Quick Reference Handbook of Formulas and Theorems for Year 10 Cambridge Science | Year 10 Cambridge 科学：公式定理速查手册

📚 Quick Reference Handbook of Formulas and Theorems for Year 10 Cambridge Science | Year 10 Cambridge 科学：公式定理速查手册

This handbook provides a concise collection of essential formulas, laws, and theorems required for Year 10 Cambridge Science. It covers physics, chemistry, and biology topics commonly encountered in the IGCSE Co-ordinated Sciences syllabus. Use this as a quick revision tool to reinforce your understanding and exam readiness.

本手册汇集了 Year 10 剑桥科学课程所需的公式、定律与定理，涵盖 IGCSE Co-ordinated Sciences 教学大纲中常见的物理、化学和生物学主题。可作为快速复习工具，帮助你巩固知识并做好考试准备。

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1. Speed, Velocity and Acceleration | 速度、速率与加速度

In kinematics, we describe motion using key quantities such as speed, velocity and acceleration. The fundamental equations are listed below.

在运动学中，我们使用速率、速度和加速度等关键量来描述运动。以下为基本方程。

Speed is a scalar quantity defined as the distance travelled per unit time.

速率是标量，定义为单位时间内通过的路程。

v = s / t

Where v is speed (m/s), s is distance (m), and t is time (s).

其中 v 为速率 (m/s)，s 为路程 (m)，t 为时间 (s)。

Velocity is a vector quantity; average velocity is given by displacement over time.

速度是矢量，平均速度等于位移除以时间。

υ = Δs / t

Δs represents displacement (m); the symbol ν is used for average velocity here.

Δs 表示位移 (m)；此处用 ν 表示平均速度。

Acceleration is the rate of change of velocity.

加速度是速度的变化率。

a = (v - u) / t

a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s), t is time (s).

a 为加速度 (m/s²)，v 为末速度，u 为初速度，t 为时间。

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2. Forces and Newton's Laws of Motion | 力与牛顿运动定律

Forces cause changes in motion. Newton's three laws form the foundation of classical mechanics.

力使运动状态发生改变。牛顿三定律奠定了经典力学的基础。

Newton's Second Law gives the relationship between resultant force, mass and acceleration.

牛顿第二定律给出了合力、质量和加速度之间的关系。

F = m a

F is the resultant force (N), m is mass (kg), a is acceleration (m/s²).

F 为合力 (N)，m 为质量 (kg)，a 为加速度 (m/s²)。

Weight is the gravitational force acting on a mass.

重力是作用在质量上的引力。

W = m g

g is the gravitational field strength (≈ 9.8 N/kg on Earth).

g 为引力场强 (地球上约为 9.8 N/kg)。

For a spring obeying Hooke's Law, the extension is proportional to the applied load within the elastic limit.

在弹性限度内，遵循胡克定律的弹簧，其伸长量与载荷成正比。

F = k x

k is the spring constant (N/m) and x is the extension (m).

k 为劲度系数 (N/m)，x 为伸长量 (m)。

Friction opposes motion and can be static or kinetic.

摩擦力阻碍运动，分为静摩擦和动摩擦。

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3. Energy, Work and Power | 能量、功与功率

Energy cannot be created or destroyed, only transferred or transformed. Work and power quantify energy transfers.

能量既不会凭空产生，也不会凭空消失，只能转移或转化。功和功率用于量化能量转移。

Work done by a constant force is the product of the force and the distance moved in the direction of the force.

恒力做功等于力与物体在力的方向上移动的距离的乘积。

W = F d

W is work (J), F is force (N), d is distance (m).

W 为功 (J)，F 为力 (N)，d 为距离 (m)。

Power is the rate of doing work or transferring energy.

功率是做功或转移能量的快慢。

P = W / t

For constant velocity, power can also be expressed as P = F v.

匀速运动时也可表示为 P = F v。

Kinetic energy of a moving object:

物体的动能：

KE = ½ m v²

Gravitational potential energy:

重力势能：

GPE = m g h

Efficiency compares useful output to total input.

效率对比有效输出与总输入。

Efficiency = (useful output / total input) × 100%

This can be applied to energy or power.

此公式可用于能量或功率计算。

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4. Density and Pressure | 密度与压强

Density describes how much mass is packed into a given volume.

密度表示单位体积内所含质量的多少。

ρ = m / V

ρ (rho) is density (kg/m³), m is mass (kg), V is volume (m³).

ρ 为密度 (kg/m³)，m 为质量 (kg)，V 为体积 (m³)。

Pressure is the force acting per unit area.

压强定义为单位面积上所受的压力。

p = F / A

Pressure in a fluid column: p = ρ g h, where h is the height of the column.

液柱产生的压强：p = ρ g h，h 为液柱高度。

Liquid pressure increases with depth and acts equally in all directions.

液体压强随深度增加而增大，并向各个方向等大地作用。

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5. Waves and Optics | 波与光学

Wave speed depends on the medium and is related to frequency and wavelength.

波速取决于介质，并与频率和波长相关。

v = f λ

v is wave speed (m/s), f is frequency (Hz), λ is wavelength (m).

v 为波速，f 为频率，λ 为波长。

The law of reflection states that the angle of incidence equals the angle of reflection.

反射定律指出，入射角等于反射角。

Refractive index n of a medium can be found by Snell's law:

介质的折射率 n 可用斯涅尔定律求得：

n = sin i / sin r

Alternatively, n = c / v, where c is the speed of light in a

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