📚 Year 10 OCR Science: Formula & Theorem Quick Reference Handbook | 十年级OCR科学：公式定理速查手册
This handbook provides a concise bilingual reference to the essential formulas and theorems covered in Year 10 OCR Gateway Science (Combined). It is designed to help you quickly look up the equations for motion, forces, energy, electricity, waves, chemistry, and biology, along with key conditions and units.
本手册为十年级OCR Gateway科学（综合）课程中的关键公式和定理提供简明中英对照速查。它旨在帮助你快速查阅运动、力、能量、电学、波、化学和生物学的方程式，并附带重要条件和单位。
1. Motion: Speed and Acceleration | 运动：速率与加速度
Speed is a scalar quantity representing how fast an object is moving, calculated as distance travelled per unit time. Acceleration is the rate of change of velocity — it is a vector quantity and can be caused by a change in speed, direction, or both.
速率是表示物体运动快慢的标量，按单位时间内通过的距离计算。加速度是速度变化的速率——它是一个矢量，可由速度大小、方向或两者的变化引起。
| Formula | Description (English / 中文) |
|---|---|
| v = s / t | average speed = distance ÷ time (平均速率 = 距离 ÷ 时间) |
| a = (v − u) / t | acceleration = (final velocity − initial velocity) ÷ time (加速度 = (末速度 − 初速度) ÷ 时间) |
Always use consistent SI units: distance in metres (m), time in seconds (s), velocity in metres per second (m/s), and acceleration in metres per second squared (m/s2). On a velocity–time graph, acceleration is the gradient, and the area under the graph gives displacement.
始终使用一致的SI单位：距离用米(m)，时间用秒(s)，速度用米每秒(m/s)，加速度用米每二次方秒(m/s2)。在速度–时间图中，加速度是斜率，图线下的面积表示位移。
2. Newton's Second Law and Weight | 牛顿第二定律与重量
Newton's second law relates the net force acting on an object to its mass and the acceleration produced. Weight is the force of gravity on an object and depends on the gravitational field strength.
牛顿第二定律将作用在物体上的净力与其质量和产生的加速度联系起来。重量是物体受到的重力，取决于引力场强度。
| Formula | Description (English / 中文) |
|---|---|
| F = m a | resultant force = mass × acceleration (合力 = 质量 × 加速度) |
| W = m g | weight = mass × gravitational field strength (重量 = 质量 × 引力场强度) |
On Earth, g ≈ 9.8 N/kg (or 10 N/kg for estimation). In Newton's second law, the acceleration is always in the direction of the resultant force. Remember that mass is a scalar (kg), while weight is a vector (N) acting towards the centre of the planet.
在地球上，g ≈ 9.8 N/kg（或估算时取10 N/kg）。在牛顿第二定律中，加速度方向总与合力的方向一致。请记住，质量是标量(kg)，而重量是矢量(N)，方向指向地心。
3. Equations of Uniform Acceleration (Higher Tier) | 匀加速运动方程（提高层）
When acceleration is constant, the following equation links displacement, initial and final velocities, and acceleration. It is particularly useful for solving problems without time.
当加速度恒定时，以下方程将位移、初速度、末速度和加速度联系起来。对于不涉及时间的问题，这个公式尤其有用。
v2 − u2 = 2 a s
where v = final velocity (m/s), u = initial velocity (m/s), a = acceleration (m/s2 tion applies only when acceleration is constant. You may also see it rearranged to find the acceleration or displacement of a moving object.
其中 v = 末速度(m/s)，u = 初速度(m/s)，a = 加速度(m/s2)，s = 位移(m)。此方程仅适用于加速度恒定的情况。你也可以将其变形，用来求解运动物体的加速度或位移。
4. Momentum (Higher Tier) | 动量（提高层）
Momentum is a property of moving objects, defined as the product of mass and velocity. It is a vector quantity and is conserved in isolated systems, meaning total momentum before a collision or explosion equals total momentum after, provided no external forces act.
动量是运动物体的一种属性，定义为质量与速度的乘积。它是矢量，在孤立系统中守恒——这意味着在没有外力作用时，碰撞或爆炸前的总动量等于之后的总动量。
| Formula | Description (English / 中文) |
|---|---|
| p = m v | momentum = mass × velocity (动量 = 质量 × 速度) |
| m1u1 + m2u2 = m1v1 + m2v2 | conservation of momentum (动量守恒): total momentum before = total momentum after |
Units of momentum are kg m/s. In an explosion, the total momentum before is zero, so the objects move apart with equal and opposite momenta. Always assign positive and negative directions for vector calculations.
动量的单位是kg m/s。在爆炸中，爆炸前总动量为零，因此物体以大小相等、方向相反的动量分开。进行矢量计算时，务必指定正方向和负方向。
5. Work, Kinetic Energy and Gravitational Potential Energy | 功、动能与重力势能
Work is done when a force moves an object through a distance in the direction of the force. Kinetic energy is the energy of motion, and gravitational potential energy is stored energy due to an object's position in a gravitational field.
当力使物体沿力的方向移动一段距离时，就做了功。动能是物体由于运动而具有的能量，重力势能是物体因处于引力场中的某个位置而储存的能量。
| Formula | Description (English / 中文) |
|---|---|
| W = F d | work done = force × distance (along line of action) (做功 = 力 × 沿力方向的距离) |
| Ek = ½ m v2 | kinetic energy = ½; × mass × (speed)2 (动能 = ½; × 质量 × 速度平方) |
| Ep = m g h | gravitational potential energy = mass × g × height (重力势能 = 质量 × g × 高度) |
gravity converts gravitational potential energy into kinetic energy (m g h = ½ m v2). In all energy transfers, energy is conserved.
当物体在没有空气阻力的情况下自由下落时，重力做的功将重力势能转化为动能（m g h = ½ m v2）。在所有的能量转移中，能量是守恒的。
6. Power and Efficiency | 功率与效率
Power is the rate at which energy is transferred or work is done. Efficiency compares the useful output energy or power with the total input, and it can be expressed as a percentage or a decimal.
功率是能量转移或做功的速率。效率将有用的输出能量或功率与总输入进行比较，可以用百分数或小数表示。
| Formula | Description (English / 中文) |
|---|---|
| P = E / t | power = energy transferred ÷ time (功率 = 转移的能量 ÷ 时间) |
| P = W / t | power = work done ÷ time (功率 = 做功 ÷ 时间) |
| Efficiency = (useful output / total input) × 100% | iency = useful output energy (or power) ÷ total input energy (or power) × 100% (效率 = 有用的输出能量 ÷ 总输入能量 × 100%) |
The unit of power is the watt (W), equivalent to J/s. No device can be 100% efficient because some energy is always dissipated as thermal energy due to friction or resistance.
功率的单位是瓦特(W)，相当于 J/s。没有任何设备可以达到100%的效率，因为由于摩擦或电阻，总会有部分能量以热能的形式耗散。
7. Electrical Circuits: Ohm's Law and Power | 电路：欧姆定律与电功率
Ohm's law relates potential difference, current, and resistance in a conductor at constant temperature. Electrical power can be calculated from current and voltage, and energy transferred in a circuit depends on the power and time.
欧姆定律描述了在恒定温度下，导体中电压、电流和电阻之间的关系。电功率可通过电流和电压计算，电路中转移的能量取决于功率和时间。
| Formula | Description (English / 中文) |
|---|---|
| V = I R | potential difference = current × resistance (电压 = 电流 × 电阻) |
| P = I V | power = current × potential difference (电功率 = 电流 × 电压) |
| P = I2 R (Higher) | power = current2 × resistance (电功率 = 电流平方 × 电阻，适用于higher tier) |
| E = P t | energy transferred = power × time (转移的能量 = 功率 × 时间) |
| Rtotal = R1 + R2 + ... | resistors in series (串联电阻) |
| 1/Rtotal = 1/R1 + 1/R2 + ... | resistors in parallel (并联电阻) |
For parallel circuits, the total resistance is always less than the smallest individual resistance. When electricity is used in the home, energy is commonly measured in kilowatt-hours (kWh).
对于并联电路，总电阻总是小于最小的单个电阻。家用电路中，电能通常以千瓦时(kWh)为单位计量。
8. Wave Speed and Properties | 波速与特性
All waves transfer energy without transferring matter. The wave speed equation links velocity, frequency and wavelength, while the period of a wave is the inverse of its frequency.
所有的波都传递能量而不传递物质。波速方程将速度、频率和波长联系起来，而波的周期是其频率的倒数。
| Formula | Description (English / 中文) |
|---|---|
| v = f λ | wave speed = frequency × wavelength (波速 = 频率 × 波长) |
| T = 1 / f | period = 1 ÷ frequency (周期 = 1 ÷ 频率) |
When a wave travels from one medium to another, its speed and wavelength may change, but its frequency remains constant. This is key to understanding refraction.
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。这是理解折射的关键。
9. Radioactive Decay and Half-Life | 放射性衰变与半衰期
Radioactive decay is a random process in which an unstable nucleus emits alpha, beta, or gamma radiation. The half-life is the time it takes for the activity (or number of radioactive nuclei) to decrease by half.
放射性衰变是一个随机过程，不稳定的原子核会发射α、β或γ辐射。半衰期是指活度（或放射性核的数量）减半所需的时间。
fraction remaining = (½)n
where n is the number of half-lives elapsed. This relationship allows you to calculate the remaining activity or mass from a given initial amount. Nuclear equations must balance the total mass number (top) and atomic number (bottom) on both sides.
其中 n 是经过的半衰期个数。利用这一关系，可从已知的初始量计算出剩余的活度或质量。书写核方程时，必须使两侧的总质量数（上标）和原子序数（下标）平衡。
10. Chemical Calculations: Moles, Mass and Concentration | 化学计算：摩尔、质量与浓度
The mole is the unit for amount of substance, linking atomic-scale particles to macroscopic mass. The concentration of a solution expresses how much solute is dissolved in a given volume of solvent.
摩尔是物质的量的单位，它将原子尺度的微粒与宏观质量联系起来。溶液的浓度表示在一定体积的溶剂中
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