📚 Formula and Theorem Quick Reference for CIE Biology Year 12 | CIE 生物 Year 12 公式定理速查手册
This handbook collects the essential formulas, ratios, and calculation rules you must master for the CIE AS Level Biology course (Year 12). Each entry provides the formula, its meaning, and a concise explanation to reinforce your quantitative skills and conceptual understanding.
本手册汇集了 CIE AS 阶段生物学（Year 12）必须掌握的核心公式、比率和计算规则。每一条目均给出公式、含义及简要说明，帮助巩固定量技能与概念理解。
1. Magnification and Actual Size | 放大倍数与实际大小
Magnification is how many times larger an image is compared to the real object. The formula relates image size (I), actual size (A), and magnification (M), always ensuring units match.
放大倍数是指图像比实物放大了多少倍。公式将图像尺寸 (I)、实际尺寸 (A) 与放大倍数 (M) 联系起来，计算时务必统一单位。
M = I / A
To find actual size from a photomicrograph, rearrange to A = I / M. Measure the image in mm, convert to µm if needed, and divide by magnification.
从显微照片求实际大小时，使用 A = I / M。以毫米测量图像，必要时转换为微米，再除以放大倍数。
Key conversion: 1 mm = 1000 µm; 1 µm = 1000 nm. Always express actual size in the appropriate biological unit.
关键换算：1 毫米 = 1000 微米；1 微米 = 1000 纳米。务必用合适的生物学单位表示实际大小。
2. Surface Area to Volume Ratio | 表面积与体积比
The surface area to volume ratio (SA:V) limits cell size and determines how efficiently substances can be exchanged by diffusion. As an object grows, its volume increases faster than its surface area, so the ratio falls.
表面积与体积比（SA:V）限制着细胞大小，并决定扩散交换物质的效率。随着物体增大，体积的增长快于表面积，因此该比值下降。
| Side length / 边长 (cm) | SA / 表面积 (cm²) | V / 体积 (cm³) | SA:V |
|---|---|---|---|
| 1 | 6 | 1 | 6:1 |
| 2 | 24 | 8 | 3:1 |
| 3 | 54 | 27 | 2:1 |
For a cube, SA = 6L² and V = L³, giving SA:V = 6/L. Small organisms and single cells rely on a high SA:V for direct diffusion; larger multicellular organisms need specialised transport systems.
对于立方体，SA = 6L²，V = L³，因此 SA:V = 6/L。小型生物和单个细胞依靠高 SA:V 进行直接扩散；大型多细胞生物则需专门的运输系统。
3. Fick’s Law of Diffusion | 菲克扩散定律
Fick’s Law summarises the factors that influence the rate of diffusion across a surface. The rate is directly proportional to the surface area and the concentration gradient, and inversely proportional to the diffusion distance.
菲克定律概括了影响跨面扩散速率的诸因素。速率与表面积和浓度梯度成正比，与扩散距离成反比。
Rate of diffusion ∝ (Surface Area × Concentration Difference) / Diffusion Distance
Symbolically: rate ∝ (A × ΔC) / d. To maximise diffusion, epithelial surfaces (alveoli, villi, gills) are thin, have a large area, and maintain a steep concentration gradient through blood flow or ventilation.
符号表示为：rate ∝ (A × ΔC) / d。为使扩散效率最大化，上皮表面（肺泡、绒毛、鳃）非常薄、面积广大，并通过血流或通风维持陡峭的浓度梯度。
4. Water Potential (Ψ) | 水势 (Ψ)
Water potential (Ψ) is the potential energy of water per unit volume and dictates the direction of osmosis. Water moves from regions of higher (less negative) water potential to regions of lower (more negative) water potential.
水势 (Ψ) 是单位体积水的势能，决定了渗透作用的方向。水从较高（负值较小）的水势区域流向较低（负值更大）的水势区域。
Ψ = Ψₛ + Ψₚ
Ψₛ is solute potential (osmotic potential), always negative or zero because dissolved solutes lower water potential. Ψₚ is pressure potential; in an open container or animal cell Ψₚ = 0, so Ψ = Ψₛ. In plant cells, turgor pressure makes Ψₚ positive.
Ψₛ 为溶质势（渗透势），因溶质降低水势，故恒为负值或零。Ψₚ 为压力势；在开放容器或动物细胞中 Ψₚ = 0，因此 Ψ = Ψₛ。植物细胞中膨压使 Ψₚ 为正值。
The more negative the Ψ, the lower the water potential. Pure water at standard pressure has Ψ = 0.
Ψ 值越负，水势越低。标准压力下的纯水 Ψ = 0。
5. Rate of Reaction and Q₁₀ | 反应速率与温度系数 Q₁₀
In enzyme kinetics, the initial rate of reaction can be estimated from the time taken for a measurable change, such as a colour change or the appearance of a product.
在酶动力学中，初始反应速率可通过可测变化所需时间估算，例如颜色变化或产物出现的时间。
Rate = 1 / t
(Where t is the time for a fixed endpoint, e.g., time for starch to disappear in the iodine test.)
（t 为到达固定终点的时间，如碘液检验中淀粉消失所需的时间。）
The temperature coefficient Q₁₀ indicates how much the rate of an enzyme-controlled reaction increases with a 10 °C rise in temperature, before denaturation.
温度系数 Q₁₀ 表示在变性之前，酶促反应速率随温度升高 10 °C 而增加的倍数。
Q₁₀ = Rate at (T + 10 °C) / Rate at T °C
For most enzyme reactions, Q₁₀ is around 2, meaning the rate approximately doubles for every 10 °C increase up to the optimum temperature.
多数酶促反应的 Q₁₀ 约为 2，即在最适温度以下，温度每升高 10 °C，速率约翻倍。
6. Cardiac Output | 心输出量
Cardiac output (CO) is the total volume of blood pumped by one ventricle per minute. It reflects the overall performance of the heart.
心输出量 (CO) 是一个心室每分钟泵出的血液总量，反映心脏的整体工作能力。
CO = Stroke Volume (SV) × Heart Rate (HR)
Stroke volume is the volume of blood ejected per beat (typically 70 mL at rest). Heart rate is the number of beats per minute. Cardiac output can increase dramatically during exercise.
每搏输出量 (SV) 是每次心跳射出的血量（静息时约 70 mL）。心率 (HR) 为每分钟心跳次数。运动时心输出量可大幅增加。
7. Pulmonary Ventilation (Minute Volume) | 肺通气量（每分通气量）
Pulmonary ventilation describes the volume of air moved into and out of the lungs per minute, an indicator of respiratory performance.
肺通气量指每分钟进出肺部的空气体积，是衡量呼吸功能的指标。
Minute Ventilation = Tidal Volume (TV) × Breathing Rate (BR)
Tidal volume is the volume of air inhaled or exhaled in one quiet breath (approx. 0.5 L at rest). Breathing rate is the number of breaths per minute. Both increase during exercise, raising minute ventilation.
潮气量 (TV) 是平静呼吸时每次吸入或呼出的气体体积（静息时约 0.5 L）。呼吸频率 (BR) 为每分钟呼吸次数。运动时两者均增大，从而提高每分通气量。
8. Mitotic Index | 有丝分裂指数
The mitotic index measures the proportion of cells undergoing mitosis in a tissue sample, used to study growth rates or detect cancerous tissue.
有丝分裂指数测量组织样本中处于有丝分裂期的细胞比例，用于研究生长速率或检测癌变组织。
Mitotic Index = Number of cells in mitosis / Total number of cells observed
Count all cells showing visible chromosomes (prophase to telophase) and divide by the total cell count. Highly active meristems (root and shoot tips) and tumours show a high mitotic index.
统计所有可见染色体的细胞（前期至末期）并除以细胞总数。活跃的分生组织（根尖和茎尖）及肿瘤的有丝分裂指数较高。
9. Percentage Change and Mean Calculations | 百分比变化与平均值
These general mathematical tools
Published by TutorHao | Year 12 Biology Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply