📚 GCSE WJEC Science: Formula Summary Handbook | GCSE WJEC 科学：公式汇总手册
This comprehensive handbook brings together all the essential formulas needed for the GCSE WJEC Science examinations, covering physics, chemistry and biology quantitative skills. Mastering these equations and understanding how to apply them is key to solving numerical problems accurately across the three sciences.
这本综合手册汇集了 GCSE WJEC 科学考试所需的所有基本公式，涵盖物理、化学和生物的定量技能。掌握这些方程并理解如何运用它们，是在三门科学中准确解决计算问题的关键。
1. Speed, Distance and Time | 速度、距离与时间
v = d / t
Where v is average speed in metres per second (m/s), d is total distance travelled in metres (m) and t is total time taken in seconds (s).
其中 v 为平均速度（米/秒，m/s），d 为总行驶距离（米，m），t 为总用时（秒，s）。
If an object moves at a constant speed, the same relationship holds. The unit of speed can also be given in km/h, but you must convert carefully: divide by 3.6 to change km/h to m/s.
如果物体做匀速运动，同样适用此关系式。速度单位也可以表示为 km/h，但必须小心换算：将 km/h 除以 3.6 即可转换为 m/s。
You can rearrange the formula to find distance (d = v × t) or time (t = d / v). Always ensure the units are consistent before substituting values.
你可以转换公式求距离（d = v × t）或时间（t = d / v）。代入数值前务必确保单位统一。
2. Acceleration | 加速度
a = Δv / t
Acceleration a (in m/s²) is the rate of change of velocity. Δv represents the change in velocity, which equals final velocity v minus initial velocity u, so Δv = v − u. The time t is measured in seconds (s).
加速度 a（单位 m/s²）是速度的变化率。Δv 表示速度的变化量，等于末速度 v 减初速度 u，即 Δv = v − u。时间 t 以秒（s）为单位。
The velocity can be taken as positive or negative depending on direction. A negative acceleration indicates deceleration, meaning the object is slowing down in the chosen positive direction.
速度可根据方向取正或负。负加速度表示减速，即物体在选定的正方向上变慢。
In uniform acceleration equations, the same formula applies only if acceleration is constant. For the WJEC exam, you are also expected to interpret velocity–time graphs to find acceleration from the gradient.
在匀加速运动中，此公式仅适用于加速度恒定的情况。在 WJEC 考试中，你还需要能够通过速度-时间图的斜率求出加速度。
3. Newton’s Second Law | 牛顿第二定律
F = m × a
Resultant force F is measured in newtons (N), mass m in kilograms (kg) and acceleration a in metres per second squared (m/s²). This equation tells us that the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass.
合力 F 的单位为牛顿（N），质量 m 的单位为千克（kg），加速度 a 的单位为米每二次方秒（m/s²）。该方程表明，物体的加速度与合力成正比，与质量成反比。
Always identify the resultant force first. If multiple forces act on an object, add them as vectors; the equation uses the net force in the direction of the acceleration.
务必首先确定合力。如果多个力作用在物体上，需按矢量相加；方程中使用的是沿加速度方向的净力。
You can rearrange to find mass (m = F / a) or acceleration (a = F / m). This relationship is fundamental for explaining how vehicles, falling objects and rockets move.
可变形求质量（m = F / a）或加速度（a = F / m）。这一关系是解释车辆、落体及火箭运动的基础。
4. Work, Energy and Power | 功、能与功率
W = F × d
Work done W is in joules (J) when a force F in newtons (N) moves an object through a distance d in metres (m), provided the force acts along the direction of motion. One joule is defined as the work done when a force of 1 N moves an object 1 m.
当力 F（牛顿，N）使物体沿力的方向移动距离 d（米，m）时，所做的功 W 单位为焦耳（J）。1 焦耳定义为 1 N 的力使物体移动 1 m 所做的功。
P = W / t or P = E / t
Power P in watts (W) is the rate at which work is done or energy is transferred. W is work done in joules (J) or E is energy transferred in joules (J), and t is time in seconds (s). One watt equals one joule per second.
功率 P（瓦特，W）是做功或能量转移的速率。W 为做功（焦耳，J）或 E 为转移的能量（J），t 为时间（秒，s）。1 瓦特等于 1 焦耳每秒。
When energy is transferred, the total amount of work done is equal to the energy converted. Use the appropriate form based on the context, such as a motor lifting a load or a lamp converting electrical energy.
能量转移时，所做的总功等于转换的能量。需根据具体情景选用恰当形式，如电动机提升重物或灯泡转换电能。
5. Gravitational Potential Energy and Kinetic Energy | 重力势能与动能
GPE = m × g × h
Gravitational potential energy (GPE) depends on mass m (kg), gravitational field strength g (N/kg, approximately 9.8 N/kg on Earth, often taken as 10 N/kg in WJEC calculations) and height h (m) above a reference level. Energy is in joules (J).
重力势能（GPE）取决于质量 m（kg）、重力场强度 g（N/kg，地球表面约 9.8 N/kg，WJEC 计算中常取 10 N/kg）以及相对于参考平面的高度 h（m）。能量单位为焦耳（J）。
KE = ½ × m × v²
Kinetic energy (KE) is the energy associated with motion, given by half the mass m (kg) times the square of the speed v (m/s). Notice that doubling the speed quadruples the kinetic energy because of the v² term.
动能（KE）是与运动相关的能量，等于质量 m（kg）的一半乘以速度 v（m/s）的平方。注意由于 v² 项的存在，速度加倍会使动能变为原来的四倍。
In many problems, energy is conserved and transfers between GPE and KE, for example a falling object or a pendulum. Ignoring air resistance, total mechanical energy remains constant.
在许多问题中，能量是守恒的，并在 GPE 和 KE 之间转化，例如落体或摆锤。忽略空气阻力时，总机械能保持不变。
6. Efficiency | 效率
Efficiency = (useful output energy / total input energy) × 100%
Efficiency compares how much of the input energy is converted into useful output. It can also be calculated using power: Efficiency = (useful power output / total power input) × 100%. It has no units and can be expressed as a percentage or a decimal between 0 and 1.
效率比较的是有多少输入能量转化为有用的输出。也可以用功率计算：效率 =（有用输出功率 / 总输入功率）× 100%。它无单位，可用百分数或 0 到 1 之间的小数表示。
No device can have an efficiency greater than 100% because of energy dissipation, mainly as thermal energy. In WJEC questions, you may be asked to identify ways to reduce wasted energy, such as lubrication or thermal insulation.
由于能量耗散（主要以热能形式），任何装置效率都不能超过 100%。在 WJEC 考题中，你可能需要提出减少能量浪费的方法，如润滑或隔热。
You must be able to rearrange the efficiency equation to find a missing quantity, e.g. useful energy = efficiency × total energy. Always check whether the efficiency is given as a decimal or a percentage.
你需要能够转换效率方程求解未知量，例如有用能量 = 效率 × 总能量。务必确认效率给定的是小数还是百分数。
7. Electrical Equations (Ohm’s Law, Power, Charge) | 电学公式（欧姆定律、功率、电荷）
V = I × R
Ohm’s law states that potential difference V in volts (V) equals current I in amperes (A) multiplied by resistance R in ohms (Ω). This holds for ohmic conductors at a constant temperature.
欧姆定律指出，电势差 V（伏特，V）等于电流 I（安培，A）乘以电阻 R（欧姆，Ω）。该定律适用于温度恒定的欧姆导体。
P = I × V
Electrical power P in watts (W) is the product of current I (A) and potential difference V (V). Using Ohm’s law, you can also write P = I² × R or P = V² / R, which are variations useful when certain quantities are unknown.
电功率 P（瓦特，W）是电流 I（A）与电势差 V（V）的乘积。结合欧姆定律，还可写出 P = I² × R 或 P = V² / R，这些变式在部分量未知时很有用。
Q = I × t
Charge Q in coulombs (C) is the current I (A) flowing for a time t (s). This equation links electricity to the number of electrons passing a point.
电荷 Q（库仑，C）等于电流 I（A）与通电时间 t（s）的乘积。该方程将电流与流经某点的电子数目联系起来。
In most WJEC problems, you will need to select the appropriate form of the power equation. Remember that the fuse rating in a plug is chosen based on the normal operating current, usually calculated from the power and voltage of the appliance.
在大多数 WJEC 题目中，你需要选择合适的功率方程。请记住，插头中保险丝的额定值是根据正常工作电流选定的，通常由电器的功率和电压计算得出。
8. Transformer Equation | 变压器公式
Vₚ / Vₛ = Nₚ / Nₛ
For an ideal transformer, the ratio of the primary voltage Vₚ to the secondary voltage Vₛ equals the ratio of the number of turns on the primary coil Nₚ to the number of turns on the secondary coil Nₛ. Both V and N are unitless ratios in this relationship, but voltage is measured in volts (V).
对于理想变压器，初级电压 Vₚ 与次级电压 Vₛ 之比等于初级线圈匝数 Nₚ 与次级线圈匝数 Nₛ 之比。在这个关系式中，V 和 N 的比值无单位，但电压的单位是伏特（V）。
Assuming 100% efficiency, the power in the primary circuit equals the power in the secondary circuit, giving Vₚ Iₚ = Vₛ Iₛ. This means a step-up transformer (Vₛ > Vₚ) has a smaller secondary current, and vice versa.
假设效率为 100%，则初级电路功率等于次级电路功率，即 Vₚ Iₚ = Vₛ Iₛ。这意味着升压变压器（Vₛ > Vₚ）的次级电流较小，反之亦然。
Transformers only work with alternating current (AC). You are expected to apply these equations to calculate missing voltage, turns or current in WJEC examination questions.
变压器只能使用交流电（AC）。在 WJEC 考试中，你需应用这些公式计算缺失的电压、匝数或电流。
9. Wave Equation | 波动方程
v = f × λ
Wave speed v in metres per second (m/s) is the product of frequency f in hertz (Hz) and wavelength λ in metres (m). This equation applies to all types of waves, including sound, light and water waves.
波速 v（米/秒，m/s）等于频率 f（赫兹，Hz）与波长 <
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