📚 Year 13 Edexcel Science: Quick Reference Handbook of Formulas and Theorems | 13年级爱德思科学：公式定理速查手册
This handbook collates the essential formulas, theorems, and relationships required for the Year 13 Edexcel A Level Physics, Chemistry, and Biology specifications. Use it as a rapid retrieval tool to reinforce your understanding, spot connections between topics, and build confidence before assessments. Each section delivers the key equations with concise context in both English and Chinese, matching the bilingual learning support TutorHao is known for.
本速查手册汇集了13年级爱德思A Level物理、化学、生物大纲所要求的核心公式、定理与重要关系。你可以将它用作快速回顾工具，巩固理解、发现专题之间的关联，并在评估前建立信心。每一个小节都以中英双语提供关键方程式及简明注释，延续TutorHao一贯的双语学习支持风格。
1. Kinematics and Mechanics | 运动学与力学
of uniformly accelerated motion are: v = u + at, s = ut + ½at², and v² = u² + 2as. Newton's second law gives F = ma, and momentum is defined as p = mv.
匀加速运动的三大方程是：v = u + at，s = ut + ½at² 以及 v² = u² + 2as。牛顿第二定律表明 F = ma，动量定义为 p = mv。
force acts. This is the principle of conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
在任何无合外力作用的封闭系统中，碰撞前的总动量等于碰撞后的总动量，这就是动量守恒原理：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
e average force multiplied by the time for which it acts: FΔt = Δp. The area under a force–time graph represents impulse.
冲量是动量的变化量，等于平均力乘以作用时间：FΔt = Δp。力–时间图下方的面积代表冲量。
2. Work, Energy and Power | 功、能与功率
splacement. Kinetic energy is KE = ½mv², and gravitational potential energy near the Earth's surface is ΔGPE = mgΔh.
恒力做功的表达式为 W = Fd cos θ，其中 θ 是力与位移的夹角。动能为 KE = ½mv²，地球表面附近的重力势能变化为 ΔGPE = mgΔh。
stem is useful energy output divided by total energy input: η = useful output / total input.
能量守恒定律指出，能量不能被创造或毁灭，只能在不同的能量储存之间转移。系统的效率为有用能量输出除以总能量输入：η = 有用输出 / 总输入。
, where v is the velocity in the direction of the force. One watt is one joule per second.
功率是做功的速率：P = W / t = Fv，其中 v 是沿力方向的速度。1瓦特等于每秒1焦耳。
3. Circular Motion and Gravitation | 圆周运动与引力
centripetal acceleration is a = v²/r = rω², and the centripetal force is F = mv²/r = mrω².
对于以恒速率 v 在半径为 r 的圆周上运动的物体，角速度 ω 满足 v = rω。向心加速度为 a = v²/r = rω²，向心力为 F = mv²/r = mrω²。
Newton' F = Gm₁m₂/r². The gravitational field strength at a distance r from a mass M is g = GM/r².
牛顿万有引力定律指出，两个质点之间的引力为 F = Gm₁m₂/r²。距质量为 M 的天体 r 处的引力场强度为 g = GM/r²。
Kepler's third law for a satellite orbiting a central body can be expressed as T² ∝ y T² = (4π²/GM) r³. For a geostationary satellite, the orbital period is exactly 24 hours.
开普勒第三定律适用于绕中心天体运行的卫星，可表示为 T² ∝ r³，精确形式为 T² = (4π²/GM) r³。对于地球同步卫星，轨道周期恰好为24小时。
4. Electric Fields and Circuits | 电场与电路
W/q, the work done per unit charge. For a uniform field between parallel plates, E = V/d.
电场强度定义为 E = F/q，即单位正电荷所受的力。两点之间的电势差为 V = W/q，即移动单位电荷所做的功。对于平行板间的匀强电场，E = V/d。
Coulomb' : F = kQ₁Q₂/r², where k = 1/(4πε₀). The electric field due to a point charge is E = kQ/r².
库仑定律给出两点电荷之间的作用力：F = kQ₁Q₂/r²，其中 k = 1/(4πε₀)。点电荷产生的电场为 E = kQ/r²。
Current is the rate of flow of charge: I = ΔQ/Δt. Ohm' trical power is P = IV = I²R = V²/R. Resistivity ρ links resistance to geometry: R = ρL/A.
电流是电荷流动的速率：I = ΔQ/Δt。欧姆定律指出，在温度一定时，对导体有 V = IR。电功率为 P = IV = I²R = V²/R。电阻率 ρ 将电阻与几何尺寸联系起来：R = ρL/A。
5. Magnetic Fields and Induction | 磁场与电磁感应
ls a magnetic force: F = Bqv sin θ, where θ is the angle between velocity and field lines.
磁场中的载流导体受到安培力：F = BIL sin θ。运动电荷受到洛伦兹力：F = Bqv sin θ，其中 θ 是速度与磁感线之间的夹角。
Magnetic flux through an area A is φ = BA cos θ. Faraday' tates that the induced e.m.f. is equal to the negative rate of change of flux linkage: ε = – or a straight conductor of length l moving at speed v perpendicular to a field B, ε = Blv.
穿过面积 A 的磁通量为 φ = BA cos θ。法拉第电磁感应定律指出，感应电动势等于磁链变化率的负值：ε = – d(Nφ)/dt。对于长度为 l 的直导体在垂直于磁场 B 的方向上以速度 v 运动，ε = Blv。
Lenz's law determines the direction of induced current: the induced current always flows in a direction that opposes the change in flux producing it. This is consistent with conservation of energy.
楞次定律决定了感应电流的方向：感应电流总是沿阻碍引起它的磁通量变化的方向流动，这与能量守恒是一致的。
6. Waves and Optics | 波与光学
eed, frequency, and wavelength: v = fλ. The refractive index of a medium is n = c/v. Snell' in θ₂. The critical angle for total internal reflection is sin θc = n₂/n₁ (where n₁ > n₂).
波速方程关联波速、频率和波长：v = fλ。介质的折射率为 n = c/v。斯涅耳定律：n₁ sin θ₁ = n₂ sin θ₂。全反射的临界角满足 sin θc = n₂/n₁（其中 n₁ > n₂）。
fraction grating, maxima occur when d sin θ = nλ, where d is the slit separation. In Young' le-slit experiment, the fringe separation is Δy = λD/d, with D the distance to the screen.
对于衍射光栅，明纹条件为 d sin θ = nλ，其中 d 是光栅常数。在杨氏双缝实验中，条纹间距为 Δy = λD/d，其中 D 为缝到屏的距离。
The intensity of a progressive wave is proportional to the square of its amplitude: I ∝ s, the energy of a photon is E = hf, which combines with the wave equation to give c = fλ.
行波的强度正比于振幅的平方：I ∝ A²。对于电磁波，光子能量为 E = hf，结合波速方程可得 c = fλ。
7. Quantum and Nuclear Physics | 量子与核物理
φ + KE_max, where φ is the work function. The threshold frequency f₀ is given by hf₀ = φ.
光子能量为 E = hf = hc/λ。光电效应由方程 hf = φ + KE_max 描述，其中 φ 是逸出功。截止频率 f₀ 满足 hf₀ = φ。
The de Broglie wavelength of a moving particle is λ = h/p, showing wave– on diffraction, the spacing of crystal planes can be calculated using nλ = 2d sin θ (Bragg's law).
运动粒子的德布罗意波长为 λ = h/p，体现了波粒二象性。在电子衍射中，晶面间距可用布拉格定律 nλ = 2d sin θ 计算。
Radioactive decay follows an exponential law: N = N₀ e-λt tivity A = λN. The half-life T₁/₂ is linked to the decay constant by T₁/₂ = ln 2 / λ. Mass–energy equivalence from special relativity is E = mc².
放射性衰变遵循指数规律：N = N₀ e-λt，活度 A = λN。半衰期 T₁/₂ 与衰变常数的关系为 T₁/₂ = ln 2 / λ。狭义相对论中的质能方程为 E = mc²。
8. Thermodynamics | 热力学
ixed mass of an ideal gas, pV/T = constant. The average kinetic energy of a molecule is ½m
理想气体状态方程为 pV = nRT，其中 n 为物质的量，R = 8.31 J mol⁻¹ K⁻¹。对于一定质量的理想气体，pV/T = 常数。分子的平均平动动能为 ½m
W is work done on the system. For an isothermal expansion of an ideal gas, ΔU = 0, so Q = –W.
热力学第一定律为 ΔU = Q + W，其中 ΔU 是内能变化，Q 是对系统加热量，W 是对系统做功量。对于理想气体等温膨胀，ΔU = 0，故 Q = –W。
The efficiency of a heat engine is η = W/Qh = 1 – Qc/Qh. The maximum theoretical efficiency (Carnot efficiency) is η = 1 – Tc/Th, where temperatures are in kelvin.
热机效率为 η = W/Qh = 1 – Qc/Qh。最大理论效率（卡诺效率）为 η = 1 – Tc/Th，其中温度均以开尔文为单位。
9. Stoichiometry and Equilibrium Constants | 化学计量与平衡常数
lumes to moles: n = V/Vm at RTP. Percentage yield = (actual yield/theoretical yield) × 100%.
物质的量 n 由 n = m/M 给出。浓度 c = n/V（mol dm⁻³）。理想气体方程也可用于将气体体积转换为物质的量：在常温常压下 n = V/Vm。产率百分比 = (实际产量/理论产量) × 100%。
For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant Kc = [C]c[D]d / [A]a[B]b. For gases, Kp is defined using partial pressures in a similar ratio. The value of K is constant at a given temperature.
对于可逆反应 aA + bB ⇌ cC + dD，平衡常数 Kc = [C]c[D]d / [A]a[B]b。对于气体，Kp 用分压以类似的比值定义。在给定温度下，K 的值是恒定的。
or weak acids, the acid dissociation constant is Ka = [H⁺][A⁻]/[HA]. pH is defined as pH = –log₁₀[H⁺]. The ionic product of water is Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K.
对于弱酸，酸解离常数为 Ka = [H⁺][A⁻]/[HA]。pH 定义为 pH = –log₁₀[H⁺]。水的离子积为 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶（298 K时）。
10. Rates of Reaction and Arrhenius | 反应速率与阿伦尼乌斯
For a reaction with rate law rate = k[A]m[B]n, the orders m and n are determined experimentally. The overall order is m + n. The rate constant k is temperature-dependent.
对于速率方程为 rate = k[A]m[B]n 的反应，级数 m 和 n 由实验确定。总反应级数为 m + n。速率常数 k 随温度变化。
The Arrhenius equation links the rate constant to temperature: k = A e-Ea/RT he activation energy and A is the pre-exponential factor. In logarithmic form: ln k = ln A – Ea/(RT).
阿伦尼乌斯方程将速率常数与温度联系起来：k = A e-Ea/RT，其中 Ea 是活化能，A 是指前因子。对数形式为：ln k = ln A – Ea/(RT)。
pend on the overall order: for zero order, mol dm⁻³ s⁻¹; for first order, s⁻¹; for second order, dm³ mol⁻¹ s⁻¹.
对于一级反应，半衰期 t₁/₂ 与浓度无关：t₁/₂ = ln 2 / k。k 的单位取决于总级数：零级为 mol dm⁻³ s⁻¹，一级为 s⁻¹，二级为 dm³ mol⁻¹ s⁻¹。
11. Biology: Respiration and Photosynthesis | 生物学：细胞呼吸与光合作用
he light-dependent reactions, photolysis of water produces protons, electrons, and oxygen. ATP is synthesised by chemiosmosis.
光合作用总反应式为 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。在光反应中，水的光解产生质子、电子和氧气。ATP 通过化学渗透合成。
lysis produces a net gain of 2 ATP and 2 NADH per glucose. The Krebs cycle and oxidative phosphorylation yield up to approximately 36–38 ATP molecules per glucose in total.
有氧呼吸可概括为 C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。糖酵解每分子葡萄糖净产生2 ATP 和2 NADH。三羧酸循环与氧化磷酸化合计每分子葡萄糖最多可产生约36–38个 ATP。
/ O₂ consumed. For carbohydrates RQ = 1.0, for lipids RQ ≈ 0.7, and for proteins RQ ≈ 0.9.
呼吸商（RQ）是产生的 CO₂ 与消耗的 O₂ 之比：RQ = 产生的 CO₂ / 消耗的 O₂。碳水化合物的 RQ = 1.0，脂类的 RQ ≈ 0.7，蛋白质的 RQ ≈ 0.9。
12. Genetics and Populations | 遗传学与种群
The Hardy– es), where p is the frequency of the dominant allele and q is the frequency of the recessive allele.
哈代-温伯格定律预测非进化种群的等位基因频率：p + q = 1（等位基因频率）且 p² + 2pq + q² = 1（基因型频率），其中 p 为显性等位基因频率，q 为隐性等位基因频率。
n ecology, the Lincoln index provides a method for estimating population size N using mark–release– the number caught and marked initially, n₂ is the number caught in the second sample, and m is the number of marked individuals recaptured.
在生态学中，林肯指数提供了一种利用标记-重捕法估算种群大小 N 的方法：N = (n₁ × n₂)/m，其中 n₁ 是初次捕获并标记的个体数，n₂ 是第二次捕获的个体数，m 是重捕到的标记个体数。
s calculated as (energy available after transfer / energy available before transfer) × 100% tion (GPP) is the total energy fixed by photosynthesis; net primary production (NPP) = GPP – respiration.
营养级之间的能量传递效率计算为（传递后的可用能量 / 传递前的可用能量） × 100%。总初级生产力（GPP）是光合作用固定的总能量；净初级生产力（NPP）= GPP – 呼吸消耗。
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