📚 AS Edexcel Science: Quick-Reference Formula & Theorem Handbook | AS Edexcel 科学：公式定理速查手册
This article collects the essential formulas, equations and key theorems required for the AS Edexcel Science curriculum, covering Physics, Chemistry and Biology. Use it as a rapid revision companion to reinforce your understanding of quantitative relationships, from SUVAT equations to mole calculations and beyond.
本文汇总了 AS Edexcel 科学课程中必须掌握的核心公式、方程式与重要定理，涵盖物理、化学和生物三大学科。使用本手册作为快速复习伴侣，有助于巩固你对运动学方程、摩尔计算等各类定量关系的理解。
1. Kinematic Equations (SUVAT) | 运动学方程 (SUVAT)
For an object moving with constant acceleration along a straight line, the five SUVAT variables — displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t) — are linked by four equations. These are valid only when acceleration is uniform.
对于沿直线以恒定加速度运动的物体，五个 SUVAT 变量——位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)——可通过四个方程相互关联。这些方程仅在加速度恒定时有效。
- v = u + a t — relates velocity and time / 关联速度与时间
- s = u t + ½ a t² — displacement with initial velocity and acceleration / 包含初速度与加速度的位移公式
- v² = u² + 2 a s — velocity–displacement relation / 速度与位移关系
- s = ½ (u + v) t — displacement from average velocity / 由平均速度求位移
Remember to choose a positive direction when assigning signs to vector quantities.
使用矢量量时，务必先选定一个正方向，赋予各量正确的正负号。
2. Forces, Momentum & Newton’s Laws | 力、动量与牛顿定律
The resultant force acting on an object equals its mass multiplied by acceleration: F = m a. For an object in equilibrium, the vector sum of all forces is zero. Momentum p is defined as p = m v and is always conserved in a closed system.
作用在物体上的合力等于其质量乘以加速度：F = m a。处于平衡状态的物体，所有力的矢量和为零。动量 p 定义为 p = m v，在封闭系统中动量总是守恒的。
The impulse of a force is the change in momentum: F Δt = Δ(m v). This relationship is especially useful for collision and explosion problems.
力的冲量等于动量的变化：F Δt = Δ(m v)。该关系在解决碰撞与爆炸问题时尤其重要。
3. Work, Energy & Power | 功、能与功率
When a force F moves an object through a displacement s in the direction of the force, the work done is W = F s. Mechanical energy exists in two key forms: kinetic energy Eₖ = ½ m v² and gravitational potential energy ΔEₚ = m g Δh.
当一个力 F 使物体沿力的方向发生位移 s 时，所做的功为 W = F s。机械能主要有两种形式：动能 Eₖ = ½ m v² 和重力势能变化 ΔEₚ = m g Δh。
Power is the rate of energy transfer: P = W / t = ΔE / t. For an object moving at constant speed against a resistive force, power can also be expressed as P = F v. The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.
功率是能量转移的速率：P = W / t = ΔE / t。对于以恒定速度克服阻力运动的物体来说，功率也可写成 P = F v。能量守恒定律指出，能量既不会凭空产生也不会凭空消失，只会从一种形式转化为另一种形式。
4. Electrical Circuits | 电路定律
The fundamental relationships in circuit analysis are Ohm’s law V = I R, the electric power law P = I V = I² R = V² / R, and the definition of resistance from resistivity: R = ρ L / A, where ρ is resistivity, L length and A cross-sectional area.
电路分析中最基础的关系是欧姆定律 V = I R、电功率公式 P = I V = I² R = V² / R 以及利用电阻率定义电阻：R = ρ L / A，其中 ρ 为电阻率、L 为长度、A 为横截面积。
For resistors in series: R_total = R₁ + R₂ + …. For resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + …. The sum of the e.m.f. around a closed loop equals the sum of the p.d. drops (Kirchhoff’s second law).
电阻串联时：R_total = R₁ + R₂ + …。电阻并联时：1/R_total = 1/R₁ + 1/R₂ + …。闭合回路中的总电动势等于总电势降落之和（基尔霍夫第二定律）。
5. Wave Properties | 波的特性
The wave equation links speed (v), frequency (f) and wavelength (λ): v = f λ. Electromagnetic waves travel through a vacuum at c = 3.00 × 10⁸ m s⁻¹. For a periodic wave, the period T is the reciprocal of frequency: T = 1 / f.
波的方程将波速 (v)、频率 (f) 和波长 (λ) 联系在一起：v = f λ。电磁波在真空中的传播速度 c = 3.00 × 10⁸ m s⁻¹。周期波的周期 T 与频率互为倒数：T = 1 / f。
In refraction, Snell’s law for a boundary between two transparent media is n₁ sin θ₁ = n₂ sin θ₂, where n is refractive index. The refractive index can also be calculated as n = c / v, the ratio of the speed of light in vacuum to the speed in the medium. Diffraction and interference patterns can be predicted using the double‑slit fringe spacing formula w = λ D / s, where w is fringe width, D is distance to screen and s is slit separation.
在折射现象中，两种透明介质界面处的斯涅耳定律为 n₁ sin θ₁ = n₂ sin θ₂，其中 n 为折射率。折射率还可表示为真空中光速与介质中光速之比：n = c / v。双缝干涉条纹间距可通过公式 w = λ D / s 预测，其中 w 为条纹宽度，D 为屏幕到双缝的距离，s 为双缝间距。
6. Mechanics of Materials | 材料力学
Hooke’s law describes the elastic deformation of a spring: F = k x, where k is the spring constant and x the extension. The elastic potential energy stored in a stretched spring is E = ½ F x = ½ k x², provided the elastic limit is not exceeded.
胡克定律描述了弹簧的弹性形变：F = k x，其中 k 为弹簧常数，x 为伸长量。在不超过弹性极限的前提下，被拉伸的弹簧所储存的弹性势能为 E = ½ F x = ½ k x²。
Stress σ and strain ε characterise material behaviour independently of sample dimensions: σ = F / A (unit Pa) and ε = ΔL / L₀ (no units). The Young modulus E is the ratio of stress to strain in the linear region: E = σ / ε.
应力 σ 与应变 ε 可以描述材料本征的力学行为，不依赖于试样尺寸：σ = F / A（单位 Pa），ε = ΔL / L₀（无量纲）。杨氏模量 E 是线弹性区域内应力与应变的比值：E = σ / ε。
7. Amount of Substance & Moles | 物质的量与摩尔计算
The mole is the SI unit for amount of substance. The number of moles n can be found from mass m and molar mass M: n = m / M. For solutions, concentration c (mol dm⁻³) and volume V (dm³) give n = c V.
摩尔是物质的量的 SI 单位。物质的量 n 可由质量 m 与摩尔质量 M 求出：n = m / M。对于溶液，浓度 c（mol dm⁻³）与体积 V（dm³）的关系为 n = c V。
At room temperature and pressure (RTP, approximately 20 °C and 101 kPa), one mole of any gas occupies a volume of about 24 dm³: V (dm³) = n × 24 or n = V / 24. The ideal gas equation is p V = n R T, where p is pressure in Pa, V is volume in m³, T is temperature in K, and R = 8.31 J mol⁻¹ K⁻¹.
在常温常压（RTP，约 20 °C、101 kPa）下，1 mol 任何气体的体积约为 24 dm³：V (dm³) = n × 24 或 n = V / 24。理想气体状态方程为 p V = n R T，其中 p 为压强 (Pa)、V 为体积 (m³)、T 为温度 (K)，R = 8.31 J mol⁻¹ K⁻¹。
Stoichiometric calculations rely on balanced chemical equations to find reacting ratios and limiting reagents. Percentage yield and atom economy are used to assess the efficiency of a reaction.
涉及化学计量计算时，必须依据配平的化学方程式确定反应物比例和限量试剂。百分产率与原子经济性可用于评价反应的效率。
8. Energetics & Enthalpy Changes | 能量学与焓变
The heat transferred in a reaction carried out in solution is often measured using a calorimeter: q = m c ΔT, where q is the heat energy (J), m is the mass of solution (g), c is the specific heat capacity (usually 4.18 J g⁻¹ °C⁻¹ for aqueous solutions) and ΔT is the temperature change (°C).
在溶液中进行的反应，其传递的热量通常用热量计测量：q = m c ΔT，其中 q 为热量 (J)，m 为溶液质量 (g)，c 为比热容（对水溶液常取 4.18 J g⁻¹ °C⁻¹），ΔT 为温度变化 (°C)。
The enthalpy change for a reaction, ΔH, relates to the heat transferred at constant pressure: ΔH = –q / n (in kJ mol⁻¹), where n is the number of moles of the limiting reactant. Hess’s law states that the total enthalpy change for a reaction is independent of the pathway taken, allowing the construction of enthalpy cycles.
反应焓变 ΔH 与恒压条件下的热量转移相关：ΔH = –q / n（单位 kJ mol⁻¹），其中 n 为限量试剂的物质的量。赫斯定律指出，化学反应的总焓变与反应路径无关，因此可以利用焓循环进行计算。
9. Chemical Equilibrium | 化学平衡
For a reversible reaction at equilibrium, the equilibrium constant Kc connects the concentrations of products and reactants. For a general reaction aA + bB ⇌ cC + dD, the expression is Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ), where square brackets denote equilibrium concentrations in mol dm⁻³.
对于达到平衡的可逆反应，平衡常数 Kc 将产物与反应物的浓度联系起来。对于一般反应 aA + bB ⇌ cC + dD，其表达式为 Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)，方括号代表平衡浓度，单位为 mol dm⁻³。
Kc depends only on temperature; changes in concentration or pressure shift the position of equilibrium but do not alter Kc. A large Kc indicates a product-favoured equilibrium, while a small Kc indicates a reactant-favoured equilibrium. Le Chatelier’s principle provides a qualitative tool for predicting the response of a system to changes.
Kc 只随温度变化；浓度或压力的改变会使平衡位置移动，但不会改变 Kc 的值。较大的 Kc 表示平衡向产物方向倾斜，较小的 Kc 则表示平衡偏向反应物一侧。勒夏特列原理是定性预测平衡系统响应外界变化的重要工具。
10. Key Biological Formulas | 生物学重要公式
In microscopy, the actual size of a specimen is related to the image size and magnification: Actual size = Image size / Magnification. Ensure both sizes are in the same units before calculation. The magnification triangle (I = A × M) is an indispensable tool for cell biology.
在显微镜使用中，标本的实际大小与图像大小及放大倍数的关系为：实际大小 = 图像大小 / 放大倍数。计算前务必保证两者单位一致。公式三角形 (I = A × M) 是细胞生物学中不可或缺的工具。
For population ecology, population growth rate can be estimated as (births − deaths) / initial population or using change in numbers over time. While the Hardy–Weinberg principle is often taught at A‑level, AS candidates should be comfortable applying simple percentage change and ratio calculations to biological data. Respiration and photosynthesis rates are frequently expressed per unit mass or per unit time.
在种群生态学中，种群增长率可估计为 (出生数 − 死亡数) / 初始种群大小，亦可通过数量随时间的变化来计算。虽然哈迪‑温伯格原理常出现在 A‑level 阶段，但 AS 考生仍需熟练掌握对生物数据进行简单的百分比变化与比率换算。呼吸速率和光合速率通常以单位质量或单位时间的形式表示。
11. Practical Skills & Uncertainties | 实用技能与不确定度
Every measurement in science carries an uncertainty. For a single reading, the absolute uncertainty is usually taken as ± half of the smallest scale division. For repeated measurements, the uncertainty can be estimated as ± half the range of the values. Percentage uncertainty is calculated as % uncertainty = (absolute uncertainty / measured value) × 100%.
科学中每一个测量值都带有不确定度。对于单次读数，绝对不确定度一般取最小刻度分度值的一半。对于多次测量，不确定度可估计为数据范围的一半。百分不确定度的计算公式为 % 不确定度 = (绝对不确定度 / 测量值) × 100%。
When values are added or subtracted, add absolute uncertainties. When values are multiplied or divided, add percentage uncertainties. A zero error is a systematic error caused by a measuring instrument that does not read zero when it should; this affects all readings in the same direction.
当数据进行加减运算时，应叠加绝对不确定度；进行乘除运算时，则叠加百分不确定度。零点误差是一种系统误差，由仪器未能在应指零处归零而导致，它会使所有测量值都朝同一方向偏离。
12. Units, Prefixes & Standard Form | 单位、词头与科学记数法
A secure command of SI units and standard form is vital across all AS Sciences. Common prefixes include milli (m, 10⁻³), micro (μ, 10⁻⁶), nano (n, 10⁻⁹), pico (p, 10⁻¹²), kilo (k, 10³), mega (M, 10⁶) and giga (G, 10⁹). Always express data in base units (kg, m, s, A, K, mol) before substituting into equations unless the formula explicitly allows other consistent units.
在所有 AS 科学学科中，牢固掌握 SI 单位与科学记数法至关重要。常见的词头有：毫 (m, 10⁻³)、微 (μ, 10⁻⁶)、纳 (n, 10⁻⁹)、皮 (p, 10⁻¹²)、千 (k, 10³)、兆 (M, 10⁶) 和吉 (G, 10⁹)。代入公式之前，通常应先将数据转换为基本单位 (kg, m, s, A, K, mol)，除非公式明确允许使用其他一致单位。
Trigonometric ratios, areas and volumes also appear frequently — for instance, the area of a circle π r² or the volume of a sphere ⁴⁄₃ π r³. Being able to manipulate these quickly saves vital time during the exam. Regular practice of converting between units and applying the correct number of significant figures will improve both accuracy and confidence.
三角函数比、面积和体积公式也经常用到——例如圆的面积 π r²、球体的体积 ⁴⁄₃ π r³。快速运用这些公式能在考试中为你节省宝贵时间。经常练习单位换算并选用正确的有效数字位数，既能提高准确性，也能增强信心。
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