📚 Year 11 OCR Science: Quick Reference Handbook of Formulas and Principles | Year 11 OCR 科学：公式定理速查手册
This handbook is your go-to revision tool for the essential formulas and principles across Physics, Chemistry and Biology in the Year 11 OCR Science course. Each section presents clear equations, standard scientific notation, unit reminders and concise explanations so that you can substitute values, rearrange expressions and solve problems confidently in your examinations.
本手册是你复习 Year 11 OCR 科学课程中物理、化学和生物核心公式与定理的快速查阅工具。每一节都给出清晰的方程、标准科学符号、单位提示以及简明解释，帮助你在考试中正确代入数值、熟练变形公式并自信地解决问题。
1. How to Use This Handbook: Units, Notation and Prefixes | 使用本手册：单位、记法与词头
Every equation in this handbook is written with the quantity, the symbol and the SI unit that must be substituted. Read the unit before you read the number. If a question gives a value in grams, centimetres or minutes, the first mark in the method is usually earned simply by converting it correctly.
本手册中的每一个方程都标明了物理量、符号以及代入时必须使用的国际单位。先看单位，再看数字。如果题目给出的是克、厘米或分钟，那么方法分中的第一分往往就是靠正确换算拿到的。
Use the table below to move between multiples and submultiples of SI units. Prefixes change the size of the unit only; they never change the equation itself.
下表用于在国际单位的不同倍数与分数单位之间换算。词头只改变单位的大小，绝不改变方程本身。
| Prefix | Symbol | Factor | Example |
| pico | p | × 10⁻¹² | 1 pm = 1 × 10⁻¹² m |
| nano | n | × 10⁻⁹ | 1 nm = 1 × 10⁻⁹ m |
| micro | μ | × 10⁻⁶ | 1 μm = 1 × 10⁻⁶ m |
| milli | m | × 10⁻³ | 1 mm = 0.001 m |
| kilo | k | × 10³ | 1 km = 1000 m |
| mega | M | × 10⁶ | 1 MW = 1 × 10⁶ W |
| giga | G | × 10⁹ | 1 GHz = 1 × 10⁹ Hz |
Very large and very small values should be written in standard form, a × 10ⁿ where 1 ≤ a < 10. Give your final answer to the same number of significant figures as the least precise value in the question, and always state the unit.
很大或很小的数值应写成标准形式 a × 10ⁿ，其中 1 ≤ a < 10。最终答案的有效数字位数应与题目中精确度最低的数值一致，并且一定要写出单位。
2. Motion: Speed, Distance, Time and Acceleration | 运动：速率、距离、时间与加速度
Understanding how objects move starts with three fundamental equations: average speed, acceleration, and the link between initial velocity, final velocity, acceleration and displacement. In uniformly accelerated motion the initial velocity is normally symbolised by u and the final velocity by v; the displacement is s and the acceleration is a.
理解物体如何运动，从三个基本方程开始：平均速率、加速度，以及初速度、末速度、加速度与位移之间的关系。在匀加速运动中，初速度通常用 u 表示，末速度用 v 表示；位移用 s，加速度用 a。
v = d / t
Average speed = distance / time. This version is used when speed is not constant: v is in m/s, d is in m and t is in s. The gradient of a distance-time graph gives speed, and the gradient of a velocity-time graph gives acceleration.
平均速率 = 距离 / 时间。当速率不恒定时使用此式：v 的单位是 m/s，d 的单位是 m，t 的单位是 s。距离—时间图的斜率给出速率，速度—时间图的斜率给出加速度。
a = Δv / t = (v − u) / t
Acceleration = change in velocity / time taken. A negative value simply means deceleration, that is, acceleration in the opposite direction to the motion. The unit is m/s² because a velocity in m/s is divided by a time in s.
加速度 = 速度变化量 / 所用时间。负值只表示减速，即加速度方向与运动方向相反。单位是 m/s²，因为是用 m/s 的速度除以 s 的时间。
The three standard equations of uniformly accelerated motion are:
匀加速运动的三个标准方程是：
v = u + at
s = ut + ½at²
v² = u² + 2as
The third equation, v² = u² + 2as, is the one that links initial and final velocity, acceleration and displacement without involving time. It is the correct choice whenever a question mentions distance travelled but gives no time.
第三个方程 v² = u² + 2as 正是把初速度、末速度、加速度与位移联系起来、而不含时间的公式。当题目给出运动距离却没有给出时间时，就应该选择它。
- Speed is a scalar; velocity is a vector and includes direction. | 速率是标量，速度是矢量，包含方向。
- Distance is the total path length; displacement is the straight-line distance in a stated direction. | 路程是轨迹总长度，位移是沿某一方向的直线距离。
- For a falling object, use g ≈ 9.8 m/s² (often taken as 10 m/s² in OCR questions). | 对于自由落体，取 g ≈ 9.8 m/s²（OCR 题目中常取 10 m/s²）。
3. Forces, Weight, Momentum and Moments | 力、重力、动量与力矩
Newton's second law states that the resultant force on an object equals its mass multiplied by its acceleration. This single relationship explains why a heavier trolley accelerates more slowly under the same push, and why a larger force produces a larger acceleration.
牛顿第二定律指出，物体所受的合力等于质量乘以加速度。这一关系解释了为什么同一推力下越重的小车加速越慢，以及为什么力越大加速度越大。
F = ma
Resultant force = mass × acceleration. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in m/s². Always work out the resultant force first by adding forces in the same direction and subtracting those in opposite directions.
合力 = 质量 × 加速度。力的单位是牛顿（N），质量单位是千克（kg），加速度单位是 m/s²。要先把同方向上的力相加、反方向上的力相减，求出合力再代入。
W = mg
Weight = mass × gravitational field strength. Weight is a force in newtons and changes with location, whereas mass in kilograms does not. On Earth, g ≈ 9.8 N/kg.
重力 = 质量 × 重力场强度。重力是以牛顿为单位的力，会随位置改变；而千克为单位的质量不会改变。在地球上 g ≈ 9.8 N/kg。
For collisions, momentum is conserved in a closed system, and the force experienced depends on how quickly the momentum changes.
在碰撞中，封闭系统内动量守恒，而物体所受的力取决于动量改变的快慢。
p = mv
F = Δp / Δt
Momentum is measured in kg m/s or N s. The second equation explains why crumple zones and airbags reduce injury: the change in momentum is spread over a longer time, so the force is smaller.
动量的单位是 kg m/s 或 N s。第二个方程解释了为什么溃缩区和安全气囊能减轻伤害：动量变化被拉长到更长时间内完成，因此作用力更小。
Moment = F × d
A moment is measured in N m and d is the perpendicular distance from the pivot to the line of action of the force. For a balanced beam, the sum of clockwise moments equals the sum of anticlockwise moments.
力矩的单位是 N m，其中 d 是从支点到力的作用线的垂直距离。对于平衡的横梁，顺时针力矩之和等于逆时针力矩之和。
4. Energy, Work, Power and Efficiency | 能量、功、功率与效率
Energy is conserved: it can be transferred between stores but never created or destroyed. In an examination, the safest way to start a calculation is to name the transfer, for example from chemical to thermal, then choose the matching equation.
能量守恒：能量可以在不同能量库之间转移，但既不能创造也不能消灭。考试中最稳妥的做法是先说出能量转移形式，例如从化学能到热能，然后选择对应的方程。
W = Fs
Work done = force × distance moved in the direction of the force. Work done is measured in joules (J) because a force in newtons is multiplied by a distance in metres. One joule is one newton metre.
功 = 力 × 沿力的方向移动的距离。功的单位是焦耳（J），因为牛顿的力乘以米的距离。1 焦耳等于 1 牛顿米。
Eₖ = ½mv²
Eₚ = mgh
Kinetic energy depends on the square of the speed, so doubling the speed quadruples the kinetic energy. Gravitational potential energy uses the height change h measured in metres, not the total height of the object above the ground.
动能与速率的平方成正比，因此速率加倍，动能变为四倍。重力势能中的高度变化 h 以米为单位，指的是高度变化量，而不是物体离地面的总高度。
P = E / t = W / t
Power = energy transferred / time taken J/s. Power measures how quickly energy is transferred, not how much energy is transferred.
功率 = 转移的能量 / 所用时间，单位是瓦特（W），1 W = 1 J/s。功率衡量的是能量转移的快慢，而不是转移了多少能量。
Efficiency = useful output energy / total input energy × 100%
Efficiency has no unit and is always less than 100% in a real device. The energy that is not usefully transferred is dissipated, usually by heating the surroundings.
效率没有单位，真实装置的效率总是小于 100%。未被有效利用的能量被耗散，通常是加热了周围环境。
For thermal calculations, use the specific heat capacity equation: E = mcΔθ, where m is mass in kg, c is specific heat capacity in J/kg °C and Δθ is the temperature change in °C.
热学计算使用比热容方程：E = mcΔθ，其中 m 是质量
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