📚 GCSE OCR Science: Formula Summary Handbook | GCSE OCR 科学：公式汇总手册
This handbook brings together all the essential equations you need to memorise for the GCSE OCR Science examinations, covering key formulas from Physics, Chemistry and Biology. Use it as a quick reference to build your confidence when tackling calculation questions.
本手册汇总了GCSE OCR科学考试必须记住的所有核心公式，涵盖物理、化学和生物。将其作为快速参考，帮助你在解答计算题时充满信心。
1. Speed, Distance, and Time | 速度、距离与时间
The relationship between speed, distance and time is one of the most fundamental in Physics. Speed describes how fast an object moves and is calculated by dividing the distance travelled by the time taken.
速度、距离和时间的关系是物理学中最基础的关系之一。速度描述物体运动的快慢，通过移动的距离除以所用时间来计算。
speed = distance ÷ time
In symbols: v = d ÷ t, where v is speed (m/s), d is distance (m), and t is time (s). The formula can be rearranged to find distance or time: d = v × t, t = d ÷ v.
符号表示为：v = d ÷ t，其中 v 是速度（米/秒），d 是距离（米），t 是时间（秒）。此公式可变形求出距离 d = v × t，或时间 t = d ÷ v。
2. Acceleration | 加速度
Acceleration is the rate at which an object changes its velocity. It can be a positive value (speeding up) or a negative value (slowing down, sometimes called deceleration). The standard formula uses the change in velocity over time.
加速度是物体速度变化的快慢。它可以是正值（加速）或负值（减速）。标准公式用速度的变化量除以时间。
a = (v − u) ÷ t
a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s), and t is the time taken (s). The difference (v − u) can also be written as Δv.
a 是加速度（米/秒²），v 是末速度（米/秒），u 是初速度（米/秒），t 是时间（秒）。差值 (v − u) 也可写作 Δv。
3. Forces and Newton’s Second Law | 力与牛顿第二定律
Newton’s Second Law relates the resultant force acting on an object to its mass and acceleration. It explains why a greater force produces a larger acceleration, and a larger mass results in a smaller acceleration for the same force.
牛顿第二定律将物体所受的合力与其质量和加速度联系起来。它解释了为什么更大的力会产生更大的加速度，而质量更大的物体在相同力作用下加速度更小。
F = m × a
F is the resultant force (N), m is the mass (kg), and a is the acceleration (m/s²). For weight, the force due to gravity is given by a special case: W = m × g, where g is gravitational field strength (N/kg, on Earth about 9.8 N/kg).
F 是合力（牛），m 是质量（千克），a 是加速度（米/秒²）。重力的特殊情形为：W = m × g，其中 g 为引力场强度（牛/千克，地球上约为 9.8 牛/千克）。
W = m × g
Be careful not to confuse mass (kg) and weight (N); mass is the amount of matter, while weight is the gravitational force acting on that mass.
注意不要混淆质量（千克）和重量（牛）；质量是物质的多少，而重量是作用在该质量上的重力。
4. Work Done and Energy Transfer | 做功与能量转移
When a force moves an object, work is done and energy is transferred. The work done is equal to the product of the force and the distance moved in the direction of the force.
当力使物体移动时，力就做了功，能量发生了转移。功等于力与沿力方向移动距离的乘积。
W = F × d
W is work done (J), F is the applied force (N), and d is the distance moved in the direction of the force (m). If the force is perpendicular to the direction of motion, no work is done.
W 是做功（焦），F 是作用力（牛），d 是沿力方向移动的距离（米）。如果力与运动方向垂直，则不做功。
5. Kinetic Energy and Potential Energy | 动能与势能
Energy can be stored in different ways. Kinetic energy depends on mass and speed, gravitational potential energy depends on mass, height and gravitational field strength, and elastic potential energy depends on spring constant and extension.
能量可以以不同形式储存。动能取决于质量和速度，重力势能取决于质量、高度和引力场强度，弹性势能取决于弹簧常数和伸长量。
KE = ½ × m × v²
KE is kinetic energy (J), m is mass (kg), v is speed (m/s). This formula shows that doubling the speed quadruples the kinetic energy.
KE 为动能（焦），m 为质量（千克），v 为速度（米/秒）。该公式表明速度加倍时动能变为原来的四倍。
GPE = m × g × h
GPE is gravitational potential energy (J), m is mass (kg), g is gravitational field strength (N/kg), h is height above the reference point (m).
GPE 为重力势能（焦），m 为质量（千克），g 为引力场强度（牛/千克），h 为相对于参考点的高度（米）。
EPE = ½ × k × x²
EPE is elastic potential energy (J), k is the spring constant (N/m), and x is the extension or compression (m). This equation is usually only assessed at Higher Tier.
EPE 为弹性势能（焦），k 为弹簧常数（牛/米），x 为伸长量或压缩量（米）。该公式通常仅在高阶层次考查。
6. Power and Efficiency | 功率与效率
Power is the rate at which energy is transferred or work is done. Efficiency describes how much of the total input energy is converted into useful output. Both concepts are key to understanding energy in systems.
功率是能量转移或做功的快慢。效率描述总输入能量中有多少转化为有用的输出。这两个概念对理解系统中的能量至关重要。
P = W ÷ t = E ÷ t
P is power (W or J/s), W is work done (J), E is energy transferred (J), and t is time (s). Power can also be calculated from energy change per second.
P 是功率（瓦或焦/秒），W 是做功（焦），E 是转移的能量（焦），t 是时间（秒）。功率也可由每秒的能量变化求得。
efficiency = useful output energy ÷ total input energy
Efficiency can be expressed as a decimal or multiplied by 100 to give a percentage. It can also be calculated using useful power output ÷ total power input.
效率可以小数表示，或乘以 100 得到百分比。也可用有用功率输出 ÷ 总功率输入计算。
7. Waves | 波
The wave equation links wave speed, frequency and wavelength. It applies to all types of waves, including sound, water and electromagnetic waves.
波速方程将波速、频率和波长联系起来。它适用于所有类型的波，包括声波、水波和电磁波。
v = f × λ
v is wave speed (m/s), f is frequency (Hz) and λ is wavelength (m). Remember that frequency is the number of complete waves per second, and wavelength is the distance from one peak to the next.
v 为波速（米/秒），f 为频率（赫兹），λ 为波长（米）。记住频率是每秒完整波的个数，波长是从一个波峰到下一个波峰的距离。
8. Electricity: Ohm’s Law and Charge | 电学：欧姆定律与电荷
Ohm’s law expresses the relationship between potential difference, current and resistance. The charge equation connects current to the flow of electric charge over time.
欧姆定律表达了电势差、电流和电阻之间的关系。电荷方程将电流与电荷随时间流动的多少联系起来。
V = I × R
V is potential difference or voltage (V), I is current (A), R is resistance (Ω). For a fixed resistor, if the voltage doubles, the current also doubles at constant resistance.
V 为电势差或电压（伏），I 为电流（安），R 为电阻（欧）。对于固定电阻，若电压加倍，在电阻不变时电流也加倍。
Q = I × t
Q is electric charge (C), I is current (A), t is time (s). This equation tells you the amount of charge passing a point in a circuit in a given time.
Q 为电荷（库），I 为电流（安），t 为时间（秒）。该公式给出给定时间内通过电路中某一点的电荷量。
E = Q × V
E is energy transferred (J), Q is charge (C), V is potential difference (V). The energy transferred when a charge moves through a component is directly proportional to the voltage.
E 为转移的能量（焦），Q 为电荷（库），V 为电势差（伏）。电荷通过元件时转移的能量与电压成正比。
9. Electrical Power and Energy | 电功率与电能
Electrical power can be calculated from current and voltage or from current and resistance. The energy used can be found from power and time.
电功率可由电流与电压，或电流与电阻算出。消耗的电能可由功率与时间求得。
P = I × V
P is power (W), I is current (A), V is potential difference (V). For a device operating at a constant voltage, doubling the current doubles the power.
P 为功率（瓦），I 为电流（安），V 为电势差（伏）。对于在恒压下工作的设备，电流加倍则功率加倍。
P = I² × R
Using V = I × R, this alternative form is useful when you know current and resistance. It shows that power loss in a resistor increases with the square of the current.
利用 V = I × R 可推导出此形式，当已知电流和电阻时很方便。它表明电阻上的功率损耗随电流的平方增加。
E = P × t
E is energy transferred (J), P is power (W), t is time (s). You can combine this with the power equations to find energy in terms of I, V and t: E = I × V × t.
E 为转移的能量（焦），P 为功率（瓦），t 为时间（秒）。可将此式与功率方程结合，得到以 I、V 和 t 表示的能量：E = I × V × t。
10. Magnification (Biology) | 放大率（生物）
In Biology, magnification is used to describe how much larger an image appears compared to the actual specimen. The magnification equation is simple but must be applied with the same units for image size and actual size.
在生物学中，放大率用于描述图像比实际标本大多少。放大率公式简单，但必须保证图像尺寸与实际尺寸使用相同的单位。
magnification = image size ÷ actual size
Often written as M = I ÷ A, where I is the size of the image (mm, µm, etc.) and A is the actual size of the object in the same unit. Magnification has no unit.
常写作 M = I ÷ A，其中 I 是图像尺寸（毫米、微米等），A 是物体的实际尺寸（相同单位）。放大率没有单位。
Always check that you have converted both measurements to the same unit (e.g. both in µm) before dividing. A common mistake is to use mixed units, which gives a wrong magnification.
务必在相除前确认两者已换算成相同单位（例如都转化为微米）。常见错误是混用单位，导致放大率
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