📚 Year 11 SQA Biology: Quick Reference Handbook of Formulas and Theorems | Year 11 SQA 生物：公式定理速查手册
Mastering quantitative skills is essential for success in SQA Biology. This handbook consolidates the key formulas, theorems, and calculation principles for Year 11 students. From microscopy measurements to energy flow in ecosystems, each section provides clear definitions, worked applications, and bilingual explanations to build confidence in numeracy-based exam questions.
掌握定量技能是在 SQA 生物考试中取得成功的关键。本手册为 Year 11 学生整理了核心公式、定理和计算原理。从显微镜测量到生态系统中的能量流动，每个部分都提供了清晰的定义、应用示例和中英双语解释，帮助建立应对计算类考试题目的信心。
1. Units and Conversions in Biology | 生物学中的单位与换算
so unit conversions are fundamental. The most common prefixes are milli (m, 10⁻³), micro (µ nano (n, 10⁻⁹). You must be able to move fluently between millimetres (mm), micrometres (µm), and nanometres (nm). Remember: 1 mm = 1000 µm, and 1 µ 1000 nm. Always express very large or very small numbers in standard form to avoid errors.
生物测量跨越多个数量级，因此单位换算十分基础。最常见的前缀有毫（m，10⁻³）、微（µ，10⁻⁶）和纳（n，10⁻⁹）。你必须能在毫米（mm）、微米（µm）和纳米（nm）之间熟练转换。请记住：1 mm = 1000 µm，1 µm = 1000 nm。始终用标准形式表示极大或极小的数字，避免出错。
When converting, multiply by powers of 1000. For example, to change 0.05 mm to µm, multiply by 1000 to obtain 50 µm. In microscopy, always check the units of eyepiece graticule calibrations before starting a calculation.
转换时，乘以 1000 的幂。例如，将 0.05 mm 转换为 µm，乘以 1000 得 50 µm。在使用显微镜时，开始计算前务必检查目镜测微尺校准所使用的单位。
2. Magnification Formula | 放大倍数公式
The linear magnification of a biological drawing or microscope image is calculated using the relationship between image size and actual size. The formula is:
生物绘图或显微镜图像的线性放大倍数通过图像大小与实际大小的关系来计算。其公式为：
Magnification = Image Size ÷ Actual Size
size: Actual Size = Image Size ÷ Magnification. Always use the same length units (usually µm or mm) before dividing.
图像大小和实际大小必须使用相同单位。重新整理该公式即可求出实际大小：实际大小 = 图像大小 ÷ 放大倍数。在相除之前，务必统一长度单位（通常为 µm 或 mm）。
tual size is 60 ÷ 400 = 0.15 mm. Convert to micrometres by multiplying by 1000, giving 150 µm.
举个计算示例，如果一个细胞在屏幕上的图像长度为 60 mm，标注的放大倍数为 ×400，则实际大小为 60 ÷ 400 = 0.15 mm。乘以 1000 转换为微米，得 150 µm。
3. Percentage Change and Averages | 百分比变化与平均值
Percentage change is widely used to compare biological data before and after an experimental treatment. The formula uses the initial and final values:
百分比变化广泛用于比较实验处理前后的生物学数据。该公式需要使用初始值和最终值：
Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100%
age) is fundamental: Mean = Sum of all values ÷ Number of values. This is essential when analysing repeats in practical work.
负百分比表示减小。始终以初始值作为分母。除百分比变化外，计算平均值也非常基础：平均值 = 所有数值之和 ÷ 数值的个数。在分析实验操作的重复数据时，这一点至关重要。
4. Rate of Reaction Calculations | 反应速率计算
The rate of a biological process, such as enzyme-catalysed reactions, photosynthesis, or respiration, is the change in a quantity per unit time. The general formula is:
生物过程的速率，例如酶催化反应、光合作用或呼吸作用，是指单位时间内某一数量的变化量。其通用公式为：
Rate = Change in Quantity ÷ Time Taken
cm³ of oxygen in 4 minutes, the rate is 12 ÷ 4 = 3 cm³/min. Always specify the units clearly (e.g., cm³ min⁻¹).
该数量可以是产生的气体体积、消耗的反应物质量，或颜色强度的变化。例如，如果酶反应在 4 分钟内产生 12 cm³ 氧气，则速率为 12 ÷ 4 = 3 cm³/min。始终明确标出单位（例如 cm³ min⁻¹）。
5. Surface Area to Volume Ratio | 表面积体积比
Surface area to volume ratio (SA:V) is a critical concept explaining why cells are small and why organisms have specialised exchange surfaces. It is calculated as:
表面积体积比 (SA:V) 是解释细胞为何如此微小、以及生物体为何拥有特化交换表面的关键概念。其计算方式为：
SA:V Ratio = Surface Area ÷ Volume
For a cube of side length L r, its SA:V ratio decreases. This reduces the efficiency of diffusion for nutrient uptake and waste removal, requiring specialised systems like lungs and gills.
对于边长为 L 的立方体，表面积 = 6L²，体积 = L³，因此 SA:V = 6 ÷ L。随着生物体变大，其 SA:V 比值降低。这会降低扩散对营养吸收和废物排出的效率，因此需要专门的系统，如肺和鳃。
6. Respiratory Quotient (RQ) | 呼吸商
The respiratory quotient indicates the type of substrate being respired by comparing the volumes of carbon dioxide produced and oxygen consumed. The formula is:
呼吸商通过比较产生的二氧化碳体积与消耗的氧气体积，指示正在被呼吸的底物类型。其公式为：
RQ = Volume of CO₂ Produced ÷ Volume of O₂ Consumed
.9. Values outside this range may suggest anaerobic respiration. Always ensure the gas volumes are measured under the same temperature and pressure conditions.
碳水化合物呼吸的 RQ 值约为 1.0；脂质呼吸约为 0.7；蛋白质呼吸约为 0.9。超出此范围的数值可能提示无氧呼吸。始终确保气体体积在相同温度和压强条件下测量。
7. Energy Transfer Efficiency | 能量传递效率
Energy is lost between trophic levels, mainly as heat through respiration, and as undigested material. The efficiency of energy transfer is calculated as a percentage:
能量在营养级之间会损失，主要通过呼吸作用以热量形式散失，以及作为未消化的物质排出。能量传递效率的计算以百分比表示：
Efficiency (%) = [Energy at Higher Trophic Level ÷ Energy at Lower Trophic Level] × 100%
In most ecosystems, transfer efficiency averages around 10%. When calculating, ensure both energy values are in the same units (e.g., kJ m⁻² yr⁻¹). This concept explains why food chains rarely exceed four or five trophic levels.
在大多数生态系统中，传递效率平均约为 10%。计算时，确保两个能量值使用相同单位（例如 kJ m⁻² yr⁻¹）。这一概念解释了为何食物链很少超过四到五个营养级。
8. Population Growth Rate | 种群增长率
Population size in a defined area changes over time due to births, deaths, immigration, and emigration. The rate of population change can be expressed as:
一定区域内种群规模会随时间因出生、死亡、迁入和迁出而变化。种群变动率可表示为：
Population Change = (Births + Immigration) − (Deaths + Emigration)
For a growth rate per individual (per capita), divide by the initial population. In SQA exam contexts, always read the data carefully to identify which four factors are provided. A positive result means population growth; a negative result means decline.
若要求单一个体的增长率（人均），则除以初始种群数量。在 SQA 考试背景下，要仔细阅读数据以明确提供了哪四个因素。正数结果意味着种群增长；负数结果意味着种群衰退。
9. Probability in Genetics | 遗传学中的概率
Mendel's laws of segregation and independent assortment are the theoretical foundation for predicting genetic outcomes. Monohybrid crosses follow predictable ratios (e.g., 3:1 for a heterozygous cross with dominance). The product rule states that the probability of two independent events occurring together is the product of their individual probabilities. The sum rule adds probabilities for mutually exclusive outcomes.
孟德尔的分离定律和自由组合定律是预测遗传结果的理论基础。单基因杂交遵循可预测的比例（例如，具有显性性状的杂合杂交为 3:1）。乘积规则指出，两个独立事件同时发生的概率等于各自概率的乘积。加和规则用于将互斥结果的概率相加。
tio is 1 AA : 2 Aa : 1 aa, giving a 3:1 phenotype ratio if A is dominant. Always express probabilities as fractions, decimals, or percentages.
使用庞纳特方格可以直观展示所有可能的配子组合。对于两个杂合亲本的杂交（Aa × Aa），基因型比为 1 AA : 2 Aa : 1 aa，若 A 为显性则表型比为 3:1。始终将概率表示为分数、小数或百分数。
10. Dilution Calculations | 稀释计算
Preparing solutions of a required concentration from a stock solution involves using the dilution equation. This is based on the principle that the amount of solute remains constant before and after adding solvent:
从储备液配制所需浓度的溶液需使用稀释方程式。其原理是加入溶剂前后，溶质的量保持不变：
C₁V₁ = C₂V₂
0 cm³ of 0.5 mol dm⁻³ solution from a 2 mol dm⁻³ stock, V₁ = (0.5 × 100) ÷ 2 = 25 cm³. You would therefore add 25 cm³ of stock to 75 cm³ of water.
其中 C₁ 为初始浓度，V₁ 为初始体积，C₂ 为最终浓度，V₂ 为最终体积。例如，要从 2 mol dm⁻³ 的储备液配制 100 cm³ 的 0.5 mol dm⁻³ 溶液，V₁ = (0.5 × 100) ÷ 2 = 25 cm³。因此，需要将 25 cm³ 储备液加入 75 cm³ 水中。
11. Osmosis and Water Movement | 渗透与水分运动
Osmosis is the net movement of water molecules through a partially permeable membrane from a region of higher water potential to a region of lower water potential. While not a numerical formula, the direction of movement can be predicted by comparing solute concentrations. Water potential decreases as solute concentration increases.
渗透是水分子通过半透膜从较高水势区域向较低水势区域的净移动。尽管不是一个数值公式，但通过比较溶质浓度可预测水分移动方向。水势随溶质浓度升高而降低。
olutions. The formula for percentage change in mass is the same as the percentage change formula: (Final Mass − Initial Mass) ÷ Initial Mass × 100%.
实验中，渗透速率常通过计算植物组织在不同溶液中质量或长度的百分比变化来量化。质量百分比变化公式与前述的百分比变化公式相同：(最终质量 − 初始质量) ÷ 初始质量 × 100%。
12. Lincoln Index (Capture-Mark-Recapture) | 林肯指数（标记重捕法）
To estimate the population size of mobile organisms, ecologists use the capture-mark-recapture method. The Lincoln Index provides the formula:
为了估计移动生物体的种群大小，生态学家使用标记重捕法。林肯指数提供的公式为：
Population Estimate (N) = (M × C) ÷ R
where M is the number of individuals captured and marked in the first sample, C is the total number captured in the second sample, and R is the number of marked individuals recaptured in the second sample. This method assumes random mixing, no migration, and no change in survival due to marking.
其中 M 为首次捕捉并标记的个体数量，C 为第二次捕捉的总数量，R 为第二次捕捉中已标记个体的数量。该方法假设标记个体随机混合、没有迁移、且标记不影响生存。
Published by TutorHao | Biology Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图