📚 Year 11 WJEC Biology: Formula & Theorem Quick-Reference Handbook | WJEC 11年级生物：公式定理速查手册
This handbook compiles all essential formulas, equations, and key theorems you need to master for the WJEC Year 11 Biology exam. Keep it handy for last-minute revision and ensure you can apply each concept confidently in calculations and structured questions.
本手册汇集了WJEC 11年级生物考试必须掌握的所有核心公式、方程式和重要定理。随身携带，用于考前快速复习，确保在计算题和简答题中能够自信地应用每一个概念。
1. Magnification Formula | 放大率公式
Magnification is the number of times larger an image appears compared to the actual size of the object. The relationship is given by: Magnification = Image size ÷ Actual size. Always convert both measurements to the same unit before calculating. Rearranging the formula allows you to find actual size or image size when the other two values are known.
放大率是指图像与物体实际尺寸相比放大的倍数。关系式为：放大率 = 图像尺寸 ÷ 实际尺寸。计算前务必把两个测量值换算成相同的单位。变换公式可以在已知其中两项时求出实际尺寸或图像尺寸。
M = I ÷ A 或 I = M × A 或 A = I ÷ M
- Typical units: image size in mm or µm; actual size usually in µm or nm. Use the triangle method to memorise the relationship.
- 常用单位：图像尺寸为毫米或微米；实际尺寸常用微米或纳米。用三角形记忆法掌握三者关系。
- Example: ll image is 20 mm wide and magnification is ×400, actual size = 20 mm ÷ 400 = 0.05 mm = 50 µm.
- 示例：若细胞图像的宽度为20毫米，放大倍数为400倍，实际尺寸 = 20 ÷ 400 = 0.05 毫米 = 50 微米。
2. Photosynthesis Rate & Balanced Equation | 光合作用速率与总反应方程式
The rate of photosynthesis can be measured by the volume of oxygen produced per unit time or the rate of carbon dioxide uptake. The balanced chemical equation summarises the process: light energy drives the conversion of carbon dioxide and water into glucose and oxygen, with chlorophyll acting as the catalyst.
光合作用速率可以通过单位时间产生的氧气体积或二氧化碳的吸收速率来测定。总反应方程式概括了这一过程：光能驱动二氧化碳和水转化为葡萄糖和氧气，叶绿素充当催化剂。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Rate calculations often involve measuring oxygen bubbles per minute from pondweed, or using a gas syringe. The formula for average rate is: Rate = Amount of product formed ÷ Time taken. Limiting factors such as light intensity, CO₂ concentration, and temperature affect the rate, following the principle of the limiting factor law.
速率计算常涉及测量水草每分钟产生的氧气气泡数，或使用气体注射器。平均值速率公式为：速率 = 产物的生成量 ÷ 所花时间。光照强度、二氧化碳浓度和温度等限制因素会影响速率，遵循限制因子定律。
| Limiting Factor | Effect on Rate |
| Light intensity | Rate increases until plateau |
| CO₂ concentration | Rate increases until plateau |
| Temperature | Rate rises to optimum then drops (enzyme denaturation) |
限制因子定律指出，在最接近其最低所需值的那个因子控制下，光合作用的速率只能达到该因子允许的范围，即使其他因子充足。
3. Respiration Equations & Respiratory Quotient (RQ) | 呼吸作用方程式与呼吸商
Aerobic respiration releases energy through the complete breakdown of glucose. The overall equation is the reverse of photosynthesis in terms of raw materials. The respiratory quotient (RQ) indicates which substrate is being respired and is calculated from the ratio of carbon dioxide produced to oxygen consumed.
有氧呼吸通过葡萄糖的完全分解释放能量。总反应方程式在原料上与光合作用互为可逆。呼吸商（RQ）显示正在被呼吸的底物类型，由产生的二氧化碳与消耗的氧气的体积比计算得出。
Aerobic: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ ATP)
Anaerobic (animals): C₆H₁₂O₆ → 2C₃H₆O₃ (lactic acid)
Anaerobic (yeast): C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
RQ formula: RQ = Volume of CO₂ produced ÷ Volume of O₂ consumed 1.0; for lipids it is about 0.7; for proteins typically 0.9. In anaerobic conditions, RQ cannot be calculated meaningfully because oxygen is not used.
RQ公式：呼吸商 = 产生的CO₂体积 ÷ 消耗的O₂体积。碳水化合物的呼吸商为1.0；脂肪约为0.7；蛋白质通常为0.9。无氧条件下因不消耗氧气，呼吸商无实际计算意义。
4. Biomass Transfer Efficiency | 生物量传递效率
In a food chain, only a small percentage of biomass is transferred from one trophic level to the next. The efficiency of this transfer can be calculated using the formula: % Efficiency = (Biomass in higher trophic level ÷ Biomass in lower trophic level) × 100. This explains the pyramid shape of biomass and why food chains rarely exceed four to five links.
在食物链中，只有一小部分生物量从一个营养级传递到下一级。传递效率可用公式：效率百分比 = （较高营养级的生物量 ÷ 较低营养级的生物量） × 100。这解释了生物量金字塔形状以及食物链很少超过四到五个环节的原因。
Biomass is measured as dry mass (g/m² or kg/m²) to eliminate water content variation. Most energy is lost through respiration, undigested waste and heat. Typical transfer efficiencies range from 5% to 20%.
生物量以干重（克/平方米或千克/平方米）计量，以消除水分差异。大部分能量因呼吸、未消化废物和热损耗而丧失。典型的传递效率在5%至20%之间。
- Example: bbit eats 200 g of grass and gains 30 g in dry biomass, efficiency = (30 ÷ 200) × 100 = 15%.
- 示例：假如一只兔子吃掉200克草，干生物量增加30克，传递效率 = （30 ÷ 200） × 100 = 15%。
5. Cardiac Output Formula | 心输出量公式
Cardiac output is the volume of blood pumped by the heart per minute. It is the product of heart rate and stroke volume. This formula helps assess fitness levels and the effect of exercise on the circulatory system.
心输出量是心脏每分钟泵出的血液量。它是心率与每搏输出量的乘积。该公式有助于评估健康水平以及运动对循环系统的影响。
Cardiac Output (CO) = Heart Rate (HR) × Stroke Volume (SV)
Heart rate is beats per minute (bpm); stroke volume is the volume of blood ejected with each beat (ml/beat). During exercise, both heart rate and stroke volume increase, leading to a higher cardiac output to deliver more oxygen to muscles.
心率单位为每分钟心跳次数；每搏输出量是心脏每次搏动射出的血量（毫升/次）。运动时心率和每搏输出量都会增加，导致心输出量上升，以便向肌肉输送更多氧气。
- At rest: typical HR = 70 bpm, SV = 70 ml, CO = 70 × 70 = 4900 ml/min ≈ 4.9 L/min.
- 安静时：典型心率70次/分，每搏输出量70毫升，心输出量 = 70 × 70 = 4900 毫升/分 ≈ 4.9 升/分。
6. Body Mass Index (BMI) | 体质指数
BMI is a screening tool used to categorise individuals as underweight, healthy weight, overweight or obese. It is calculated from a person's mass and height. The formula is essential for discussing health risks linked to body fat.
BMI是一种筛查工具，用于将个体分为偏瘦、健康体重、超重或肥胖。由人的体重和身高计算得出。该公式是讨论与体脂相关的健康风险时不可或缺的基础。
BMI = Mass (kg) ÷ Height² (m²)
| BMI range | Classification |
| Below 18.5 | Underweight |
| 18.5 – 24.9 | Healthy weight |
| 25 – 29.9 | Overweight |
| 30 and above | Obese |
BMI does not distinguish between muscle and fat, so it has limitations. However, it remains a useful population-level indicator. Higher BMI correlates with an increased risk of cardiovascular disease and type 2 diabetes.
BMI不区分肌肉和脂肪，因此存在局限性。尽管如此，它仍是一种有用的群体指标。较高的BMI值与心血管疾病和2型糖尿病风险增加相关。
7. Population Estimation – Lincoln Index | 种群数量估计 – 林肯指数
The Lincoln Index is used to estimate the population size of mobile animals through mark–release–recapture sampling. The method relies on the assumption that marked and unmarked individuals mix randomly and that no significant immigration, emigration or mortality occurs between samples.
林肯指数用于通过标记–释放–重捕法估算移动性动物的种群数量。此方法依赖的假设是，标记与未标记个体随机混合，且两次取样之间没有显著的迁入、迁出或死亡。
stimate = (Number in first sample × Number in second sample) ÷ Number of marked recaptures
econd sample, and m₂ = number of marked individuals in second sample. The formula then is: N = (n₁ × n₂) ÷ m₂.
设 n₁ = 第一次取样中捕获并标记的个体数，n₂ = 第二次取样中捕获的总数，m₂ = 第二次取样中带有标记的个体数。则公式为：N = (n₁ × n₂) ÷ m₂。
- Assumptions: marks are not lost or harmful; marked individuals mix fully; sampling is random; population is closed (no births, deaths, migration).
- 假设条件：标记不会脱落或对生物有害；标记个体充分混合；随机取样；种群封闭（无出生、死亡和迁移）。
8. Genetic Probability & Punnett Squares | 遗传概率与庞纳特方格
Monohybrid inheritance follows Mendel’s laws. A Punnett square predicts the probability of offspring genotypes and phenotypes. The basic theorem states that alleles segregate during gamete formation, so each gamete carries only one allele for each gene.
单基因遗传遵循孟德尔定律。庞纳特方格用于预测后代基因型和表现型的概率。基本定理是：等位基因在配子形成时分离，因此每个配子只携带每个基因的一个等位基因。
o is 1 GG : 2 Gg : 1 gg. If the dominant allele G determines a trait, the phenotypic ratio is 3 dominant : 1 recessive. Probability calculations are often expressed as fractions or percentages.
对于两个杂合子亲本（Gg × Gg）的杂交，基因型比例为1 GG : 2 Gg : 1 gg。若显性等位基因G决定性状，表现型比例为3显性 : 1隐性。概率计算通常以分数或百分比表示。
Probability (offspring) = Number of squares with the genotype ÷ Total squares
For example, the probability of a homozygous recessive offspring (gg) is ¼ or 25%. Dihybrid crosses follow the principle of independent assortment, where allele pairs for different genes separate independently.
例如，纯合隐性后代（gg）的概率为¼或25%。双因子杂交遵循自由组合定律，即不同基因的等位基因对独立分离。
9. Osmosis & Diffusion Principles | 渗透与扩散原理
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. It is a passive process requiring no energy. The rate of diffusion is influenced by temperature, surface area, concentration difference and diffusion distance, as summarised in Fick's Law.
扩散是粒子从高浓度区域向低浓度区域的净移动，沿浓度梯度进行，直至达到平衡。这是一个被动过程，不需要能量。扩散速率受温度、表面积、浓度差和扩散距离的影响，可由菲克定律概括。
Rate of diffusion ∝ (Surface area × Concentration difference) ÷ Diffusion distance
Osmosis is a special case of diffusion involving the movement of water molecules through a partially permeable membrane from a dilute to a more concentrated solution. The water potential gradient drives osmosis, and the concept of water potential (Ψ) is measured in kilopascals (kPa). Animal cells burst (lysis) in pure water, while plant cells become turgid and are protected by their cell wall.
渗透是扩散的一种特殊形式，涉及水分子通过选择性透过膜从稀溶液向较浓溶液移动。水势梯度驱动渗透，水势（Ψ）以千帕（kPa）计量。动物细胞在纯水中会胀破（溶血），而植物细胞变得硬挺，受到细胞壁的保护。
10. Enzyme Lock-and-Key Model & Q10 Coefficient | 酶的锁钥模型与温度系数 Q10
The lock-and-key theory describes enzyme specificity: the active site of an enzyme has a complementary shape to its specific substrate, forming an enzyme-substrate complex. The induced fit model modifies this slightly, but WJEC mainly references the lock-and-key analogy. Enzymes lower activation energy and are not consumed in the reaction.
锁钥学说描述了酶的专一性：酶的活性位点与其特定底物的形状互补，形成酶-底物复合物。诱导契合模型对此略有修改，但WJEC主要引用锁钥比喻。酶降低活化能，且在反应中不被消耗。
The Q10 temperature coefficient measures the rate of a reaction change over a 10°C interval. It helps quantify the effect of temperature on enzyme-catalysed reactions before denaturation occurs.
温度系数Q10衡量反应速率在每10°C温度变化中的变化倍数。它有助于在变性发生前量化温度对酶促反应的影响。
Q10 = Rate at (T + 10°C) ÷ Rate at T°C
For many enzymatic reactions, Q10 is about 2, meaning the rate doubles for every 10°C rise within the optimum range. Above the optimum temperature, the active site denatures, and the rate falls sharply. pH also affects enzyme activity, with most human enzymes having an optimum near pH 7.
对许多酶促反应而言，Q10值约为2，意味着在适宜范围内温度每升高10°C，速率翻倍。超过最适温度时活性位点变性，速率急剧下降。pH值同样影响酶活性，多数人体酶的最适pH值在7左右。
11. Natural Selection – Core Theorem | 自然选择 – 核心定理
Charles Darwin’s theory of evolution by natural selection is a central theorem in biology. It states that within a population, there is variation. Individuals with characteristics better suited to the environment have a selective advantage; they are more likely to survive, reproduce, and pass on their advantageous alleles to offspring.
达尔文的自然选择进化论是生物学的核心定理。它指出，种群内部存在变异。具有更适应环境特征的个体具有选择优势；它们更有可能存活、繁殖并将其有利的等位基因传递给后代。
Over many generations, the frequency of advantageous alleles increases, leading to adaptation and eventually evolution of new species if populations become isolated. Antibiotic resistance in bacteria is a classic example: exposure to an antibiotic creates a strong selection pressure favouring resistant strains.
经过多代之后，有利等位基因的频率增加，导致适应，若种群隔离最终可能导致新物种形成。细菌的抗生素耐药性是经典实例：暴露于抗生素产生强大的选择压力，有利于耐药菌株。
Key evidence for evolution includes fossils, DNA sequence comparisons and the observation of antibiotic-resistant bacteria. Speciation can occur due to geographical isolation, leading to reproductive isolation and separate evolutionary paths.
进化论的关键证据包括化石、DNA序列比较以及对抗生素耐药菌的观察。物种形成可能因地理隔离而发生，导致生殖隔离并走向不同的进化路径。
12. Pyramids & Productivity Theorems | 金字塔与生产力定理
Ecological pyramids represent the structure of food chains in terms of number, biomass or energy. The pyramid of energy is always upright because energy is lost at each trophic level, primarily through respiration and heat. The 10% rule is a simplified theorem stating that only about 10% of the energy is transferred between trophic levels, though actual values vary.
生态金字塔以数量、生物量或能量来表示食物链的结构。能量金字塔总是正立的，因为能量在每一个营养级通过呼吸和热损失而减少。10%法则是一个简化的定理，表明能量在营养级之间的传递率仅有约10%，尽管实际值会有所变化。
Gross primary production (GPP) is the total light energy converted by plants; net primary production (NPP) remains after subtracting respiration (R): NPP = GPP – R. This formula explains the available biomass for herbivores.
总初级生产量（GPP）是植物转化的总光能；净初级生产量（NPP）在减去呼吸消耗（R）后剩余：NPP = GPP – R。该公式解释了可供草食动物利用的生物量。
Pyramid diagrams must be drawn to scale, with bars centred and labelled. An understanding of productivity helps explain why short food chains are more efficient for feeding large populations; less energy is lost as heat.
金字塔图必须按比例绘制，条形居中并标注。理解生产力有助于解释为什么短食物链在供养大量人口时更有效；因为以热形式损失的能量更少。
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