Year 12 AQA Science: Formula & Theorem Quick Reference Handbook | Year 12 AQA 科学：公式定理速查手册

📚 Year 12 AQA Science: Formula & Theorem Quick Reference Handbook | Year 12 AQA 科学：公式定理速查手册

This handbook provides a concise, bilingual collection of essential formulas, laws, and theorems from the Year 12 AQA Science curriculum. It covers Physics, Chemistry, and Biology topics that frequently appear in assessments, helping you revise core quantitative relationships and scientific principles efficiently.

本手册精选了 Year 12 AQA 科学课程中的核心公式、定律和定理，并以中英双语呈现。内容涵盖物理、化学和生物中常考的重要关系式与原理，旨在帮助你高效复习量化关系和科学基本原则。

1. Physical Quantities & Units | 物理量与国际单位

All physical quantities are expressed in SI base units or derived units. Prefixes are used to scale units for very large or very small quantities.

所有物理量均以国际单位制基本单位或导出单位表示。对于极大或极小的量，常使用词头来缩放单位。

Physical Quantity	SI Unit	Symbol
Mass	kilogram	kg
Length	metre	m
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol

Common prefixes: kilo (k, 10³), mega (M, 10⁶), giga (G, 10⁹), centi (c, 10⁻²), milli (m, 10⁻³), micro (μ, 10⁻⁶), nano (n, 10⁻⁹), pico (p, 10⁻¹²).

常见词头：千 (k, 10³)、兆 (M, 10⁶)、吉 (G, 10⁹)、厘 (c, 10⁻²)、毫 (m, 10⁻³)、微 (μ, 10⁻⁶)、纳 (n, 10⁻⁹)、皮 (p, 10⁻¹²)。

very term must have the same base units. Use square brackets for units, e.g., [v] = m s⁻¹.

物理方程的同质性：方程中每一项的基本单位必须相同。常用方括号表示单位，如 [v] = m s⁻¹。

---

2. Kinematics & Dynamics | 运动学与动力学

For constant acceleration a, the SUVAT equations link displacement s, initial velocity u, final velocity v, and time t.

对于匀加速直线运动，SUVAT 方程将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系起来。

v = u + a t

Equation without displacement: v = u + at.

不含位移的公式：v = u + at。

s = u t + ½ a t²

Displacement with time: s = u t + ½ a t².

含时间的位移公式：s = u t + ½ a t²。

v² = u² + 2 a s

Equation without time: v² = u² + 2as.

不含时间的公式：v² = u² + 2as。

s = ½ (u + v) t

Average velocity displacement: s = ½ (u + v) t.

平均速度位移：s = ½ (u + v) t。

Newton' cond law: resultant force F = m a, where m is mass. Momentum p = m v. Impulse = F Δt = Δp.

牛顿第二定律：合力 F = m a，其中 m 为质量。动量 p = m v。冲量 = F Δt = Δp。

m in an isolated system: total momentum before collision = total momentum after collision.

在孤立系统中动量守恒：碰撞前的总动量 = 碰撞后的总动量。

For two objects: m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂.

对于两个物体：m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂。

---

3. Materials & Deformation | 材料与形变

Hooke' ied force F, up to the limit of proportionality. F = k Δx, where k is the spring constant.

胡克定律：在比例极限内，伸长量 Δx 与施加的力 F 成正比。F = k Δx，其中 k 为劲度系数。

/ A (force per cross-sectional area). Strain ε = ΔL / L₀ (extension over original length).

应力 σ = F / A（单位截面积的力）；应变 ε = ΔL / L₀（伸长量与原长之比）。

= σ / ε = (F L₀) / (A ΔL). It describes stiffness of a material within the elastic limit.

杨氏模量 E = σ / ε = (F L₀) / (A ΔL)，用于描述材料在弹性范围内的刚度。

Elastic strain energy stored = ½ F Δx = ½ k (Δx)², equal to the area under the force‑extension graph.

弹性应变能 = ½ F Δx = ½ k (Δx)²，等于力‑伸长图下方的面积。

Ultimate tensile strength and breaking stress characterise material failure beyond the elastic region.

抗拉强度和断裂应力表征材料在超过弹性范围后的破坏行为。

---

4. Waves & Optics | 波动与光学

Wave speed v = f λ, where f is frequency, λ is wavelength. Period T = 1 / f.

波速 v = f λ，其中 f 为频率，λ 为波长。周期 T = 1 / f。

For all waves, intensity I = Power / Area. For a point source, I ∝ 1 / r² (inverse‑square law).

所有波均满足强度 I = 功率 / 面积。对于点源，I ∝ 1 / r²（平方反比定律）。

Refractive index n = c / v_s, where c is speed in vacuum. Snell's law: n₁ sin θ₁ = n₂ sin θ₂.

折射率 n = c / v_s，c 为真空光速。斯涅耳定律：n₁ sin θ₁ = n₂ sin θ₂。

Critical angle θc for total internal reflection: sin θc = n₂ / n₁ (n₁ > n₂).

全反射临界角 θc：sin θc = n₂ / n₁（要求 n₁ > n₂）。

Young's double‑slit fringe spacing: w = (λ D) / s, where D is slit‑screen distance, s is slit separation.

杨氏双缝干涉条纹间距：w = (λ D) / s，D 为缝与屏的距离，s 为双缝间距。

Diffraction grating maxima: n λ = d sin θ, where d is grating spacing, n is order number.

衍射光栅明纹条件：n λ = d sin θ，d 为光栅常数，n 为级次。

---

5. Electricity & Circuits | 电路与电流

Current I = ΔQ / Δt. Potential difference V = W / Q. Ohm's law: V = I R for ohmic conductors at constant temperature.

电流 I = ΔQ / Δt；电势差 V = W / Q。欧姆定律：对于恒温下的欧姆导体，V = I R。

Resistance R = ρ L / A, where ρ is resistivity, L is length, A is cross‑sectional area.

电阻 R = ρ L / A，ρ 为电阻率，L 为导体长度，A 为截面积。

Electrical power P = V I = I² R = V² / R. Energy transferred E = P t = V I t.

电功率 P = V I = I² R = V² / R。能量转移 E = P t = V I t。

Kirchhoff' eaving. Second law: sum of e.m.f. around any closed loop = sum of p.d. drops (Σε = Σ I R).

基尔霍夫第一定律：流入节点的电流之和 = 流出节点的电流之和。第二定律：任意闭合回路中电动势的代数和 = 各元件电压降的代数和 (Σε = Σ I R)。

For series resistors: R_total = R₁ + R₂ + ... For parallel resistors: 1 / R_total = 1 / R₁ + 1 / R₂ + ... .

串联电阻：R_total = R₁ + R₂ + ... ；并联电阻：1 / R_total = 1 / R₁ + 1 / R₂ + ... 。

Potential divider: V_out = V_in × [R₂ / (R₁ + R₂)], where R₂ is the resistor across which the output voltage is taken.

分压电路：V_out = V_in × [R₂ / (R₁ + R₂)]，其中 R₂ 是输出电压所取的电阻。

---

广告 / Sponsored

6. Quantum Phenomena & Particles | 量子现象与粒子

Photon energy E = h f = h c / λ, where h is the Planck constant (6.63×10⁻³⁴ J s).

光子能量 E = h f = h c / λ，h 为普朗克常数（6.63×10⁻³⁴ J s）。

Photoelectric effect: h f = Φ + E_k(max), where Φ is work function and E_k(max) is the maximum kinetic energy of emitted electrons.

光电效应方程：h f = Φ + E_k(max)，Φ 为逸出功，E_k(max) 为光电子的最大动能。

Threshold frequency f₀ = Φ / h. Stopping potential V_s satisfies E_k(max) = e V_s.

截止频率 f₀ = Φ / h。遏止电势差 V_s 满足 E_k(max) = e V_s。

De Broglie wavelength λ = h / p = h / (m v), showing the wave‑particle duality of matter.

德布罗意波长 λ = h / p = h / (m v)，体现了物质波粒二象性。

electron falls from a higher energy level E₂ to a lower level E₁, such that h f = E₂ − E₁.

原子能级：电子从高能级 E₂ 跃迁到低能级 E₁ 时会辐射光子，满足 h f = E₂ − E₁。

Annihilation and pair production relate mass m to energy via E = m c².

湮灭与粒子对产生通过质能方程 E = m c² 联系起来。

---

7. Chemical Calculations & Energetics | 化学计量与能量学

M is molar mass. Gas volume at RTP: V = n × 24.0 dm³ mol⁻¹ (or V = n × 24,000 cm³ mol⁻¹).

物质的量 n = m / M，m 为质量，M 为摩尔质量。常温常压下气体体积：V = n × 24.0 dm³ mol⁻¹（或 V = n × 24,000 cm³ mol⁻¹）。

/ V (mol dm⁻³). Ideal gas equation: p V = n R T, where R = 8.31 J K⁻¹ mol⁻¹, T in kelvin.

浓度 c = n / V (mol dm⁻³)。理想气体状态方程：p V = n R T，R = 8.31 J K⁻¹ mol⁻¹，T 为开尔文温度。

Percentage yield = (actual yield / theoretical yield) × 100%. Atom economy = (molar mass of desired product / total molar mass of reactants) × 100%.

产率 = (实际产量 / 理论产量) × 100%。原子经济性 = (目标产物摩尔质量 / 反应物总摩尔质量) × 100%。

at exchanged, m is mass of solution, c is specific heat capacity (usually 4.18 J g⁻¹ K⁻¹ for water).

焓变 q = m c ΔT，q 为热量变化，m 为溶液质量，c 为比热容（水通常取 4.18 J g⁻¹ K⁻¹）。

ΔH = − q / n at constant pressure. Hess's law: the total enthalpy change for a reaction is independent of the route taken.

ΔH = − q / n（恒压）。盖斯定律：反应的总焓变与途径无关。

Bond enthalpy estimation: ΔH ≈ Σ(bond enthalpies broken) − Σ(bond enthalpies formed).

键能估算法：ΔH ≈ Σ(断裂键键能) − Σ(生成键键能)。

---

8. Kinetics & Equilibria | 动力学与平衡

te of reaction = change in concentration / time. For a reaction A → products, rate = k [A]^m, where k is the rate constant, m is the order with respect to A.

反应速率 = 浓度变化 / 时间。对于反应 A → 产物，速率 = k [A]^m，k 为速率常数，m 为对于 A 的反应级数。

The rate‑determining step is the slowest step in a reaction mechanism and dictates the rate equation.

速率控制步骤是反应机理中最慢的一步，决定了速率方程的数学形式。

For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant Kc = [C]^c [D]^d / ([A]^a [B]^b), at a given temperature.

对于可逆反应 aA + bB ⇌ cC + dD，在一定温度下，平衡常数 Kc = [C]^c [D]^d / ([A]^a [B]^b)。

Le Chatelier's principle: if a system at equilibrium is subjected to a change in concentration, pressure or temperature, the position of equilibrium shifts to oppose the change.

勒夏特列原理：若平衡系统受到浓度、压力或温度的改变，平衡位置将朝着减弱这种改变的方向移动。

The effect of temperature on Kc: for an exothermic reaction (ΔH < 0), increasing temperature decreases Kc; for an endothermic reaction (ΔH > 0), increasing temperature increases Kc.

温度对 Kc 的影响：放热反应 (ΔH < 0) 升温使 Kc 减小；吸热反应 (ΔH > 0) 升温使 Kc 增大。

---

9. Organic Chemistry Rules | 有机化学规则

Markovnikov's rule: in addition of HX to an unsymmetrical alkene, the hydrogen attaches to the carbon with the greater number of hydrogen atoms already present.

马氏规则：在 HX 与不对称烯烃的加成中，氢原子加在含氢较多的碳原子上。

Saytzeff's rule: in elimination reactions, the major product is the more substituted alkene (more stable).

查依采夫规则：在消去反应中，主要产物是取代基更多的烯烃（更稳定）。

genoalkane → alcohol (nucleophilic substitution), alcohol → halogenoalkane (nucleophilic substitution).

官能团转换是 Year 12 有机合成的核心：烯烃 → 醇（水合）、醇 → 烯烃（消去）、卤代烷 → 醇（亲核取代）、醇 → 卤代烷（亲核取代）。

IUPAC nomenclature: identify the longest carbon chain, number to give the lowest locants to functional groups and side chains, and list substituents alphabetically.

IUPAC 命名法：找出最长的碳链，从靠近官能团的一端开始编号以使编号最小，取代基按字母顺序排列。

Isomerism: structural isomers have the same molecular formula but different connectivity; E/Z isomers arise from restricted rotation around a double bond with two different groups on each carbon.

异构现象：结构异构体分子式相同而原子连接顺序不同；E/Z 异构体源于双键的旋转受阻，且每个双键碳上连有两个不同的基团。

---

10. Genetics & Probability | 遗传学与概率

Mendel's law of segregation: each individual possesses two alleles for a trait, which separate during gamete formation, so that a gamete carries only one allele.

孟德尔分离定律：个体具有一对等位基因，在配子形成时

Published by TutorHao | Year 12 Science Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）