📚 Year 12 SQA Sciences: Quick Reference Formula & Theorem Handbook | SQA Year 12 科学公式定理速查手册
This handbook brings together the key formulae, theorems, and principles from SQA Higher Physics, Chemistry, and Biology at Year 12 level. Each section provides a rapid reference with clear expressions, followed by paired Chinese translations for bilingual revision.
本手册汇集了 Year 12 SQA 高阶物理、化学、生物考试中最核心的公式、定理和原理。每一部分提供清晰表达式，并附有中英对照，方便快速查阅与双语复习。
1. Motion and Forces | 运动与力
For constant linear acceleration, the following kinematic equations are used:
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u+v)t
（常加速度直线运动公式：末速度、位移与时间的关系。）
Newton's second law of motion links net force, mass, and acceleration:
F = ma
牛顿第二定律将合外力、质量与加速度联系起来。
Weight is the gravitational force acting on a mass:
W = mg
重力是作用在物体上的引力，大小为质量乘以重力场强度。
For a body on a slope at equilibrium or accelerating, the component of weight parallel to the plane is mg sinθ, and the perpendicular component is mg cosθ. Friction may be accounted for, but the Higher course emphasises resultant force analysis.
物体在斜面上时，重力沿斜面分量为 mg sinθ，垂直分量为 mg cosθ。课程重点在于用合力进行分析，常忽略摩擦细节。
2. Momentum and Energy | 动量与能量
Linear momentum is the product of mass and velocity:
p = mv
线动量等于质量与速度的乘积。
Impulse equals the change in momentum and is also the product of average force and contact time:
Ft = mv − mu
冲量等于动量的变化，也等于平均力乘以作用时间。
Kinetic energy of a moving object:
Eₖ = ½mv²
物体的动能公式。
Gravitational potential energy near Earth's surface:
Eₚ = mgh
地表附近的重力势能。
Work done by a constant force over a displacement:
W = Fd cosθ
恒力做功等于力在位移方向的分量乘以位移。
Power is the rate of energy transfer or work done:
P = E/t = W/t
功率表示能量转化或做功的快慢。
The principle of conservation of energy states that total energy in a closed system remains constant, transforming between kinetic, potential, and heat forms but never lost.
能量守恒定律指出，封闭系统内的总能量保持不变，只从一种形式转化为另一种形式。
3. Circular Motion and Gravitation | 圆周运动与引力
Angular velocity relates angular displacement to time:
ω = θ/t
角速度是角度随时间的变化率。
Linear speed and angular speed are connected by the radius:
v = rω
线速度与角速度通过半径关联。
Centripetal acceleration is directed towards the centre of the circle:
a = v²/r = rω²
向心加速度指向圆心，可用线速度或角速度表达。
Centripetal force required to keep an object moving in a circle:
F = mv²/r = mrω²
维持圆周运动所需的向心力公式。
Newton's law of universal gravitation for two point masses:
F = G M m / r²
万有引力定律适用于两质点间的作用力。
The gravitational field strength at a point depends on the mass of the source and the distance from it:
g = GM / r²
重力场强度由中心天体质量与距离平方决定。
4. Electricity and Circuits | 电学与电路
Current, charge, and time are related by:
I = Q/t
电流等于单位时间内流过导体截面的电荷量。
Ohm's law for a resistor at constant temperature:
V = IR
欧姆定律表示电压与电流成正比，电阻恒定。
Resistors in series and parallel combine as:
Rtotal = R₁ + R₂ + ...
1/Rtotal = 1/R₁ + 1/R₂ + ...
串联电阻总阻值为各电阻之和；并联电阻总阻值的倒数为各电阻倒数之和。
Electrical power can be expressed in several forms:
P = IV = I²R = V²/R
电功率的多种表达式，适用于纯电阻电路。
A real cell has internal resistance r; the terminal voltage V is lower than the emf E when current flows:
E = V + Ir
真实电池有内阻，端电压等于电动势减去内阻压降。
Capacitance is charge stored per unit potential difference:
C = Q/V
电容定义为单位电压下储存的电荷量。
Energy stored in a charged capacitor:
E = ½QV = ½CV²
电容器储存的能量公式。
Potential divider output voltage:
Vout = (R₂ / (R₁+R₂)) × Vin
分压器输出电压由两个电阻的比值决定。
5. Waves and Optics | 波与光学
The wave equation relates speed, frequency, and wavelength:
v = f λ
波速等于频率与波长的乘积。
Period is the reciprocal of frequency:
T = 1/f
周期是频率的倒数。
Snell's law of refraction between two media:
n = sin i / sin r
折射定律：折射率等于入射角正弦与折射角正弦之比。
Refractive index can also be expressed as the ratio of speeds:
n = c / v
绝对折射率等于真空中光速与介质中光速之比。
Critical angle for total internal reflection:
sin c = 1/n
全反射临界角的正弦值等于折射率的倒数。
For a diffraction grating, constructive interference occurs at angles given by:
d sinθ = nλ
光栅方程：光栅间距乘以衍射角的正弦等于整数倍波长。
Path difference for constructive interference is nλ, and for destructive interference it is (n + ½)λ.
相长干涉的光程差为整数倍波长，相消干涉的光程差为半波长的奇数倍。
6. Quantum and Particles | 量子与粒子
A photon's energy is directly proportional to its frequency:
E = hf
光子能量与频率成正比，比例常数为普朗克常数。
Using the wave equation, this becomes:
E = hc/λ
光子能量也用波长表达。
Einstein's photoelectric equation accounts for the work function of the metal:
hf = φ + Eₖ(max)
爱因斯坦光电效应方程：入射光子能量等于逸出功加上最大动能。
The de Broglie wavelength of a moving particle shows wave–particle duality:
λ = h / p
德布罗意波长公式将粒子的动量与波长联系起来。
7. Stoichiometry and the Mole | 化学计量与摩尔
The number of moles from a given mass:
n = m / M
物质摩尔数等于质量除以摩尔质量。
The number of moles from solution concentration and volume:
n = cV
摩尔数也等于溶液浓度乘以体积（注意单位统一为升）。
Molar volume of a gas at room temperature and pressure (RTP) is used to find volume:
V (dm³) = n × 24
在室温和常压下，气体摩尔体积约为 24 dm³ mol⁻¹。
Percentage yield of a reaction compares actual to theoretical yield:
% yield = (actual mass / theoretical mass) × 100
产率衡量实际产量与理论产量的接近程度。
Atom economy evaluates how much of the reactants end up in the desired product:
% atom economy = (molar mass of desired product / total molar mass of reactants) × 100
原子经济性评估反应物中有多少原子转化为目标产物。
8. Enthalpy and Equilibrium | 焓变与平衡
Enthalpy change from calorimetry data uses q = mcΔT:
q = mcΔT
通过量热实验计算热量变化。
The molar enthalpy change is then determined, with sign indicating exothermic or endothermic:
ΔH = −q / n
摩尔焓变等于负的热量除以摩尔数（放热为负）。
Hess's law states that the total enthalpy change for a reaction is independent of the pathway taken. It allows enthalpy changes to be calculated from known data.
盖斯定律指出，化学反应的总焓变只与始态和终态有关，与途径无关。
The equilibrium constant Kc for a general reaction aA + bB ⇌ cC + dD is:
Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ
平衡常数表达式，各物质浓度以化学计量数为指数。
9. Acids, Bases and pH | 酸、碱与pH
pH is defined as the negative logarithm of the hydrogen ion concentration:
pH = −log[H⁺]
pH 定义为氢离子浓度的负对数。
To find the concentration from pH:
[H⁺] = 10⁻ᵖᴴ
由 pH 反算氢离子浓度。
The ionic product of water at 25 °C is:
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴
水的离子积常数，为 1.0×10⁻¹⁴。 Published by TutorHao | Year 12 Science Revision Series | aleveler.com
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