📚 Year 12 CCEA Biology: Formula & Theorem Quick Reference | Year 12 CCEA 生物：公式定理速查手册
This quick reference guide compiles the essential formulas and key principles required for Year 12 CCEA AS Biology. Use these summaries to review calculations for magnification, physiology, ecology, genetics and data analysis. Each section presents the formula in bold, followed by worked-style explanations in both English and Chinese to reinforce understanding before your exams.
这份速查手册汇总了 Year 12 CCEA AS 生物学所需的关键公式和重要定理。通过重温放大倍数、生理学、生态学、遗传学和数据分析的计算，每节均以粗体呈现公式，并配以中英双语说明，帮助巩固理解、备战考试。
1. Magnification and Actual Size | 放大倍数与实际尺寸
Actual Size = Image Size ÷ Magnification
实际尺寸 = 图像尺寸 ÷ 放大倍数
All three quantities must be expressed in the same length unit. If the image size is measured in millimetres and you need the actual size in micrometres, convert after calculation: 1 mm = 1000 µm. Rearranging gives Magnification = Image Size ÷ Actual Size.
三个量必须使用相同的长度单位。如果图像尺寸以毫米为单位，而你需要以微米表示实际尺寸，可以在计算后换算：1 mm = 1000 µm。变形可得 放大倍数 = 图像尺寸 ÷ 实际尺寸。
In scale-bar questions, measure the bar length in mm, convert to µm if the scale is given in µm, then divide by the labelled distance on the bar.
遇到比例尺题目时，先测量比例尺图像长度 (mm)，若标注为微米则换算为微米，再除以比例尺标注的实际距离。
2. Calculating Percentage Change | 计算百分比变化
Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100%
百分比变化 = [(终值 − 初值) ÷ 初值] × 100%
This formula is widely used in osmosis experiments and enzyme activity reports. A negative value indicates a decrease. Always clearly state whether the change is an increase or decrease.
该公式常用于渗透实验和酶活性报告。负值表示减少。务必明确说明变化属于增加还是减少。
3. Surface Area to Volume Ratio | 表面积与体积比
SA:V Ratio = Surface Area ÷ Volume
表面积体积比 = 表面积 ÷ 体积
Smaller organisms or cells have a larger SA:V ratio, which promotes efficient diffusion of oxygen, nutrients and waste. You may be required to calculate this ratio for cubes, spheres or cylinders using geometry formulas.
较小的生物或细胞具有较大的表面积体积比，有利于氧气、营养物质和废物的高效扩散。考试可能要求利用几何公式计算立方体、球体或圆柱的该比值。
For a cube of side L: Surface area = 6L², Volume = L³, so SA:V = 6 / L. As size increases, the ratio decreases.
边长为 L 的立方体：表面积 = 6L²，体积 = L³，因此 SA:V = 6 / L。尺寸越大，比值越小。
4. Cardiac Output | 心输出量
Cardiac Output = Heart Rate × Stroke Volume
心输出量 = 心率 × 每搏输出量
Cardiac output is the volume of blood pumped by one ventricle per minute. Stroke volume is the volume ejected per beat. In CCEA AS questions, you may be asked to calculate any of the three variables when two are known.
心输出量指一侧心室每分钟泵出的血液体积。每搏输出量为每次心跳射出的血量。在 CCEA AS 题目中，已知其中两个量即可求出第三个。
5. Pulmonary Ventilation | 肺通气量
Pulmonary Ventilation = Tidal Volume × Breathing Rate
肺通气量 = 潮气量 × 呼吸频率
This represents the volume of air moved into the lungs per minute. Tidal volume is the amount of air inhaled or exhaled in one normal breath. Ensure units are consistent (e.g. cm³ min−¹).
该公式表示每分钟进出肺的空气量。潮气量是正常呼吸时每次吸入或呼出的气量。请注意单位统一（如 cm³ min−¹）。
6. Respiratory Quotient (RQ) | 呼吸商
RQ = Volume of CO&sub2; produced ÷ Volume of O&sub2; consumed
RQ = 产生的 CO&sub2; 体积 ÷ 消耗的 O&sub2; 体积
RQ values indicate the main respiratory substrate: RQ = 1.0 for carbohydrates, RQ ≈ 0.7 for lipids, and RQ ≈ 0.8 for proteins. A mixture of substrates gives intermediate values. Questions often require interpreting RQ data from a respirometer.
RQ 值可指示主要呼吸底物：碳水化合物 RQ = 1.0，脂质约 0.7，蛋白质约 0.8。混合底物则呈中间值。考题常要求解读呼吸计数据得出 RQ 值。
7. Simpson’s Index of Diversity | 辛普森多样性指数
D = 1 − ∑( n / N )²
D = 1 − ∑( n / N )²
Where n = number of individuals of a particular species, N = total number of organisms of all species. Values range from 0 (low diversity) to almost 1 (high diversity). Higher D reflects greater species richness and evenness.
其中 n = 某一物种的个体数，N = 所有物种的总个体数。D 值范围从 0（多样性低）到接近 1（多样性高）。D 值越高，反映物种丰富度和均匀度越大。
In CCEA AS exams, you may need to calculate D for a habitat and comment on biodiversity. Remember that high D suggests a stable, complex ecosystem.
在 CCEA AS 考试中，可能需要计算某生境的 D 值并评价其生物多样性。D 值高意味着生态系统稳定、复杂。
8. Genetic Ratios & Punnett Squares | 遗传比例与庞纳特方格
Monohybrid cross (pure-breeding parents, complete dominance): F&sub2; phenotypic ratio = 3 : 1. Genotypic ratio = 1 : 2 : 1.
单基因杂交（纯合亲本，完全显性）：F&sub2; 表型比 = 3 : 1。 基因型比 = 1 : 2 : 1。
Dihybrid cross (heterozygous for both traits, independent assortment): F&sub2; phenotypic ratio = 9 : 3 : 3 : 1.
双基因杂交（双杂合，自由组合）： F&sub2; 表型比 = 9 : 3 : 3 : 1。
Test cross for a heterozygous monohybrid: Phenotypic ratio = 1 : 1. For a dihybrid test cross: 1 : 1 : 1 : 1. Always link ratios to Mendel’s laws of segregation and independent assortment.
杂合单基因测交： 表型比 = 1 : 1。双基因测交：1 : 1 : 1 : 1。务必将这些比例与孟德尔分离定律和自由组合定律联系起来。
9. Calculating Mean & Standard Deviation | 计算平均值与标准差
Mean = ∑x ÷ n
平均值 = ∑x ÷ n
To describe spread around the mean, use standard deviation:
要描述数据围绕平均值的离散程度，使用 标准差：
s = √[ ∑(x&indsub;ḷ − x̅)² ÷ (n − 1) ]
s = √[ ∑(xḳ − x̅)² ÷ (n − 1) ]
s = sample standard deviation, x̅ = mean, xḳ = each individual value, n = sample size. A smaller standard deviation indicates more consistent results. In practical write-ups, you often add error bars showing ± 1 s on bar charts.
s = 样本标准差，x̅ = 平均值，xḳ = 每个独立数值，n = 样本容量。标准差越小，结果越一致。在实验报告中，常在柱状图上添加 ± 1 s 的误差棒。
10. Enzyme Rate of Reaction | 酶促反应速率
Rate = 1 ÷ Time (for a fixed change, e.g. colour disappearance)
速率 = 1 ÷ 时间（用于固定变化，如颜色消失）
When measuring gas production, rate = volume of product formed ÷ time. Always use initial rates when substrate concentration is still high to avoid limiting factors. You may be asked to plot an initial rate curve against substrate concentration and describe the effect of competitive vs. non-competitive inhibitors.
当测量气体产生时，速率 = 生成产物的体积 ÷ 时间。始终使用初始速率（底物浓度尚高时）以避免限制因素。试题可能要求绘制起始速率对底物浓度的曲线，并说明竞争性抑制剂与非竞争性抑制剂的影响。
The lock-and-key and induced-fit models explain specificity. The induced-fit model proposes an enzyme’s active site changes shape slightly to fit the substrate, which then stresses bonds and lowers activation energy.
锁钥模型和诱导契合模型解释了酶的专一性。诱导契合模型提出酶的活性部位轻微变形以适应底物，从而拉紧化学键并降低活化能。
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