📚 Year 10 AQA Science: Quick Reference Handbook of Formulas and Theorems | Year 10 AQA 科学：公式定理速查手册
This handbook provides a concise revision guide covering the essential formulas, laws, and theorems required for Year 10 AQA Science (GCSE Combined Science or separate sciences). It is designed for quick reference before exams, helping students recall the key quantitative relationships and fundamental principles across Physics, Chemistry, and Biology.
本手册提供了一份简明复习指南，涵盖 Year 10 AQA 科学（GCSE 联合科学或单独科学）所需的基本公式、定律和定理。旨在方便考试前快速查阅，帮助学生回忆物理、化学和生物中关键的定量关系和基本原理。
1. Physics - Equations of Motion | 物理 – 运动学方程
In GCSE Physics, motion with constant acceleration is described by the SUVAT equations. These equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
在 GCSE 物理中，匀加速直线运动可由 SUVAT 方程描述。这些方程涉及位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。
v = u + at
This equation directly links final velocity to initial velocity and acceleration over time. It is often used when the displacement is not needed.
该方程直接将末速度与初速度、加速度和时间联系起来。通常在不需要位移时使用。
s = ut + ½ at²
This equation calculates displacement when the initial velocity, acceleration, and time are known. The term ½ at² accounts for the additional distance covered due to acceleration.
当已知初速度、加速度和时间时，可用该方程计算位移。项 ½ at² 表示由于加速而额外移动的距离。
v² = u² + 2as
This equation is useful when time is not given or required. It links final velocity to initial velocity, acceleration, and displacement.
当未给出或不需要时间时，可使用该方程。它将末速度与初速度、加速度和位移联系起来。
s = (v + u)/2 × t
. It is derived from the fact that average velocity = (v + u)/2 for constant acceleration.
该方程利用平均速度求位移。它源于对于匀加速度，平均速度 = (v + u)/2。
2. Physics - Forces and Newton's Laws | 物理 – 力与牛顿定律
Newton's first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a resultant force. This principle of inertia explains why seatbelts are needed in a car.
牛顿第一定律指出，一切物体总保持静止或匀速直线运动状态，除非有合力作用使其改变。这一惯性原理解释了为什么汽车中需要安全带。
F = ma
Newton's second law: the resultant force (F) on an object is equal to its mass (m) multiplied by its acceleration (a). This explains why a heavier object requires a greater force to achieve the same acceleration.
牛顿第二定律：物体所受合力 (F) 等于其质量 (m) 乘以加速度 (a)。这解释了为什么更重的物体需要更大的力才能获得相同的加速度。
Newton's third law: for every action force, there is an equal and opposite reaction force. These forces act on different objects and are of the same type.
牛顿第三定律：每一个作用力都有一个大小相等、方向相反的反作用力。这两个力作用在不同物体上，且属于同种类型。
W = m g
Weight (W) is the force due to gravity on an object's mass (m). On Earth, the gravitational field strength g is approximately 9.8 N/kg, often rounded to 10 N/kg in calculations.
重量 (W) 是由于重力作用在物体质量 (m) 上的力。在地球上，重力场强 g 约为 9.8 N/kg，在计算中通常取 10 N/kg。
F = k e
Hooke's Law: the extension (e) of a spring is directly proportional to the force (F) applied, up to the limit of proportionality. The spring constant k indicates the stiffness of the spring.
胡克定律：在比例限度内，弹簧的伸长量 (e) 与施加的力 (F) 成正比。弹簧常数 k 表示弹簧的劲度系数。
3. Physics - Energy, Work and Power | 物理 – 能量、功和功率
Eₖ = ½ m v²
Kinetic energy (Eₖ) is the energy of motion. An object of mass m moving at velocity v possesses kinetic energy equal to half the product of mass and the square of its velocity.
动能 (Eₖ) 是运动的能量。质量为 m、速度为 v 的物体具有的动能等于质量与速度平方乘积的一半。
Eₚ = m g h
Gravitational potential energy (Eₚ) is the energy stored in an object lifted through a height h against gravity. It depends on mass, gravitational field strength, and height.
重力势能 (Eₚ) 是物体克服重力被举高到高度 h 后储存的能量。它取决于质量、重力场强和高度。
W = F s
Work done (W) is the energy transferred when a force (F) moves an object through a distance (s) in the direction of the force. Work is measured in joules (J).
做功 (W) 是指力 (F) 使物体沿力的方向移动一段距离 (s) 所转移的能量。功以焦耳 (J) 为单位。
P = W / t = ΔE / t
Power (P) is the rate of doing work or the rate of energy transfer. It is calculated as work done or energy transferred divided by time.
功率 (P) 是做功或能量转移的速率。它等于所做的功或转移的能量除以时间。
Efficiency = Useful output energy / Total input energy
Efficiency is a measure of how well a device transfers energy without wasting it. It can be expressed as a ratio or a percentage by multiplying by 100.
效率是衡量设备转移能量而不浪费能量的指标。可用比值表示，或乘以 100 表示为百分比。
4. Physics - Electricity and Circuit Formulas | 物理 – 电学与电路公式
The key formulas relating charge, current, voltage, resistance, and power for GCSE circuits are summarised below. These are essential for analysing both series and parallel circuits.
以下总结了 GCSE 电路中关于电荷、电流、电压、电阻和功率的关键公式。这些对于分析串联和并联电路至关重要。
| Formula | Description |
|---|---|
| Q = I t | Charge (C) = current (A) × time (s) |
| V = I R | Voltage (V) = current (A) × resistance (Ω) |
| P = V I | Power (W) = voltage (V) × current (A) |
| P = I² R | Power dissipated in a resistor |
| E = V I t | Energy transferred (J) = voltage × current × time |
| Rtotal = R₁ + R₂ + … | Resistors in series |
| 1/Rtotal = 1/R₁ + 1/R₂ + … | Resistors in parallel |
Note that in series circuits, current is the same everywhere, and the supply voltage is shared. In parallel circuits, each branch receives the full supply voltage, and current divides.
请注意，在串联电路中，各处电流相同，电源电压被分配；在并联电路中，每条支路承受全部电源电压，电流则分流。
5. Physics - Waves and Optics | 物理 – 波与光学
v = f λ
th λ. All electromagnetic waves travel at the same speed in a vacuum, about 3.0 × 10⁸ m/s.
波速方程：波速 v 等于频率 f 与波长 λ 的乘积。所有电磁波在真空中传播速度相同，约为 3.0 × 10⁸ m/s。
T = 1 / f
The period T is the time taken for one complete wave cycle. It is the reciprocal of the frequency.
周期 T 是完成一个完整波循环所需的时间。它是频率的倒数。
n = sin i / sin r
Snell's law relates the angle of incidence i and angle of refraction r when light passes from one medium to another. The refractive index n is a property of the material.
斯涅尔定律关联了光从一种介质进入另一种介质时的入射角 i 和折射角 r。折射率 n 是材料的属性。
sin c = 1 / n
When light travels from a denser medium into air, the critical angle c can be found using this equation. If the angle of incidence exceeds c, total internal reflection occurs.
当光从光密介质射入空气时，可用该方程求出临界角 c。若入射角大于 c，则发生全内反射。
6. Chemistry - Moles and Quantitative Chemistry | 化学 – 摩尔与定量化学
n = m / Mr
The number of moles n can be calculated from the mass m of a substance and its relative formula mass Mr. This is fundamental to all stoichiometric calculations.
物质的量 n 可由物质的质量 m 及其相对式量 Mr 计算。这是所有化学计量计算的基础。
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