📚 Year 12 WJEC Science: Formula & Theorem Quick Reference Handbook | WJEC 12 年级科学：公式定理速查手册
This handbook gathers the essential formulas, laws and theorems that appear most often in the Year 12 WJEC Science curriculum, covering Physics, Chemistry and Biology. It is written as a quick revision reference: each section states the equation, defines every symbol, and flags the exam conventions that examiners expect to see. Use it alongside past papers rather than instead of them, and always quote units in your final answer.
本手册汇总了 WJEC 12 年级科学课程中最常出现的核心公式、定律与定理，覆盖物理、化学与生物学三大科目。它以速查复习资料的形式编写：每一节给出方程、逐一定义符号，并指出考官希望看到的考试约定。请把它与历年真题配合使用，而不是替代真题，并且在最终答案中务必写出单位。
1. Kinematics Equations | 运动学方程
Kinematics describes motion using displacement, velocity and acceleration without asking what causes the motion. For motion with constant acceleration, four equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). WJEC candidates are expected to select the correct equation from the quantities given in the question.
运动学用位移、速度和加速度描述运动，而不追问运动的成因。对于匀加速运动，四个方程把位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）联系起来。WJEC 考生需要根据题目给出的已知量选择正确的方程。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
sitive direction: any vector pointing the opposite way must be entered with a negative sign. Near the Earth' m s⁻², and for a projectile the horizontal and vertical motions are treated independently.
这组方程称为 SUVAT 方程。代入数值之前必须先规定正方向：凡与正方向相反的矢量都要带负号。在地球表面附近，自由落体加速度通常取 g = 9.81 m s⁻²；处理抛体运动时，水平方向与竖直方向要分别独立处理。
- v = u + at — choose this when t is known but s is not.（当已知 t、未知 s 时选用。）
- s = ut + ½at² — choose this when v is unknown.（当未知 v 时选用。）
- v² = u² + 2as — choose this when t is not mentioned.（当题目不提 t 时选用。）
- s = ½(u + v)t — choose this when a is unknown but the average velocity is useful.（当未知 a、而平均速度可用时选用。）
A graph check is always worth marks: the gradient of a displacement-time graph gives velocity, the gradient of a velocity-time graph gives acceleration, and the area under a velocity-time graph gives displacement.
图表分析往往能稳拿分数：位移-时间图的斜率等于速度，速度-时间图的斜率等于加速度，速度-时间图下的面积等于位移。
2. Newton's Laws of Motion | 牛顿运动定律
Newton's three laws underpin all of classical mechanics and appear in every WJEC Physics paper. The first law states that an object remains at rest, or moves with constant velocity, unless a resultant force acts on it. The second law quantifies the link between force, mass and acceleration, and the third law states that forces always arise in equal and opposite pairs acting on two different bodies.
牛顿三大定律是经典力学的基石，在每一份 WJEC 物理试卷中都会出现。第一定律指出：除非有合外力作用，物体将保持静止或匀速直线运动。第二定律定量描述力、质量与加速度的关系。第三定律指出：力总是成对出现，大小相等、方向相反，且分别作用在两个不同的物体上。
Fresultant = ma
W = mg
Fmax = μR
m s⁻². Weight W is the gravitational force on a mass, with g = 9.81 N kg⁻¹ near the Earth' roportional to the normal contact force R, with μ the coefficient of friction and no unit.
在合力方程中，F 以牛顿为单位，m 以千克为单位，a 以 m s⁻² 为单位。重力 W 是作用在质量上的引力，地表附近 g = 9.81 N kg⁻¹。摩擦力被建模为与法向接触力 R 成正比的最大值，μ 为摩擦系数，没有单位。
- Newton's first law — inertia; a body keeps its velocity unless the resultant force is non-zero.（惯性：合力为零时物体速度不变。）
- Newton's second law — acceleration is proportional to the resultant force and inversely proportional to mass.（加速度与合力成正比，与质量成反比。）
- Newton's third law — action and reaction act on different bodies, so they never cancel each other.（作用力与反作用力作用在不同物体上，因此永远不会相互抵消。）
Terminal velocity is the standard application: a falling object accelerates until drag grows to equal its weight, the resultant force becomes zero, and the acceleration falls to zero.
收尾速度是标准应用场景：下落物体加速，直到阻力增大到等于重力，合力变为零，加速度随之降为零。
3. Momentum, Impulse and Collisions | 动量、冲量与碰撞
Momentum is a vector quantity defined as the product of mass and velocity. In any closed system with no external resultant force, total momentum is conserved, which makes collisions and explosions standard calculation tasks in WJEC papers.
动量是矢量，定义为质量与速度的乘积。在任何不受合外力的封闭系统中，总动量守恒，因此碰撞与爆炸类计算是 WJEC 试卷中的常见题型。
p = mv
F Δt = Δp = mv − mu
The impulse equation says that a force acting for a time Δt produces a change in momentum equal to the area under a force-time graph. This explains why crumple zones and airbags reduce injury: they lengthen the collision time, so the peak force on the occupants is smaller for the same momentum change.
冲量方程表明，力在时间 Δt 内作用所产生的动量变化，等于力-时间图下的面积。这解释了为何溃缩区和安全气囊能减轻伤害：它们延长了碰撞时间，因此在动量变化相同的情况下，乘员受到的峰值力更小。
| Type of collision | Momentum | Kinetic energy |
| Perfectly elastic（完全弹性碰撞） | Conserved（守恒） | Conserved（守恒） |
| Inelastic（非弹性碰撞） | Conserved（守恒） | Reduced（减少） |
| Explosion（爆炸） | Conserved（守恒） | Increases（增加） |
When solving one-dimensional collision problems, choose a positive direction, write the total momentum before and after as equal, and keep the signs of velocities consistent throughout the working.
解一维碰撞题时，先选定正方向，写出碰撞前后的总动量并令其相等，并且全程保持速度符号一致。
4. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application through a distance. Energy is the capacity to do work and is conserved in a closed system, though it may transfer between stores such as kinetic, gravitational potential, elastic and thermal.
当力的作用点发生位移时，力就做了功。能量是做功的本领，在封闭系统中总量守恒，但可以在动能、重力势能、弹性势能和热能等能量储库之间转移。
W = Fs cos θ
Ek = ½mv²
ΔEp = mgΔh
P = W ÷ t = Fv
ergy transfer, and the form P = Fv is convenient whenever an object moves at constant velocity against a resistive force.
在功的方程中，θ 是力与位移之间的夹角，因此与运动方向垂直的力不做功。功率是能量转移的速率，当物体以恒定速度克服阻力运动时，使用 P = Fv 这一形式最为方便。
efficiency = useful output energy ÷ total input energy × 100%
Efficiency is always less than 100% in real machines because some energy is dissipated to the thermal store, usually by friction or electrical resistance. Note that efficiency is a ratio, so it has no unit.
真实机械的效率总是低于 100%，因为一部分能量通过摩擦或电阻耗散到热能储库中。注意效率是比值，因此没有单位。
5. Waves, Optics and Refraction | 波动、光学与折射
Waves transfer energy without transferring matter. WJEC questions usually require you to move between wave speed, frequency, period and wavelength, and then to apply refraction and interference relationships in optics.
波传递能量而不传递物质。WJC 类题目通常要求你在波速、频率、周期与波长之间换算，然后应用光学中的折射和干涉关系式。
v = fλ
T = 1 ÷ f
n = c ÷ v
n₁ sin θ₁ = n₂ sin θ₂
ares the speed of light in a vacuum c = 3.00 × 10⁸ m s⁻¹ with the speed in that material, and Snell's law links the angles on either side of a boundary.
在波方程中，v 是波速，单位为 m s⁻¹；f 是频率，单位为赫兹；λ 是波长，单位为米。材料的折射率 n 把真空中的光速 c = 3.00 × 10⁸ m s⁻¹ 与该材料中的光速相比，斯涅尔定律则把界面两侧的角度联系起来。
sin C = 1 ÷ n
w = λD ÷ s
Total internal reflection occurs when light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle C. In the double-slit equation, w is the fringe spacing, D the slit-to-screen distance and s the slit separation; all lengths must be in metres.
全内反射发生在光由光密介质射向光疏介质、且入射角大于临界角 C 时。在双缝方程中，w 是条纹间距，D 是缝到屏的距离，s 是双缝间距；所有长度必须统一为米。
6. Electricity: Ohm's Law and Circuits | 电学：欧姆定律与电路
Direct current circuits are built on two ideas: charge is conserved at every junction and energy is conserved around every loop. Ohm's law applies to a conductor at constant temperature, and the internal resistance of a source explains why terminal voltage falls as current rises.
直流电路建立在两个基本思想之上：在任一节点电荷守恒，沿任一回路能量守恒。欧姆定律适用于温度恒定的导体，而电源的内阻解释了为什么电流增大时端电压会下降。
V = IR
P = VI = I²R = V² ÷ R
ε = I(R + r)
Vterminal = ε − Ir
Here V is the potential difference in volts, I the current in amperes, R the resistance in ohms, ε the electromotive force of the source and r its internal resistance. The three forms of the power equation are interchangeable, but only one of them will match the quantities you have been given.
其中 V 是电位差，单位为伏特；I 是电流，单位为安培；R 是电阻，单位为欧姆；ε 是电源电动势；r 是内阻。功率公式的三种形式可以互换，但只有一种与你手上的已知量相匹配。
| Quantity | Series（串联） | Parallel（并联） |
| Current（电流） | Same everywhere（处处相同） | Splits between branches（各支路分流） |
| Voltage（电压） | Splits between components（各元件分压） | Same across each branch（各支路相同） |
| Resistance（电阻） | R = R₁ + R₂ + R₃ | 1/R = 1/R₁ + 1/R₂ + 1/R₃ |
For a potential divider, Vout = Vin dependent resistor placed in the divider converts a temperature or light-level change into a measurable voltage change, which is the basis of many sensor questions.
对于分压电路，Vout = Vin × R₂ ÷ (R₁ + R₂)。把热敏电阻或光敏电阻接入分压电路，就能把温度或光强的变化转换成可测量的电压变化，这是许多传感器题目的基础。
7. Thermal Physics and Gas Laws | 热学与气体定律
Thermal physics deals with energy transfer from a hotter to a cooler body, measured through specific heat capacity and specific latent heat. The kinetic model then connects the macroscopic gas laws to the random motion of molecules.
热学研究能量由高温物体向低温物体的传递，用比热容和比潜热来度量。随后，动力学模型把宏观的气体定律与分子的无规则运动联系起来。
Q = mcΔT
Q = ml
pV = nRT
pV = NkT
In the heating equation, Q is the energy transferred in joules, m the mass in kilograms, c the specific heat capacity in J kg⁻¹ K⁻¹ and ΔT the temperature change in kelvin. For a change of state, l is the specific latent heat in J kg⁻¹ and the temperature stays constant throughout the change.
在加热方程中，Q 是传递的能量，单位为焦耳；m 是质量，单位为千克；c 是比热容，单位为 J kg⁻¹ K⁻¹；ΔT 是温度变化，单位为开尔文。发生物态变化时，l 是比潜热，单位为 J kg⁻¹，且整个过程中温度保持不变。
p₁V₁ ÷ T₁ = p₂V₂ ÷ T₂
The combined gas equation gives Boyle's law when T is constant, Charles's law when p is constant and Gay-Lussac' , and the gas constant R = 8.31 J mol⁻¹ K⁻¹ should be quoted to three significant figures.
组合气体方程在 T 恒定时给出玻意耳定律，在 p 恒定时给出查理定律，在 V 恒定时给出盖-吕萨克定律。代入之前必须用 T = θ + 273.15 把温度换算为开尔文，气体常数 R = 8.31 J mol⁻¹ K⁻¹ 通常保留三位有效数字。
8. Amount of Substance and Stoichiometry | 物质的量与化学计量
pers award marks for correct working rather than only for the final value, so always show the balanced equation and the mole ratio you have used.
化学计算全部建立在摩尔之上，摩尔是含有 6.02 × 10²³ 个粒子的物质的量。WJEC 试卷对正确的推演过程同样给分，而不仅看最终数值，因此务必写出配平方程和你所使用的摩尔比。
n = m ÷ M
n = c × V ÷ 1000
n = V ÷ 24.0 (gas at room temperature and pressure)
number of particles = n × 6.02 × 10²³
In these relationships n is the amount in moles, m the mass in grams, M the molar mass in g mol⁻¹, c the concentration in mol dm⁻³ and V the volume. In the titration form, V must be in cm³ because of the factor of 1000 that converts cm³ to dm³.
在这些关系中，n 是物质的量，单位为摩尔；m 是质量，单位为克；M 是摩尔质量，单位为 g mol⁻¹；c 是浓度，单位为 mol dm⁻³；V 是体积。在滴定计算式中，V 必须以 cm³ 为单位，因为换算时需要乘以 1000 把 cm³ 转换为 dm³。
- Percentage yield = actual mass ÷ theoretical mass × 100%.（产率 = 实际质量 ÷ 理论质量 × 100%。）
- Atom economy = molar mass of desired product ÷ total molar mass of all products × 100%.（原子经济性 = 目标产物摩尔质量 ÷ 全部产物摩尔质量之和 × 100%。）
- Avogadro constant = 6.02 × 10²³ mol⁻¹.（阿伏伽德罗常数 = 6.02 × 10²³ mol⁻¹。）
9. Energetics and Hess's Law | 能量学与盖斯定律
Energetics concerns the enthalpy changes that accompany reaction. An exothermic reaction releases energy to the surroundings and has a negative ΔH, while an endothermic reaction absorbs energy and has a positive ΔH.
能量学研究伴随反应发生的焓变。放热反应向环境释放能量，ΔH 为负值；吸热反应吸收能量，ΔH 为正值。
q = mcΔT
ΔH = −q ÷ n
ΔH = Σ bond energies broken − Σ bond energies formed
In calorimetry, q is the heat energy released in joules, m the mass of the solution in grams, c the specific heat capacity of water, taken as 4.18 J g⁻¹ K⁻¹, and ΔT the temperature rise. Dividing by the number of moles gives the molar enthalpy change, and the negative sign is needed because the reaction releases energy to the solution.
在量热法中，q 是释放的热能，单位为焦耳；m 是溶液质量，单位为克；c 是水的比热容，取 4.18 J g⁻¹ K⁻¹；ΔT 是温度升高值。除以摩尔数即得摩尔焓变；由于反应向溶液放热，所以需要加负号。
Hess's law states that the enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. It allows you to construct an energy cycle and calculate an unknown enthalpy change from standard enthalpies of formation or combustion.
盖斯定律指出：只要始态与终态相同，反应的焓变与路径无关。借助该定律可以构建能量循环，用标准生成焓或标准燃烧焓求出未知的焓变。
10. Kinetics and Chemical Equilibrium | 动力学与化学平衡
Kinetics explains how fast a reaction proceeds, while equilibrium describes the position of a reversible reaction once the forward and reverse rates become equal. Both topics are assessed with data interpretation, so units and graph shapes carry marks.
动力学解释反应进行的快慢，而平衡描述可逆反应在正、逆反应速率相等时所处的状态。这两个主题都以数据解读的形式考查，因此单位和图形形状都会给分。
rate = Δ[conc] ÷ Δt 更多咨询请联系16621398022（同微信）
Kc = [C]c[D]d ÷ [A]a[B]b
Kw = [H
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