📚 Year 10 CIE Science: Formula & Theorem Quick Reference Guide | Year 10 CIE 科学：公式定理速查手册
This quick reference handbook gathers all essential formulas, equations and key theorems from the Year 10 CIE Co-ordinated Sciences syllabus. It is designed to help you revise efficiently and apply the right relationship in every calculation. Use it alongside past papers to build speed and accuracy.
本速查手册汇集了 Year 10 CIE 协调科学课程中所有重要公式、方程和关键定理，旨在帮助你高效复习，并在每一道计算题中准确选用正确的关系式。建议搭配历年真题使用，以提升解题速度与准确度。
1. Motion and Forces | 运动与力
Average speed is the total distance travelled divided by the total time taken. It tells you how fast an object moves overall.
v = d / t
平均速度等于总路程除以总时间，表示物体运动的整体快慢程度。
Acceleration is the rate at which velocity changes. It can be a positive speed-up or a negative slow-down.
a = (v - u) / t
加速度是速度变化的快慢程度。当末速度 v 大于初速度 u 时物体加速，反之减速。
Newton's second law states that the resultant force acting on an object equals its mass multiplied by its acceleration.
F = m a
牛顿第二定律：作用在物体上的合力等于物体的质量乘以加速度。力 (F) 的单位是牛顿 (N)，质量 (m) 的单位是千克 (kg)，加速度 (a) 的单位是米每二次方秒 (m/s²)。
Weight is the gravitational force exerted by a planet on an object. It depends on the local gravitational field strength g.
W = m g
重量是行星对物体施加的引力，在地球表面附近 g ≈ 9.8 N/kg（常简化为 10 N/kg）。
Momentum is a measure of the 'quantity of motion' and is conserved in isolated systems.
p = m v
动量是物体质量和速度的乘积，在封闭系统内动量守恒。
2. Energy, Work and Power | 能量、功与功率
Kinetic energy (KE) is the energy an object possesses due to its motion.
Eₖ = ½ m v²
动能等于物体质量的一半乘以速度的平方。
Gravitational potential energy (GPE) is stored by an object raised above a reference level.
ΔEₚ = m g Δh
重力势能的变化等于质量 (m) 乘以重力场强 (g) 再乘以高度变化 (Δh)。
Work done is the energy transferred when a force moves an object through a distance in the direction of the force.
W = F d
功等于力与沿力方向移动距离的乘积。1 焦耳 (J) = 1 N·m。
Power is the rate at which energy is transferred or work is done.
P = E / t or P = W / t
功率是能量转换或做功的快慢，单位瓦特 (W) 等于焦耳每秒 (J/s)。
Efficiency compares useful output energy (or power) to total input energy (or power).
Efficiency = (useful output / total input) × 100%
效率等于有用输出能量（或功率）除以总输入能量（或功率），用百分比表示。
3. Density, Pressure and Moments | 密度、压强与力矩
Density measures how much mass is packed into a given volume.
ρ = m / V
密度 (ρ) 是质量 (m) 与体积 (V) 的比值，常用单位 kg/m³ 或 g/cm³。
Pressure is the force applied perpendicular to a surface per unit area.
P = F / A
压强等于垂直于表面的力除以受力面积，单位帕斯卡 (Pa)，1 Pa = 1 N/m²。
Liquid pressure increases with depth and fluid density.
P = h ρ g
液体内部压强由深度 h、液体密度 ρ 和重力场强 g 共同决定，相同深度处各方向压强相等。
The moment of a force about a pivot is the turning effect of that force.
Moment = F × d
力矩是力乘以力到支点的垂直距离，单位为 N·m。杠杆平衡时顺时针力矩等于逆时针力矩。
4. Thermal Physics | 热学
Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1°C.
Q = m c Δθ
物质吸收或放出的热量 (Q) 等于质量 (m) 乘以比热容 (c) 再乘以温度变化 (Δθ)。
Specific latent heat is the energy required to change the state of 1 kg of a substance without a temperature change.
Q = m L
熔化潜热 (Lf) 和汽化潜热 (Lv) 分别用于固-液和液-气变化过程中，温度保持不变。
Boyle’s law: for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume.
p₁ V₁ = p₂ V₂
玻意耳定律：一定质量气体在温度不变时，压强与体积成反比。
Charles’ law: at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.
V₁ / T₁ = V₂ / T₂
查理定律：压强不变时，气体的体积与绝对温度 (T, 单位 K) 成正比。
The pressure law (Gay-Lussac’s law): at constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature.
p₁ / T₁ = p₂ / T₂
压力定律：体积不变时，一定质量气体的压强与绝对温度成正比。
5. Waves | 波动
The wave equation links wave speed, frequency and wavelength for all periodic waves.
v = f λ
波速 (v) 等于频率 (f) 乘以波长 (λ)。单位：v 为 m/s，f 为 Hz，λ 为 m。
Frequency is the number of complete oscillations per second and is the reciprocal of the period.
f = 1 / T
频率与周期互成倒数，周期 T 是完成一次完整振动所需的时间。
Refractive index n describes how much a medium bends light.
n = sin i / sin r
折射率等于入射角的正弦除以折射角的正弦，两角都从法线量度。
The critical angle for total internal reflection occurs when the angle of refraction is 90°.
sin c = 1 / n
全内反射的临界角 c 满足 sin c = 1/n，光从光密介质射向光疏介质时才会发生。
6. Electricity | 电学
Electric current is the rate of flow of charge.
I = Q / t
电流 (I) 等于电荷量 (Q) 除以时间 (t)，单位安培 (A) = 库仑每秒 (C/s)。
Ohm’s law: voltage across a resistor is directly proportional to current at constant temperature.
V = I R
欧姆定律：电压 (V) 等于电流 (I) 乘以电阻 (R)，单位伏特 (V) = 安培 × 欧姆 (Ω)。
Electrical power is the product of current and voltage.
P = I V
电功率 (P) 等于电流乘以电压，单位瓦特 (W)。结合欧姆定律可得 P = I²R 或 P = V²/R。
Energy transferred by an electrical circuit depends on power and time.
E = I V t
电能等于电流、电压与时间的乘积，单位焦耳 (J)。
Resistors in series and parallel combine differently.
Rₜₒₜₐₗ = R₁ + R₂ + ... (series)
1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + ... (parallel)
串联电路总电阻等于各电阻之和；并联电路总电阻的倒数等于各电阻倒数之和。
7. Magnetism and Electromagnetism | 磁学与电磁学
The transformer equation relates the voltages to the turns ratio of the primary and secondary coils.
Vₚ / Vₛ = Nₚ / Nₛ
理想变压器中，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。
For a 100% efficient transformer, input power equals output power.
Vₚ Iₚ = Vₛ Iₛ
在无能量损耗时，初级功率等于次级功率，电流与电压成反比。
The size of the force on a current-carrying conductor in a magnetic field is given by Fleming’s left-hand rule context.
F = B I L
力 (F) 与磁感应强度 (B)、电流 (I) 及导体在磁场中的有效长度 (L) 成正比，方向由左手定则判定。
Moving a conductor across magnetic field lines induces an e.m.f. – Faraday’s law.
法拉第电磁感应定律：导体切割磁感线时会产生感应电动势，其快慢影响电动势大小。
8. Atomic Physics | 原子物理
Alpha decay reduces the mass number by 4 and atomic number by 2.
ᴬᵦX → ᴬ⁻⁴ᵦ⁻²Y + ⁴₂He
α 衰变：母核放出 α 粒子（氦核），质量数减 4，质子数减 2。
Beta decay increases the atomic number by 1 while the mass number stays the same.
ᴬᵦX → ᴬᵦ⁺¹Y + ⁰₋₁e + ν̄
β⁻ 衰变：中子转变为质子，放出电子和反中微子，质量数不变，质子数加 1。
Gamma emission involves no change in mass or atomic number; it often follows alpha or beta decay.
γ 射线是电磁波，发射时不改变原子核的组成，仅释放多余能量。
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