📚 Year 10 Edexcel Science: Formula & Theorem Quick Reference Handbook | Year 10 Edexcel 科学：公式定理速查手册
This quick reference handbook compiles all the essential formulas and theorems you need to master for the Year 10 Edexcel Science curriculum. Whether you are tackling physics problems on motion and energy, chemistry calculations involving moles and concentrations, or the key equations that link physical quantities, having these relationships at your fingertips will sharpen your problem-solving and boost your exam confidence. Each formula is broken down with symbol meanings, SI units and a worked example to show exactly how it is applied.
这本速查手册汇编了 Year 10 Edexcel 科学课程必须掌握的所有核心公式和定理。无论是处理物理中的运动与能量问题、进行化学摩尔与浓度计算，还是运用联系各物理量的关键方程，随时查阅这些关系都能增强你的解题能力与应考信心。每个公式都详列符号含义、国际单位并给出示例，清晰展示如何正确应用。
1. Speed Equation | 速度公式
v = s / t
Average speed is the total distance travelled divided by the time taken. It is a scalar quantity and does not involve direction. The equation is valid for uniform motion or for calculating the mean speed over a journey.
平均速度等于总运动距离除以所用时间。速度是标量，不涉及方向。该公式适用于匀速运动或计算全程的平均速率。
Symbols: v – average speed (metres per second, m/s); s – distance travelled (metres, m); t – time taken (seconds, s).
符号：v – 平均速度（米/秒，m/s）；s – 路程（米，m）；t – 所用时间（秒，s）。
Example: A runner completes 400 m in 50 s. Average speed v = 400 m / 50 s = 8 m/s.
示例：一名跑步者用50 s跑完400 m。平均速度 v = 400 m / 50 s = 8 m/s。
2. Acceleration | 加速度公式
a = (v − u) / t
Acceleration is the rate of change of velocity. It is a vector quantity, meaning direction matters. The formula uses the final velocity v, initial velocity u and the time interval t. A negative value indicates deceleration.
加速度是速度的变化率。它是矢量，方向至关重要。公式用到末速度 v、初速度 u 和时间间隔 t。负值表示减速。
Symbols: a – acceleration (metres per second squared, m/s²); v – final velocity (m/s); u – initial velocity (m/s); t – time (s).
符号：a – 加速度（米/秒²，m/s²）；v – 末速度（m/s）；u – 初速度（m/s）；t – 时间（s）。
Example: A car speeds up from 10 m/s to 25 m/s in 5 s. a = (25 − 10) / 5 = 3 m/s².
示例：一辆汽车在5 s内从10 m/s加速到25 m/s。a = (25 − 10) / 5 = 3 m/s²。
3. Newton’s Second Law | 牛顿第二定律
F = m × a
The resultant force acting on an object is directly proportional to its mass and the acceleration produced. One newton is the force needed to accelerate a 1 kg mass by 1 m/s².
作用在物体上的合力与其质量和产生的加速度成正比。1牛顿是使1 kg质量产生1 m/s²加速度所需的力。
Symbols: F – resultant force (newtons, N); m – mass (kilograms, kg); a – acceleration (m/s²).
符号：F – 合力（牛顿，N）；m – 质量（千克，kg）；a – 加速度（m/s²）。
Example: A 1200 kg car accelerates at 2 m/s². The driving force F = 1200 × 2 = 2400 N.
示例：一辆1200 kg的汽车以2 m/s²加速。驱动力 F = 1200 × 2 = 2400 N。
4. Weight | 重量
W = m × g
Weight is the force of gravity acting on a mass. It is measured in newtons and depends on the gravitational field strength g, which on Earth is approximately 10 N/kg (more precisely 9.8 N/kg).
重量是作用在质量上的引力。它以牛顿为单位，取决于引力场强度 g。在地球表面，g 约等于10 N/kg（更精确为9.8 N/kg）。
Symbols: W – weight (N); m – mass (kg); g – gravitational field strength (newtons per kilogram, N/kg).
符号：W – 重量（N）；m – 质量（kg）；g – 引力场强度（牛/千克，N/kg）。
Example: A 50 kg student on Earth has a weight W = 50 × 10 = 500 N.
示例：地球上一位50 kg的学生重量 W = 50 × 10 = 500 N。
5. Gravitational Potential Energy (GPE) | 重力势能
GPE = m × g × h
Gravitational potential energy is the energy stored by an object due to its height above a reference level. The work done to lift the object is equal to the gain in GPE, assuming no energy losses.
重力势能是物体因所在高度而储存的能量。在无能量损失的情况下，抬高物体所做的功等于其增加的重力势能。
Symbols: GPE – gravitational potential energy (joules, J); m – mass (kg); g – gravitational field strength (N/kg); h – vertical height (metres, m).
符号：GPE – 重力势能（焦耳，J）；m – 质量（kg）；g – 引力场强度（N/kg）；h – 垂直高度（m）。
Example: A 2 kg book placed on a 1.5 m shelf gains GPE = 2 × 10 × 1.5 = 30 J.
示例：一本2 kg的书放在1.5 m的架子上，获得 GPE = 2 × 10 × 1.5 = 30 J。
6. Kinetic Energy (KE) | 动能
KE = ½ × m × v²
Kinetic energy is the energy an object possesses because of its motion. The equation shows that doubling the speed quadruples the kinetic energy, highlighting that speed has a squared relationship with KE.
动能是物体因运动而具有的能量。该公式显示，速度加倍会使动能变为原来的四倍，表明动能与速度的平方成正比。
Symbols: KE – kinetic energy (J); m – mass (kg); v – speed (m/s).
符号：KE – 动能（J）；m – 质量（kg）；v – 速度（m/s）。
Example: A 0.5 kg ball moving at 4 m/s has KE = 0.5 × 0.5 × 4² = 0.5 × 0.5 × 16 = 4 J.
示例：一个0.5 kg的球以4 m/s运动，动能 KE = 0.5 × 0.5 × 4² = 0.5 × 0.5 × 16 = 4 J。
7. Work Done | 做功
W = F × d
Work is done when a force moves an object through a distance in the direction of the force. One joule is the work done when a force of 1 N moves its point of application 1 m in the direction of the force.
当力使物体沿力的方向移动一段距离时，这个力做了功。1焦耳等于1 N的力使物体沿力的方向移动1 m所做的功。
Symbols: W – work done (J); F – force applied (N); d – distance moved in the direction of the force (m).
符号：W – 做功（J）；F – 施加的力（N）；d – 沿力的方向移动的距离（m）。
Example: A 20 N force pushes a box 3 m across a floor. Work done W = 20 × 3 = 60 J.
示例：一个20 N的力将箱子沿地面推行3 m。做功 W = 20 × 3 = 60 J。
8. Power | 功率
P = E / t or P = W / t
Power is the rate of doing work or transferring energy. The two forms are equivalent because work done is equal to the energy transferred. The unit watt is one joule per second.
功率是做功或转移能量的速率。两种形式等价，因为做功等于转移的能量。单位瓦特表示每秒转移1焦耳。
Symbols: P – power (watts, W); E – energy transferred (J); W – work done (J); t – time (s).
符号：P – 功率（瓦特，W）；E – 转移的能量（J）；W – 做功（J）；t – 时间（s）。
Example: A motor lifts a weight, doing 2400 J of work in 12 s. Power P = 2400 / 12 = 200 W.
示例：一台电动机提升重物，12 s内做功2400 J。功率 P = 2400 / 12 = 200 W。
9. Ohm’s Law | 欧姆定律
V = I × R
Ohm’s law links the potential difference across a conductor, the current flowing through it and its resistance. It holds for ohmic conductors at constant temperature. Resistance is measured in ohms (Ω).
欧姆定律将导体两端的电势差、流经的电流和电阻联系起来。它适用于恒温条件下的欧姆导体。电阻的单位是欧姆（Ω）。
Symbols: V – potential difference or voltage (volts, V); I – current (amperes, A); R – resistance (ohms, Ω).
符号：V – 电势差或电压（伏特，V）；I – 电流（安培，A）；R – 电阻（欧姆，Ω）。
Example: A resistor carries a current of 2 A when a voltage of 10 V is applied. R = V / I = 10 / 2 = 5 Ω.
示例：一个电阻器在10 V电压下通过2 A的电流。R = V / I = 10 / 2 = 5 Ω。
10. Density | 密度
ρ = m / V
Density is mass per unit volume. It is a characteristic property of a substance and can be used to identify materials. Solids and liquids typically have densities expressed in g/cm³ or kg/m³.
密度是单位体积的质量。它是物质的一种特性，可用于鉴别材料。固体和液体的密度常用 g/cm³ 或 kg/m³ 表示。
Symbols: ρ – density (kilograms per cubic metre, kg/m³, or grams per cubic centimetre, g/cm³); m – mass (kg or g); V – volume (m³ or cm³).
符号：ρ – 密度（千克/立方米，kg/m³，或克/立方厘米，g/cm³）；m – 质量（kg或g）；V – 体积（m³或cm³）。
Example: A 100 cm³ piece of aluminium has a mass of 270 g. Density ρ = 270 g / 100 cm³ = 2.7 g/cm³.
示例：一块100 cm³的铝质量为270 g。密度 ρ = 270 g / 100 cm³ = 2.7 g/cm³。
11. The Mole and Molar Mass | 摩尔与摩尔质量
n = m / M
The mole is the unit for amount of substance. One mole contains 6.02 × 10²³ particles. Molar mass M is the mass of one mole of a substance and is numerically equal to the relative formula mass in grams per mole.
摩尔是物质的量的单位。1 mol 包含 6.02 × 10²³ 个微粒。摩尔质量 M 是1 mol 物质的质量，数值上等于相对式量，单位为克/摩尔（g/mol）。
Symbols: n – amount of substance (mol); m – mass (grams, g); M – molar mass (grams per mole, g/mol).
符号：n – 物质的量（mol）；m – 质量（克，g）；M – 摩尔质量（克/摩尔，g/mol）。
Example: Carbon dioxide (CO₂) has M = 44 g/mol. What amount is 22 g of CO₂? n = 22 / 44 = 0.5 mol.
示例：二氧化碳（CO₂）的 M = 44 g/mol。22 g CO₂ 是多少摩尔？ n = 22 / 44 = 0.5 mol。
12. Concentration of a Solution | 溶液浓度
c = n / V
Concentration expresses how much solute is dissolved in a given volume of solution. The standard unit is moles per cubic decimetre (mol/dm³), often referred to as molarity. Volume must be in dm³, so volumes in cm³ must be divided by 1000.
浓度表示单位体积溶液中溶质的量。标准单位是摩尔/立方分米（mol/dm³），常称摩尔浓度。体积必须用 dm³，若以 cm³ 给出应除以1000。
Symbols: c – concentration (mol/dm³); n – amount of solute (mol); V – volume of solution (dm³).
符号：c – 浓度（mol/dm³）；n – 溶质的物质的量（mol）；V – 溶液体积（dm³）。
Example: 0.4 mol of sodium hydroxide is dissolved to make 2 dm³ of solution. c = 0.4 / 2 = 0.2 mol/dm³.
示例：将0.4 mol氢氧化钠溶于水，配成2 dm³溶液。c = 0.4 / 2 = 0.2 mol/dm³。
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