📚 Year 12 SQA Science: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This comprehensive quick reference handbook brings together the most important formulas, theorems, and key principles from the Year 12 SQA Science curriculum. Designed for rapid revision and daily use, it covers kinematics, dynamics, energy, waves, electricity, chemical calculations, equilibrium, thermodynamics, and nuclear processes. Each entry is presented as a clear English explanation followed by its Chinese equivalent, ensuring you understand the concept deeply and can recall it accurately under exam conditions.
本综合速查手册汇集了 SQA 12 年级科学课程中最重要的公式、定理和关键原理。手册专为快速复习与日常使用而设计，涵盖运动学、动力学、能量、波动、电学、化学计算、平衡、热力学及核过程。每个条目均以清晰的英文说明后接对应的中文解释，确保你深入理解概念并在考试中准确回忆。
1. Kinematics Equations | 运动学方程
Kinematics describes motion without considering its causes. The three core equations of motion for constant acceleration in a straight line link initial velocity u, final velocity v, acceleration a, displacement s, and time t. Always define a positive direction before using them.
运动学描述物体的运动而不涉及引起运动的原因。对于匀变速直线运动，三个核心运动方程将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系起来。使用前务必先规定正方向。
v = u + at
This equation relates final velocity to initial velocity, acceleration and time. It is used when displacement is not required.
该方程将末速度与初速度、加速度和时间关联，用于不涉及位移的情况。
s = ut + ½at²
Use this relation when you know initial velocity, acceleration and time but need to find displacement. The quadratic dependence on time is characteristic of accelerated motion.
当你知道初速度、加速度和时间但需要求位移时使用。位移对时间的二次依赖是加速运动的特征。
v² = u² + 2as
This time-independent equation connects initial and final velocities with acceleration and displacement. It is particularly helpful when time is not given.
该不含时间的方程将初末速度与加速度和位移联系起来。在未给出时间的情况下特别有用。
2. Newton's Laws of Motion | 牛顿运动定律
Newton's three laws form the foundation of classical mechanics. The first law states that an object remains at rest or in uniform motion unless acted upon by an unbalanced force. The second law quantifies the relationship between force, mass, and acceleration. The third law describes action--reaction pairs.
牛顿三定律构成了经典力学的基础。第一定律指出，除非受到不平衡力的作用，物体将保持静止或匀速直线运动状态。第二定律定量描述了力、质量和加速度的关系。第三定律描述了作用力与反作用力对。
F = ma
This is the mathematical statement of Newton's second law: the net force acting on an object equals the product of its mass and acceleration. The force must be in newtons, mass in kg, acceleration in m/s².
这是牛顿第二定律的数学表述：作用在物体上的合外力等于物体质量与加速度的乘积。力须以牛顿为单位，质量以千克，加速度以米/秒²为单位。
perpendicular components. The weight of an object is W = mg, where g = 9.8 m/s² on Earth.
分析问题时，画出受力分析图并将所有力分解为垂直方向的分力。物体的重量为 W = mg，地球上 g = 9.8 米/秒²。
netic friction, f = μₖN, where μ is the coefficient of friction and N is the normal force.
须包含拉力、摩擦力、法向反作用力和外加力。对于静摩擦力，f ≤ μₛN；对于动摩擦力，f = μₖN，其中 μ 为摩擦系数，N 为法向力。
3. Work, Energy and Power | 功、能量和功率
Work is done when a force moves its point of application. The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. Kinetic energy, gravitational potential energy, and work done against resistive forces are central to problem solving.
当力使其作用点移动时，就做了功。能量守恒定律指出，能量既不能创造也不能消灭，只能从一种形式转化为另一种形式。动能、重力势能以及克服阻力所做的功是解题的核心。
W = Fd cosθ
Work done equals the product of the force, the displacement, and the cosine of the angle between them. The unit is the joule (J).
功等于力、位移及两者夹角余弦的乘积。单位为焦耳（J）。
KE = ½mv² and GPE = mgh
Kinetic energy depends on mass and the square of speed. Gravitational potential energy near the Earth's surface is calculated from mass, gravitational field strength, and height.
动能取决于质量和速度的平方。地表附近的重力势能由质量、重力场强度和高度计算。
P = W / t = Fv
Power is the rate of doing work. The unit is the watt (W). For an object moving at constant speed against a force, power equals force times velocity.
功率是做功的速率。单位是瓦特（W）。对于克服某个力匀速运动的物体，功率等于力乘以速度。
rvation: total initial energy = total final energy + work done against dissipative forces.
在非保守情况下，克服摩擦力所做的功转化为热量：ΔE = 传递的热量。始终应用能量守恒：初始总能量 = 末总能量 + 克服耗散力所做的功。
4. Waves and Optics | 波动与光学
Waves transfer energy without transferring matter. The wave equation links speed, frequency and wavelength. Understanding reflection, refraction, diffraction and interference is essential for the SQA Higher course.
波传递能量而不传递物质。波动方程将波速、频率和波长联系起来。理解反射、折射、衍射和干涉对 SQA Higher 课程至关重要。
v = fλ
Wave speed (m/s) equals frequency (Hz) multiplied by wavelength (m). This applies to all waves, including sound, water and electromagnetic waves.
波速（m/s）等于频率（Hz）乘以波长（m）。这适用于所有波，包括声波、水波和电磁波。
n = sin i / sin r
Snell' ht passes from a vacuum (or air) into that medium. It also equals the ratio of speeds: n = c / v, where c is the speed of light in vacuum.
斯涅尔折射定律：当光从真空（或空气）进入某介质时，该介质的折射率 n 等于入射角正弦与折射角正弦之比。它也等于光速之比：n = c / v，其中 c 为真空光速。
. At angles greater than the critical angle, no light is refracted out of the denser medium.
全内反射的临界角 θc 由 sin θc = 1 / n 给出。当入射角大于临界角时，没有光线从光密介质折射出去。
coherent sources: d sinθ = mλ; for destructive: d sinθ = (m + ½)λ, where m is an integer.
相干光源的干涉中，加强干涉的程差：d sinθ = mλ；减弱干涉：d sinθ = (m + ½)λ，m 为整数。
5. Electricity and Circuits | 电学与电路
Electric circuits obey Ohm's law for ohmic conductors at constant temperature. The behaviour of series and parallel resistors, along with the relationships between charge, current, voltage, energy and power, are tested regularly.
对于欧姆导体，在恒温下电路遵守欧姆定律。串联和并联电阻的特性，以及电荷、电流、电压、能量和功率之间的关系，是经常考查的内容。
V = IR
Ohm's law: the potential difference across an ohmic conductor is proportional to the current passing through it. The resistance R is constant.
欧姆定律：欧姆导体两端的电势差与通过的电流成正比。电阻 R 恒定。
I = Q / t
Electric current is the rate of flow of charge. One ampere equals one coulomb per second.
电流是电荷流动的速率。1 安培等于 1 库仑/秒。
| Series | Parallel |
|---|---|
| Rtotal = R₁ + R₂ + ... | 1/Rtotal = 1/R₁ + 1/R₂ + ... |
| Vtotal = V₁ + V₂ + ... | V is the same across each branch |
| Current I the same everywhere | Itotal = I₁ + I₂ + ... |
P = IV = I²R = V²/R and E = Pt
Electrical power is the product of current and voltage. Electrical energy transferred is power multiplied by time, measured in joules or kilowatt-hours.
电功率是电流与电压的乘积。传递的电能是功率乘以时间，单位为焦耳或千瓦时。
Kirchhoff's laws: junction rule (Σ Iin = Σ Iout) and loop rule (Σ ΔV = 0 around any closed loop). Use these to solve complex circuits.
基尔霍夫定律：节点电流定律（Σ Iin = Σ Iout）和回路电压定律（任一闭合回路 Σ ΔV = 0）。用它们求解复杂电路。
6. The Mole and Stoichiometry | 摩尔与化学计量
The mole is the SI unit for amount of substance. Stoichiometry uses balanced equations to calculate masses, volumes and concentrations of reactants and products. Master these relationships to handle quantitative chemistry with confidence.
摩尔是物质的量的 SI 单位。化学计量法利用配平的方程计算反应物和产物的质量、体积和浓度。掌握这些关系，就能自信地处理定量化学。
n = m / M
Number of moles equals mass in grams divided by molar mass in g/mol. This is the most fundamental formula linking mass and amount.
物质的量等于以克为单位的质量除以以 g/mol 为单位的摩尔质量。这是联系质量与物质的量最基本的公式。
n = V / Vₘ (for gases at room temperature and pressure)
conditions, one mole of any gas occupies approximately 24 dm³. Vₘ ≈ 24 dm³ mol⁻¹ at r.t.p.
在标准状况下，1 摩尔任何气体大约占据 24 dm³。在室温和常压下，Vₘ ≈ 24 dm³ mol⁻¹。
c = n / V (concentration in mol dm⁻³)
ember: c₁V₁ = c₂V₂ for dilutions and neutralisation reactions where the mole ratio is 1:1.
浓度将溶质的物质的量与溶液体积联系起来。这在滴定中广泛使用。记住：当摩尔比为 1:1 时，稀释和中和反应满足 c₁V₁ = c₂V₂。
Percent yield = (actual yield / theoretical yield) × 100% Atom economy = (molar mass of desired product / sum of molar masses of all reagents) × 100%.
产率百分数 =（实际产量 / 理论产量）× 100%。原子经济性 =（所需产物的摩尔质量 / 所有反应物摩尔质量之和）× 100%。
7. Chemical Equilibrium and Le Chatelier's Principle | 化学平衡与勒夏特列原理
At dynamic equilibrium, the rates of the forward and reverse reactions are equal. The equilibrium constant Kc expresses the ratio of product concentrations to reactant concentrations at equilibrium. Le Chatelier's principle predicts how a system at equilibrium responds to changes.
在动态平衡时，正反应和逆反应的速率相等。平衡常数 Kc 表达了平衡时产物浓度与反应物浓度之比。勒夏特列原理可预测平衡系统对条件变化的响应。
For aA + bB ⇌ cC + dD, Kc = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ)
The square brackets denote equilibrium concentrations in mol dm⁻³. The value of Kc is temperature dependent only. Changing pressure or concentration shifts the position of equilibrium but does not change Kc.
方括号表示以 mol dm⁻³ 为单位的平衡浓度。Kc 的值仅取决于温度。改变压强或浓度会移动平衡位置，但不改变 Kc。
- Temperature increase: equilibrium shifts in the endothermic direction.
- 温度升高：平衡向吸热方向移动。
- Pressure increase (gaseous systems): equilibrium shifts towards the side with fewer gas molecules.
- 压强增大（气体体系）：平衡向气体分子数较少的一侧移动。
- Concentration increase of a reactant: equilibrium shifts to consume the added reactant.
- 增大反应物浓度：平衡向消耗所加反应物的方向移动。
A catalyst provides an alternative pathway with lower activation energy, speeding up both forward and reverse reactions equally. It does not affect the equilibrium position or Kc.
催化剂提供了活化能较低的替代路径，同等加快正逆反应速率，但不影响平衡位置或 Kc。
8. Reaction Rates | 反应速率
The rate of a chemical reaction measures how quickly reactants are used up or products are formed. SQA Higher requires understanding of collision theory, activation energy, and the interpretation of rate-concentration graphs.
化学反应速率衡量反应物消耗或产物生成的快慢。SQA Higher 要求理解碰撞理论、活化能，并能解释速率-浓度图。
Rate = Δ[concentration] / Δt
Average rate is calculated from the change in concentration divided by the time interval. The instantaneous rate is found from the gradient of a tangent to the concentration-time curve.
平均速率由浓度变化除以时间间隔算得。瞬时速率则由浓度-时间曲线切线的斜率求得。
neral rate equation: Rate = k [A]ₓₓ[B]ₓ, where k is the rate constant and x, y are orders.
对于许多反应，速率与一种或多种反应物浓度的某次方成正比。通用速率方程：Rate = k [A]ₓₓ[B]ₓ，其中 k 为速率常数，x、y 为反应级数。
energy (Ea); increasing concentration/pressure increases collision frequency; a catalyst lowers Ea. The Arrhenius equation is not required at this level, but the qualitative effect must be understood.
影响速率的因素：升高温度增加能量 ≥ 活化能（Ea）的碰撞次数；增大浓度/压强增加碰撞频率；催化剂降低 Ea。本级不要求阿伦尼乌斯方程，但必须理解上述定性影响。
9. Thermodynamics and Enthalpy | 热力学与焓
Enthalpy change (ΔH) is the heat energy change at constant pressure. Exothermic reactions release heat to the surroundings, having a negative ΔH. Endothermic reactions absorb heat, showing a positive ΔH. SQA Higher expects you to perform calculations using experimental data and bond enthalpies.
焓变（ΔH）是恒压下的热量变化。放热反应向环境释放热量，ΔH 为负。吸热反应吸收热量，ΔH 为正。SQA Higher 要求你使用实验数据和键焓进行计算。
q = mcΔT
Heat transferred is calculated from mass, specific heat capacity c, and temperature change. This equation is used in calorimetry to find the enthalpy change of a reaction.
传递的热量由质量、比热容 c 和温度变化计算。该方程用于量热法中，以求得反应的焓变。
ΔH = - q / n (or ΔH = + q / n, depending on definition of system and surroundings)
Enthalpy change per mole is obtained by dividing the heat change by the number of moles of the limiting reactant. Always include the sign.
每摩尔的焓变由热量变化除以限制反应物的物质的量得到。务必标明符号。
ΔH ≈ Σ (bond energies of bonds broken) – Σ (bond energies of bonds formed)
This average bond enthalpy method provides an estimate of ΔH for gas-phase reactions. Bond breaking is endothermic, bond forming is exothermic.
平均键焓法可为气相反应提供 ΔH 的估算值。断键吸热，成键放热。
Hess's law states that the total enthalpy change for a reaction is independent of the route taken. Use it to calculate unknown ΔH values from known enthalpies of formation or combustion.
赫斯定律指出，反应的总焓变与途径无关。利用该定律，可通过已知的生成焓或燃烧焓计算未知的 ΔH。
10. Radioactive Decay and Half-Life | 放射性衰变与半衰期
Unstable nuclei undergo radioactive decay, emitting alpha, beta, or gamma radiation. The activity of a source is the number of decays per unit time. Understanding half-life and nuclear equations is essential for this topic.
不稳定的原子核会发生放射性衰变，放出 α、β 或 γ 辐射。源的活度是单位时间的衰变数。理解半衰期和核方程对此主题至关重要。
A = - dN/dt = λN
Activity A is proportional to the number of undecayed nuclei N, where λ is the decay constant. The SI unit of activity is the becquerel (Bq).
活度 A 与尚未衰变的核子数 N 成正比，λ 为衰变常数。活度的 SI 单位是贝克勒尔（Bq）。
t₁/₂ = ln 2 / λ ≈ 0.693 / λ
The half-life is the time taken for the number of undecayed nuclei (or the activity) to halve. It is a constant for a given radioisotope.
半衰期是未衰变核子数（或活度）减半所需的时间。对于给定的放射性同位素，它是常数。
er n half-lives, the fraction remaining is (1/2)ⁿ. These relationships allow calculation of remaining activity or age in radiometric dating.
指数衰变：N = N₀ e⁻(λt)。经过 n 个半衰期后，剩余份额为 (1/2)ⁿ。这些关系可用于计算剩余活度或放射性测年的年代。
nucleon number and total proton number. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He for alpha decay.
核方程须在总核子数和总质子数上守恒。例如 α 衰变：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。
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