📚 SQA National 5 Science Quick Reference Handbook: Formulas & Theorems | SQA 国家5级科学公式定理速查手册
This handbook brings together the essential formulas, laws and theorems needed for Year 11 SQA Science, covering physics and chemistry. Use it as a fast revision checklist to strengthen your calculation skills and conceptual understanding before assessments.
本手册汇集了 Year 11 SQA 科学（物理与化学）所需的关键公式、定律和定理。它可作为快速复习清单，帮助你在测评前巩固计算技巧和概念理解。
1. Kinematics Equations | 运动学公式
For objects moving in a straight line with constant acceleration, three equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).
对于匀加速直线运动，以下三个方程将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系起来。
v = u + at: Use this to find final velocity after a known time when initial velocity and acceleration are constant.
v = u + at: 当初速度和加速度恒定时，用来求经过已知时间后的末速度。
s = ut + ½at²: Calculates displacement. The term ½at² accounts for the extra distance covered due to acceleration.
s = ut + ½at²: 计算位移。½at² 项表示加速度带来的额外位移。
v² = u² + 2as: Relates final velocity directly to displacement without needing time.
v² = u² + 2as: 直接关联末速度与位移，不涉及时间。
2. Newton’s Laws of Motion | 牛顿运动定律
First Law (Inertia): An object remains at rest or moves with constant velocity unless acted upon by an unbalanced force.
第一定律（惯性）: 除非受到非平衡力，物体将保持静止或匀速直线运动。
Second Law: The net force equals mass times acceleration. This is the core equation for analysing dynamics: F = ma.
第二定律: 合力等于质量乘加速度。这是分析动力学的核心方程：F = ma。
Third Law: If object A exerts a force on object B, then B exerts an equal and opposite force on A. These forces act on different bodies.
第三定律: 若物体 A 对 B 施加力，则 B 同时对 A 施加大小相等、方向相反的力。这两个力作用在不同物体上。
3. Weight, Mass and Gravitational Field Strength | 重量、质量与引力场强
Weight equation: W = mg. Weight (W) is the gravitational force on a mass (m), measured in newtons (N). On Earth, the gravitational field strength g ≈ 9.8 N/kg.
重量公式: W = mg。重量 W 是作用在质量 m 上的引力，单位牛顿 (N)。地球表面引力场强 g 约为 9.8 N/kg。
Mass is a scalar quantity and does not change with location; weight is a vector and varies with g.
质量是标量，不随地点变化；重量是矢量，随 g 改变。
4. Work, Energy and Power | 功、能与功率
Work done: W = Fd, where force F moves an object through distance d in the direction of the force. Work is measured in joules (J).
功: W = Fd，力 F 沿其方向使物体移动距离 d，功的单位为焦耳 (J)。
Gravitational potential energy: Ep = mgh. Lifting a mass m through a vertical height h increases its stored energy.
重力势能: Ep = mgh。将质量 m 竖直提升 h 高度会增加其储存能量。
Kinetic energy: Ek = ½mv². Moving objects possess energy proportional to mass and the square of speed.
动能: Ek = ½mv²。运动物体的能量与质量及速度的平方成正比。
Power: P = E/t (or P = W/t). Power is the rate of energy transfer, measured in watts (W). 1 W = 1 J/s.
功率: P = E/t（或 P = W/t）。功率是能量转移的速率，单位瓦特 (W)。1 W = 1 J/s。
5. Ohm’s Law and Electrical Power | 欧姆定律与电功率
Ohm’s Law: V = IR. For an ohmic conductor at constant temperature, potential difference V (volts) equals current I (amps) multiplied by resistance R (ohms).
欧姆定律: V = IR。对于恒温下的欧姆导体，电压 V（伏特）等于电流 I（安培）乘以电阻 R（欧姆）。
Electrical power: P = IV = I²R = V²/R. Choose the form that matches the data you have.
电功率: P = IV = I²R = V²/R。根据已知数据选择相应形式。
Energy transferred in a circuit can be calculated using E = Pt or E = IVt.
电路中的能量转移可用 E = Pt 或 E = IVt 计算。
6. Series and Parallel Circuits | 串联与并联电路
Series circuits: Current is the same at all points: I₁ = I₂ = I_total. Voltage splits: V_total = V₁ + V₂. Total resistance adds: R_total = R₁ + R₂.
串联电路: 各处电流相等：I₁ = I₂ = I_total。电压分配：V_total = V₁ + V₂。总电阻相加：R_total = R₁ + R₂。
Parallel circuits: Voltage across each branch is equal to the supply voltage. Current splits: I_total = I₁ + I₂. Total resistance is found from the reciprocal sum: 1/R_total = 1/R₁ + 1/R₂.
并联电路: 各支路电压等于电源电压。电流分流：I_total = I₁ + I₂。总电阻由倒数求和得出：1/R_total = 1/R₁ + 1/R₂。
7. Wave Properties | 波的特性
Wave speed equation: v = fλ. Speed v (m/s) equals frequency f (Hz) multiplied by wavelength λ (m). This applies to all types of waves.
波速公式: v = fλ。波速 v（米/秒）等于频率 f（赫兹）乘波长 λ（米）。适用于所有波。
Period and frequency: T = 1/f. The period T is the time for one complete wave cycle.
周期与频率: T = 1/f。周期 T 是完成一个完整波形所需的时间。
Distance, speed and time: d = vt can also be used for waves travelling through a medium.
路程、速率与时间: 波在介质中传播时也可用 d = vt。
In refraction, frequency remains constant; wavelength and speed change.
折射过程中，频率保持不变，波长和波速会改变。
8. Gas Laws and the Kinetic Model | 气体定律与分子动理论
Boyle’s Law (constant temperature): p₁V₁ = p₂V₂. Pressure and volume are inversely proportional.
波义耳定律（恒温）: p₁V₁ = p₂V₂。压强与体积成反比。
Charles’ Law (constant pressure): V₁ / T₁ = V₂ / T₂. Volume is directly proportional to absolute temperature (in kelvin).
查理定律（恒压）: V₁ / T₁ = V₂ / T₂。体积与绝对温度（开尔文）成正比。
Gay-Lussac’s Law (constant volume): p₁ / T₁ = p₂ / T₂. Pressure is directly proportional to absolute temperature.
盖-吕萨克定律（恒容）: p₁ / T₁ = p₂ / T₂。压强与绝对温度成正比。
Combined gas law: p₁V₁/T₁ = p₂V₂/T₂. This is valid for a fixed mass of gas.
组合气体定律: p₁V₁/T₁ = p₂V₂/T₂。适用于一定质量的气体。
The kinetic model explains these behaviours using the motion of particles: temperature relates to average kinetic energy, and pressure arises from collisions with container walls.
分子动理论用粒子运动解释这些行为：温度与平均动能相关，压强由粒子撞击容器壁产生。
9. Mole Calculations in Chemistry | 化学中的摩尔计算
Mass and moles: n = m / M, where n is the number of moles (mol), m is mass (g), and M is the gram formula mass (g/mol). Alternatively, m = n × M.
质量与摩尔: n = m / M，n 为物质的量（摩尔），m 为质量（克），M 为克式量（g/mol）。也可写作 m = n × M。
Gram formula mass is the relative formula mass expressed in grams.
克式量是以克为单位的相对式量。
The Avogadro constant L = 6.02 × 10²³ mol
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