📚 Year 9 CCEA Science Formula & Theorem Quick Reference | Year 9 CCEA 科学：公式定理速查手册
This quick reference handbook brings together the essential formulas, equations and key theorems you will meet in Year 9 CCEA Science. It covers the most important relationships in Physics, Chemistry and Biology – from speed and acceleration to electrical circuits, chemical quantities and biological processes. Each section presents the formula first in words, then in symbols, along with the units you need to know. Keep this guide handy for homework, end‑of‑topic tests and revision.
这份速查手册汇集了 Year 9 CCEA 科学课程中你必须掌握的核心公式、方程式和重要定理。内容涵盖物理、化学和生物中最关键的关系——从速度和加速度到电路、化学计量以及生命过程。每个章节先用文字表达公式，再给出符号形式，并标明你需要知道的单位。无论是家庭作业、单元测验还是统考复习，这份指南都能随时为你提供支持。
1. Speed, Distance and Time | 速度、距离与时间
The average speed of an object is the distance it travels divided by the time taken. In everyday situations we often use kilometres per hour (km/h), but in science calculations the standard unit is metres per second (m/s).
物体的平均速度等于它移动的距离除以所用的时间。生活中常用千米每小时 (km/h)，但在科学计算中标准单位是米每秒 (m/s)。
speed = distance ÷ time
速度 = 距离 ÷ 时间
In symbols we write v = d / t, where v is speed in m/s, d is distance in metres (m) and t is time in seconds (s).
用符号表示为 v = d / t，其中 v 为速度 (m/s)，d 为距离 (m)，t 为时间 (s)。
You can rearrange the formula to find distance (d = v × t) or time (t = d / v). Always make sure the units match before you calculate.
你可以通过变形求出距离 (d = v × t) 或时间 (t = d / v)。计算前务必统一单位。
2. Acceleration | 加速度
Acceleration tells us how quickly the velocity of an object changes. It can be a positive value (speeding up) or negative (slowing down, sometimes called deceleration).
加速度描述物体速度变化的快慢。它可以是正值（加速），也可以是负值（减速，有时称作负加速度）。
acceleration = change in velocity ÷ time taken
加速度 = 速度变化量 ÷ 所用时间
In symbols: a = (v − u) / t, where a is acceleration in m/s², v is final velocity (m/s), u is initial velocity (m/s) and t is time (s).
用符号表示为：a = (v − u) / t，其中 a 为加速度 (m/s²)，v 为末速度 (m/s)，u 为初速度 (m/s)，t 为时间 (s)。
= 0. If it comes to a stop, v = 0. The formula works for uniform (constant) acceleration.
如果物体从静止出发，u = 0；如果它最终停下，v = 0。该公式适用于匀加速（加速度恒定）运动。
3. Forces, Mass and Weight | 力、质量与重量
A resultant force causes an object to accelerate. The size of the acceleration depends on the mass of the object and the size of the force. This is summed up by Newton’s Second Law.
合力使物体产生加速度。加速度的大小取决于物体的质量和力的大小。这可以用牛顿第二定律来概括。
force = mass × acceleration
力 = 质量 × 加速度
F = m × a, where F is force in newtons (N), m is mass in kilograms (kg) and a is acceleration in m/s².
F = m × a，其中 F 为力 (N)，m 为质量 (kg)，a 为加速度 (m/s²)。
Weight is the force due to gravity. The gravitational field strength on Earth is approximately 10 N/kg.
重量是由重力产生的力。地球表面的重力场强度约为 10 N/kg。
weight = mass × gravitational field strength
重量 = 质量 × 重力场强度
W = m × g, where W is weight in N, m in kg and g ≈ 10 N/kg on Earth.
W = m × g，其中 W 为重量 (N)，m 为质量 (kg)，地球表面 g ≈ 10 N/kg。
4. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object through a distance. Energy is transferred when work is done.
力使物体沿力的方向移动一段距离，我们就说力做了功。做功的过程伴随着能量转移。
work done = force × distance moved in the direction of the force
功 = 力 × 沿力方向移动的距离
W = F × d, where W is work in joules (J), F in N and d in m.
W = F × d，其中 W 为功 (J)，F 为力 (N)，d 为距离 (m)。
Kinetic energy is the energy an object has because of its motion.
动能是物体由于运动而具有的能量。
kinetic energy = ½ × mass × velocity²
动能 = ½ × 质量 × 速度²
Eₖ = ½ m v², where Eₖ is in J, m in kg and v in m/s.
Eₖ = ½ m v²，其中 Eₖ 单位为 J，m 为 kg，v 为 m/s。
Gravitational potential energy is the energy stored in an object raised above the ground.
重力势能是物体被举高时所储存的能量。
change in GPE = mass × gravitational field strength × change in height
重力势能的变化 = 质量 × 重力场强度 × 高度变化
ΔEₚ = m g Δh, with energy in J, m in kg, g in N/kg and Δh in m.
ΔEₚ = m g Δh，能量单位为 J，m 为 kg，g 为 N/kg，Δh 为 m。
Power is the rate at which work is done or energy is transferred.
功率表示做功或能量转移的快慢。
power = work done ÷ time taken or power = energy transferred ÷ time
功率 = 功 ÷ 时间 或 功率 = 转移的能量 ÷ 时间
P = W / t or P = E / t, with P in watts (W), W/E in J and t in s.
P = W / t 或 P = E / t，P 单位为瓦特 (W)，W/E 为 J，t 为 s。
Efficiency compares useful output energy to total input energy.
效率将有用的输出能量与总输入能量进行比较。
efficiency = (useful output energy ÷ total input energy) × 100%
效率 = (有用的输出能量 ÷ 总输入能量) × 100%
5. Density and Pressure | 密度与压强
Density is a measure of how much mass is packed into a given volume. It is a property of a material and can be used to identify substances.
密度衡量单位体积内所含质量的多少。它是物质的一种特性，可用于鉴别物质。
density = mass ÷ volume
密度 = 质量 ÷ 体积
ρ = m / V, where ρ is density in kg/m³ or g/cm³, m is mass in kg or g, and V is volume in m³ or cm³.
ρ = m / V，其中 ρ 为密度 (kg/m³ 或 g/cm³)，m 为质量 (kg 或 g)，V 为体积 (m³ 或 cm³)。
Pressure is the force acting perpendicularly per unit area. Solids exert pressure on surfaces, while fluids exert pressure in all directions.
压强是垂直作用在单位面积上的力。固体对接触面产生压强，而流体向各个方向施加压强。
pressure = force ÷ area
压强 = 力 ÷ 面积
p = F / A, where p is pressure in pascals (Pa) or N/m², F is force in N and A is area in m².
p = F / A，p 为压强 (Pa 或 N/m²)，F 为力 (N)，A 为面积 (m²)。
6. Moments | 力矩
A moment is the turning effect of a force about a pivot. It depends on two factors: the size of the force and the perpendicular distance from the pivot to the line of action of the force.
力矩是力使物体绕支点转动的效应。它取决于两个因素：力的大小以及支点到力作用线的垂直距离。
moment of a force = force × perpendicular distance from pivot
力矩 = 力 × 支点到力作用线的垂直距离
M = F × d, where M is moment in newton metres (N m), F is force in N and d is the perpendicular distance in m.
M = F × d，M 为力矩 (N m)，F 为力 (N)，d 为垂直距离 (m)。
The principle of moments states that for an object in equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments.
力矩原理指出：处于平衡状态的物体，对于任意支点，顺时针力矩之和等于逆时针力矩之和。
total clockwise moment = total anticlockwise moment
总顺时针力矩 = 总逆时针力矩
7. Electricity – Ohm's Law and Electrical Power | 电学 – 欧姆定律与电功率
Ohm’s Law links the current flowing through a conductor, the voltage across it and its resistance, provided the temperature stays constant.
欧姆定律描述了在温度不变的条件下，流过导体的电流、导体两端的电压以及电阻之间的关系。
voltage = current × resistance
电压 = 电流 × 电阻
V = I × R, where V is voltage in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω).
V = I × R，V 为电压 (V)，I 为电流 (A)，R 为电阻 (Ω)。
Electrical power tells us how quickly a component transfers energy. It can be calculated using current and voltage.
电功率表示电路元件转移能量的快慢，可用电流和电压计算。
power = current × voltage
电功率 = 电流 × 电压
P = I × V, with P in W, I in A and V in V.
P = I × V，P 为 W，I 为 A，V 为 V。
The energy transferred by a device depends on its power and how long it is used.
用电器转移的能量取决于其功率大小和用电时间。
energy transferred = power × time or E = I × V × t
转移的能量 = 功率 × 时间 或 E = I × V × t
E is in joules (J), P in W, t in s, I in A and V in V.
E 的单位为焦耳 (J)，P 为 W，t 为 s，I 为 A，V 为 V。
8. Series and Parallel Circuits | 串联与并联电路
Understanding how resistors add up in different circuit arrangements is essential for analysing circuits.
理解电阻在不同电路连接方式中的累加规律，对分析电路至关重要。
In a series circuit, the total resistance is simply the sum of the individual resistances. The current is the same at every point.
在串联电路中，总电阻等于各个电阻之和。电路中各处电流相等。
Rtotal = R₁ + R₂ + R₃ + …
R总 = R₁ + R₂ + R₃ + …
The supply voltage is shared between the components: Vtotal = V₁ + V₂ + …
电源电压在各元件之间分配：V总 = V₁ + V₂ + …
In a parallel circuit, the total resistance is found using the reciprocal formula. The voltage across each branch is the same as the supply voltage.
在并联电路中，总电阻可用倒数公式求出。各支路两端的电压相等，且等于电源电压。
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
1 / R总 = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
The total current from the supply splits between the branches: Itotal = I₁ + I₂ + …
干路总电流等于各支路电流之和：I总 = I₁ + I₂ + …
9. Chemical Calculations and Equations | 化学计算与方程式
Relative atomic mass (Ar) compares the mass of an atom to 1/12 of the mass of a carbon‑12 atom. It has no units.
相对原子质量 (Ar) 是将原子的质量与碳‑12 原子质量的 1/12 进行比较，没有单位。
Relative formula mass (Mr) is the sum of the relative atomic masses of all the atoms in a formula unit. It is used for ionic compounds and giant structures.
相对式量 (Mr) 是化学式单元中所有原子的相对原子质量之和。可用于离子化合物和巨型结构。
Mr = Σ Ar of all atoms in the formula
Mr = 化学式中所有原子的 Ar 之和
Example: for H₂O, Mr = (2 × 1) + 16 = 18.
例如：H₂O 的 Mr = (2 × 1) + 16 = 18。
The law of conservation of mass states that in a chemical reaction, the total mass of the reactants equals the total mass of the products. No atoms are lost or made.
质量守恒定律指出：在化学反应中，反应物的总质量等于生成物的总质量。原子既不会消失也不会凭空产生。
Balancing equations ensures the same number of each type of atom on both sides. A balanced equation uses coefficients before formulas.
配平方程式确保方程式两边各类原子的数目相同。平衡的方程式在各化学式前加上计量数。
Example: 2H₂ + O₂ → 2H₂O
例子：2H₂ + O₂ → 2H₂O
10. Photosynthesis and Respiration | 光合作用与呼吸作用
Photosynthesis is the process by which plants make glucose using light energy. Carbon dioxide and water are the reactants; glucose and oxygen are the products.
光合作用是植物利用光能制造葡萄糖的过程。反应物是二氧化碳和水，生成物是葡萄糖和氧气。
Word equation:
文字方程式：
carbon dioxide + water → glucose + oxygen
二氧化碳 + 水 → 葡萄糖 + 氧气
Balanced symbol equation (with light and chlorophyll):
配平的符号方程式（需要光和叶绿素）：
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Aerobic respiration releases energy from glucose using oxygen. It takes place in the mitochondria of cells.
有氧呼吸利用氧气从葡萄糖中释放能量。这一过程发生在细胞的线粒体中。
Word equation:
文字方程式：
glucose + oxygen → carbon dioxide + water (+ energy)
葡萄糖 + 氧气 → 二氧化碳 + 水（+ 能量）
Balanced symbol equation:
配平的符号方程式：
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
The two processes are essentially reverse of each other in terms of chemical equations, but they take place in different organelles and at different times.
从化学方程式看，这两个过程互为逆反应，但它们发生在不同的细胞器中且时间不同。
11. Microscopy and Magnification | 显微镜与放大率
When using a light microscope, you can calculate the magnification or the actual size of a specimen using a simple formula. This is essential for drawing scale diagrams and interpreting micrographs.
使用光学显微镜时，你可以用一个简单公式计算放大率或标本的实际大小。这对于绘制比例图和解读显微照片至关重要。
magnification = size of image ÷ size of real object
放大率 = 图像大小 ÷ 实物大小
In symbols: M = I / A is image size and A is actual size. Both I and A must be in the same units (usually mm or µm).
用符号表示：M = I / A，其中 M 为放大率（无单位，常写作 ×），I 为图像尺寸，A 为实际尺寸。I 和 A 单位必须一致（通常用 mm 或 µm）。
You can rearrange the formula: A = I / M and I = M × A. Always remember to convert all lengths to the same unit before substituting.
你可以变形公式：A = I / M 以及 I = M × A。代入前务必把所有长度单位统一。
If the image is measured in mm and the actual size in µm, recall that 1 mm = 1000 µm. This conversion is a common requirement in CCEA practical assessments.
如果图像以毫米 (mm) 计量而实际尺寸以微米 (µm) 计量，注意 1 mm = 1000 µm。这一换算是 CCEA 实验考核中的常见要求。
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