WJEC Pre-U Science: Formula & Theorem Quick Reference Handbook | WJEC 大学预科科学：公式定理速查手册

📚 WJEC Pre-U Science: Formula & Theorem Quick Reference Handbook | WJEC 大学预科科学：公式定理速查手册

This handbook brings together the essential formulae and theorems needed for the WJEC Pre-University Science curriculum. It covers key equations from physics, chemistry and biology, each presented with clear context and practical meaning – ideal for quick revision and classroom reference.

本手册汇集了 WJEC 大学预科科学课程所需的核心公式与定理。内容涵盖物理、化学和生物学的关键方程，每个公式都配有清晰的语境与实用说明，非常适合快速复习和课堂查阅。

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1. Kinematics Equations | 运动学方程

The first equation of uniformly accelerated motion allows you to determine final velocity when initial velocity, acceleration and time are known – fundamental in any motion analysis.

v = u + a t

匀加速运动的第一个公式可在已知初速度、加速度和时间时求出末速度，是所有运动分析的基础。

The displacement–time relation with constant acceleration is given by the second equation, which neatly includes the term for the contribution of acceleration over time squared.

s = u t + ½ a t²

第二个公式给出了恒加速度下位移与时间的关系，其中包含加速度对时间的平方贡献项。

A third equation expresses displacement as the average velocity multiplied by the time interval, highlighting a simple conceptual bridge between kinematics and average motion.

s = ½ (u + v) t

第三个公式将位移表示为平均速度与时间的乘积，突出了平均运动这一简单的概念桥梁。

The velocity–displacement equation, v² = u² + 2 a s, is particularly useful when time is not given; it directly links the change in speed to the distance covered.

v² = u² + 2 a s

速度–位移公式 v² = u² + 2 a s 在未给出时间时特别有用，它将速度的变化与所经距离直接联系在一起。

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2. Newton’s Laws and Momentum | 牛顿定律与动量

Newton’s second law in its most common form states that the net force acting on an object equals its mass times acceleration – the quantitative link between force and motion.

F = m a

牛顿第二定律最常用的形式指出，作用在物体上的合力等于其质量乘以加速度，这是力与运动之间的定量联系。

Momentum, a vector quantity defined as the product of mass and velocity, is conserved in all isolated systems, underpinning collision and explosion calculations.

p = m v

动量是定义为质量与速度乘积的矢量，在所有孤立系统中守恒，是碰撞和爆炸计算的基础。

The impulse–momentum theorem shows that the change in momentum equals the average net force multiplied by the time interval over which it acts – crucial in safety engineering.

F Δt = Δp

冲量–动量定理表明，动量的变化等于平均合力与其作用时间的乘积，这在安全工程中至关重要。

Newton’s third law reminds us that forces always occur in interacting pairs: if body A exerts a force on body B, body B exerts an equal and opposite force on body A.

牛顿第三定律提醒我们，力总是成对出现的：若物体 A 对物体 B 施加一个力，物体 B 必对 A 施加一个大小相等、方向相反的力。

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3. Work, Energy and Power | 功、能与功率

Work done by a constant force is the product of the force component along the direction of motion and the displacement – the primary pathway of energy transfer in mechanics.

W = F s cos θ

恒力所做的功等于力在运动方向上的分量与位移的乘积，是力学中能量传递的主要途径。

Kinetic energy, the energy of motion, is given by ½ m v²; any change in this quantity directly reflects the net work done on the object.

Eₖ = ½ m v²

动能即运动能量，由 ½ m v² 给出；该值的变化直接反映了对物体所做的净功。

Gravitational potential energy near Earth’s surface is calculated with Eₚ = m g h, linking mass, height and the gravitational field strength g (≈ 9.8 N kg⁻¹).

Eₚ = m g h

地球表面附近的重力势能用 Eₚ = m g h 计算，将质量、高度和重力场强度 g（≈ 9.8 N kg⁻¹）联系起来。

Power is the rate of doing work or transferring energy; in mechanics it can be expressed as force times velocity for an object moving at constant speed.

P = W / t = F v

功率是做功或传递能量的速率；在力学中，对于一个匀速运动的物体，可表示为力与速度的乘积。

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4. Electricity and Circuits | 电学与电路

Ohm’s law connects the potential difference across a conductor, the current flowing through it and its resistance – the central rule for resistive DC circuits.

V = I R

欧姆定律将导体两端的电势差、流过导体的电流及其电阻联系起来，是直流电阻电路的核心规律。

Electrical power can be calculated from voltage and current, and using Ohm’s law it can also be expressed in terms of current and resistance or voltage and resistance.

P = V I = I² R = V² / R

电功率可由电压和电流计算，结合欧姆定律还可用电流与电阻或电压与电阻表示。

When resistors are added in series, the total resistance is simply the sum of the individual resistances – a direct application of energy conservation.

R_total = R₁ + R₂ + R₃ + …

电阻串联时，总电阻就是各个电阻值之和，这是能量守恒的直接应用。

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5. Ideal Gas Law and Thermodynamics | 理想气体定律与热力学

The ideal gas equation, p V = n R T, links the pressure, volume and temperature of an ideal gas to the amount of substance in moles – a cornerstone of thermal physics.

p V = n R T

理想气体方程 p V = n R T 将气体的压强、体积、温度与物质的量（摩尔）联系起来，是热物理的基石。

In thermodynamics the first law is expressed as ΔU = Q – W: the change in internal energy equals the heat added to the system minus the work done by the system.

ΔU = Q – W

热力学第一定律表达为 ΔU = Q – W：内能的变化等于系统吸收的热量减去系统对外做的功。

The efficiency of any heat engine is always less than 1; for an ideal Carnot engine it can be expressed using the temperatures of the hot and cold reservoirs.

η = 1 – (T_cold / T_hot)

任何热机的效率总小于 1；理想卡诺热机的效率可用热源与冷源的温度表示。

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6. Moles and Stoichiometric Calculations | 摩尔与化学计量计算

The mole is the gateway to quantitative chemistry: the number of moles equals the mass of a substance divided by its molar mass.

n = m / M

摩尔是定量化学的入口：物质的量（摩尔数）等于物质的质量除以其摩尔质量。

For solutions, the concentration in mol dm⁻³ is given by the number of moles divided by the volume of the solution in dm³ – a fundamental equation for volumetric analysis.

c = n / V

对于溶液，浓度（mol dm⁻³）等于溶质的物质的量除以溶液的体积（dm³），是容量分析的基本公式。

The ideal gas equation can also be rearranged to give the molar volume of an ideal gas at standard temperature and pressure, approximately 22.4 dm³ mol⁻¹.

理想气体方程也可重新整理，得到标准状况下理想气体的摩尔体积约为 22.4 dm³ mol⁻¹。

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7. Equilibrium Constant Kc and Le Chatelier’s Principle | 平衡常数 Kc 与勒夏特列原理

For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant Kc is expressed in terms of the molar concentrations of products and reactants, each raised to the power of its stoichiometric coefficient.

Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ

对于可逆反应 aA + bB ⇌ cC + dD，平衡常数 Kc 用产物和反应物的平衡浓度表示，各浓度以化学计量系数为指数。

Le Chatelier’s principle states that if a system at equilibrium is subjected to a change in concentration, pressure or temperature, the equilibrium will shift so as to partially counteract the imposed change.

勒夏特列原理指出，若一个处于平衡状态的体系受到浓度、压强或温度的改变，平衡将朝着部分抵消这一改变的方向移动。

A particularly important application is the influence of temperature on Kc: for an exothermic reaction (ΔH negative), increasing temperature lowers Kc; for an endothermic reaction (ΔH positive), increasing temperature raises Kc.

一个特别重要的应用是温度对 Kc 的影响：对于放热反应（ΔH 为负），升高温度会降低 Kc；对于吸热反应（ΔH 为正），升高温度会增大 Kc。

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8. Organic Functional Groups and General Formulas | 有机官能团与通式

Alkanes, the simplest homologous series, follow the general formula CₙH₂ₙ₊₂; their saturated nature makes them relatively unreactive except under extreme conditions.

CₙH₂ₙ₊₂ (alkane)

烷烃是最简单的同系列，通式为 CₙH₂ₙ₊₂；其饱和特性使它们相对不活泼，除极端条件外不易反应。

Alkenes contain at least one carbon–carbon double bond and have the general formula CₙH₂ₙ; this unsaturation is the basis of addition reactions such as hydrogenation and halogenation.

CₙH₂ₙ (alkene)

烯烃至少含有一个碳碳双键，通式为 CₙH₂ₙ；这种不饱和性是加成反应（如氢化和卤化）的基础。

Alcohols contain the hydroxyl (–OH) functional group; primary alcohols have the general formula CₙH₂ₙ₊₁OH and can be oxidised to aldehydes and carboxylic acids.

CₙH₂ₙ₊₁OH (primary alcohol)

醇含有羟基 (–OH) 官能团；伯醇的通式为 CₙH₂ₙ₊₁OH，可被氧化为醛和羧酸。

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9. Respiration and Photosynthesis Equations | 呼吸与光合作用方程

Aerobic respiration in living cells releases energy by the oxidation of glucose; the overall word and balanced symbol equations capture the transformation of glucose and oxygen into carbon dioxide, water and ATP.

C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O + energy

活细胞中的有氧呼吸通过氧化葡萄糖释放能量；总文字和配平的符号方程概括了葡萄糖和氧气转化为二氧化碳、水和 ATP 的过程。

Photosynthesis is the process by which green plants convert light energy into chemical energy, synthesising glucose from carbon dioxide and water with the release of oxygen.

6 CO₂ + 6 H₂O →light→ C₆H₁₂O₆ + 6 O₂

光合作用是绿色植物将光能转化为化学能的过程，从二氧化碳和水合成葡萄糖并释放氧气。

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10. Hardy–Weinberg Equilibrium Theorem | 哈迪–温伯格平衡定理

The Hardy–Weinberg theorem provides a null model for population genetics, stating that allele and genotype frequencies in a large, randomly mating population remain constant from generation to generation in the absence of evolutionary forces.

哈迪–温伯格定理为群体遗传学提供了一个零假设模型，指出在一个大且随机交配的群体中，若无进化力量作用，等位基因频率和基因型频率代代保持不变。

For a gene with two alleles, if p is the frequency of the dominant allele and q is the frequency of the recessive allele, the relationship p + q = 1 holds true.

p + q = 1

对于一个具有两个等位基因的基因，若 p 为显性等位基因的频率，q 为隐性等位基因的频率，则有 p + q = 1。

The expected genotype frequencies under random mating are given by the expansion of (p + q)²: homozygous dominant p², heterozygous 2pq, and homozygous recessive q².

p² + 2pq + q² = 1

随机交配下的预期基因型频率由 (p + q)² 展开给出：显性纯合子 p²，杂合子 2pq，隐性纯合子 q²。

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