📚 Year 9 Edexcel Science: Formula & Theorem Quick Reference Handbook | Edexcel 9年级科学：公式定理速查手册
This handbook gathers the essential formulas and laws from the Year 9 Edexcel Science curriculum. It covers physics, chemistry and biology – from speed and energy to Ohm’s law and magnification. Use it to check equations quickly, practise rearrangements and build a solid foundation for GCSE years.
本手册汇集了Edexcel 9年级科学课程中的核心公式和定律，涵盖物理、化学和生物三大领域――从速度、能量到欧姆定律和放大率计算。你可以用它快速查阅公式、练习变换，为GCSE阶段打下坚实基础。
1. Speed and Acceleration | 速度与加速度
Speed tells you how fast an object is moving. It is the distance travelled per unit of time, and acceleration is the rate at which speed changes.
速度表示物体运动的快慢，是单位时间内通过的距离；加速度则是速度变化的快慢。
Average speed: v = d / t, where v is speed, d is distance and t is time. Speed is measured in metres per second (m/s).
平均速度：v = d / t，其中 v 为速度，d 为距离，t 为时间。速度的单位是米每秒（m/s）。
Acceleration: a = (v − u) / t, where a is acceleration, v is final speed, u is initial speed and t is the time taken. Acceleration is measured in m/s².
加速度：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。加速度的单位是米每二次方秒（m/s²）。
On a distance–time graph, speed equals the gradient. On a speed–time graph, acceleration equals the gradient, and the area under the line gives the distance travelled.
在距离−时间图中，速度等于斜率；在速度−时间图中，加速度等于斜率，图线下方面积表示所通过的距离。
2. Forces and Newton’s Laws | 力与牛顿定律
Forces cause changes in motion. Newton’s second law links force, mass and acceleration, while weight is the force of gravity on a mass.
力是改变运动状态的原因。牛顿第二定律建立了力、质量和加速度的关系，而重量是重力对质量的作用力。
Newton’s second law: F = m × a, where F is the resultant force in newtons (N), m is mass in kilograms (kg) and a is acceleration in m/s².
牛顿第二定律：F = m × a，其中 F 为合力，单位牛顿（N）；m 为质量，单位千克（kg）；a 为加速度，单位 m/s²。
Weight: W = m × g, where g is the gravitational field strength on Earth (approximately 9.8 N/kg, often rounded to 10 N/kg in calculations). Weight is a force measured in newtons.
重量：W = m × g，其中 g 为地球表面重力场强度（约 9.8 N/kg，计算中常取 10 N/kg）。重量是一种力，单位为牛顿。
Pressure: p = F / A, where p is pressure in pascals (Pa), F is the normal force and A is the area. A smaller area produces a larger pressure for the same force.
压强：p = F / A，其中 p 为压强，单位帕斯卡（Pa）；F 为垂直作用力，A 为面积。相同力下面积越小压强越大。
3. Work, Energy and Power | 功、能量与功率
Energy is transferred when work is done. Mechanical work, kinetic energy and gravitational potential energy all share the unit joule (J). Power measures how quickly energy is transferred.
做功伴随着能量转移。机械功、动能和重力势能的单位都是焦耳（J）。功率则衡量能量转移的快慢。
Work done: W = F × d, where work W is in joules, F is the force applied in newtons and d is the distance moved in the direction of the force.
功：W = F × d，其中功 W 单位为焦耳，F 为施加的力（牛顿），d 为沿力方向移动的距离（米）。
Kinetic energy: Eₖ = ½ m v². Doubling the speed quadruples the kinetic energy, which is vital for understanding stopping distances.
动能：Eₖ = ½ m v²。速度变为两倍，动能将变为四倍，这对于理解刹车距离十分关键。
Gravitational potential energy: Eₚ = m g h, where h is the change in height. Energy is stored when an object is lifted against gravity.
重力势能：Eₚ = m g h，其中 h 为高度变化。物体被举高时储存了重力势能。
Power: P = E / t or P = W / t. Power is measured in watts (W), where 1 W = 1 J/s.
功率：P = E / t 或 P = W / t，单位瓦特（W），1 W = 1 J/s。
4. Electricity: Current, Voltage and Resistance | 电流、电压与电阻
Electric circuits rely on the flow of charge. The relationships between current, voltage, resistance and power are described by a small set of equations that you will use repeatedly.
电路依赖电荷的流动。电流、电压、电阻和功率之间的关系由几个常用方程描述，你需要反复使用它们。
Charge and current: Q = I × t, where Q is electric charge in coulombs (C), I is current in amperes (A) and t is time in seconds (s).
电荷与电流：Q = I × t，其中 Q 为电荷量，单位库仑（C）；I 为电流，单位安培（A）；t 为时间，单位秒（s）。
Ohm’s law: V = I × R, where V is potential difference (voltage) in volts (V), I is current and R is resistance in ohms (Ω). Resistance reduces the current for a given voltage.
欧姆定律：V = I × R，其中 V 为电势差（电压），单位伏特（V）；I 为电流；R 为电阻，单位欧姆（Ω）。在一定电压下，电阻越大电流越小。
Electrical power: P = V × I. By combining with Ohm’s law you can also write P = I² R and P = V² / R. These are useful for comparing energy dissipation in components.
电功率：P = V × I。结合欧姆定律，还可以写成 P = I² R 和 P = V² / R，用于比较元件中的能量耗散。
5. Waves: Speed, Frequency and Wavelength | 波：波速、频率与波长
All waves obey the wave equation. Whether you are dealing with sound, water or light, the same formula connects their speed, frequency and wavelength.
所有波都遵循波动方程。无论是声波、水波还是光波，波速、频率和波长之间的关系都相同。
Wave speed equation: v = f λ, where v is wave speed in m/s, f is frequency in hertz (Hz) and λ (lambda) is wavelength in metres (m).
波速公式：v = f λ，其中 v 为波速，单位 m/s；f 为频率，单位赫兹（Hz）；λ 为波长，单位米（m）。
Frequency is the number of complete waves passing a point per second. Period (T) is the time for one complete wave: T = 1 / f.
频率是每秒通过某点的完整波数。周期（T）是一个完整波所需的时间：T = 1 / f。
When a wave travels from one medium to another, its speed and wavelength may change, but its frequency stays the same.
当波从一种介质进入另一种介质时，波速和波长可能改变，但频率保持不变。
6. Density and States of Matter | 密度与物态
Density links mass and volume, and it helps identify substances and predict whether objects will float or sink. The particle model explains changes of state.
密度将质量和体积联系起来，有助于识别物质并判断物体浮沉。粒子模型可以解释物态变化。
Density: ρ = m / V, where ρ (rho) is density in kg/m³, m is mass in kg and V is volume in m³. Water has a density of about 1000 kg/m³.
密度：ρ = m / V，其中 ρ 为密度，单位 kg/m³；m 为质量，单位 kg；V 为体积，单位 m³。水的密度约为 1000 kg/m³。
Changing the state of a substance (melting, freezing, boiling, condensing) does not change its mass, so if the volume changes, the density will also change.
物质状态变化（熔化、凝固、沸腾、凝结）不改变质量，因此若体积发生变化，密度也会随之改变。
7. Chemical Quantities and Conservation | 化学计量与守恒
In a chemical reaction, mass is always conserved. You can use relative atomic masses and formula masses to track the atoms and work out reacting masses.
化学反应中质量始终守恒。借助相对原子质量和化学式量，你可以追踪原子并计算反应质量。
Law of conservation of mass: total mass of reactants = total mass of products. No atoms are lost or gained, only rearranged.
质量守恒定律：反应物总质量 = 生成物总质量。原子不会消失或新增，只是重新组合。
Relative atomic mass (Aᵣ): the average mass of an atom compared to 1/12 the mass of carbon‑12. Relative formula mass (Mᵣ): sum of Aᵣ values of all atoms in a formula. Both have no units.
相对原子质量（Aᵣ）：原子的平均质量与碳‑12原子质量的1/12相比的比值。相对化学式量（Mᵣ）：化学式中所有原子 Aᵣ 的总和。两者均无单位。
Rate of reaction can be measured by the change in mass of a reactant or product per unit time: rate ≈ Δ(mass or volume) / Δtime.
反应速率可通过反应物或生成物质量（或体积）在单位时间内的变化衡量：速率 ≈ Δ(质量或体积) / Δ时间。
8. Magnification and Biology Measurements | 放大率与生物学测量
When using microscopes, the magnification formula helps relate the image size to the real size of a specimen. Biological equations for photosynthesis and respiration show energy transformations.
使用显微镜时，放大率公式将图像尺寸与实际样本尺寸联系起来。光合作用和呼吸作用的方程式则展示了能量转换。
Magnification: M = I / A, where M is magnification (no unit), I is image size and A is actual size, both in the same length unit. You may also see triangle formula: I = M × A.
放大率：M = I / A，其中 M 为放大率（无单位），I 为图像尺寸，A 为实际尺寸，两者单位相同。也可记作 I = M × A。
Photosynthesis word equation: carbon dioxide + water → glucose + oxygen (in the presence of light and chlorophyll). Symbol equation: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.
光合作用文字式：二氧化碳 + 水 → 葡萄糖 + 氧气（需光和叶绿素）。符号方程式：6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂。
Aerobic respiration word equation: glucose + oxygen → carbon dioxide + water (+ energy). Symbol equation: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O.
有氧呼吸文字式：葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）。符号方程式：C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O。
9. Energy Transfers and Efficiency | 能量转移与效率
Energy cannot be created or destroyed – it is conserved, but it can be transferred usefully or wasted. Efficiency measures how well a device converts input energy into useful output.
能量既不能创造也不会消灭――它守恒，但转移时可分为有用输出和浪费。效率衡量器件将输入能量转化为有用输出的程度。
Efficiency: Efficiency = (useful output energy transfer / total input energy transfer) × 100%. This ratio can also be expressed in terms of power: Efficiency = (useful power output / total power input) × 100%.
效率：效率 = (有用输出能量 ÷ 总输入能量) × 100%。也可用功率表示：效率 = (有用输出功率 ÷ 总输入功率) × 100%。
Energy transfers in systems involve stores such as kinetic, thermal, chemical, gravitational potential and elastic potential. Sankey diagrams help visualise these transfers.
系统中的能量转移涉及动能、热能、化学能、重力势能和弹性势能等能量仓库。桑基图有助于直观展示这些转移。
10. Units, Prefixes and Conversions | 单位、前缀与换算
Correct units matter. Always state the unit with your answer and learn the standard prefixes so you can convert confidently between metres, kilometres, grams and kilograms.
正确的单位至关重要。答案总要带上单位，并记住标准前缀，以便自信地在米、千米、克、千克等单位间换算。
- Length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
- 长度：1 千米 = 1000 米, 1 米 = 100 厘米, 1 厘米 = 10 毫米。
- Mass: 1 kg = 1000 g, 1 g = 1000 mg.
- 质量：1 千克 = 1000 克, 1 克 = 1000 毫克。
- Time: 1 min = 60 s, 1 h = 3600 s.
- 时间：1 分钟 = 60 秒, 1 小时 = 3600 秒。
- Volume: 1 m³ = 1 000 000 cm³, 1 litre = 1000 cm³ = 0.001 m³.
- 体积：1 立方米 = 1 000 000 立方厘米, 1 升 = 1000 立方厘米 = 0.001 立方米。
- Prefixes: kilo (k) = 10³, centi (c) = 10⁻², milli (m) = 10⁻³, micro (µ) = 10⁻⁶.
- 前缀：千 (k) = 10³, 厘 (c) = 10⁻², 毫 (m) = 10⁻³, 微 (µ) = 10⁻⁶。
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