📚 AS Eduqas Science: Formula & Theorem Quick Reference Handbook | AS Eduqas 科学：公式定理速查手册
This handbook consolidates the essential formulas, equations, and key theorems for the AS Eduqas Science specification, covering Physics, Chemistry, and Biology. Use it as a fast revision tool to check understanding and recall before exams. Each section pairs concise explanations with practical examples, ensuring you can apply knowledge to unfamiliar contexts.
本手册汇总了AS Eduqas科学考试大纲中的核心公式、方程式和关键定理，涵盖物理、化学和生物三个学科。可作为考前快速复习工具，用于检验理解和记忆。每个部分都将简洁的解释与实际例子相结合，确保你能够将知识应用于陌生情境。
1. Physics – Mechanics & Kinematics | 物理 – 力学与运动学
The SUVAT equations apply only when acceleration is constant. They link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Remember to choose a consistent positive direction.
SUVAT方程仅适用于加速度恒定的情况。它们将位移(s)、初速度(u)、末速度(v)、加速度(a)和时间(t)联系起来。请务必选定一致的正方向。
v = u + at
Use this when time, initial velocity, and acceleration are known. For example, a car accelerating from 10 m/s at 2 m/s² for 5 s reaches 20 m/s.
当已知时间、初速度和加速度时使用此式。例如，一辆汽车以2 m/s²的加速度从10 m/s加速5秒，末速度为20 m/s。
s = ut + ½ at²
This gives displacement when initial and final velocities are not directly needed. It is frequently tested in projectile motion where horizontal and vertical components are separated.
该式可在不需要直接使用末速度时求得位移。在抛体运动中经常考查，需要将水平和竖直分量分开处理。
v² = u² + 2as
Ideal for problems where time is not given. For instance, a ball thrown upward with 15 m/s will reach a maximum height of about 11.5 m (taking g = -9.8 m/s²).
适用于未给出时间的问题。例如，以15 m/s向上抛出的小球，能达到的最大高度约为11.5米（取g = -9.8 m/s²）。
2. Physics – Forces & Newton’s Laws | 物理 – 力与牛顿定律
Newton’s second law defines the relationship between resultant force, mass, and acceleration. Momentum is conserved in closed systems, making it a powerful tool for collision analysis.
牛顿第二定律定义了合力、质量和加速度之间的关系。在封闭系统中动量守恒，这使其成为碰撞分析的有力工具。
F = ma
A resultant force of 10 N acting on a 2 kg trolley produces an acceleration of 5 m/s². Always resolve forces into perpendicular components before applying this equation.
10 N的合力作用于2 kg的小车上，产生5 m/s²的加速度。在应用该公式前，始终将力分解为垂直分量。
p = mv
Momentum (p) is a vector. In an elastic collision, both momentum and kinetic energy are conserved; in an inelastic collision, only momentum is conserved.
动量(p)是矢量。在弹性碰撞中，动量和动能均守恒；在非弹性碰撞中，仅动量守恒。
Impulse = Δp = FΔt
The area under a force–time graph equals the impulse. Airbags increase stopping time, reducing the average force on a passenger.
力-时间图下的面积等于冲量。安全气囊延长了停止时间，从而减小了乘客所受的平均力。
3. Physics – Waves & Optics | 物理 – 波动与光学
The wave equation links frequency, wavelength, and speed. Refractive index explains how light bends at boundaries and determines the critical angle for total internal reflection.
波动方程将频率、波长和波速联系起来。折射率解释了光在界面处的偏折规律，并决定了全反射的临界角。
v = fλ
For electromagnetic waves in a vacuum, v = c = 3.00 × 10⁸ m/s. A radio wave of frequency 100 MHz has a wavelength of 3.0 m.
对于真空中的电磁波，v = c = 3.00 × 10⁸ m/s。频率为100 MHz的无线电波，其波长为3.0米。
n = c / vₛ
Refractive index n is the ratio of the speed of light in a vacuum to its speed in the medium. Diamond has n ≈ 2.42, giving a low critical angle and dazzling sparkle.
折射率n是光在真空中的速度与介质中速度的比值。钻石的n约为2.42，因此临界角小，产生耀眼的闪光。
n₁ sin θ₁ = n₂ sin θ₂
Snell’s law. When light travels from water (n=1.33) to air, the critical angle is sin⁻¹(1/1.33) ≈ 48.8°.
斯涅尔定律。当光从水(n=1.33)射向空气时，临界角为sin⁻¹(1/1.33) ≈ 48.8°。
4. Chemistry – Quantitative Chemistry & Moles | 化学 – 定量化学与摩尔
The mole is the bridge between macroscopic masses and the number of particles. Mastery of these formulas is essential for titration calculations, yield determination, and gas volume problems.
摩尔是宏观质量与微粒数目之间的桥梁。掌握这些公式对于滴定计算、产率测定和气体体积问题至关重要。
n = m / M
Amount (mol) = mass (g) ÷ molar mass (g/mol). For 8.0 g of oxygen (O₂, M = 32 g/mol), n = 0.25 mol.
物质的量（mol）= 质量（g）÷ 摩尔质量（g/mol）。8.0 g氧气（O₂，M = 32 g/mol），n = 0.25 mol。
n = V (dm³) / 24 at RTP
At room temperature and pressure, 1 mol of any gas occupies approximately 24 dm³. Use this to convert between gas volume and amount.
在常温常压下，1 mol任何气体大约占据24 dm³的体积。利用此关系可在气体体积和物质的量之间进行转换。
n = cV
For solutions, amount = concentration (mol/dm³) × volume (dm³). Always convert volumes to dm³ before substituting.
对于溶液，物质的量 = 浓度（mol/dm³）× 体积（dm³）。代入前务必将体积单位转换为dm³。
5. Chemistry – Energetics & Enthalpy | 化学 – 能量学与焓
Enthalpy changes accompany chemical and physical processes. The sign convention is crucial: negative for exothermic reactions, positive for endothermic.
化学反应和物理过程伴随焓变。符号惯例至关重要：放热反应为负值，吸热反应为正值。
q = mcΔT
Heat transferred (J) to a solution or water is calculated from mass, specific heat capacity (usually 4.18 J/g·°C for water), and temperature change.
传递给溶液或水的热量（J）由质量、比热容（水通常为4.18 J/g·°C）和温度变化计算得出。
ΔH = –q / n
The enthalpy change per mole is found by dividing the heat released (with sign) by the amount of limiting reactant. Remember to include the unit kJ/mol.
每摩尔的焓变通过将释放的热量（带符号）除以限制反应物的物质的量得到。记得带上单位kJ/mol。
Hess’s Law: ΔHₚₐₜₕ₁ = ΔHₚₐₜₕ₂
The total enthalpy change for a reaction is independent of the route taken. Use enthalpy cycles to find an unknown ΔH from known combustion or formation data.
反应的总焓变与所经途径无关。使用焓循环图，可从已知的燃烧或生成焓数据求出未知的ΔH。
6. Chemistry – Rates & Equilibrium | 化学 – 速率与平衡
The rate of a reaction can be expressed by the change in concentration per unit time. The equilibrium constant K꜀ indicates the position of equilibrium for homogeneous systems.
反应速率可用单位时间内浓度的变化来表示。平衡常数K꜀表示均相系统中平衡的位置。
Rate = Δ[product] / Δt
Instantaneous rate is the gradient of a concentration–time graph. The initial rate is often measured to deduce orders of reaction.
瞬时速率是浓度-时间图上的切线斜率。通常测量初始速率以推断反应级数。
K꜀ = [products] / [reactants] (with stoichiometric powers)
For aA + bB ⇌ cC + dD, K꜀ = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ. Solids and pure liquids are omitted. A large K꜀ favours products.
对于aA + bB ⇌ cC + dD，K꜀ = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ。固体和纯液体不写入表达式。K꜀值大表明平衡偏向产物。
Le Chatelier’s principle predicts the shift in equilibrium when conditions change. For an exothermic reaction, increasing temperature decreases K꜀.
勒夏特列原理预测了条件改变时平衡移动的方向。对于放热反应，升高温度会降低K꜀。
7. Chemistry – Organic Functional Groups | 化学 – 有机官能团
Functional groups determine chemical behaviour. This table summarises the common classes tested in AS Organic Chemistry.
官能团决定化学性质。下表总结了AS有机化学中常考的类别。
| Homologous Series | Functional Group | Suffix/Prefix | Example |
|---|---|---|---|
| Alkene | C=C | -ene | Ethene |
| Alcohol | –OH | -ol | Ethanol |
| Carboxylic acid | –COOH | -oic acid | Ethanoic acid |
| Haloalkane | –X (F, Cl, Br, I) | fluoro-/chloro- etc. | Chloroethane |
| Ketone | >C=O | -one | Propanone |
For IUPAC naming, first identify the longest carbon chain containing the principal functional group, then number to give the group the lowest locant.
进行IUPAC命名时，首先找出包含主官能团的最长碳链，然后编号使官能团位次最小。
8. Biology – Cell Structure & Microscopy | 生物 – 细胞结构与显微镜
Magnification and resolution underpin our understanding of cell ultrastructure. Eukaryotic and prokaryotic cells share common features but differ in complexity.
放大倍数和分辨率是我们理解细胞超微结构的基础。真核细胞与原核细胞有共同特征，但复杂程度不同。
Magnification = Image size ÷ Actual size
Convert all measurements to the same unit before calculation. A mitochondrion 1 µm long appearing as 10 mm in a diagram has a magnification of ×10,000.
计算前将所有测量值转换为相同单位。一个长1 µm的线粒体在图中显示为10 mm，其放大倍数为×10,000。
The surface area to volume ratio limits cell size. As a cell grows, its SA:V decreases, reducing the efficiency of exchange; this is why large organisms need transport systems.
表面积与体积之比限制了细胞的大小。细胞越大，SA:V越小，物质交换效率降低；这就是大型生物需要运输系统的原因。
Prokaryotes lack membrane-bound organelles. Their DNA is circular and free in the cytoplasm, and they possess 70S ribosomes, compared with 80S in eukaryotes.
原核生物没有膜包被的细胞器。它们的DNA呈环状，游离在细胞质中，核糖体为70S，而真核生物为80S。
9. Biology – Biological Molecules & Enzymes | 生物 – 生物分子与酶
Carbohydrates, lipids, proteins, and nucleic acids are the four major classes. Condensation and hydrolysis reactions are involved in forming and breaking bonds.
糖类、脂质、蛋白质和核酸是四大类生物分子。缩合反应和水解反应分别参与化学键的形成和断裂。
Enzymes are globular proteins with active sites complementary to specific substrates. The lock-and-key and induced-fit models explain catalysis; the induced-fit model stresses conformational changes in the enzyme.
酶是球状蛋白质，其活性位点与特定底物互补。锁钥模型和诱导契合模型解释催化作用；诱导契合模型强调酶构象的改变。
V = Vmax [S] / (Km + [S])
The Michaelis–Menten equation describes the relationship between rate and substrate concentration. Km is the substrate concentration at half Vmax, indicating enzyme affinity.
米氏方程描述了反应速率与底物浓度之间的关系。Km是半最大反应速率时的底物浓度，反映酶与底物的亲和力。
Competitive inhibitors raise Km but Vmax unchanged; non-competitive inhibitors lower Vmax without affecting Km. Temperature and pH extremes disrupt tertiary structure, causing denaturation.
竞争性抑制剂使Km增大而Vmax不变；非竞争性抑制剂降低Vmax但不影响Km。极端的温度和pH会破坏三级结构，导致变性。
10. Biology – Genetics & Inheritance | 生物 – 遗传学与遗传
Monohybrid crosses follow the principles of Mendel. The Hardy–Weinberg principle provides a mathematical model for allele frequencies in populations (for exam boards that include it). Check your specification: Eduqas may require a basic understanding of inheritance patterns but not full population genetics; still, the principle reinforces understanding of dominant and recessive alleles.
单基因杂交遵循孟德尔原理。哈迪-温伯格原理为种群等位基因频率提供了一个数学模型（部分考试局要求）。请核对你的教学大纲：Eduqas可能要求基础遗传规律，不一定有完整种群遗传学；但该原理能强化对显性和隐性等位基因的理解。
p + q = 1; p² + 2pq + q² = 1
Where p is the frequency of the dominant allele and q of the recessive allele. Use this to predict genotype frequencies in a non-evolving population.
其中p是显性等位基因的频率，q是隐性等位基因的频率。用于预测非进化种群中的基因型频率。
Codominance gives a 1:2:1 phenotype ratio in the F2 generation when two heterozygous individuals are crossed. Sex-linkage often results in males expressing X-linked recessive traits more frequently.
共显性在杂合子杂交时，F2代表型比例为1:2:1。伴性遗传常导致男性更多地表现出X连锁隐性性状。
Draw Punnett squares to determine probability. In a cross between two carriers (Tt × Tt) for a recessive condition, the chance of an affected child is 1/4.
绘制庞纳特方格以确定概率。对于隐性遗传病，两个携带者（Tt × Tt）生育患病孩子的概率为1/4。
11. Biology – Transport & Gas Exchange | 生物 – 运输与气体交换
Fick’s law unifies factors affecting diffusion rate. Adaptations like thin exchange surfaces, large surface area, and steep concentration gradients maximise efficiency.
菲克定律概括了影响扩散速率的因素。薄的交换表面、大的表面积和陡的浓度梯度等适应特征使效率最大化。
Rate of diffusion ∝ (Surface area × Concentration difference) / Thickness of membrane
In the human lung, alveoli provide a huge surface area (~70 m²), a thin squamous epithelium, and a dense capillary network maintaining a steep O₂/CO₂ gradient.
在人肺中，肺泡提供了巨大的表面积（约70平方米）、薄层鳞状上皮和密集的毛细血管网，维持着陡的O₂/CO₂浓度梯度。
Mass flow in plants (transpiration stream) is driven by evaporation from leaves, creating tension (cohesion–tension theory). Xylem vessels are dead, hollow tubes strengthened with lignin.
植物中的集流（蒸腾流）由叶片蒸发产生拉力（内聚力-张力理论）。木质部导管是死的中空管道，由木质素加固。
The human heart is a double pump, with the left ventricle wall thicker to generate higher pressure for systemic circulation. Cardiac output = stroke volume × heart rate.
人体心脏是双泵结构，左心室壁更厚以产生更高的体循环压力。心输出量 = 每搏输出量 × 心率。
12. Biology – Ecology & Energy Transfer | 生物 – 生态学与能量传递
Energy flows through ecosystems via trophic levels. Only a small percentage is transferred between levels, limiting the length of food chains.
能量通过营养级在生态系统中流动。只有很小一部分能量在相邻级之间传递，这限制了食物链的长度。
Net primary production (NPP) = Gross primary production (GPP) – Respiratory losses (R)
NPP represents the energy available to primary consumers. It is measured in kJ m⁻² yr⁻¹. Agricultural ecosystems aim to maximise NPP by minimising losses.
净初级生产量（NPP）代表可供初级消费者利用的能量。单位为kJ m⁻² yr⁻¹。农业生态系统通过减少损失来最大化NPP。
The efficiency of energy transfer between two trophic levels is (energy available after transfer ÷ energy available before transfer) × 100. Typically, efficiencies range from 5–20%.
两个营养级之间的能量传递效率 = （传递后的能量 ÷ 传递前的能量）× 100。典型效率在5%至20%之间。
The carbon cycle involves photosynthesis, respiration, decomposition, and combustion. Deforestation reduces CO₂ fixation, while burning fossil fuels adds CO₂, contributing to climate change.
碳循环包括光合作用、呼吸作用、分解作用和燃烧。砍伐森林减少了CO₂的固定，而燃烧化石燃料增加了CO₂，导致气候变化。
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