📚 A-Level CCEA Science: Essential Formula Handbook | A-Level CCEA 科学：必背公式汇总手册
Mastering the essential formulas in Physics, Chemistry, and Biology is the key to scoring high in CCEA A-Level Science. This handbook brings together must-know equations from all three disciplines, with clear explanations and practical tips — perfect for last-minute revision or building deep understanding. Keep it handy, test yourself daily, and walk into the exam hall with confidence.
掌握物理、化学和生物的核心公式是征服 CCEA A-Level 科学考试的关键。这份手册汇聚了三大学科的必背方程，并配有清晰的阐释和实用贴士——非常适合考前冲刺或深入理解。随身携带、每日自测，自信步入考场。
1. Physics: Kinematics & Dynamics | 物理：运动学与动力学
The SUVAT equations describe uniformly accelerated motion. v = u + at links final velocity v, initial velocity u, acceleration a and time t.
匀加速运动的 SUVAT 方程。 v = u + at 关联末速度 v、初速度 u、加速度 a 和时间 t。
s = ut + ½at²
This gives displacement s when acceleration is constant.
当加速度恒定时，此式给出位移 s。
v² = u² + 2as
Useful when time is unknown.
未知时间时非常实用。
s = ½(u + v)t
Average velocity multiplied by time yields displacement.
平均速度乘以时间得出位移。
Newton's second law F = ma gives resultant force F for mass m and acceleration a. Weight is W = mg (g = 9.81 m s⁻² on Earth).
牛顿第二定律 F = ma 给出质量为 m、加速度为 a 时的合力。重力 W = mg（地球上 g ≈ 9.81 m s⁻²）。
um p = mv is conserved in collisions. Impulse FΔt = Δp links force and change in momentum.
动量 p = mv 在碰撞中守恒。冲量 FΔt = Δp 将力与动量变化联系起来。
2. Physics: Work, Energy & Power | 物理：功、能与功率
W = Fs cos θ
Work done W equals force F times displacement s times the cosine of the angle between them.
功 W 等于力 F 乘以位移 s 再乘以它们夹角 θ 的余弦。
Kinetic energy KE = ½mv², gravitational potential energy GPE = mgh (h is height). The principle of conservation of energy is fundamental: total energy remains constant in a closed system.
动能 KE = ½mv²，重力势能 GPE = mgh（h 为高度）。能量守恒原理是根本：封闭系统中总能量保持不变。
P = W/t = Fv
Power P is the rate of doing work. For a constant force moving at speed v, P = Fv.
功率 P 是做功的速率。对于以恒定速度 v 移动的恒力，P = Fv。
Efficiency = (useful energy output / total energy input) × 100%.
效率 =（有用能量输出 / 总能量输入）× 100%。
3. Physics: Waves & Optics | 物理：波与光学
v = f λ
Wave speed v equals frequency f multiplied by wavelength λ.
波速 v 等于频率 f 乘以波长 λ。
Refractive index n = sin i / sin r, where i is angle of incidence and r is angle of refraction.
折射率 n = sin i / sin r，其中 i 为入射角，r 为折射角。
n = c / v
Also, n equals the speed of light in vacuum c divided by speed in medium v.
此外，n 等于真空光速 c 除以介质中光速 v。
Critical angle for total internal reflection: sin θc = 1/n.
全内反射的临界角： sin θc = 1/n。
For double-slit interference, fringe spacing Δy = λD / d, where D is slit-to-screen distance and d is slit separation.
双缝干涉条纹间距 Δy = λD / d，其中 D 为缝屏距离，d 为双缝间距。
4. Physics: Electricity & Circuits | 物理：电学与电路
V = IR
Ohm's law: potential difference V across a resistor equals current I multiplied by resistance R.
欧姆定律：电阻两端的电势差 V 等于电流 I 乘以电阻 R。
Electrical power P = IV = I²R = V²/R. Energy transferred E = IVt.
电功率 P = IV = I²R = V²/R。传输的能量 E = IVt。
Resistance of a uniform wire: R = ρL / A, where ρ is resistivity, L length, A cross-sectional area.
均匀导线的电阻： R = ρL / A，ρ 为电阻率，L 为长度，A 为横截面积。
Resistors in series: Rtotal = R₁ + R₂ + ... ; in parallel: 1/Rtotal = 1/R₁ + 1/R₂ + ...
串联电阻：Rₜₒₜₐₗ = R₁ + R₂ + …；并联电阻：1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + …
Terminal pd V = ε - Ir, where ε is emf and r internal resistance.
路端电压 V = ε - Ir，其中 ε 为电动势，r 为内阻。
5. Physics: Thermal Physics & Gases | 物理：热物理与气体
Heat energy change: ΔQ = mcΔθ, where m is mass, c specific heat capacity, Δθ temperature change.
热量变化：ΔQ = mcΔθ，m 为质量，c 为比热容，Δθ 为温度变化。
Latent heat: ΔQ = mL, where L is specific latent heat (fusion or vaporisation).
潜热：ΔQ = mL，L 为比潜热（熔化或汽化）。
pV = nRT
Ideal gas law: pressure p, volume V, amount n (mol), gas constant R (8.31 J K⁻¹ mol⁻¹), thermodynamic temperature T.
理想气体定律：压强 p、体积 V、物质的量 n（摩尔）、气体常数 R（8.31 J K⁻¹ mol⁻¹）、热力学温度 T。
Mean kinetic energy of a gas molecule: KEₐᵥₑ = (3/2)kT, where k is Boltzmann constant.
气体分子的平均动能：KEₐᵥₑ = (3/2)kT，k 为玻尔兹曼常数。
6. Physics: Nuclear & Quantum Physics | 物理：原子核与量子物理
E = mc²
Mass-energy equivalence links mass m and energy E, with c the speed of light.
质能方程关联质量 m 和能量 E，c 为光速。
ber of undecayed nuclei N = N₀ e⁻λᵗ, where λ is decay constant. Half-life t₁/₂ = ln 2 / λ.
放射性衰变：未衰变核数目 N = N₀ e⁻λᵗ，λ 为衰变常数。半衰期 t₁/₂ = ln 2 / λ。
Photon energy E = hf = hc/λ, Planck constant h = 6.63 × 10⁻³⁴ J s.
光子能量 E = hf = hc/λ，普朗克常数 h = 6.63 × 10⁻³⁴ J s。
The de Broglie wavelength λ = h / p = h / mv demonstrates wave-particle duality.
德布罗意波长 λ = h / p = h / mv 揭示了波粒二象性。
7. Chemistry: Moles & Stoichiometry | 化学：摩尔与化学计量
n = m / M
Amount of substance n (mol) equals mass m divided by molar mass M.
物质的量 n（摩尔）等于质量 m 除以摩尔质量 M。
Concentration c = n / V, typically in mol dm⁻³, where V is volume of solution.
浓度 c = n / V，单位常用 mol dm⁻³，V 为溶液体积。
olume at RTP (room temp & pressure): V(gas) = n × 24 dm³ mol⁻¹. At STP use 22.4 dm³ mol⁻¹.
室温常压下气体体积：V(气体) = n × 24 dm³ mol⁻¹。标准状况下用 22.4 dm³ mol⁻¹。
pV = nRT
Ideal gas equation for any gas; remember to use consistent units.
适用于任何气体的理想气体方程；注意使用一致的单位。
Percentage yield = (actual yield / theoretical yield) × 100%; atom economy = (mass of desired product / total mass of reactants) × 100%.
产率 =（实际产量 / 理论产量）× 100%；原子经济性 =（目标产物质量 / 反应物总质量）× 100%。
8. Chemistry: Energetics & Kinetics | 化学：能量学与动力学
ΔH = ΣH(products) - ΣH(reactants)
lpy change calculated from formation enthalpies. Use q = mcΔT for calorimetry experiments.
标准焓变由生成焓计算。量热实验使用 q = mcΔT。
ΔHreaction = Σ(bond energies broken) - Σ(bond energies formed).
反应焓变 = Σ(断裂键能) - Σ(生成键能)。
ΔG = ΔH - TΔS
Gibbs free energy determines feasibility: ΔG < 0 for a spontaneous reaction.
吉布斯自由能决定反应可行性：自发反应需 ΔG < 0。
Rate equation: rate = k[A]ᵐ[B]ⁿ on. The Arrhenius equation ln k = -Eₐ/(RT) + ln A links rate constant k and temperature T.
速率方程：rate = k[A]ᵐ[B]ⁿ，m 和 n 为反应级数。阿伦尼乌斯方程 ln k = -Eₐ/(RT) + ln A 关联速率常数 k 与温度 T。
9. Chemistry: Equilibrium & Redox | 化学：平衡与氧化还原
Equilibrium constant Kc for aA + bB ⇌ cC + dD:
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ
Kc is temperature-dependent. A large Kc indicates equilibrium favours products.
Kc 随温度变化。大 Kc 表示平衡倾向于产物。
pH = -log₁₀[H⁺]; [H⁺] = 10⁻ᵖᴴ. For strong acids, [H⁺] = concentration of acid.
pH = -log₁₀[H⁺]；[H⁺] = 10⁻ᵖᴴ。强酸中 [H⁺] 等于酸的浓度。
Ionic product of water: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K.
水的离子积：Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴（298 K 时）。
In redox, oxidation number changes track electron transfer. Reducing agents lose electrons, oxidising agents gain electrons.
氧化还原中，氧化数的变化反映电子转移。还原剂失电子，氧化剂得电子。
10. Biology: Magnification & Measurement | 生物：放大与测量
Magnification = Image size / Actual size
Always convert units to the same scale (e.g., mm to µm: ×1000).
务必统一单位（如 mm 转 µm：×1000）。
nts using haemocytometer: Cells per ml = average count per square × dilution factor × 10⁴.
血球计数板计数：每毫升细胞数 = 每格平均计数 × 稀释倍数 × 10⁴。
of reaction (e.g., enzyme activity) = change in substrate or product concentration / time.
反应速率（如酶活性）= 底物或产物浓度变化 / 时间。
ut = heart rate × stroke volume. Breathing rate and tidal volume link to ventilation rate.
心输出量 = 心率 × 每搏输出量。呼吸频率与潮气量决定肺通气量。
11. Biology: Population Genetics & Statistical Tests | 生物：群体遗传学与统计检验
Hardy–Weinberg principle:
p + q = 1 ; p² + 2pq + q² = 1
p and q are allele frequencies. p², 2pq, q² predict genotype frequencies in a non-evolving population.
p 和 q 为等位基因频率。p²、2pq、q² 预测非进化群体中的基因型频率。
Chi-squared test: χ² = Σ((O - E)² / E), where O = observed, E = expected. Compare with critical value at n-1 degrees of freedom.
卡方检验：χ² = Σ((O - E)² / E)，O 为观察值，E 为期望值。与自由度为 n-1 的临界值比较。
impson’s Index of Diversity: D = 1 - Σ(n/N)², higher value indicates greater biodiversity.
辛普森多样性指数：D = 1 - Σ(n/N)²，数值越高表明生物多样性越丰富。
12. Data Analysis & Uncertainties | 数据分析与不确定度
Percentage uncertainty = (absolute uncertainty / measurement) × 100% ents: for addition/subtraction add absolute uncertainties; for multiplication/division add % uncertainties.
百分不确定度 =（绝对不确定度 / 测量值）× 100%。组合测量时，加减运算叠加绝对不确定度；乘除运算叠加百分不确定度。
Mean value x̄ = Σx / n. Standard deviation s = √(Σ(x - x̄)²/(n-1)). Precision is indicated by range or standard deviation.
平均值 x̄ = Σx / n。标准差 s = √(Σ(x - x̄)²/(n-1))。精密度由极差或标准差体现。
gradient = Δy/Δx. Intercept gives useful physical quantities (e.g., y-intercept for emf).
作图时绘制最佳拟合线，斜率 = Δy/Δx。截距常给出有用的物理量（如电动势由 y 截距得出）。
Always quote final answers to the same number of significant figures as the least precise measurement. Keep units consistent.
最终答案的有效数字应与最不精确的测量值保持一致。务必统一单位。
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