📚 Quick Reference Handbook: Key Formulas and Principles for SQA Year 10 Biology | SQA Year 10 生物：公式定理速查手册
Welcome to your essential quick-reference guide for SQA Year 10 Biology (typically National 5 equivalent). This handbook consolidates all the key formulas, principles, and numerical skills you need to master laboratory calculations, data analysis, and core biological concepts. From magnification to enzyme kinetics, and from genetic probabilities to energy transfer efficiency, each section presents the formula clearly, explains how to use it, and highlights common pitfalls. Keep this resource handy for revision, homework, and exam preparation.
欢迎使用你的 SQA Year 10 生物学（通常对标 National 5）必备速查手册。本手册汇总了所有关键公式、原理和数值计算技能，助你掌握实验室计算、数据分析及核心生物学概念。从放大倍率到酶动力学，从遗传概率到能量传递效率，每个小节清晰给出公式、解释用法并提示常见误区。复习、作业和备考时，请随时查阅本资源。
1. Magnification Calculations | 放大倍率计算
The magnification of a drawing, photomicrograph, or image can be calculated if you know the image size and the actual specimen size. Both measurements must be expressed in identical units before division.
若已知图像尺寸和标本实际尺寸，可计算绘图、显微照片或图像的放大倍率。两者单位必须统一后方可相除。
Magnification = Image size ÷ Actual size
放大倍率 = 图像尺寸 ÷ 实际尺寸
For example, if a cell image measures 60 mm on paper and its true length is 0.2 mm, the magnification is 60 ÷ 0.2 = 300×. Always convert to the smallest common unit (often µm). Remember that 1 mm = 1000 µm.
例如，若纸上细胞图像长 60 mm，实际长度为 0.2 mm，则放大倍率为 60 ÷ 0.2 = 300×。始终换算成最小共同单位（常为 µm）。注意 1 mm = 1000 µm。
Rearranging the equation allows you to find actual size: Actual size = Image size ÷ Magnification. This is essential when reading scales from micrographs.
公式变形可求实际尺寸：实际尺寸 = 图像尺寸 ÷ 放大倍率。在读取显微图比例尺时这很关键。
2. Genetic Crosses and Punnett Squares | 遗传杂交与庞纳特方格
Mendel’s law of segregation states that alleles separate during gamete formation, each gamete carrying only one allele for each gene. A monohybrid cross follows one characteristic, determined by a single gene with dominant (e.g., B) and recessive (b) alleles.
孟德尔分离定律指出，配子形成时等位基因分离，每个配子仅携带一个基因的一个等位基因。单基因杂交跟踪由一对显性（如 B）和隐性（b）等位基因决定的单一性状。
Use a Punnett square to predict offspring genotypes and phenotypes. For parents both heterozygous (Bb), the expected genotypic ratio is 1 BB : 2 Bb : 1 bb, and the phenotypic ratio for a dominant-recessive trait is 3 : 1.
用庞纳特方格预测子代基因型与表现型。若亲本均为杂合（Bb），预期基因型比为 1 BB : 2 Bb : 1 bb，显隐性性状的表现型比为 3 : 1。
Probability of a specific genotype can be expressed as a fraction or percentage; for example, the chance of a homozygous recessive offspring from two heterozygotes is ¼ or 25%.
特定基因型的概率可用分数或百分数表示；例如两个杂合亲本产生纯合隐性后代的概率为 ¼ 或 25%。
3. Population Density and Sampling | 种群密度与采样
To estimate population size in a habitat, ecologists use sampling techniques such as quadrats (for plants and slow-moving organisms) and capture-mark-recapture (for mobile animals). The basic formula for population density is straightforward.
生态学家使用样方法（针对植物和缓慢生物）和标志重捕法（针对移动动物）等采样技术估算栖息地内种群数量。种群密度基本公式很简单。
Population density = Total number counted ÷ Area sampled
种群密度 = 计数总数 ÷ 采样面积
For quadrat sampling, calculate the mean number of individuals per quadrat and multiply by the total area divided by the quadrat area. Always express density per unit area (e.g., per m²).
样方采样中，先算出每个样方个体平均数，再乘以（总面积 ÷ 样方面积）。密度始终以单位面积（例如每平方米）表示。
In the capture-mark-recapture (Lincoln index) method: Population estimate = (Number caught in first sample × Number caught in second sample) ÷ Number of marked individuals recaptured. Ensure the assumptions (closed population, marks not lost) are met.
标志重捕法（林肯指数）：种群估算值 = (首次捕获数 × 第二次捕获数) ÷ 重捕中标记个体数。须满足假设（封闭种群、标志不脱落）。
4. Enzyme Activity and Rate Calculations | 酶活性与速率计算
The rate of an enzyme-controlled reaction can be determined by measuring the amount of product formed (or substrate used) per unit time. The formula is a direct rate calculation.
通过测定单位时间内产物生成量（或底物消耗量）可确定酶促反应速率。公式为直接速率计算。
Rate = Change in quantity (product or substrate) ÷ Time taken
速率 = 数量变化（产物或底物） ÷ 所用时间
When a graph of product concentration against time is plotted, the initial rate is the gradient of the tangent at time zero. This represents the fastest rate before substrate becomes limiting or product inhibition occurs.
绘制产物浓度-时间曲线图时，初始速率是零时刻切线的斜率，代表底物尚未成为限制因素或产物抑制发生前的最快速率。
Units for rate depend on the measurement; common examples are cm³ O₂ min⁻¹, mg substrate min⁻¹, or absorbance units s⁻¹. Always label axes and state units clearly.
速率单位取决于测量指标；常见的有 cm³ O₂ min⁻¹、mg 底物 min⁻¹ 或吸光度单位 s⁻¹。务必明确标注坐标轴及单位。
5. Percentage Change in Mass (Osmosis Experiments) | 质量百分比变化（渗透实验）
When investigating the effect of solute concentration on tissue (e.g., potato cylinders), calculating percentage change in mass allows fair comparison between samples of different starting masses. It shows the direction and magnitude of net water movement.
研究溶质浓度对组织（如土豆条）影响时，计算质量百分比变化可以在不同起始质量的样本间进行公平比较，显示净水分移动的方向和程度。
Percentage change in mass = (Final mass – Initial mass) / Initial mass × 100%
质量百分比变化 =（最终质量 – 初始质量）/ 初始质量 × 100%
A positive value indicates mass gain (water entering by osmosis when external solute concentration is lower); a negative value indicates mass loss (water leaving when external solute concentration is higher). The concentration where mass change is zero is an estimate of the isotonic point.
正值表明质量增加（外部溶质浓度较低时水因渗透进入）；负值表明质量减少（外部溶质浓度较高时水流失）。质量变化为零时的浓度即为等渗点的估算值。
Always blot the tissues dry before weighing and use at least three replicates to calculate a mean percentage change, improving reliability.
称重前务必将组织吸干，并至少使用三个重复计算平均百分比变化，以提高可靠性。
6. Photosynthesis and Limiting Factors | 光合作用与限制因素
The rate of photosynthesis is influenced by light intensity, carbon dioxide concentration, and temperature. The law of limiting factors states that at any given moment, the process is limited by the factor in shortest supply.
光合作用速率受光照强度、二氧化碳浓度和温度影响。限制因素定律指出：在任何时刻，反应速率受最缺乏的因素制约。
A simplified word equation summarises the overall process, and it helps when working with energy conversions or biomass accumulation.
Carbon dioxide + Water → Glucose + Oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
(This occurs in the presence of light and chlorophyll)
（该过程在光和叶绿素存在下发生）
The rate can be measured by oxygen production (bubbles per minute or volume using a gas syringe) or by the increase in dry biomass of a plant over time. When light intensity is the independent variable, the relationship is initially proportional; at the light saturation point, another factor becomes limiting.
速率可通过氧气产量（每分钟气泡数或使用气体注射器的体积）或植物干生物量随时间增加来测定。当光照强度为自变量时，初始阶段呈正比；在光饱和点，另一因素成为限制。
7. Energy Transfer and Biomass Efficiency | 能量传递与生物量效率
In ecosystems, energy passes along food chains but a large proportion is lost at each trophic level through respiration, excretion, and uneaten parts. Efficiency of transfer can be calculated using the following formula.
在生态系统中，能量沿食物链传递，但每一营养级都因呼吸、排泄和未被取食部分损失大量能量。传递效率可用以下公式计算。
Efficiency (%) = (Energy or biomass transferred to next level ÷ Energy or biomass available at previous level) × 100
效率 (%) =（传递至下一级的能量或生物量 ÷ 前一级可用的能量或生物量）× 100
Typically, only about 10% of energy is transferred between trophic levels. This explains why food chains rarely exceed four or five levels and why pyramids of biomass or energy are always upright.
通常营养级间仅约 10% 的能量得以传递。这解释了食物链为何很少超过四到五级，以及生物量或能量金字塔为何总是正立的。
Net primary production (NPP) in plants can be expressed as: NPP = Gross primary production (GPP) – Plant respiration. This biomass is what becomes available to primary consumers.
植物净初级生产量 (NPP) 可表示为：NPP = 总初级生产量 (GPP) – 植物呼吸消耗。该生物量成为初级消费者的可获资源。
8. Surface Area to Volume Ratio | 表面积与体积比
As an object or organism increases in size, its volume grows faster than its surface area. This ratio is critical for understanding transport limitations in cells and organisms, such as diffusion, heat exchange, and oxygen uptake.
当物体或生物体增大时，其体积增速快于表面积。该比值对于理解细胞和生物体中扩散、热交换和氧气摄入等运输限制至关重要。
Surface area : Volume ratio = Total surface area ÷ Volume
表面积 : 体积比 = 总表面积 ÷ 体积
For a simple cube of side L, surface area = 6L² and volume = L³, giving a ratio that simplifies to 6/L. This shows that a small cube has a much larger ratio than a large cube, and thus a faster rate of diffusion across its surface.
对于边长为 L 的简单立方体，表面积 = 6L²，体积 = L³，比值简化为 6/L。这表明小立方体的比值远大于大立方体，因而其表面扩散速率更快。
Single-celled organisms rely on their high surface area:volume ratio to supply oxygen and remove wastes by diffusion alone. Multicellular organisms require specialised exchange surfaces (lungs, gills, villi) and transport systems to overcome diffusion distances.
单细胞生物依靠高表面积与体积比，仅凭扩散即可供应氧气并排除废物。多细胞生物则需要特化的交换表面（肺、鳃、绒毛）和运输系统来克服扩散距离。
9. Heart Rate and Cardiac Output | 心率与心输出量
During exercise, heart rate and stroke volume increase to deliver more oxygen to working muscles. Cardiac output is a fundamental physiological measure linking these variables.
运动时，心率与每搏输出量增加，为工作肌肉输送更多氧气。心输出量是联系这些变量的基本生理指标。
Cardiac output (CO) = Heart rate (HR) × Stroke volume (SV)
心输出量 (CO) = 心率 (HR) × 每搏输出量 (SV)
Heart rate is measured in beats per minute (bpm); stroke volume is the volume of blood pumped per beat (ml beat⁻¹). Typical resting values are HR ≈ 70 bpm, SV ≈ 70 ml, giving CO ≈ 4900 ml min⁻¹ (4.9 L min⁻¹).
心率以每分钟心跳次数 (bpm) 度量；每搏输出量为每搏泵血量 (ml beat⁻¹)。典型静息值为 HR ≈ 70 bpm，SV ≈ 70 ml，得 CO ≈ 4900 ml min⁻¹ (4.9 L min⁻¹)。
After exercise, calculating recovery time and percentage change from resting values helps assess fitness. Always consider units and convert to litres if required by the exam question.
运动后，计算恢复时间及相对于静息值的百分比变化有助于评估体能状况。始终注意单位，若考题需要可转换为升。
10. Variables, Averages and Data Handling | 变量识别、平均值与数据处理
Every valid investigation must identify the independent variable (what you change), the dependent variable (what you measure) and the control variables (what must be kept constant). This ensures fair testing and reliable conclusions.
每个有效探究都必须识别自变量（你所改变的量）、因变量（你测量的结果）和控制变量（必须保持不变的因素），以确保公平测试与可靠结论。
Repeated measurements are used to calculate an arithmetic mean. The formula for the mean is simple, but you must be able to identify and handle anomalous results appropriately.
Mean = Sum of all values ÷ Number of values
平均值 = 所有数值之和 ÷ 数值个数
For example, if five transpiration readings are 2.3, 2.5, 7.8, 2.4, 2.3 cm³, you should identify 7.8 as an outlier, omit it, and calculate the mean from the remaining four values = 2.375 cm³. Always justify omission based on atypical magnitude.
例如，若五次蒸腾读数分别为 2.3、2.5、7.8、2.4、2.3 cm³，应识别 7.8 为异常值并剔除，用剩余四个数值计算平均值 = 2.375 cm³。剔除时必须给出基于异常幅度的理由。
Present data in line graphs, bar charts or scatter graphs as appropriate. The independent variable goes on the x-axis, the dependent on the y-axis. Always draw a line of best fit (curved or straight) and avoid ‘dot-to-dot’ unless specifically instructed.
根据数据类型选用折线图、条形图或散点图呈现。自变量在 x 轴，因变量在 y 轴。务必绘制最佳拟合线（曲线或直线），除非专门要求，否则避免逐点连接。
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