📚 A-Level WJEC Science: Formula Reference Guide | A-Level WJEC 科学公式参考手册
This comprehensive formula handbook has been specially designed for students following the WJEC A‑Level Science specifications. It brings together the essential equations from Physics and Chemistry, presenting each one with a clear description so you can revise efficiently. Use this guide alongside past papers to reinforce your understanding and improve your problem‑solving confidence.
这份综合公式手册专为遵循 WJEC A‑Level 科学规范的学生设计。它汇集了物理和化学的核心方程，并为每一个提供清晰说明，以便你高效复习。将本指南与历年真题配合使用，可强化理解并提升解题信心。
1. Motion and Forces | 运动与力
v = u + a t
Relates final velocity (v) to initial velocity (u), constant acceleration (a) and time (t). Suitable for problems where displacement is not required.
将末速度(v)与初速度(u)、恒定加速度(a)和时间(t)关联起来。适用于不涉及位移的问题。
s = u t + ½ a t²
Calculates displacement (s) when initial velocity, acceleration and time are known. The term ½ a t² accounts for the additional distance covered due to acceleration.
当已知初速度、加速度和时间时，用于计算位移(s)。项 ½ a t² 代表因加速度而产生的额外位移。
v² = u² + 2 a s
Connects final velocity, initial velocity, acceleration and displacement without involving time. Useful when time is not given.
在不涉及时间的情况下将末速度、初速度、加速度和位移联系起来。当时间未知时很有用。
s = ½ (u + v) t
Displacement equals average velocity multiplied by time. This SUVAT equation is valid only when acceleration is constant.
位移等于平均速度乘以时间。该匀速运动方程仅当加速度恒定时成立。
F = m a
Newton’s second law: the net force acting on an object equals its mass times its acceleration. Remember to use resultant force for F.
牛顿第二定律：作用在物体上的合力等于质量乘以加速度。注意 F 指的是合外力。
p = m v
Linear momentum (p) is the product of mass and velocity. Momentum is conserved in isolated systems.
线性动量(p)是质量与速度的乘积。在孤立系统中动量守恒。
F Δt = Δp
he change in momentum. This is the derivation of Newton’s second law in terms of momentum.
冲量(力 × 时间)等于动量的变化量。这是牛顿第二定律的动量表述形式。
2. Work, Energy and Power | 功、能与功率
W = F d cos θ
on of displacement and the displacement. When force and displacement are aligned, W = F d.
恒力做的功等于力在位移方向上的分量与位移的乘积。当力与位移方向一致时，W = F d。
Eₖ = ½ m v²
Kinetic energy depends on mass and the square of speed. All moving objects possess kinetic energy.
动能取决于质量与速度的平方。所有运动物体都具有动能。
ΔEₚ = m g Δh
avitational field strength × change in height. Use g = 9.81 m s⁻² unless stated otherwise.
靠近地球表面时重力势能的变化等于质量 × 重力场强度 × 高度变化。除非另有说明，取 g = 9.81 m s⁻²。
P = W / t = F v
work. For an object moving at constant velocity against a force, power = force × velocity.
功率是做功的速率。对于以恒定速度克服阻力运动的物体，功率 = 力 × 速度。
3. Circular Motion | 圆周运动
ω = θ / t = 2π / T = 2π f
Angular velocity (ω) is the rate of change of angular displacement, measured in rad s⁻¹. It is related to period (T) and frequency (f).
角速度(ω)是角位移的变化率，单位为 rad s⁻¹。它与周期(T)和频率(f)有关。
v = ω r
Linear speed (v) of an object moving in a circle of radius r is the product of angular velocity and radius.
沿半径为 r 的圆周运动的物体线速度(v)等于角速度与半径的乘积。
a = v² / r = ω² r
Centripetal acceleration points towards the centre of the circle. Both forms are useful depending on the given quantities.
向心加速度指向圆心。两种形式根据已知量选用。
F = m v² / r = m ω² r
Centripetal force is the resultant force causing circular motion. It is not a separate force but is provided by tension, gravity, friction, etc.
向心力是产生圆周运动的合力。它并非独立的力，而是由张力、重力、摩擦力等提供。
4. Simple Harmonic Motion (SHM) | 简谐运动
a = – ω² x
The defining equation of SHM: acceleration is proportional to displacement and directed towards the equilibrium position. ω is the angular frequency.
简谐运动的定义方程：加速度与位移成正比且方向指向平衡位置。ω 为角频率。
v = ± ω √A² – x²
nt x in SHM; A is the amplitude. Maximum speed occurs at the equilibrium position (x = 0).
简谐运动中在给定位移 x 处的速度；A 为振幅。最大速度出现在平衡位置(x = 0)。
T = 2π / ω = 1 / f
Period T is the time for one complete oscillation. For a mass‑spring system, T = 2π √m/k; for a simple pendulum, T = 2π √L/g.
周期 T 是一次完整振动所需的时间。对于弹簧振子，T = 2π √m/k；对于单摆，T = 2π √L/g。
Eₜₒₜₐₗ = ½ m ω² A²
The total mechanical energy in undamped SHM remains constant and is proportional to the square of the amplitude.
无阻尼简谐运动中的总机械能保持恒定，并与振幅的平方成正比。
5. Waves and Optics | 波与光学
v = f λ
The wave speed equation: frequency (f) multiplied by wavelength (λ). Applies to all progressive waves.
波速公式：频率(f)乘以波长(λ)。适用于所有行波。
n₁ sin θ₁ = n₂ sin θ₂
Snell’s law of refraction. n₁ and n₂ are the refractive indices of the two media; θ₁ and θ₂ are the angles to the normal.
斯涅尔折射定律。n₁、n₂ 为两种介质的折射率；θ₁、θ₂ 分别为入射角和折射角。
n = c / v
Absolute refractive index of a medium is the ratio of the speed of light in vacuum (c) to its speed in the medium (v).
介质的绝对折射率是光在真空中的速度(c)与光在介质中的速度(v)之比。
d sin θ = n λ
Diffraction grating equation: d is the slit spacing, θ is the angle of the nth order maximum, and n is the order number.
衍射光栅方程：d 为狭缝间距，θ 为第 n 级明纹的衍射角，n 为级次。
6. Electric Circuits | 电路
V = I R
Ohm’s law: potential difference across a resistor equals current times resistance, valid provided temperature remains constant.
欧姆定律：电阻器两端的电势差等于电流乘以电阻，前提是温度保持恒定。
P = I V = I² R = V² / R
Electrical power dissipated in a component. Choose the appropriate form based on the known quantities.
元器件中耗散的电功率。根据已知量选择合适的形式。
Rₛ = R₁ + R₂ + …
Resistors in series: total resistance is the sum of individual resistances.
串联电阻：总电阻等于各电阻之和。
1/Rₚ = 1/R₁ + 1/R₂ + …
Resistors in parallel: the reciprocal of total resistance equals the sum of the reciprocals of individual resistances.
并联电阻：总电阻的倒数等于各电阻倒数之和。
ε = I (R + r)
The emf (ε) of a cell supplies energy per unit charge. Terminal p.d. equals ε – I r, where r is the internal resistance.
电池的电动势(ε)是每单位电荷提供的能量。路端电压等于 ε – I r，其中 r 为内阻。
7. Gravitational and Electric Fields | 重力场与电场
F = G M m / r²
Newton’s law of gravitation: the force between two point masses is proportional to the product of masses and inversely proportional to the square of their separation.
牛顿万有引力定律：两质点间的引力与质量乘积成正比，与距离的平方成反比。
g = F / m = G M / r²
Gravitational field strength (g) is force per unit mass. Near a planet’s surface it is approximately uniform.
重力场强度(g)是单位质量的力。在行星表面附近，它近似为匀强场。
F = (1 / 4πε₀) ( Q₁ Q₂ / r² )
Coulomb’s law for the force between two point charges. ε₀ is the permittivity of free space.
库仑定律描述两点电荷之间的力。ε₀ 为真空电容率。
E = F / q = (1 / 4πε₀) (Q / r²)
Electric field strength (E) is force per unit positive charge. For a radial field around a point charge, it follows an inverse‑square law.
电场强度(E)是单位正电荷所受的力。对于点电荷周围的径向电场，服从平方反比定律。
V = (1 / 4πε₀) (Q / r)
Electric potential (V) at a distance r from a point charge. Potential is a scalar; the zero is taken at infinity.
距点电荷 r 处的电势(V)。电势是标量；无穷远处为零势点。
8. Electromagnetic Induction | 电磁感应
Φ = B A cos θ
Magnetic flux (Φ) through a surface is the flux density (B) multiplied by the perpendicular area component. Measured in weber (Wb).
穿过一个面的磁通量(Φ)等于磁感应强度(B)乘以与该面垂直的面积分量。单位为韦伯(Wb)。
ε = – N ΔΦ / Δt
Faraday’s law: the induced emf is proportional to the rate of change of flux linkage (NΦ). The minus sign indicates Lenz’s law.
法拉第定律：感生电动势与磁链(NΦ)的变化率成正比。负号体现了楞次定律。
Vₛ / Vₚ = Nₛ / Nₚ
For an ideal transformer, the ratio of secondary voltage to primary voltage equals the turns ratio. Power input equals power output.
对于理想变压器，副边电压与原边电压之比等于匝数比。输入功率等于输出功率。
9. Nuclear Physics | 核物理
E = m c²
Mass– ivalence. In nuclear reactions, the mass defect Δm appears as released energy: ΔE = Δm c².
质能等价。在核反应中，质量亏损 Δm 表现为释放的能量：ΔE = Δm c²。
N = N₀ e–λ t
is the number of undecayed nuclei after time t, λ is the decay constant. Activity A = λ N.
指数衰变规律：N 为经过时间 t 后未衰变的原子核数，λ 为衰变常量。活度 A = λ N。
T½ = ln 2 / λ
Half‑life is the time taken for half the radioactive nuclei to decay. It is constant for a given isotope.
半衰期是半数放射性原子核衰变所需的时间。对于给定的同位素，它是一个常量。
10. Chemical Quantities and Gas Laws | 化学计量与气体定律
n = m / M
Amount of substance (mol) equals mass (g) divided by molar mass (g mol⁻¹). The foundation of all stoichiometric calculations.
物质的量(mol)等于质量(g)除以摩尔质量(g mol⁻¹)。这是所有化学计量计算的基础。
n = V / Vₘ
pressure (RTP), one mole of any gas occupies approximately 24 dm³. Use Vₘ = 24 dm³ mol⁻¹.
在常温常压下，1 摩尔任何气体的体积约为 24 dm³。使用 Vₘ = 24 dm³ mol⁻¹。
c = n / V
Concentration of a solution (mol dm⁻³) is the amount of solute divided by the volume of solution in dm³.
溶液的浓度(mol dm⁻³)等于溶质的物质的量除以溶液的体积(单位 dm³)。
P V = n R T
gas equation. Ensure units are consistent: P in Pa, V in m³, T in K. R = 8.31 J mol⁻¹ K⁻¹.
理想气体状态方程。确保单位一致：压强 P 用 Pa，体积 V 用 m³，温度 T 用 K。R = 8.31 J mol⁻¹ K⁻¹。
11. Thermochemistry and Rates | 热化学与反应速率
ΔH = ΣΔHf(products) – ΣΔHf(reactants)
Standard enthalpy change of reaction using standard enthalpies of formation. A negative ΔH indicates an exothermic reaction.
使用标准生成焓计算反应的标准焓变。ΔH 为负值表示放热反应。
q = m c ΔT
Heat energy transferred when a substance changes temperature. c is the specific heat capacity (J g⁻¹ K⁻¹ or J kg⁻¹ K⁻¹).
物质温度改变时传递的热量。c 为比热容（单位 J g⁻¹ K⁻¹ 或 J kg⁻¹ K⁻¹）。
ΔH = – q / n
For a reaction carried out in solution, the enthalpy change per mole is calculated from the measured temperature rise.
对于在溶液中进行的反应，每摩尔的焓变可由测得的温度变化计算得出。
rate = k [A]ᵐ [B]ⁿ
Rate equation: k is the rate constant; m and n are orders of reaction determined experimentally, not from the stoichiometric coefficients.
速率方程：k 为速率常数；m 和 n 是由实验确定的反应级数，而非来自化学计量系数。
k = A e–Eₐ/RT
Arrhenius equation: shows how the rate constant depends on temperature and activation energy (Eₐ). The exponential factor accounts for the fraction of molecules with sufficient energy.
阿伦尼乌斯公式：表明速率常数如何取决于温度和活化能(Eₐ)。指数因子代表拥有足够能量的分子比例。
12. Equilibria and Acids–Bases | 平衡与酸碱
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ
Equilibrium constant in terms of concentration. Pure solids and liquids are omitted. Kc is temperature‑dependent.
浓度平衡常数。纯固体和纯液体不出现在表达式中。Kc 随温度变化。
Kₐ = [H⁺][A⁻] / [HA]
Acid dissociation constant for a weak acid HA. The larger Kₐ, the stronger the acid. pKₐ = –log₁₀ Kₐ.
弱酸 HA 的酸解离常数。Kₐ 越大，酸性越强。pKₐ = –log₁₀ Kₐ。
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (at 25 °C)
product of water. In pure water and neutral solutions, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³.
水的离子积。在纯水和中性溶液中，[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³。
pH = –log₁₀ [H⁺]
Definition of pH. For strong monoprotic acids, [H⁺] equals the acid concentration. For weak acids, use Kₐ.
pH 的定义。对于强一元酸，[H⁺] 等于酸的浓度；对于弱酸，需使用 Kₐ 计算。
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