📚 KS3 CIE Science: Formula & Theorem Quick Reference Handbook | KS3 CIE 科学：公式定理速查手册
This quick reference handbook brings together the essential formulas, definitions and key theorems from the KS3 CIE Science curriculum. Covering physics, chemistry and biology, it is designed to help you revise efficiently and apply core principles with confidence. Each section presents concepts in clear, paired English–Chinese explanations so you can easily check facts and practise using scientific equations.
本速查手册汇集了 KS3 CIE 科学课程中的核心公式、定义和重要定理，涵盖物理、化学与生物领域，旨在帮助你高效复习并自信地运用基本原理。每个小节都以清晰的中英配对解释呈现概念，方便你快速查阅知识点并练习使用科学方程式。
1. Motion and Speed | 运动与速度
An object is in motion when its position changes relative to a reference point. Speed describes how fast it moves, without considering direction. The formula for average speed links the total distance travelled to the time taken.
当物体相对于参考点的位置发生变化时，它就是运动的。速度描述物体运动的快慢，不考虑方向。平均速度的公式将总路程与所用时间联系起来。
v = d / t
On a distance–time graph, a straight sloping line represents constant speed. The gradient of the line equals the speed. A horizontal line means the object is stationary.
在距离—时间图中，一条倾斜的直线表示匀速运动。直线的斜率等于速度。水平线表示物体静止。
Velocity is speed in a given direction. An object moving in a circle at constant speed has a changing velocity because its direction is changing continuously.
速度是带有方向的速度。物体以恒定速率做圆周运动时，由于方向不断改变，其速度也在变化。
2. Forces and Newton’s Laws | 力与牛顿定律
A force is a push or a pull that can change an object’s speed, direction or shape. Forces are measured in newtons (N). When multiple forces act on an object, the resultant force determines its motion.
力是一种推或拉的作用，可以改变物体的速度、方向或形状。力的单位是牛顿 (N)。当多个力作用在物体上时，合力决定其运动状态。
Resultant force = mass × acceleration (F = m a)
Newton’s first law states that an object remains at rest or in uniform motion unless a resultant force acts on it. The second law gives the relationship F = m a. The third law tells us that for every action there is an equal and opposite reaction.
牛顿第一定律指出，除非受到合力作用，否则物体将保持静止或匀速直线运动。第二定律给出了 F = m a 的关系。第三定律告诉我们，每一个作用力都有一个大小相等、方向相反的反作用力。
Weight is the gravitational force on a mass. It is calculated using:
重量是作用在质量上的重力。计算公式为：
W = m g
where g ≈ 10 N/kg on Earth (or 9.8 N/kg for greater accuracy). Mass is measured in kilograms (kg); weight is measured in newtons.
在地球上，g ≈ 10 N/kg（更精确值为 9.8 N/kg）。质量以千克 (kg) 为单位，重量以牛顿为单位。
3. Energy, Work and Power | 能量、功与功率
Energy is the ability to do work. It exists in many forms – kinetic, gravitational potential, thermal, chemical and more. The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed.
能量是做功的能力。它以多种形式存在——动能、重力势能、热能、化学能等。能量守恒定律指出，能量不能被创造或消灭，只能被转移或转化。
Work is done when a force moves an object. The amount of work done equals the energy transferred.
当力使物体移动时就做了功。做功的多少等于转移的能量。
Work done = force × distance (W = F d)
Gravitational potential energy (GPE) is the energy stored in an object because of its height above the ground:
重力势能 (GPE) 是物体由于离地高度而储存的能量：
GPE = m g h
Kinetic energy (KE) is the energy of a moving object:
动能 (KE) 是运动物体具有的能量：
KE = ½ m v²
Power is the rate at which work is done or energy is transferred:
功率是做功或能量转移的快慢：
P = W / t or P = E / t
The unit of power is the watt (W), where 1 W = 1 J/s.
功率的单位是瓦特 (W)，1 W = 1 J/s。
4. Density and Pressure | 密度与压强
Density measures how much mass is packed into a given volume. It helps identify materials and predict whether an object will float or sink.
密度衡量一定体积内所含质量的多少。它有助于鉴别材料，并可预测物体会浮还是沉。
ρ = m / V
The symbol ρ (rho) represents density; m is mass in kg, V is volume in m³. The SI unit is kg/m³, although g/cm³ is also common.
符号 ρ (rho) 表示密度；m 是质量 (kg)，V 是体积 (m³)。国际单位为 kg/m³，也常用 g/cm³。
Pressure is the force applied perpendicular to a surface per unit area:
压强是垂直作用在单位面积上的力：
p = F / A
Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m². A larger force or a smaller area gives a higher pressure.
压强的单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。力越大或受力面积越小，压强越大。
In liquids, pressure increases with depth and density:
在液体中，压强随深度和液体密度的增加而增大：
p = h ρ g
Here h is the depth of the liquid, ρ its density and g the gravitational field strength.
其中 h 是液体深度，ρ 是液体的密度，g 是引力场强度。
5. Electricity Basics | 电学基础
Electric current is the flow of electric charge. In a metal wire, it is the movement of electrons. Current (I) is measured in amperes (A).
电流是电荷的流动。在金属导线中，它是电子的移动。电流 (I) 的单位是安培 (A)。
Voltage (potential difference) is the energy transferred per unit charge. It is measured in volts (V).
电压（电势差）是单位电荷转移的能量，单位是伏特 (V)。
Resistance (R) measures how difficult it is for current to flow, measured in ohms (Ω). Ohm’s law links these quantities:
电阻 (R) 衡量电流流动的难易程度，单位是欧姆 (Ω)。欧姆定律将它们联系在一起：
V = I R
In series circuits, current is the same everywhere; total resistance is the sum of individual resistances. In parallel circuits, voltage is the same across each branch, and total current splits between the branches.
在串联电路中，电流处处相等；总电阻等于各电阻之和。在并联电路中，各支路电压相同，总电流在支路间分配。
Electrical power is the rate at which electrical energy is transferred:
电功率是电能转移的速率：
P = I V
This can be combined with Ohm’s law to give P = I² R or P = V² / R.
结合欧姆定律，可得 P = I² R 或 P = V² / R。
6. Waves | 波
Waves transfer energy without transferring matter. They can be transverse, like light waves and water ripples, or longitudinal, like sound waves.
波传递能量而不传递物质。它们可以是横波，例如光波和水波；也可以是纵波，例如声波。
The wave speed equation relates the frequency and wavelength of a wave:
波速公式将波的频率和波长联系起来：
v = f λ
Here v is wave speed in m/s, f is frequency in hertz (Hz), and λ (lambda) is wavelength in metres. The period T of a wave is the reciprocal of frequency: T = 1 / f.
其中 v 是波速 (m/s)，f 是频率 (Hz)，λ (lambda) 是波长 (m)。波的周期 T 是频率的倒数：T = 1 / f。
Reflection occurs when a wave bounces off a surface; refraction happens when it changes speed as it passes from one medium to another, bending the wave.
反射发生在波从表面弹回时；折射发生在波穿过不同介质速度改变时，波会弯曲。
7. States of Matter and Particle Model | 物质状态与粒子模型
Matter exists as solid, liquid or gas. In solids, particles are arranged in a regular pattern and vibrate in fixed positions. In liquids, particles are close but can move past each other. In gases, particles are far apart and move quickly in all directions.
物质以固态、液态或气态存在。固体中，粒子规则排列并在固定位置振动。液体中，粒子靠近但能相互滑动。气体中，粒子相距很远并快速向各个方向运动。
Changes of state – melting, freezing, boiling, condensation, sublimation – occur at specific temperatures. The energy added or removed during a change of state does not raise the temperature but breaks or forms bonds between particles.
物态变化——熔化、凝固、沸腾、冷凝、升华——在特定温度下发生。物态变化时吸收或释放的能量不改变温度，而是破坏或形成粒子间的键。
Diffusion is the movement of particles from a region of higher concentration to a region of lower concentration, faster in gases than in liquids and faster at higher temperatures.
扩散是粒子从高浓度区域向低浓度区域的运动，气体中比液体中更快，温度越高越快。
8. Chemical Reactions and Equations | 化学反应与方程式
A chemical reaction involves the rearrangement of atoms to form new substances. The law of conservation of mass states that the total mass of reactants equals the total mass of products.
化学反应涉及原子的重新排列，形成新物质。质量守恒定律指出，反应物的总质量等于生成物的总质量。
Chemical equations show the reactants and products using symbols and formulas. They must be balanced so that the number of atoms of each element is the same on both sides.
化学方程式用符号和化学式表示反应物和生成物。方程式必须配平，使每种元素的原子个数在两边相等。
Example of a combustion reaction:
燃烧反应示例：
CH₄ + 2O₂ → CO₂ + 2H₂O
Types of reactions encountered at KS3 include combustion, neutralisation, thermal decomposition, oxidation and displacement. The speed of a reaction can be affected by temperature, concentration, surface area and the use of a catalyst.
KS3 阶段遇到的反应类型包括燃烧、中和、热分解、氧化和置换。反应速率受温度、浓度、表面积以及催化剂使用的影响。
9. Acids, Bases and pH | 酸、碱与 pH
Acids are substances that release hydrogen ions (H⁺) in water. Common acids include hydrochloric acid (HCl), sulfuric acid (H₂SO₄) and nitric acid (HNO₃). Bases neutralise acids; an alkali is a soluble base that releases hydroxide ions (OH⁻).
酸是在水中释放氢离子 (H⁺) 的物质。常见酸包括盐酸 (HCl)、硫酸 (H₂SO₄) 和硝酸 (HNO₃)。碱能中和酸；可溶性碱称为碱，释放氢氧根离子 (OH⁻)。
The pH scale ranges from 0 to 14. Acids have a pH less than 7, neutral solutions have pH 7, and alkalis have a pH greater than 7.
pH 标度的范围是 0 到 14。酸的 pH 小于 7，中性溶液的 pH 等于 7，碱的 pH 大于 7。
In a neutralisation reaction, an acid reacts with an alkali to produce a salt and water:
在中和反应中，酸与碱反应生成盐和水：
acid + alkali → salt + water
For example, hydrochloric acid + sodium hydroxide → sodium chloride + water: HCl + NaOH → NaCl + H₂O.
例如，盐酸 + 氢氧化钠 → 氯化钠 + 水：HCl + NaOH → NaCl + H₂O。
10. Cells and Life Processes | 细胞与生命过程
All living organisms are made of cells. Animal cells contain a nucleus, cytoplasm, cell membrane and mitochondria. Plant cells additionally have a cell wall, a large permanent vacuole and chloroplasts for photosynthesis.
所有生物体都由细胞组成。动物细胞含有细胞核、细胞质、细胞膜和线粒体。植物细胞还有细胞壁、大液泡和进行光合作用的叶绿体。
Living organisms carry out seven life processes, often remembered as MRS GREN: Movement, Respiration, Sensitivity, Growth, Reproduction, Excretion and Nutrition.
生物体进行七种生命活动，常被记为 MRS GREN：运动、呼吸、感应、生长、繁殖、排泄和营养。
Cells are organised into tissues, tissues into organs, and organs into organ systems. For example, muscle cells form muscle tissue, which builds the heart – an organ that, together with blood vessels, makes up the circulatory system.
细胞组织成组织，组织组成器官，器官再构成器官系统。例如，肌细胞构成肌肉组织，肌肉组织构建心脏——与血管一起组成循环系统。
11. Photosynthesis and Respiration | 光合作用与呼吸
Photosynthesis is the process by which green plants and some organisms use light energy to convert carbon dioxide and water into glucose and oxygen. It takes place in chloroplasts containing chlorophyll.
光合作用是绿色植物和某些生物利用光能将二氧化碳和水转化为葡萄糖和氧气的过程，发生在含有叶绿素的叶绿体中。
The word equation for photosynthesis is:
光合作用的文字表达式为：
carbon dioxide + water → glucose + oxygen
The balanced chemical equation is:
配平的化学方程式为：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Respiration is the process that releases energy from glucose. Aerobic respiration uses oxygen:
呼吸作用是释放葡萄糖中能量的过程。有氧呼吸需要氧气：
glucose + oxygen → carbon dioxide + water (+ energy)
Anaerobic respiration in animals produces lactic acid; in yeast it produces ethanol and carbon dioxide (fermentation).
动物的无氧呼吸产生乳酸；酵母的无氧呼吸产生乙醇和二氧化碳（发酵）。
12. Ecology and Food Chains | 生态学与食物链
Ecology studies how organisms interact with each other and their environment. A food chain shows the feeding relationships and energy flow between organisms. Each arrow represents energy transfer.
生态学研究生物彼此之间以及与环境如何相互作用。食物链展示生物间的摄食关系和能量流动，每个箭头代表能量传递。
A simple food chain might be: grass → rabbit → fox. Producers (like grass) make their own food via photosynthesis. Consumers eat other organisms; herbivores eat plants, carnivores eat animals, and omnivores eat both.
一个简单的食物链可以是：草 → 兔 → 狐狸。生产者（如草）通过光合作用制造食物。消费者以其他生物为食；食草动物吃植物，食肉动物吃动物，杂食动物两者都吃。
Decomposers, such as bacteria and fungi, break down dead matter, recycling nutrients back into the ecosystem. Energy is lost at each trophic level, mainly as heat, so food chains rarely have more than five trophic levels.
分解者（如细菌和真菌）分解死亡生物，将营养物质循环回生态系统。能量在每一个营养级都会损失，主要以热的形式散失，因此食物链很少超过五个营养级。
Bioaccumulation is the build-up of toxic substances, such as pesticides, in the tissues of organisms at higher trophic levels.
生物累积是指有毒物质（如农药）在较高营养级生物的组织中积累的现象。
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