📚 Year 13 WJEC Science: Formula & Theorem Quick-Reference Handbook | WJEC Year 13 科学：公式定理速查手册
As Year 13 students prepare for their WJEC Science examinations, having a concise collection of essential formulas and theorems is invaluable. This quick-reference handbook covers key relationships from physics, chemistry, and biology that are frequently assessed. Use it to check your recall, solve numerical problems, and understand the cornerstone principles of each topic.
对于正在准备 WJEC 科学考试的 Year 13 学生来说，拥有一本精炼的公式定理速查手册至关重要。本手册涵盖了物理、化学和生物中经常考查的关键关系式。你可以用它来检验记忆、求解计算题，并理解每个主题的基石原理。
1. Mechanics & Circular Motion | 力学与圆周运动
The equations of uniform acceleration describe motion under constant acceleration, where u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement.
匀加速运动方程描述匀加速度下的运动，其中 u 为初速度，v 为末速度，a 为加速度，t 为时间，s 为位移。
v = u + at
v² = u² + 2as
s = ut + ½at²
Newton’s second law states that the net force on an object equals the rate of change of its momentum, expressed as F = Δp/Δt, which simplifies to F = ma for constant mass. Momentum is defined as p = mv.
牛顿第二定律指出物体所受的合外力等于其动量变化率，表达式为 F = Δp/Δt，若质量恒定则可简化为 F = ma。动量定义为 p = mv。
F = ma
p = mv
For an object moving in a circle at constant speed, a centripetal force acts towards the centre. The magnitude of this force and the corresponding acceleration depend on the tangential speed v, radius r, and angular velocity ω.
对于匀速圆周运动的物体，向心力指向圆心。向心力和向心加速度的大小取决于切向速度 v、半径 r 和角速度 ω。
F = mv² / r
a = v² / r = rω²
v = rω, T = 2π / ω
2. Electric Circuits & Fields | 电路与电场
Ohm’s law relates the current I through a conductor to the potential difference V across it and its resistance R. For uniform wires, resistance can be calculated using resistivity ρ, length l, and cross-sectional area A.
欧姆定律将流过导体的电流 I、导体两端的电势差 V 和电阻 R 联系起来。对于均匀导线，电阻可以通过电阻率 ρ、长度 l 和横截面积 A 计算。
V = IR
R = ρl / A
Power dissipated in a component can be expressed in terms of current and voltage or current and resistance. Kirchhoff’s current law states that the sum of currents entering a junction equals the sum leaving (ΣI in = ΣI out), while the voltage law states that the sum of emfs equals the sum of potential drops around any closed loop (Σε = ΣIR).
元件耗散的功率可用电流和电压或电流和电阻表示。基尔霍夫电流定律表明，流入节点的电流之和等于流出电流之和；电压定律表明，沿任一闭合回路，电动势之和等于电势降落之和。
P = IV = I²R = V² / R
In an electric field, the field strength E is the force per unit charge. For a uniform field between parallel plates, E = V/d. Coulomb’s law gives the force between two point charges Q and q separated by distance r, where ε₀ is the permittivity of free space.
在电场中，电场强度 E 是单位电荷所受的力。对于平行板间的匀强电场，E = V/d。库仑定律给出两个点电荷 Q 与 q 相距 r 时的作用力，其中 ε₀ 为真空介电常数。
E = F / q
E = V / d
F = kQq / r², k = 1 / (4πε₀)
For capacitors, capacitance C is the charge stored per unit voltage. The energy stored and the time constant for an RC circuit are also listed.
对于电容器，电容 C 是单位电压下储存的电荷量。储能公式和 RC 电路的时间常数也一并列出。
C = Q / V
Energy stored = ½CV²
Time constant τ = RC
3. Thermal Physics & Ideal Gases | 热物理与理想气体
The ideal gas equation links pressure p, volume V, number of moles n, gas constant R, and absolute temperature T. It can also be expressed using the Boltzmann constant k and number of molecules N.
理想气体状态方程关联了压强 p、体积 V、物质的量 n、气体常数 R 和绝对温度 T。它也能用玻尔兹曼常数 k 和分子数 N 表达。
pV = nRT
pV = NkT
The average kinetic energy of a gas molecule is proportional to absolute temperature. The root-mean-square speed crms is derived from the mean square speed ⟨c²⟩.
气体分子的平均动能与绝对温度成正比。方均根速率 crms 由均方速率 ⟨c²⟩ 导出。
½ m⟨c²⟩ = ³⁄₂ kT
crms = √(3kT / m) = √(3RT / M)
The first law of thermodynamics states that the change in internal energy ΔU equals the heat added to the system Q plus the work done on the system W. For a gas expanding against a constant external pressure, W = −pΔV.
热力学第一定律表明，内能变化 ΔU 等于系统吸收的热量 Q 加上对系统所做的功 W。对于气体对抗恒定外压膨胀，W = −pΔV。
ΔU = Q + W
W = −pΔV (for work done by the gas, adjust sign convention accordingly)
4. Simple Harmonic Motion & Waves | 简谐运动与波动
Simple harmonic motion (SHM) occurs when the restoring force is proportional to the displacement and directed towards the equilibrium position. The acceleration a is given by a = −ω²x, where ω is the angular frequency.
当恢复力与位移成正比且指向平衡位置时，物体做简谐运动。加速度 a 由 a = −ω²x 给出，其中 ω 为角频率。
a = −ω²x
x = A cos(ωt + φ) or x = A sin(ωt + φ’)
v = ±ω√(A² − x²)
The periods of a mass–spring system and a simple pendulum depend on mass, spring constant, length, and gravitational field strength g.
弹簧振子和单摆的周期分别取决于质量、劲度系数、摆长和重力场强度 g。
T = 2π√(m / k)
T = 2π√(L / g)
For all waves, the speed v relates to frequency f and wavelength λ. In double-slit interference, fringe spacing Δx depends on wavelength, slit-screen distance D, and slit separation d. For a diffraction grating, maxima occur when d sin θ = nλ.
对所有波，波速 v 与频率 f 和波长 λ 相关。在双缝干涉中，条纹间距 Δx 取决于波长、缝屏距离 D 和缝间距 d。对于衍射光栅，极大条件为 d sin θ = nλ。
v = fλ
Δx = λD / d
d sin θ = nλ
5. Nuclear & Particle Physics | 核物理与粒子物理
Einstein’s mass–energy equivalence is the foundation of nuclear energy calculations. In radioactive decay, the number of undecayed nuclei N follows an exponential law with decay constant λ.
爱因斯坦的质能方程是核能计算的基础。在放射性衰变中，未衰变原子核数 N 遵循以衰变常量 λ 为特征的指数规律。
E = mc²
N = N
Published by TutorHao | Year 13 Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导