📚 Year 12 WJEC Science: Quick Reference Handbook of Formulas and Theorems | Year 12 WJEC 科学：公式定理速查手册
This handy reference guide compiles the essential formulas and theorems for Year 12 WJEC Science, bringing together core equations from physics, chemistry, and biology in one place. Designed for quick revision and problem solving, the handbook covers the key relationships you need to master for your AS-level studies.
本便捷参考手册汇总了 Year 12 WJEC 科学课程必备的公式与定理，将物理、化学和生物的核心方程式集于一处。本手册专为快速复习与解题而设计，涵盖 AS 阶段必须掌握的关键关系。
1. Kinematics | 运动学
For objects moving with constant acceleration along a straight line, the SUVAT equations relate displacement s, initial velocity u, final velocity v, acceleration a, and time t.
对于沿直线作匀加速运动的物体，SUVAT 方程组将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系在一起。
v = u + at
s = ut + ½ at²
v² = u² + 2as
s = (u + v)t / 2
The four equations assume acceleration is constant and motion is in one dimension. Always check that the units are consistent (metres, seconds, m s⁻²) before substituting values.
上述四个方程适用于加速度恒定的一维运动。代入数值前务必检查单位是否一致（米、秒、米每二次方秒）。
s⁻², and the sign convention must be carefully applied to upward and downward directions.
物体在重力作用下自由下落时，加速度 a 用 g = 9.81 m s⁻² 替代，并需谨慎处理向上和向下方向的正负号约定。
2. Forces and Newton's Laws | 力与牛顿定律
Newton's second law states that the resultant force on an object is equal to the rate of change of its momentum. For constant mass, this simplifies to the well‑known form.
牛顿第二定律指出，物体所受合外力等于其动量的变化率。当质量不变时，简化为常见形式。
F = ma
Net force F is measured in newtons (N), mass m in kilograms (kg), and acceleration a in m s⁻². A resultant force causes acceleration in the same direction.
合力 F 的单位是牛（N），质量 m 用千克（kg），加速度 a 用 m s⁻²。合外力产生与其同方向的加速度。
weight = mg
The weight of an object is the gravitational force exerted by the Earth; g is the gravitational field strength (9.81 N kg⁻¹ at the surface).
物体的重量是地球施加的重力；g 为重力场强度（地表约为 9.81 N kg⁻¹）。
ar directions. Resolving components uses trigonometric ratios: Fₓ = F cos θ, Fᵧ = F sin θ.
物体平衡时，所有力在两个垂直方向上的分量均须抵消。力的分解使用三角函数比：Fₓ = F cos θ，Fᵧ = F sin θ。
3. Work, Energy and Power | 功、能量与功率
Work done by a constant force is the product of the force and the displacement in the direction of the force.
恒力做功等于力与物体沿力方向位移的乘积。
W = Fs cos θ
en force and displacement are parallel, θ = 0° and W = Fs. Work is measured in joules (J).
力与位移同向时，θ = 0°，W = Fs。功的单位是焦耳（J）。
Eₖ = ½ mv²
Kinetic energy depends on mass and the square of speed. Always convert mass to kg and speed to m s⁻¹.
动能取决于质量与速度的平方。质量须转换为 kg，速度转换为 m s⁻¹。
ΔEₚ = mgΔh
The change in gravitational potential energy near Earth's surface equals mass × g × vertical height change.
地表附近重力势能的变化等于质量 × g × 垂直高度变化。
power = work done / time = energy transfer / time
Power is the rate of doing work or transferring energy; the SI unit is the watt (W).
功率是做功或传递能量的速率；SI 单位是瓦特（W）。
4. Waves | 波
The wave speed equation links frequency and wavelength for all periodic waves.
波速公式将频率与波长联系起来，适用于所有周期波。
v = f λ
z), and wavelength λ (m). For electromagnetic waves in a vacuum, v = c = 3.00 × 10⁸ m s⁻¹.
波速 v（m s⁻¹）、频率 f（Hz）和波长 λ（m）。真空中电磁波的波速 v = c = 3.00 × 10⁸ m s⁻¹。
Refraction is governed by Snell's law, where n is the refractive index.
折射遵循斯涅耳定律，n 为折射率。
n₁ sin θ₁ = n₂ sin θ₂
en the angle of incidence exceeds the critical angle, given by sin θc = n₂ / n₁ (n₁ > n₂).
光从介质 1 进入介质 2 时，角度从法线量起。入射角大于临界角时发生全内反射，临界角满足 sin θc = n₂ / n₁（n₁ > n₂）。
5. Electricity | 电学
Ohm's law relates potential difference, current, and resistance at constant temperature.
欧姆定律描述恒定温度下电压、电流与电阻的关系。
V = IR
Potential difference V (volts), current I (amperes), resistance R (ohms). For components that obey Ohm's law, the I–V graph is a straight line through the origin.
电压 V（伏特）、电流 I（安培）、电阻 R（欧姆）。服从欧姆定律的元件，其 I–V 特性图为过原点的直线。
P = IV = I²R = V² / R
Electrical power dissipated in a resistor can be expressed in three equivalent forms. Use the version that matches the data given.
电阻器消耗的电功率有三种等价表达式。选择与已知数据匹配的公式使用。
In series circuits, current is the same everywhere and resistances add: Rtotal rallel circuits, the reciprocal of the total resistance equals the sum of reciprocals: 1/Rtotal = 1/R₁ + 1/R₂ + ... .
串联电路中电流处处相等，总电阻 Rtotal = R₁ + R₂ + ... 。并联电路中，总电阻的倒数等于各支路电阻倒数之和：1/Rtotal = 1/R₁ + 1/R₂ + ... 。
6. Atomic and Nuclear Physics | 原子与核物理
Radioactive decay is a random process described by an exponential law relating the number of undecayed nuclei N to time t, where λ is the decay constant.
放射性衰变是一种随机过程，可用未衰变原子核数目 N 随时间 t 的指数规律描述，λ 为衰变常量。
N = N₀ e⁻λt
A = A₀ e⁻λt
Activity A is the number of decays per unit time, measured in becquerels (Bq). The half‑life T½ is the time for half the nuclei to decay.
活度 A 是单位时间的衰变次数，单位为贝克勒尔（Bq）。半衰期 T½ 是原子核衰变一半所需的时间。
λ T½ = ln 2
Use this relationship to find the decay constant from the half‑ is equivalent to 1.661 × 10⁻²⁷ kg, and using E = mc², 1 u converts to 931.5 MeV of energy.
利用该关系可从半衰期求衰变常量，或反之。统一原子质量单位 1 u 等于 1.661 × 10⁻²⁷ kg，通过 E = mc² 换算可得 1 u 对应 931.5 MeV 能量。
7. Chemical Amount of Substance | 物质的量
The mole is the SI unit for amount of substance, linking the number of particles to an easily measurable mass.
摩尔是物质的量的 SI 单位，将粒子数与容易测量的质量联系起来。
n = m / M
Amount n (mol) equals mass m (g) divided by molar mass M (g mol⁻¹). Avogadro's constant Nᴀ = 6.022 × 10²³ mol⁻¹ gives the number of particles in one mole.
物质的量 n（mol）等于质量 m（g）除以摩尔质量 M（g mol⁻¹）。阿伏伽德罗常量 Nᴀ = 6.022 × 10²³ mol⁻¹ 给出 1 mol 物质所含的粒子数。
n = c V
) × volume V (dm³). Use this to prepare standard solutions or to interpret titration data.
对溶液而言，物质的量等于浓度 c（mol dm⁻³）乘以体积 V（dm³）。利用此式可配制标准溶液或解释滴定数据。
p V = n R T
.314 J mol⁻¹ K⁻¹) and absolute temperature T (K). Always convert to kelvin (K = °C + 273).
理想气体状态方程将压强 p（Pa）、体积 V（m³）、物质的量 n（mol）、气体常数 R（8.314 J mol⁻¹ K⁻¹）和绝对温度 T（K）联系起来。温度必须换算为开尔文（K = °C + 273）。
8. Energetics | 热化学
Enthalpy change ΔH is the heat transferred in a reaction at constant pressure. Standard enthalpy changes are given with standard conditions (100 kPa, 298 K, solutions at 1 mol dm⁻³).
焓变 ΔH 是恒压下反应传递的热量。标准焓变在标准条件（100 kPa、298 K、溶液浓度为 1 mol dm⁻³）下测定。
q = m c ΔT
ΔH = – q / n
Heat exchanged q is calculated from mass m of the solution, specific heat capacity c (usually 4.18 J g⁻¹ K⁻¹ for water) and temperature change ΔT. Divide by the amount n that reacted to obtain ΔH.
传递的热量 q 由溶液质量 m、比热容 c（水通常取 4.18 J g⁻¹ K⁻¹）和温度变化 ΔT 计算。除以反应的物质的量 n 即得 ΔH。
ΔH°ⱼ = Σ ∆H°𝒻(products) – Σ ∆H°𝒻(reactants)
Hess's law allows us to determine unknown enthalpy changes using standard enthalpies of formation or combustion. The overall enthalpy change for a reaction is independent of the route taken.
盖斯定律允许我们利用标准生成焓或燃烧焓计算未知的焓变。反应的总焓变与路径无关。
9. Chemical Equilibrium | 化学平衡
For a reversible reaction at equilibrium, the equilibrium constant Kc expresses the ratio of product to reactant concentrations, each raised to the power of its stoichiometric coefficient.
可逆反应达平衡时，平衡常数 Kc 表示产物浓度与反应物浓度的比值，各项以其化学计量系数为指数。
aA + bB ⇌ cC + dD
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ
Only species in the gas or aqueous phase appear in the expression; solids and pure liquids are omitted. Kc is affected only by temperature. A change in concentration or pressure shifts the position of equilibrium but does not alter the value of Kc.
仅气相或溶液中的物种出现在表达式中，固体和纯液体不写入。Kc 只受温度影响。浓度或压力的变化会改变平衡位置，但不改变 Kc 的数值。
10. Acids and Bases | 酸碱
The pH scale measures the hydrogen ion concentration in aqueous solution.
pH 标度用于衡量水溶液中的氢离子浓度。
pH = – log[H⁺]
[H⁺] = 10⁻ᴾᴴ
A change of one pH unit corresponds to a ten‑fold change in [H⁺]. For strong acids, [H⁺] equals the acid concentration.
pH 每改变一个单位，[H⁺] 浓度变化十倍。对强酸，[H⁺] 等于酸的浓度。
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (at 298 K)
r Kw underpins the neutral point. In pure water [H⁺] = [OH⁻] = 10⁻⁷ mol dm⁻³, giving pH 7.
水的离子积 Kw 决定了中性条件。纯水中 [H⁺] = [OH⁻] = 10⁻⁷ mol dm⁻³，pH = 7。
For weak acids, the acid dissociation constant Ka gives the extent of dissociation:
Ka = [H⁺][A⁻] / [HA]
We often use pKa = – log Ka, analogous to pH.
对于弱酸，酸解离常数 Ka 描述解离程度；常用 pKa = – log Ka，与 pH 类似。
11. Genetics: The Hardy‑Weinberg Principle | 遗传学：哈迪‑温伯格定律
The Hardy‑Weinberg principle predicts allele and genotype frequencies in a large, randomly mating population with no mutation, selection, gene flow or genetic drift.
哈迪‑温伯格定律预测一个大型随机交配、无突变、无选择、无基因流动和遗传漂变的种群中的等位基因频率与基因型频率。
p + q = 1
p² + 2pq + q² = 1
llele. The genotype frequencies for homozygous dominant, heterozygous and homozygous recessive are p², 2pq and q² respectively.
设 p 为显性等位基因频率，q 为隐性等位基因频率。纯合显性、杂合和纯合隐性的基因型频率分别为 p²、2pq 和 q²。
These equations are used to estimate carrier frequencies for genetic disorders and to test whether a population is evolving at a particular locus.
这些方程可用来估算遗传病携带者频率，并检验某基因座位上的种群是否在进化。
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