📚 Year 10 WJEC Science: Formula & Theorem Quick Reference Handbook | Year 10 WJEC 科学：公式定理速查手册
This handbook is your essential quick-reference guide to the key formulas, theorems and equations you will encounter in Year 10 WJEC Science. Whether you are tackling Physics, Chemistry or Biology, having these relationships at your fingertips will boost your confidence in calculations, practical work and examinations. All formulas are given in standard notation, with SI units highlighted throughout. Use this resource alongside your class notes and past papers for effective revision.
本手册是你 Year 10 WJEC 科学课程中关键公式、定理和方程的基本速查指南。无论你面对的是物理、化学还是生物学，随时掌握这些关系将提升你在计算、实验操作和考试中的信心。所有公式均以标准符号表示，并始终标注国际单位制。请将本书与你的课堂笔记和历年试题配合使用，以实现高效复习。
1. Speed, Distance and Time | 速度、距离和时间
Speed is a measure of how fast an object is moving. The relationship between average speed, distance travelled and time taken is one of the most fundamental in physics.
速度是衡量物体运动快慢的量。平均速度、移动距离和所用时间之间的关系是物理学中最基础的关系之一。
The core equation is:
核心方程为：
v = s / t
where v is speed, s is the distance travelled in a straight line, and t is the time taken. In SI units, speed is measured in metres per second (m/s), distance in metres (m) and time in seconds (s).
其中 v 为速度，s 为直线移动距离，t 为所用时间。在国际单位制中，速度单位为米每秒 (m/s)，距离为米 (m)，时间为秒 (s)。
To calculate distance: s = v × t. To calculate time: t = s / v. Always ensure units are consistent – convert minutes to seconds and kilometres to metres before substituting into the formula.
计算距离：s = v × t。计算时间：t = s / v。务必保持单位一致——在代入公式前，应先将分钟转换为秒、千米转换为米。
2. Acceleration and Newton's Second Law | 加速度与牛顿第二定律
Acceleration describes how quickly the velocity of an object changes. It is defined as the rate of change of velocity.
加速度描述物体速度变化的快慢，其定义为速度的变化率。
a = (v - u) / t
where a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s) and t is time (s). Deceleration is simply negative acceleration.
式中 a 为加速度 (m/s²)，v 为末速度 (m/s)，u 为初速度 (m/s)，t 为时间 (s)。减速即为负的加速度。
Newton's Second Law links force, mass and acceleration. The formula is fundamental to explaining how objects move.
牛顿第二定律将力、质量和加速度联系起来。该公式是解释物体运动的基础。
F = m × a
where F is the resultant force in newtons (N), m is mass in kilograms (kg) and a is acceleration in m/s². This tells us that a larger force produces a greater acceleration, and a more massive object accelerates less for the same force.
式中 F 为合力，单位为牛顿 (N)，m 为质量 (kg)，a 为加速度 (m/s²)。该公式表明：力越大，加速度越大；在相同力作用下，质量越大的物体加速度越小。
3. Weight, Mass and Gravity | 重量、质量与重力
Weight is the force acting on an object due to gravity. It is directly proportional to mass.
重量是由于重力作用在物体上的力，它与质量成正比。
W = m × g
where W is weight in newtons (N), m is mass in kilograms (kg) and g is the gravitational field strength. On Earth's surface, g ≈ 9.8 N/kg (often approximated as 10 N/kg in WJEC calculations).
式中 W 为重量 (N)，m 为质量 (kg)，g 为引力场强度。在地球表面，g 约等于 9.8 N/kg（在 WJEC 计算中常用 10 N/kg 近似）。
Note that mass is a measure of the amount of matter and does not change with location, while weight varies with the strength of gravity. Be careful not to confuse mass and weight in extended writing questions.
注意，质量是物体所含物质的量，不随位置改变，而重量随引力强弱变化。在长篇作答中切勿混淆质量与重量。
4. Work Done, Energy Transfer and Power | 做功、能量转移与功率
Work is done when a force causes an object to move in the direction of the force. The amount of work done equals the energy transferred.
当力使物体沿力的方向移动时便做了功。做功的多少等于转移的能量。
W = F × d
where W is work done in joules (J), F is the force applied in newtons (N) and d is the distance moved in the direction of the force in metres (m).
式中 W 为做功 (J)，F 为作用力 (N)，d 为物体沿力方向移动的距离 (m)。
Power is the rate at which work is done or energy is transferred. The equation is:
功率是做功或能量转移的速率，其公式为：
P = E / t
or P = W / t, where P is power in watts (W), E or W is energy or work in joules (J), and t is time in seconds (s). A watt is equivalent to one joule per second.
或 P = W / t，式中 P 为功率 (W)，E 或 W 为能量或功 (J)，t 为时间 (s)。一瓦特相当于每秒一焦耳。
Efficiency can be expressed as a percentage:
效率可用百分比表示：
Efficiency = (useful output energy / total input energy) × 100%
onship also applies to power: Efficiency = (useful power output / total power input) × 100%.
该关系也适用于功率：效率 = (有用输出功率 / 总输入功率) × 100%。
5. Kinetic Energy and Gravitational Potential Energy | 动能与重力势能
Kinetic energy (Eₖ) is the energy possessed by a moving object. Gravitational potential energy (Eₚ) is the energy stored in an object because of its position in a gravitational field.
动能 (Eₖ) 是运动物体具有的能量。重力势能 (Eₚ) 是物体因在引力场中的位置而储存的能量。
Eₖ = ½ m v²
where m is mass (kg) and v is speed (m/s). The unit is the joule (J). Notice that doubling the speed quadruples the kinetic energy.
式中 m 为质量 (kg)，v 为速度 (m/s)，单位为焦耳 (J)。请注意，速度加倍会使动能增加为四倍。
Eₚ = m g h
where m is mass (kg), g is gravitational field strength (N/kg) and h is the change in height (m). This formula assumes uniform gravitational field and is valid near the Earth's surface.
式中 m 为质量 (kg)，g 为引力场强度 (N/kg)，h 为高度变化 (m)。该公式假设均匀引力场，适用于地球表面附近。
In many problems, energy is transferred between these two stores, and you may assume no energy is lost if told there is negligible friction or air resistance.
在许多问题中，能量在这两种储存之间相互转换。若题目说明摩擦或空气阻力可忽略不计，则可假定无能量损失。
6. Ohm's Law and Electrical Resistance | 欧姆定律与电阻
Ohm's Law relates potential difference (voltage), current and resistance for an ohmic conductor at constant temperature.
欧姆定律描述了恒温下欧姆导体两端电压、通过电流和电阻之间的关系。
V = I × R
where V is potential difference in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω).
式中 V 为电势差 (V)，I 为电流 (A)，R 为电阻 (Ω)。
From this you can rearrange to find resistance: R = V / I, or current: I = V / R. Components that do not follow Ohm's Law include diodes and filament lamps, whose resistance changes with temperature.
由此可变形求得电阻：R = V / I，或电流：I = V / R。不遵循欧姆定律的元件包括二极管和灯丝灯泡，它们的电阻随温度变化。
Always check your units: if current is given in milliamperes (mA), convert to amperes by dividing by 1000 before using the equation.
请务必检查单位：若电流以毫安 (mA) 给出，应先除以 1000 转换为安培再代入公式。
7. Electrical Power and Energy Transferred | 电功率与电能转移
Electrical power is the rate at which electrical energy is transferred by a circuit. The two most commonly used formulas are:
电功率是电路转移电能的速率。最常用的两个公式如下：
P = I × V
where P is power in watts (W), I is current in amperes (A) and V is potential difference in volts (V).
式中 P 为功率 (W)，I 为电流 (A)，V 为电势差 (V)。
P = I² × R
This alternative form is obtained by combining Ohm's Law with P = I V. It is especially useful when the current and resistance are known.
将欧姆定律与 P = I V 结合即可得到此形式。当已知电流和电阻时，该式尤为实用。
Energy transferred by an electrical device can be calculated using:
用电器消耗的电能可通过下式计算：
E = P × t
where E is energy in joules (J), P is power in watts (W) and t ger amounts of energy, kilowatt-hour (kWh) may be used; remember that 1 kWh = 3.6 × 10⁶ J.
式中 E 为能量 (J)，P 为功率 (W)，t 为时间 (s)。对于较大的能量值，可使用千瓦时 (kWh)；注意 1 kWh = 3.6 × 10⁶ J。
8. Wave Speed, Frequency and Wavelength | 波速、频率与波长
The speed of a wave is related to its frequency and wavelength through the universal wave equation. This applies to sound waves, water waves and electromagnetic waves.
波的速度与其频率和波长通过普适波方程相关联。该公式适用于声波、水波和电磁波。
v = f × λ
where v is wave speed in metres per second (m/s), f is frequency in hertz (Hz) and λ (lambda) is the wavelength in metres (m).
式中 v 为波速 (m/s)，f 为频率 (Hz)，λ (兰姆达) 为波长 (m)。
To find frequency: f = v / λ. To find wavelength: λ = v / f. Remember that frequency refers to the number of complete waves passing a point per second, while wavelength is the distance between two successive identical points on a wave, such as crest to crest.
求频率：f = v / λ；求波长：λ = v / f。请记住：频率指每秒通过某点的完整波的数量，波长则是波上两个相邻相同点（如波峰到波峰）之间的距离。
9. Density | 密度
Density is a measure of how much mass is contained in a given volume. It is a characteristic property of materials and helps identify substances.
密度是衡量单位体积内包含多少质量的量。它是材料的一种特征性质，有助于鉴别物质。
ρ = m / V
where ρ (rho) is density in kilograms per cubic metre (kg/m³), m is mass in kilograms (kg) and V is volume in cubic metres (m³). In the laboratory, density is often also expressed in g/cm³.
式中 ρ (柔) 为密度 (kg/m³)，m 为质量 (kg)，V 为体积 (m³)。在实验中，密度常以 g/cm³ 表示。
rregular solids, use the displacement method and the formula for volume of a cylinder or sphere as needed.
换算关系：1 g/cm³ = 1000 kg/m³。对于规则固体，体积可由长×宽×高计算；对于不规则固体，可采用排水法，并根据需要运用圆柱体或球体体积公式。
10. The Mole and Molar Mass | 摩尔与摩尔质量
The mole is the unit for amount of substance in chemistry. It provides a bridge between the microscopic world of atoms and the macroscopic world of grams and kilograms.
摩尔是化学中物质的量的单位。它在原子等微观世界与克/千克等宏观世界之间架起了桥梁。
n = m / M
where n is the amount of substance in moles (mol), m is the mass of the substance in grams (g) and M is the molar mass in grams per mole (g/mol). Molar mass is numerically equal to the relative atomic mass (Aᵣ) or relative formula mass (Mᵣ) of the substance.
式中 n 为物质的量 (mol)，m 为物质的质量 (g)，M 为摩尔质量 (g/mol)。摩尔质量在数值上等于该物质的相对原子质量 (Aᵣ) 或相对式量 (Mᵣ)。
To find mass: m = n × M. To find molar mass: M = m / n. You will often use this relationship to convert between mass and moles in chemical equations and titrations.
求质量：m = n × M；求摩尔质量：M = m / n。在化学方程式和滴定计算中，常需利用此关系在质量和摩尔之间进行转换。
11. Concentration of Solutions | 溶液浓度
Concentration expresses how much solute is dissolved in a given volume of solution. In WJEC Chemistry, both mol/dm³ and g/dm³ units are used.
浓度表示一定体积溶液中溶解了多少溶质。在 WJEC 化学中，mol/dm³ 和 g/dm³ 两种单位都会用到。
For molar concentration:
摩尔浓度公式：
c = n / V
where c is concentration in mol/dm³, n is amount of solute in mol and V
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