This compact handbook collects the essential formulas, equations and core theorems required for the KS3 CAIE Science curriculum. Use it to review physics calculations, chemical reactions and key biological principles quickly and accurately.
这本速查手册汇集了 KS3 CAIE 科学课程中必备的公式、方程式与核心定理，方便快速、准确地复习物理计算、化学反应和生物学基本原理。
📚 KS3 CAIE Science: Formulas and Theorems Quick Reference | KS3 CAIE 科学：公式定理速查手册
1. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is the foundation of describing motion. Average speed is found by dividing the total distance travelled by the total time taken.
速度、距离和时间的关系是描述运动的基础。平均速度可由总路程除以总时间求得。
average speed = total distance ÷ total time
In symbols this is often written as v = d / t, where v is speed, d is distance and t is time. The SI unit of speed is metres per second (m/s), but kilometres per hour (km/h) is also common.
用符号常写作 v = d / t，其中 v 代表速度，d 代表距离，t 代表时间。速度的国际单位是米每秒 (m/s)，千米每小时 (km/h) 也常使用。
To rearrange the formula for distance: distance = speed × time, or d = v × t.
变换公式可求距离：距离 = 速度 × 时间，即 d = v × t。
To calculate the time taken: time = distance ÷ speed, t = d / v.
求所需时间：时间 = 距离 ÷ 速度，t = d / v。
On a distance–time graph, the slope (gradient) gives the speed. A straight, sloping line indicates constant speed; a horizontal line means the object is stationary.
在距离－时间图上，斜率（梯度）表示速度。一条倾斜的直线代表匀速运动；水平线表示物体静止。
2. Acceleration | 加速度
Acceleration describes how quickly the velocity of an object changes. It is the change in velocity divided by the time taken for that change.
加速度描述物体速度变化的快慢，等于速度的变化量除以发生该变化所用的时间。
acceleration = change in velocity ÷ time taken
Symbol form: a = (v − u) / t, where a is acceleration, v is final velocity, u is initial velocity and t is time. The SI unit is m/s².
符号形式：a = (v − u) / t，其中 a 为加速度，v 为末速度，u 为初速度，t 为时间。国际单位为 m/s²。
If an object speeds up, acceleration is positive; if it slows down, acceleration is negative (deceleration).
物体加速时加速度为正；减速时加速度为负（减速度）。
For an object starting from rest (u = 0), the final velocity after time t is v = a × t .
物体从静止（u = 0）出发，经过时间 t 后的末速度为 v = a × t 。
3. Force, Mass and Newton’s Second Law | 力、质量与牛顿第二定律
The resultant force acting on an object equals the product of its mass and acceleration. This relationship is Newton’s Second Law of Motion.
作用在物体上的合外力等于物体质量与加速度的乘积。这就是牛顿第二运动定律。
resultant force = mass × acceleration
In symbols: F = m × a, where F is force in newtons (N), m is mass in kilograms (kg) and a is acceleration in m/s².
符号形式：F = m × a，其中 F 是力（单位牛顿 N），m 是质量（单位千克 kg），a 是加速度（单位 m/s²）。
If the forces on an object are balanced, the resultant force is zero, so the object remains at rest or moves at constant speed.
若物体受到的力相互平衡，合外力为零，物体将保持静止或匀速直线运动。
To find mass: m = F ÷ a. To find acceleration: a = F ÷ m.
求质量用 m = F ÷ a，求加速度用 a = F ÷ m。
4. Weight and Gravity | 重量与重力
Weight is the force of gravity acting on an object’s mass. It differs from mass – mass is the amount of matter and is measured in kilograms.
重量是作用在物体质量上的重力。它与质量不同——质量表示物质的多少，单位是千克。
weight = mass × gravitational field strength
Symbol equation: W = m × g, where W is weight in newtons (N), m is mass in kg, and g is the gravitational field strength. On Earth, g ≈ 9.8 N/kg, often rounded to 10 N/kg for KS3.
符号方程：W = m × g，W 为重量（牛顿 N），m 为质量 (kg)，g 为引力场强度。地球表面 g ≈ 9.8 N/kg，在 KS3 阶段常取 10 N/kg。
Your mass stays the same anywhere, but your weight changes depending on the gravity of the planet.
质量在任何地方都不变，但重量会随行星引力而改变。
5. Density | 密度
Density measures how much mass is packed into a certain volume. It helps explain why some objects float while others sink.
密度度量单位体积内所含的质量，帮助解释为何有些物体会浮起、有些会下沉。
density = mass ÷ volume
ρ = m / V, where ρ is density (kg/m³ or g/cm³), m is mass (kg or g) and V is volume (m³ or cm³).
ρ = m / V，其中 ρ 代表密度（单位 kg/m³ 或 g/cm³），m 为质量，V 为体积。
To find mass: m = ρ × V. To find volume: V = m / ρ.
求质量：m = ρ × V；求体积：V = m / ρ。
An object floats in a fluid if its density is less than the fluid’s density; it sinks if its density is greater.
物体的密度小于流体密度时会漂浮；大于流体密度时则会下沉。
6. Pressure | 压强
Pressure tells us how concentrated a force is over a given area. For solids, pressure is simply the force divided by the area over which it acts.
压强表示力在作用面积上的集中程度。对于固体，压强等于作用力除以受力面积。
pressure = force ÷ area
P = F / A, where P is pressure in pascals (Pa), F is force in newtons (N) and A is area in square metres (m²). 1 Pa = 1 N/m².
P = F / A，P 为压强（帕斯卡 Pa），F 为力 (N)，A 为面积 (m²)。1 Pa = 1 N/m²。
In liquids, pressure also depends on depth and density: P = h × ρ × g, where h is the depth of the liquid, ρ is its density and g is gravitational field strength.
在液体中，压强还取决于深度和密度：P = h × ρ × g，其中 h 是液体深度，ρ 是液体密度，g 是引力场强度。
7. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object through a distance in the direction of the force. Energy is transferred when work is done.
当力使物体沿力的方向移动一段距离时，力就对物体做了功。做功的过程伴随着能量的转移。
work done = force × distance moved in direction of force
W = F × d, where work W is in joules (J), force F in newtons (N) and distance d in metres (m).
W = F × d，功 W 的单位为焦耳 (J)，力 F 为牛顿 (N)，距离 d 为米 (m)。
Kinetic energy (movement energy): Eₖ = ½ × m × v². Gravitational potential energy (stored due to height): Eₚ = m × g × h, where h is height above a reference point.
动能（运动的能量）：Eₖ = ½ × m × v²。重力势能（因高度而储存的能量）：Eₚ = m × g × h，其中 h 为参考面以上的高度。
Power is the rate of doing work or transferring energy: power = work done ÷ time or P = E / t. The unit is the watt (W); 1 W = 1 J/s.
功率是做功或能量转移的速率：功率 = 功 ÷ 时间 或 P = E / t。单位是瓦特 (W)，1 W = 1 J/s。
The principle of conservation of energy states that energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed.
能量守恒原理表明，能量可以转移、储存或耗散，但无法被创造或消灭。
8. Electrical Circuits (Ohm’s Law and Power) | 电路（欧姆定律与电功率）
Ohm’s Law relates voltage, current and resistance in a circuit at constant temperature.
欧姆定律描述了恒定温度下电路中电压、电流和电阻之间的关系。
voltage = current × resistance
V = I × R, where V is voltage in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω).
V = I × R，V 为电压（伏特 V），I 为电流（安培 A），R 为电阻（欧姆 Ω）。
Rearrange to find current: I = V / R. To find resistance: R = V / I.
求电流：I = V / R；求电阻：R = V / I。
Electrical power: P = I × V, also expressed as P = I² × R and P = V² / R. Power is measured in watts (W).
电功率：P = I × V，也可写成 P = I² × R 和 P = V² / R。功率单位是瓦特 (W)。
The charge transferred is Q = I × t, where Q is electric charge in coulombs (C) and t is time in seconds (s).
转移的电荷量：Q = I × t，Q 为电荷（库仑 C），t 为时间（秒 s）。
For resistors in series: Rₜₒₜₐₗ = R₁ + R₂ + …. For two resistors in parallel: 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂.
电阻串联：Rₜₒₜₐₗ = R₁ + R₂ + …。两个电阻并联：1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂。
9. Moments (Turning Effect) | 力矩（转动效应）
A moment is the turning effect of a force around a pivot. It depends on both the size of the force and the perpendicular distance from the pivot.
力矩是力绕支点产生的转动效应，它取决于力的大小以及力的作用线到支点的垂直距离。
moment of a force = force × perpendicular distance from pivot
M = F × d, where moment M is in newton metres (N m), force F in newtons (N) and d is the perpendicular distance in metres (m).
M = F × d，力矩 M 的单位为牛顿·米 (N m)，力 F 为牛顿 (N)，垂直距离 d 为米 (m)。
The principle of moments: for a system in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments. This is used to calculate unknown forces or distances in levers and seesaws.
力矩原理：系统平衡时，顺时针力矩之和等于逆时针力矩之和。可用来计算杠杆或跷跷板中未知的力或距离。
10. Chemical Reactions and Conservation of Mass | 化学反应与质量守恒
During a chemical reaction, atoms are rearranged but not created or destroyed. The total mass of reactants always equals the total mass of products – the law of conservation of mass.
化学反应过程中，原子重新排列而不会被创造或消灭。反应物的总质量永远等于生成物的总质量——这就是质量守恒定律。
To represent this accurately, we use balanced symbol equations. For example, magnesium burns in oxygen to form magnesium oxide: 2Mg + O₂ → 2MgO.
为准确表示反应，我们使用配平的符号方程式。例如，镁在氧气中燃烧生成氧化镁：2Mg + O₂ → 2MgO。
The relative formula mass (Mᵣ) of a compound is the sum of the relative atomic masses (Aᵣ) of all atoms in its formula. This helps calculate reacting masses.
化合物的相对化学式质量 (Mᵣ) 是其化学式中所有原子的相对原子质量 (Aᵣ) 之和，可用于计算反应质量。
Common hazard symbols on reagents help us handle chemicals safely, but recognising that atoms are conserved is the key concept behind all equations.
试剂上的常见危险符号帮助我们安全使用化学品，但认识到原子守恒是所有方程式背后的核心概念。
11. Photosynthesis and Respiration | 光合作用与呼吸作用
Photosynthesis is the process by which green plants and some organisms use light energy to convert carbon dioxide and water into glucose and oxygen.
光合作用是绿色植物及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。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Word equation: carbon dioxide + water → glucose + oxygen, in the presence of light and chlorophyll.
文字方程式：二氧化碳 + 水 → 葡萄糖 + 氧气，需要光和叶绿体。
Aerobic respiration takes place in the mitochondria of cells, releasing energy from glucose: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (+ energy as ATP).
有氧呼吸发生在细胞的线粒体中，从葡萄糖中释放能量：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O（+ 以 ATP 形式释放的能量）。
Word equation: glucose + oxygen → carbon dioxide + water (+ energy).
文字方程式：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。
12. Cell Theory and Key Biological Principles | 细胞学说与关键生物学原理
Modern cell theory states three fundamental principles that form the basis of biology.
现代细胞学说包含三条基本原理，构成生物学的基础。
1. All living organisms are composed of one or more cells. 2. The cell is the basic unit of structure and organisation in organisms. 3. All cells arise from pre-existing cells.
1. 所有生物体均由一个或多个细胞组成。2. 细胞是生物体结构和组织的基本单位。3. 所有细胞都来自已有的细胞。
When using a light microscope, total magnification is given by: total magnification = eyepiece lens magnification × objective lens magnification.
使用光学显微镜时，总放大倍数为：总放大倍数 = 目镜放大倍数 × 物镜放大倍数。
To estimate cell size: actual size = image size ÷ magnification. Make sure units are consistent; micrometers (µm) are often used for cells, where 1 mm = 1000 µm.
估算细胞实际大小：实际尺寸 = 图像尺寸 ÷ 放大倍数。注意单位要一致；细胞大小常用微米 (µm)，1 mm = 1000 µm。
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