📚 AQA Year 11 Science: Formula and Theorem Quick Reference Handbook | AQA 十一年级科学：公式定理速查手册
This handbook compiles all the essential formulas and key theorems required for AQA Year 11 Combined Science (Trilogy) and the separate sciences. Use it as a rapid revision aid to lock in those must‑know equations for Physics, Chemistry and Biology. Each entry is paired with clear definitions and standard SI units, so you can check your understanding instantly.
本手册汇集了AQA十一年级综合科学（Trilogy）及单独科学课程要求的所有核心公式和关键定理。它可作为快速复习伴侣，帮助你牢牢掌握物理、化学和生物中必须记住的方程。每个条目都配有清晰的定义和标准国际单位，方便你随时检验理解。
1. Speed, Distance and Acceleration | 速度、距离与加速度
The relationship between distance travelled, speed and time is fundamental. When an object moves at constant speed, distance is simply speed multiplied by time.
s = v × t
距离等于速度乘以时间。符号s代表距离（单位米，m），v代表速度（单位米/秒，m/s），t代表时间（单位秒，s）。
Acceleration measures how quickly velocity changes. It is the rate of change of velocity per unit time.
a = Δv ÷ t
加速度等于速度变化量除以时间。a表示加速度（单位米/秒²，m/s²），Δv是速度变化量（末速度减初速度），t是时间。
For uniform acceleration, the linking equation without time is provided in the exam. It connects initial velocity, final velocity, acceleration and displacement.
v² − u² = 2 × a × s
匀加速直线运动中，末速度的平方减去初速度的平方等于两倍加速度乘位移。v为末速度（m/s），u为初速度（m/s），a为加速度（m/s²），s为位移（m）。
2. Forces, Weight and Pressure | 力、重量与压强
Newton’s second law captures the link between resultant force, mass and acceleration. Unbalanced forces cause objects to accelerate.
F = m × a
合外力等于质量乘以加速度。F的单位是牛顿（N），m为质量（kg），a为加速度（m/s²）。
vity on a mass and depends on the gravitational field strength, g. On Earth, g ≈ 9.8 N/kg.
W = m × g
重量等于质量乘引力场强。W单位是牛顿，m单位千克，g单位N/kg。
The extension of a spring is directly proportional to the force applied, up to its limit of proportionality (Hooke’s Law).
F = k × e
弹簧受到的力等于弹簧常数乘以伸长量。F为力（N），k为弹簧常数（N/m），e为伸长量（m）。
Pressure measures how concentrated a force is over an area. It is especially useful in fluids and solids.
p = F ÷ A
压强等于法向力除以受力面积。p单位帕斯卡（Pa）或N/m²，F单位牛顿（N），A单位平方米（m²）。
The moment of a force describes its turning effect around a pivot.
M = F × d
力矩等于力乘以力臂（力的作用线到支点的垂直距离）。M单位牛顿米（Nm），F单位为N，d单位为m。
3. Energy Stores and Work | 能量储存与做功
Kinetic energy is the energy possessed by a moving object. It depends on mass and the square of speed.
Eₖ = ½ × m × v²
动能等于二分之一乘以质量乘速度的平方。Eₖ单位焦耳（J），m单位kg，v单位m/s。
Gravitational potential energy is stored when an object is raised against gravity.
Eₚ = m × g × h
重力势能等于质量乘引力场强乘高度。Eₚ单位焦耳（J），g取9.8 N/kg，h为高度变化（m）。
Work done is the energy transferred when a force moves an object. Work is equal to force multiplied by distance moved along the line of action.
W = F × s
做功等于力乘以沿力方向移动的距离。W单位焦耳（J），F单位牛顿（N），s单位米（m）。
4. Power and Efficiency | 功率与效率
Power is the rate of energy transfer or the rate of doing work. Two equivalent equations are used.
P = E ÷ t
功率等于转移的能量除以时间。P单位瓦特（W）或J/s，E单位焦耳，t单位秒。
P = W ÷ t
功率也等于做功除以时间。此处W为功（J）。
Efficiency compares useful output transfer to total input transfer. It can be written as a ratio or a percentage.
Efficiency = useful output energy transfer ÷ total input energy transfer
效率等于有用输出能量或功率除以总输入能量或功率。效率无单位（或×100%）。
5. Electricity: Charge, Current and Potential Difference | 电学：电荷、电流与电势差
Electric current is the rate of flow of charge. The size of charge transferred depends on current and time.
Q = I × t
电荷量等于电流乘以时间。Q单位库仑（C），I单位安培（A），t单位秒（s）。
Ohm’s Law relates potential difference, current and resistance for an ohmic conductor at constant temperature.
V = I × R
电势差等于电流乘以电阻。V单位伏特（V），I单位A，R单位欧姆（Ω）。
For resistors connected in series, the total resistance is simply the sum of individual resistances.
Rₜₒₜₐₗ = R₁ + R₂ + …
串联电路的总电阻等于各电阻之和。R单位欧姆。
6. Electrical Power and Energy Transfer | 电功率与电能转移
Electrical power can be expressed using potential difference and current, or using current and resistance.
P = V × I
电功率等于电势差乘以电流。P单位瓦特（W）。
P = I² × R
电功率也等于电流的平方乘以电阻。
Energy transferred by an electrical appliance depends on power and time, or on charge and potential difference.
E = P × t
电能等于功率乘以时间。E单位焦耳（J），也可用千瓦时（kWh）。
E = Q × V
电能也等于流过的电荷量乘以电势差。
7. Waves | 波
Wave speed, frequency and wavelength are linked for all types of waves, including sound and electromagnetic waves.
v = f × λ
波速等于频率乘以波长。v单位m/s，f单位赫兹（Hz），λ单位米（m）。
The period of a wave is the reciprocal of frequency. This is useful when reading oscilloscope traces.
T = 1 ÷ f
周期等于频率的倒数。T单位秒（s）。
8. Density | 密度
Density is mass per unit volume and helps identify materials. It is constant for a given substance under fixed conditions.
ρ = m ÷ V
密度等于质量除以体积。ρ单位kg/m³或g/cm³，m单位kg或g，V单位m³或cm³。
9. Chemical Calculations: Moles and Mass | 化学计算：摩尔与质量
The mole is the central unit for counting particles in Chemistry. The mass of one mole of a substance is its relative formula mass in grams.
n = m ÷ Mᵣ
物质的量（摩尔）等于物质的质量除以相对分子质量（或相对原子质量）。n单位mol，m单位g，Mᵣ单位g/mol。
Percentage yield quantifies how much product was actually made compared to the theoretical maximum.
Percentage yield = (actual yield ÷ theoretical yield) × 100
产率等于实际产量除以理论产量再乘以100%。
Atom economy measures the proportion of starting atoms that end up in the desired product. A higher atom economy means a greener process.
Atom economy = (Mᵣ of desired product ÷ sum of Mᵣ of all products) × 100
原子经济性等于目标产物的相对分子质量除以所有产物相对分子质量之和再乘以100%。
10. Concentration and Volume of Gases | 浓度与气体体积
Concentration expressed in grams per dm³ is useful for making standard solutions.
Concentration (g/dm³) = mass (g) ÷ volume (dm³)
质量浓度等于溶质质量除以溶液体积，单位g/dm³。
In titrations, concentration in mol/dm³ links moles and volume.
Concentration (mol/dm³) = n ÷ V (dm³)
摩尔浓度等于溶质的物质的量除以溶液体积，单位mol/dm³。
At room temperature and pressure (RTP), one mole of any gas occupies 24 dm³.
Gas volume (dm³) = n × 24
气体体积等于物质的量乘以24 dm³/mol。在常温和常压下适用。
11. Rates of Reaction | 反应速率
The mean rate of a reaction can be calculated by measuring how much reactant is used or product is formed over time.
Mean rate = quantity of reactant used ÷ time
平均反应速率等于反应物的消耗量除以时间。也可用产物生成量计算。单位取决于测量量，如g/s或cm³/s。
On a graph of amount against time, the rate at a specific point is found from the gradient (slope) of the tangent.
在量-时间图上，某时刻的瞬时速率等于该点切线的斜率。
12. Biology: Magnification and Key Processes | 生物学：放大率与关键过程
Magnification formula is essential for microscope drawings and interpreting scale bars.
Magnification = image size ÷ real object size
放大率等于图像尺寸除以实物尺寸。两者单位必须一致，无单位。
Photosynthesis and aerobic respiration are represented by word and balanced symbol equations. You should recall the reactants and products.
光合作用与有氧呼吸的文字方程式及配平的符号方程式需要熟记。
Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
光合作用：二氧化碳 + 水 → 葡萄糖 + 氧气（在光和叶绿体作用下）。
Aerobic respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
有氧
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