境中生长更慢。
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