AS WJEC Science: Formula & Theorem Quick Reference Handbook | AS WJEC 科学：公式定理速查手册

📚 AS WJEC Science: Formula & Theorem Quick Reference Handbook | AS WJEC 科学：公式定理速查手册

This compact reference guide brings together the essential formulae, equations and theorems you must recall for the AS WJEC Science examinations. Covering key topics from physics, chemistry and biology, each entry is presented with a concise English explanation followed immediately by its Chinese equivalent, allowing rapid revision and bilingual understanding.

这本紧凑的速查手册汇总了 AS WJEC 科学考试中必须牢记的核心公式、方程与定理。内容涵盖物理、化学和生物的关键主题，每个条目均以简明的英文解释与其对应的中文解释紧密配对，方便快速复习和双语理解。

1. Physical Quantities, Units and Definitions | 物理量、单位与定义

Speed is the rate of change of distance: v = d / t

速度是距离的变化率：v = d / t

Acceleration is the rate of change of velocity: a = (v – u) / t

加速度是速度的变化率：a = (v – u) / t

Density links mass and volume: ρ = m / V

密度将质量与体积联系起来：ρ = m / V

Weight is the gravitational force on a mass: W = mg (g = 9.81 m s⁻² on Earth)

重量是作用在质量上的引力：W = mg（地球上 g = 9.81 m s⁻²）

Moment of a force about a pivot: Moment = F × d (perpendicular distance)

力对支点的力矩：力矩 = F × d（垂直距离）

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2. Kinematics – Uniform Acceleration | 运动学 – 匀加速运动

First SUVAT equation: v = u + a t

第一个匀加速方程：v = u + a t

Second SUVAT equation: s = u t + ½ a t²

第二个匀加速方程：s = u t + ½ a t²

Third SUVAT equation: v² = u² + 2 a s

第三个匀加速方程：v² = u² + 2 a s

Fourth SUVAT equation: s = ½ (u + v) t

第四个匀加速方程：s = ½ (u + v) t

For an object falling freely from rest, u = 0 and a = g.

对于从静止自由下落的物体，u = 0，a = g。

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3. Forces and Newton’s Laws | 力与牛顿定律

Newton’s second law: F = m a (resultant force = mass × acceleration)

牛顿第二定律：F = m a（合力 = 质量 × 加速度）

Frictional force limit: F ≤ μ R, where μ is the coefficient of friction and R is the normal reaction.

摩擦力极限：F ≤ μ R，其中 μ 为摩擦系数，R 为法向反作用力。

Hooke’s law for springs: F = k Δx (force ∝ extension up to the limit of proportionality)

弹簧的胡克定律：F = k Δx（在弹性限度内力与伸长量成正比）

Momentum: p = m v

动量：p = m v

Impulse is the change in momentum: Impulse = F t = Δ p

冲量等于动量的变化量：冲量 = F t = Δ p

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4. Energy, Work and Power | 能量、功与功率

Work done by a constant force: W = F d cosθ

恒力做功：W = F d cosθ

Kinetic energy: Eₖ = ½ m v²

动能：Eₖ = ½ m v²

Gravitational potential energy: Eₚ = m g h

重力势能：Eₚ = m g h

Elastic potential energy stored in a stretched spring: E = ½ F Δx = ½ k Δx²

拉伸弹簧中储存的弹性势能：E = ½ F Δx = ½ k Δx²

Power is the rate of doing work: P = W / t = F v

功率是做功的快慢：P = W / t = F v

Efficiency: Efficiency = (useful output / total input) × 100%

效率：效率 =（有用输出 / 总输入）× 100%

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5. Waves | 波

Wave speed: v = f λ (speed = frequency × wavelength)

波速：v = f λ（波速 = 频率 × 波长）

Period and frequency are inverses: T = 1 / f

周期与频率互为倒数：T = 1 / f

Intensity of a wave: I = P / A (power per unit area)

波的强度：I = P / A（单位面积的功率）

Refractive index and Snell’s law: n₁ sin θ₁ = n₂ sin θ₂

折射率与斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂

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6. Electricity | 电学

Ohm’s law: V = I R (potential difference = current × resistance)

欧姆定律：V = I R（电压 = 电流 × 电阻）

Electrical power: P = I V = I² R = V² / R

电功率：P = I V = I² R = V² / R

Resistors in series: R_total = R₁ + R₂ + …

电阻串联：R_total = R₁ + R₂ + …

Resistors in parallel: 1 / R_total = 1 / R₁ + 1 / R₂ + …

电阻并联：1 / R_total = 1 / R₁ + 1 / R₂ + …

Electromotive force and internal resistance: ε = I (R + r)

电动势与内阻：ε = I (R + r)

Charge, current and time: Q = I t

电荷量、电流与时间：Q = I t

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7. Materials and Mechanical Properties | 材料与力学性能

Stress: σ = F / A (force per unit cross-sectional area)

应力：σ = F / A（单位截面积的力）

Strain: ε = ΔL / L₀ (extension over original length)

应变：ε = ΔL / L₀（伸长量与原长之比）

Young modulus: E = σ / ε (up to the limit of proportionality)

杨氏模量：E = σ / ε（在比例极限内）

Density: ρ = m / V

密度：ρ = m / V

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8. Atomic Physics and Radioactivity | 原子物理与放射性

Photon energy: E = h f (h = 6.63 × 10⁻³⁴ J s)

光子能量：E = h f（h = 6.63 × 10⁻³⁴ J s）

Wave equation for light: c = f λ (c = 3.00 × 10⁸ m s⁻¹ in vacuum)

光波方程：c = f λ（真空中 c = 3.00 × 10⁸ m s⁻¹）

Mass–energy equivalence: E = m c²

质能方程：E = m c²

Activity and decay constant: A = λ N

活度与衰变常数：A = λ N

Exponential decay law: N = N₀ e⁻^{λ t}

指数衰变定律：N = N₀ e⁻^{λ t}

Half-life: T₁/₂ = ln 2 / λ

半衰期：T₁/₂ = ln 2 / λ

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9. Chemical Calculations: The Mole | 化学计算：摩尔

Amount of substance: n = m / M (mass in g, molar mass in g mol⁻¹)

物质的量：n = m / M（质量 g，摩尔质量 g mol⁻¹）

Concentration: c = n / V (volume in dm³)

浓度：c = n / V（体积单位 dm³）

Molar gas volume at RTP (room temperature and pressure): V = n × 24 d m³

常温常压下气体摩尔体积：V = n × 24 dm³

Ideal gas equation: p V = n R T (R = 8.31 J mol⁻¹ K⁻¹)

理想气体状态方程：p V = n R T（R = 8.31 J mol⁻¹ K⁻¹）

Dilution of solutions: c₁ V₁ = c₂ V₂

溶液稀释：c₁ V₁ = c₂ V₂

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10. Energetics and Thermochemistry | 能量学与热化学

Heat energy transferred: q = m c ΔT (m = mass of solution, c = specific heat capacity)

热量传递：q = m c ΔT（m = 溶液质量，c = 比热容）

Enthalpy change per mole: ΔH = −q / n (exothermic → negative sign)

每摩尔焓变：ΔH = −q / n（放热用负号）

Enthalpy change using bond energies: ΔH = Σ (bond energies broken) − Σ (bond energies formed)

利用键能计算焓变：ΔH = Σ（断裂键的键能）− Σ（形成键的键能）

Hess’s law: the total enthalpy change is independent of the route taken.

赫斯定律：总焓变与反应途径无关。

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11. Yield, Atom Economy and Organic Formulae | 产率、原子经济性与有机物通式

Percentage yield: % yield = (actual yield / theoretical yield) × 100%

产率百分比：产率 % =（实际产量 / 理论产量）× 100%

Atom economy: % tom economy = (molar mass of desired product / sum of molar masses of all reactants) × 100%

原子经济性：原子经济性 % =（目标产物摩尔质量 / 所有反应物摩尔质量之和）× 100%

General formula for alkanes: Cₙ H₂ₙ₊₂

烷烃通式：Cₙ H₂ₙ₊₂

General formula for alkenes: Cₙ H₂ₙ

烯烃通式：Cₙ H₂ₙ

General formula for alcohols (saturated): Cₙ H₂ₙ₊₁ OH

饱和醇通式：Cₙ H₂ₙ₊₁ OH

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12. Biological Calculations: Magnification and Dilutions | 生物计算：放大倍数与稀释

Magnification: M = I / A where I = image size, A = actual size (both in same units)

放大倍数：M = I / A，I 为图像尺寸，A 为实际尺寸（单位需一致）

Converting units for microscopy: 1 mm = 1000 µm, 1 µm = 1000 nm

显微镜单位换算：1 mm = 1000 µm，1 µm = 1000 nm

Dilution factor in serial dilutions: DF = V_total / V_sample

连续稀释中的稀释因子：DF = V_total / V_sample

The equation C₁V₁ = C₂V₂ also applies to biological solutions.

等式 C₁V₁ = C₂V₂ 同样适用于生物溶液。

Rate of enzyme-controlled reaction: can be approximated as change in product concentration over time, but no single simple formula; instead use rate = Δ[product] / Δt.

酶促反应速率：可近似为产物浓度随时间的变化，无单一简单公式，通常用 rate = Δ[产物] / Δt 表示。

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