Formula & Theorems Quick Reference Handbook | 公式定理速查手册

📚 Formula & Theorems Quick Reference Handbook | 公式定理速查手册

This handbook provides a concise summary of the essential formulas and key theorems you will encounter in KS3 Edexcel Science. Mastering these will help you solve problems confidently across physics, chemistry and biology, and build a strong foundation for future studies.

本手册为 KS3 Edexcel 科学中需要掌握的重要公式和核心定理提供了简明总结。掌握这些内容将帮助你自信地解答物理、化学和生物中的各类问题，并为今后的学习打下坚实基础。

1. Speed Formula | 速度公式

Speed describes how fast an object moves. It is calculated by dividing the total distance travelled by the time taken. The formula is:

Speed = Distance ÷ Time

速度描述物体运动的快慢。它可以用总路程除以所花费的时间来计算。公式为：

速度 = 距离 ÷ 时间

In symbols, we write v = d / t, where v is speed in metres per second (m/s), d is distance in metres (m) and t is time in seconds (s). You can also use kilometres per hour (km/h) for longer journeys.

用符号表示为 v = d / t，其中 v 表示速度（单位：米/秒，m/s），d 表示距离（米，m），t 表示时间（秒，s）。对于较长的行程，也可以使用千米/小时 (km/h)。

To find distance, rearrange the formula: Distance = Speed × Time. To find time: Time = Distance ÷ Speed. These versions help you plan journeys and interpret motion graphs.

若要求距离，可将公式变形：距离 = 速度 × 时间。若要求时间：时间 = 距离 ÷ 速度。这些变形公式有助于规划行程和解读运动图像。

Example: A car travels 200 metres in 8 seconds. Its speed is 200 ÷ 8 = 25 m/s. In km/h, this is 25 × 3.6 = 90 km/h.

例：一辆汽车在8秒内行驶了200米，其速度为 200 ÷ 8 = 25 m/s。换算为 km/h，即 25 × 3.6 = 90 km/h。

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2. Density Formula | 密度公式

Density measures how much mass is packed into a given volume. Solids and liquids with high density feel heavy for their size, while low-density materials feel light.

密度衡量单位体积中所含质量的大小。高密度的固体或液体在相同体积下更重，而低密度材料则较轻。

Density = Mass ÷ Volume

密度 = 质量 ÷ 体积

In symbols: ρ = m / V (the Greek letter rho, ρ, stands for density). Mass is measured in kilograms (kg) or grams (g), volume in cubic metres (m³) or cubic centimetres (cm³). Density units are then kg/m³ or g/cm³.

用符号表示为 ρ = m / V（希腊字母 ρ 表示密度）。质量的单位为千克 (kg) 或克 (g)，体积的单位为立方米 (m³) 或立方厘米 (cm³)，因此密度的常用单位是 kg/m³ 或 g/cm³。

To find mass or volume, rearrange: Mass = Density × Volume, Volume = Mass ÷ Density. This is useful when identifying unknown substances by their density.

求质量或体积时可变形：质量 = 密度 × 体积，体积 = 质量 ÷ 密度。通过密度可以鉴别未知物质。

Example: A block of metal has a mass of 540 g and a volume of 200 cm³. Its density is 540 ÷ 200 = 2.7 g/cm³. This matches the density of aluminium.

例：一块金属的质量为 540 g，体积为 200 cm³，则其密度为 540 ÷ 200 = 2.7 g/cm³，与铝的密度一致。

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3. Pressure Formula | 压强公式

Pressure tells us how concentrated a force is over an area. A small area gives a large pressure for the same force, which is why sharp knives cut easily but flat shoes do not sink into soft ground.

压强表示力在面积上的集中程度。同样的力作用在较小的面积上会产生较大的压强，这就是为什么锋利的刀容易切割，而平底鞋不易陷入软地的原因。

Pressure = Force ÷ Area

压强 = 力 ÷ 面积

In symbols: P = F / A. Force (F) is measured in newtons (N), area (A) in square metres (m²). The unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m². Sometimes force is in newtons and area in cm², giving N/cm².

用符号表示为 P = F / A。力 (F) 的单位是牛顿 (N)，面积 (A) 的单位是平方米 (m²)。压强的单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。有时力用牛顿、面积用 cm²，压强单位则为 N/cm²。

Example: A force of 600 N acts on an area of 0.5 m². The pressure is 600 ÷ 0.5 = 1200 Pa. If the same force acts on 0.1 m², pressure becomes 600 ÷ 0.1 = 6000 Pa — much greater.

例：一个 600 N 的力作用在 0.5 m² 的面积上，压强为 600 ÷ 0.5 = 1200 Pa。若同样的力作用在 0.1 m² 上，压强则为 600 ÷ 0.1 = 6000 Pa，大得多。

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4. Moment of a Force | 力矩公式与力矩原理

A moment is the turning effect of a force. It depends on two things: the size of the force and the perpendicular distance from the pivot to the line of action of the force.

力矩是力的转动效应，取决于两个因素：力的大小以及支点到力的作用线的垂直距离。

Moment = Force × Perpendicular distance from pivot

力矩 = 力 × 支点的垂直距离

In symbols: M = F × d, where moment (M) is in newton metres (N m), force (F) in newtons (N) and distance (d) in metres (m). The distance must be the shortest (perpendicular) distance.

用符号表示为 M = F × d，力矩 (M) 的单位是牛顿米 (N m)，力 (F) 的单位是牛顿 (N)，距离 (d) 的单位是米 (m)。距离必须取最短的（垂直）距离。

The Principle of Moments states that for an object to be balanced (in equilibrium), the total clockwise moment equals the total anticlockwise moment about the pivot:

力矩原理指出，当物体平衡（处于平衡状态）时，绕支点的总顺时针力矩等于总逆时针力矩：

Sum of clockwise moments = Sum of anticlockwise moments

顺时针力矩之和 = 逆时针力矩之和

Example: A seesaw has a 300 N child sitting 2 m from the pivot on the left. To balance, a 200 N child sits on the right. Using moments: 300 × 2 = 200 × d, so d = 600 ÷ 200 = 3 m from the pivot.

例：跷跷板上，一个重 300 N 的孩子坐在支点左侧 2 m 处。为了平衡，一个重 200 N 的孩子坐在右侧。根据力矩：300 × 2 = 200 × d，解得 d = 600 ÷ 200 = 3 m 离支点。

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5. Work Done | 做功公式

Work is done when a force moves an object in the direction of the force. Energy is transferred during this process. The amount of work done equals the energy transferred.

当力使物体沿力的方向移动时，力就对物体做了功。这个过程中发生了能量转移，做功的大小等于转移的能量。

Work done = Force × Distance moved in the direction of the force

做功 = 力 × 沿力的方向移动的距离

In symbols: W = F × d. Work done (W) is measured in joules (J), force (F) in newtons (N) and distance (d) in metres (m). 1 Joule is defined as 1 Newton of force moving an object 1 metre.

用符号表示为 W = F × d。做功 (W) 的单位是焦耳 (J)，力 (F) 的单位是牛顿 (N)，距离 (d) 的单位是米 (m)。1 焦耳定义为 1 牛顿的力使物体移动 1 米所做的功。

Example: A person pushes a crate with a force of 50 N over a distance of 4 m. The work done is 50 × 4 = 200 J. The same amount of energy is transferred to the crate as kinetic energy and heat.

例：一个人用 50 N 的力推动箱子移动了 4 m，所做的功为 50 × 4 = 200 J。同样有 200 J 的能量转化为箱子的动能和热能。

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6. Power Formula | 功率公式

Power measures how quickly work is done or how fast energy is transferred. A powerful machine does the same amount of work in less time.

功率衡量做功的快慢或能量转移的速率。一台功率大的机器能在更短的时间内完成相同的功。

Power = Work done ÷ Time

功率 = 做功 ÷ 时间

Alternatively, Power = Energy transferred ÷ Time. The symbol for power is P, and the unit is the watt (W). One watt equals one joule per second (J/s). Larger powers are given in kilowatts (kW), where 1 kW = 1000 W.

也可写成：功率 = 转移的能量 ÷ 时间。功率的符号是 P，单位是瓦特 (W)。1 瓦特 = 1 焦耳/秒 (J/s)。较大的功率常用千瓦 (kW)，1 kW = 1000 W。

Example: A motor lifts a weight, doing 600 J of work in 25 seconds. Its power output is 600 ÷ 25 = 24 W. In kW, this is 0.024 kW.

例：一台电动机提升重物，在 25 秒内做了 600 J 的功，则其输出功率为 600 ÷ 25 = 24 W，即 0.024 kW。

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7. Ohm’s Law | 欧姆定律

Ohm’s Law describes the relationship between voltage, current and resistance in an electrical circuit. For a conductor at constant temperature, the current flowing through it is directly proportional to the voltage across it.

欧姆定律描述了电路中电压、电流和电阻之间的关系。对于温度恒定的导体，通过它的电流与其两端的电压成正比。

Voltage = Current × Resistance

电压 = 电流 × 电阻

In symbols: V = I × R. Voltage (V) is measured in volts (V), current (I) in amperes or amps (A), and resistance (R) in ohms (Ω). You can rearrange to I = V / R or R = V / I to calculate unknown components.

用符号表示为 V = I × R。电压 (V) 的单位是伏特 (V)，电流 (I) 的单位是安培 (A)，电阻 (R) 的单位是欧姆 (Ω)。公式可变形为 I = V / R 或 R = V / I，用于计算未知的电路元件。

Example: A lamp has a resistance of 12 Ω and a current of 0.5 A flows through it. The voltage across the lamp is V = 0.5 × 12 = 6 V. Many devices rely on this fixed relationship to work safely.

例：一盏灯的电阻为 12 Ω，通过它的电流为 0.5 A，则灯两端的电压为 V = 0.5 × 12 = 6 V。许多设备依靠这一确定关系才能安全工作。

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8. Law of Conservation of Mass | 质量守恒定律

The Law of Conservation of Mass states that in a chemical reaction, the total mass of the reactants is exactly equal to the total mass of the products. Atoms are neither created nor destroyed; they are simply rearranged to form new substances.

质量守恒定律指出，在化学反应中，反应物的总质量恰好等于生成物的总质量。原子既不会被创造也不会被消灭，它们只是重新排列形成了新的物质。

This means if you start with 10 g of substance A and 4 g of substance B, the products will have a total mass of 14 g, provided no gas escapes from the reaction vessel. In open systems, a gas may appear to make mass change, but if all reactants and products are collected, the mass remains constant.

这意味着如果你用 10 g 的物质 A 和 4 g 的物质 B 反应，只要没有气体从反应容器中逸出，生成物的总质量就是 14 g。在开放体系中，气体可能会使质量看起来改变，但若收集所有反应物和生成物，质量仍然守恒。

Example: When magnesium burns in oxygen, the mass of the magnesium oxide produced equals the combined mass of the magnesium and the oxygen that reacted. This principle underpins all chemical equations.

例：镁在氧气中燃烧时，生成的氧化镁的质量等于参与反应的镁和氧气的质量之和。这一定律是所有化学方程式的基础。

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9. Chemical Formula Basics | 化学式基础

A chemical formula shows which elements are present in a compound and how many atoms of each element combine together. The subscript numbers (written slightly below the line) tell us the number of atoms.

化学

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