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

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

Mastering the crucial formulas and theorems in Year 12 AQA Science is key to success across physics, chemistry, and biology. This handbook collates the most important quantitative relationships, laws, and models you need to memorise and apply. From Newton’s laws and the mole concept to the Hardy-Weinberg principle, each entry is explained concisely, with paired English and Chinese explanations for clarity and revision efficiency.

掌握 Year 12 AQA 科学中关键的公式与定理，是在物理、化学和生物学科中取得成功的关键。本手册汇集了你需要记忆和应用的最重要的定量关系、定律和模型。从牛顿定律和摩尔概念到哈代-温伯格原理，每个条目都有简明的中英双语解释，帮助你清晰理解、高效复习。

1. Physics – Mechanics & Motion | 物理 – 力学与运动

Newton’s second law relates resultant force, mass, and acceleration. It is the foundation of linear dynamics and appears in many mechanics problems.

牛顿第二定律将合力、质量和加速度联系起来。它是线性动力学的基础，出现在许多力学问题中。

F = m × a

Where F is resultant force (N), m is mass (kg), a is acceleration (m s⁻²). This vector equation means that the acceleration is directly proportional to the net force and inversely proportional to mass.

其中 F 是合力（N），m 是质量（kg），a 是加速度（m s⁻²）。这个矢量方程意味着加速度与净力成正比，与质量成反比。

The equations of motion for constant acceleration allow calculation of displacement, velocity, and time without considering forces directly.

匀加速的运动学方程可以在不直接考虑力的情况下计算位移、速度和时间。

v = u + a t  s = ½(u + v)t  s = u t + ½ a t²  v² = u² + 2 a s

Here u is initial velocity, v final velocity, a acceleration, t time, s displacement. Remember to choose a consistent sign convention.

这里 u 是初速度，v 是末速度，a 是加速度，t 是时间，s 是位移。记住要选择一致的符号约定。

Momentum and impulse are key in collisions. The change in momentum equals the impulse of the force.

动量和冲量在碰撞问题中至关重要。动量的变化等于力的冲量。

p = m v  Δp = F Δt

Momentum is conserved in isolated systems, which is essential for solving explosion and collision problems.

在孤立系统中动量守恒，这对解决爆炸和碰撞问题至关重要。

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2. Physics – Waves & Optics | 物理 – 波与光学

The wave equation links speed, frequency, and wavelength for all progressive waves. It is widely tested across different contexts.

波动方程把行波的速度、频率和波长联系起来，它在各种情境中都被广泛考查。

v = f × λ

v is wave speed (m s⁻¹), f frequency (Hz), λ wavelength (m). This applies to sound, light, and water waves.

v 是波速（m s⁻¹），f 是频率（Hz），λ 是波长（m）。这适用于声波、光波和水波。

The double‑slit interference formula gives the fringe spacing for coherent light.

双缝干涉公式给出了相干光的条纹间距。

w = λ D / s

w is the fringe spacing, λ wavelength, D slit‑screen distance, s slit separation. This demonstrates the wave nature of light.

w 是条纹间距，λ 是波长，D 是缝到屏幕的距离，s 是缝间距。这证明了光的波动性。

Refractive index determines how much light bends at a boundary and relates to the critical angle.

折射率决定了光在边界处弯曲的程度，并与临界角有关。

n = c / v  sin θ_c = 1 / n

c is speed of light in vacuum, v in medium. The critical angle θ_c applies only when light goes from a denser to a rarer medium.

c 是真空中的光速，v 是介质中的光速。临界角 θ_c 仅在光从光密介质射向光疏介质时适用。

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3. Physics – Electricity & Circuits | 物理 – 电学与电路

Ohm’s law defines the relationship between voltage, current, and resistance for ohmic conductors.

欧姆定律定义了欧姆导体的电压、电流和电阻之间的关系。

V = I × R

V is potential difference (V), I current (A), R resistance (Ω). For ohmic devices at constant temperature, R is constant.

V 是电势差（V），I 是电流（A），R 是电阻（Ω）。对于恒温下的欧姆器件，R 恒定。

Power in electrical circuits can be expressed in three equivalent forms; use the one that fits the given data.

电路中的功率可以用三种等价形式表示；选用与已知数据匹配的那个。

P = V I  P = I² R  P = V² / R

These follow from combining Ohm’s law with the definition of power as energy transferred per unit time.

这些公式来源于将欧姆定律与功率作为单位时间能量转移的定义相结合。

Resistivity links a material’s intrinsic property to resistance, length, and cross‑sectional area.

电阻率把材料的本征属性与电阻、长度和横截面积联系起来。

R = ρ L / A

ρ is resistivity (Ω m), L length, A cross‑sectional area. This explains why long, thin wires have higher resistance.

ρ 是电阻率（Ω m），L 是长度，A 是横截面积。这解释了为何长而细的导线电阻更大。

Internal resistance of a cell causes the terminal potential difference to drop when current flows.

电源的内阻使端电压在有电流流过时下降。

ε = V + I r  ε = I (R + r)

ε is electromotive force (emf), r internal resistance, V terminal pd across the external resistor R.

ε 是电动势（emf），r 是内阻，V 是外电阻 R 两端的端电压。

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4. Physics – Materials & Thermal | 物理 – 材料与热学

Hooke’s law describes the elastic behaviour of springs and wires up to the limit of proportionality.

胡克定律描述了弹簧和金属丝在比例极限内的弹性行为。

F = k ΔL

F is force (N), k spring constant (N m⁻¹), ΔL extension (m). Elastic potential energy stored is E = ½ k ΔL².

F 是力（N），k 是弹性常数（N m⁻¹），ΔL 是伸长量（m）。储存的弹性势能为 E = ½ k ΔL²。

Stress, strain, and Young modulus characterise the stiffness of a material independently of its dimensions.

应力、应变和杨氏模量表征了材料不受尺寸影响的刚度特性。

σ = F / A  ε = ΔL / L  E = σ / ε

σ is stress (Pa), ε strain (no units), E Young modulus (Pa). This is valid in the linear elastic region.

σ 是应力（Pa），ε 是应变（无量纲），E 是杨氏模量（Pa）。这在线弹性区域内有效。

The specific heat capacity equation quantifies the energy needed to raise the temperature of a substance.

比热容方程量化了提高物质温度所需的能量。

Q = m c Δθ

Q is thermal energy (J), m mass (kg), c specific heat capacity (J kg⁻¹ K⁻¹), Δθ temperature change.

Q 是热能（J），m 是质量（kg），c 是比热容（J kg⁻¹ K⁻¹），Δθ 是温度变化。

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5. Chemistry – Quantitative Chemistry & Moles | 化学 – 定量化学与摩尔

The mole is the central unit in chemistry; Avogadro’s constant links number of particles to amount of substance.

摩尔是化学中的核心单位；阿伏伽德罗常数将粒子数与物质的量联系起来。

n = N / Nₐ  Nₐ = 6.02 × 10²³ mol⁻¹

n is amount (mol), N number of particles, Nₐ Avogadro’s constant. The mass of one mole of a substance is its molar mass M in g mol⁻¹.

n 是物质的量（mol），N 是粒子数，Nₐ 是阿伏伽德罗常数。一摩尔物质的质量是其摩尔质量 M，单位为 g mol⁻¹。

The ideal gas equation connects pressure, volume, temperature, and amount of a gas, assuming no intermolecular forces.

理想气体状态方程在假设无分子间力的情况下，把气体的压力、体积、温度和物质的量联系起来。

p V = n R T

p is pressure (Pa), V volume (m³), n amount (mol), R = 8.31 J mol⁻¹ K⁻¹, T temperature (K). Always convert to correct units.

p 是压力（Pa），V 是体积（m³），n 是物质的量（mol），R = 8.31 J mol⁻¹ K⁻¹，T 是温度（K）。务必转换成正确的单位。

Concentration calculations are fundamental for titrations and solution preparation.

浓度计算是滴定和溶液配制的基础。

c = n / V  n = m / M

c is concentration (mol dm⁻³), n amount (mol), V volume (dm³). Combine to find mass needed: m = c V M.

c 是浓度（mol dm⁻³），n 是物质的量（mol），V 是体积（dm³）。结合可求得所需质量：m = c V M。

The percentage yield and atom economy assess the efficiency of a reaction.

产率和原子利用率用于评估反应的效率。

% yield = (actual yield / theoretical yield) × 100  % atom economy = (M_desired / M_total reactants) × 100

These green chemistry metrics help evaluate sustainability.

这些绿色化学指标有助于评估可持续性。

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6. Chemistry – Energetics & Thermodynamics | 化学 – 能量学与热力学

Enthalpy change ΔH is measured by calorimetry. The heat transferred is calculated from temperature change.

焓变 ΔH 通过量热法测定。传递的热量由温度变化计算得出。

q = m c ΔT

q is heat energy (J), m mass of solution (g), c specific heat capacity (4.18 J g⁻¹ K⁻¹ for water), ΔT temperature change. Then ΔH = – q / n (exothermic gives negative sign).

q 是热量（J），m 是溶液质量（g），c 是比热容（水的为 4.18 J g⁻¹ K⁻¹），ΔT 是温度变化。然后 ΔH = – q / n（放热为负号）。

Hess’s law allows enthalpy change for a reaction to be calculated via alternative routes, using enthalpies of formation or combustion.

赫斯定律允许通过生成焓或燃烧焓等替代路径计算反应的焓变。

ΔH_reaction = Σ ΔfH(products) – Σ ΔfH(reactants)

Use algebraic addition for a cycle; careful with signs and stoichiometric coefficients.

使用代数加法构建循环；注意符号和化学计量系数。

Bond enthalpy calculations estimate ΔH by breaking and making bonds.

键焓计算通过断键和成键来估算 ΔH。

ΔH ≈ Σ (bond enthalpies broken) – Σ (bond enthalpies made)

These are average values and apply to gases only, so they provide approximate results.

这些是平均值，仅适用于气态，因此结果仅为近似值。

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7. Chemistry – Kinetics & Equilibrium | 化学 – 动力学与平衡

The rate equation for a reaction shows the relationship between rate and reactant concentrations. Orders are experimentally determined.

反应的速率方程显示了速率与反应物浓度之间的关系。反应级数由实验确定。

rate = k [A]ᵐ [B]ⁿ

k is rate constant, [A], [B] are concentrations (mol dm⁻³), m and n are orders. Overall order = m + n.

k 是速率常数，[A]、[B] 是浓度（mol dm⁻³），m 和 n 是反应级数。总级数 = m + n。

The Arrhenius equation links rate constant to temperature and activation energy.

阿伦尼乌斯方程把速率常数与温度和活化能联系起来。

k = A e^(−Eₐ / R T)  ln k = −Eₐ / R T + ln A

Eₐ is activation energy (J mol⁻¹), T temperature (K), R gas constant. A plot of ln k vs 1/T gives a straight line of slope −Eₐ / R.

Eₐ 是活化能（J mol⁻¹），T 是温度（K），R 是气体常数。以 ln k 对 1/T 作图可得斜率为 −Eₐ / R 的直线。

For dynamic equilibrium, the equilibrium constant Kc or Kp quantifies the position of equilibrium.

对于动态平衡，平衡常数 Kc 或 Kp 用于量化平衡的位置。

For aA + bB ⇌ cC + dD: Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ

Concentrations are at equilibrium; units depend on stoichiometry. Temperature is the only factor that changes the value of K.

浓度取平衡时的值；单位取决于化学计量数。温度是唯一能改变 K 值的因素。

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8. Chemistry – Organic & Mechanisms | 化学 – 有机与机理

Functional groups determine the characteristic reactions of organic molecules. Homologous series share general formulas.

官能团决定了有机分子的特征反应。同系列共享通式。

• Alkanes: CₙH₂ₙ₊₂ (saturated) | 烷烃: CₙH₂ₙ₊₂（饱和）
• Alkenes: CₙH₂ₙ (one double bond) | 烯烃: CₙH₂ₙ（一个双键）
• Alcohols: CₙH₂ₙ₊₁OH | 醇: CₙH₂ₙ₊₁OH

You must be able to recognise and name the functional group from the formula and vice versa.

你必须能从分子式识别并命名官能团，反之亦然。

Mechanisms describe the stepwise movement of electron pairs. Curly arrows show electron movement from nucleophile to electrophile.

反应机理描述了电子对的分步运动。弯箭头表示从亲核试剂到亲电试剂的电子移动。

Nucleophilic substitution: Nu⁻ + R–X → R–Nu + X⁻

In SN2, the nucleophile attacks the carbon opposite to the leaving group (backside attack).

在 SN2 中，亲核试剂从离去基团的反面进攻碳（背面进攻）。

Electrophilic addition of HX to alkenes follows Markovnikov’s rule: the hydrogen attaches to the carbon with more hydrogen atoms already.

烯烃与 HX 的亲电加成遵循马氏规则：氢原子加到本来就含有较多氢原子的碳上。

Markovnikov addition: major product forms via the more stable carbocation.

The carbocation stability order is tertiary > secondary > primary > methyl, due to inductive effects.

碳正离子稳定性顺序为叔 > 仲 > 伯 > 甲基，这是由于诱导效应。

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9. Biology – Biological Molecules & Enzymes | 生物 – 生物分子与酶

Magnification calculations are used to determine the actual size of a specimen from a microscope image.

放大倍数计算用于通过显微镜图像确定标本的实际大小。

Magnification = Image size / Actual size

Remember to convert all measurements to the same unit (usually micrometres, µm).

记住将所有测量值转换为相同单位（通常是微米 µm）。

The Michaelis-Menten equation describes the rate of enzyme-catalysed reactions, but for AQA, you apply the concept of Vmax and Km.

米氏方程描述了酶催化反应的速率，但在 AQA 中，你只需要应用 Vmax 和 Km 的概念。

Initial rate ∝ enzyme concentration (when substrate is in excess)

At low substrate concentration, rate is proportional to [S]; at high [S], rate tends to Vmax.

当底物浓度低时，速率与 [S] 成正比；高 [S] 时，速率趋向 Vmax。

Competitive inhibitors increase Km (apparent affinity decreases), Vmax unchanged; non-competitive inhibitors lower Vmax, Km unchanged.

竞争性抑制剂使 Km 升高（表观亲和力下降），Vmax 不变；非竞争性抑制剂降低 Vmax，Km 不变。

The dilution factor formula is useful in serial dilutions for practical work.

稀释倍数公式在系列稀释的实验中非常有用。

C₁V₁ = C₂V₂

This ensures the amount of solute remains constant before and after dilution.

这保证了稀释前后溶质的量不变。

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10. Biology – Cells & Transport | 生物 – 细胞与转运

Water potential determines the direction of osmosis. It is measured in pressure units (kPa).

水势决定了渗透的方向。它以压力单位（kPa）来度量。

ψ = ψ_s + ψ_p

ψ is water potential, ψ_s solute potential (always negative or zero), ψ_p pressure potential (usually positive in turgid cells). Water moves from higher to lower water potential.

ψ 是水势，ψ_s 是溶质势（总为负或零），ψ_p 是压力势（在胀大的细胞中通常为正）。水从水势高处向水势低处流动。

The mitotic index is a formula that quantifies cell division in a tissue.

有丝分裂指数是定量描述组织中细胞分裂的公式。

Mitotic index = (Number of cells in mitosis / Total number of cells) × 100

A high mitotic index indicates rapid cell proliferation, often seen in meristematic or cancerous tissues.

高的有丝分裂指数表明细胞增殖迅速，常见于分生组织或癌变组织。

Surface area to volume ratio explains why cells are small and why organisms need specialised exchange surfaces.

表面积与体积比解释了为什么细胞很小，以及为什么生物体需要特化的交换表面。

SA:V ratio = Surface area / Volume

As size increases, SA:V ratio decreases, making diffusion less efficient. Fick’s law summarises diffusion rate:

随着尺寸增大，SA:V 比下降，导致扩散效率降低。菲克定律总结了扩散速率：

Rate of diffusion ∝ (Surface area × Concentration gradient) / Diffusion distance

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11. Biology – Genetics & Evolution | 生物 – 遗传与进化

The Hardy-Weinberg principle is used to calculate allele and genotype frequencies in a population that is not evolving.

哈代-温伯格原理用于计算未进化群体中的等位基因和基因型频率。

p² + 2pq + q² = 1  p + q = 1

p is frequency of dominant allele, q recessive allele. p², 2pq, q² correspond to genotype frequencies. Assumptions: no mutation, no migration, random mating, large population, no selection.

p 是显性等位基因频率，q 是隐性等位基因频率。p²、2pq、q² 对应基因型频率。假设条件：无突变、无迁移、随机交配、大群体、无选择。

Chi-squared test determines whether observed results differ significantly from expected results based on a genetic hypothesis.

卡方检验用于判断观察结果是否与基于遗传假说的预期结果有显著差异。

χ² = Σ (O − E)² / E

O is observed frequency, E expected. Compare calculated χ² with critical value at appropriate degrees of freedom (df = number of categories – 1).

O 是观察频率，E 是预期频率。将计算出的 χ² 值与相应自由度（df = 类别数 – 1）下的临界值比较。

Selection pressures cause changes in allele frequency, leading to evolution. The formula for selection coefficient (s) measures relative fitness reduction.

选择压力导致等位基因频率变化，从而引发进化。选择系数（s）衡量的是相对适合度的降低程度。

s = 1 − w, where w = relative fitness of a genotype.

This helps model directional and stabilising selection.

这有助于建模定向选择和稳定化选择。

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