📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook brings together the most essential formulas, theorems and equations from the Year 12 CCEA Science curriculum. Whether you are revising for a mock exam or preparing for your final GCSE assessments, having these key relationships at your fingertips will save you time and boost your confidence. All formulas are stated in their standard form, and we have added brief reminders about when and how to use them, as well as the units involved.
这本速查手册汇集了 Year 12 CCEA 科学课程中最关键的公式、定理和方程。无论你正在准备模拟考试还是最终评估，随时查阅这些核心关系式都能为你节省时间、增强信心。所有公式均以标准形式给出，我们还补充了关于使用条件、使用场景以及相关单位的简要提示。
1. Motion – Speed, Velocity and Acceleration | 运动 – 速度、速率与加速度
In the topic of motion, you must be able to distinguish between speed and velocity and to calculate acceleration. Speed is a scalar quantity, while velocity is a vector. Acceleration describes how quickly the velocity of an object changes.
在运动部分，你必须能够区分速率与速度，并计算加速度。速率是标量，速度是矢量。加速度描述物体速度变化的快慢。
speed = distance ÷ time v = s / t
Units: speed (m/s), distance (m), time (s). This formula applies to uniform (constant) motion. For average speed, use total distance and total time.
单位：速度单位 m/s，距离单位 m，时间单位 s。此公式适用于匀速运动。计算平均速度时，使用总距离和总时间。
acceleration = change in velocity ÷ time a = (v − u) / t
Units: acceleration (m/s²), initial velocity u (m/s), final velocity v (m/s), time t (s). This formula is used for constant acceleration.
单位：加速度 m/s²，初速度 u (m/s)，末速度 v (m/s)，时间 t (s)。用于匀加速运动。
Another useful equation for uniform acceleration: v² = u² + 2 a s, where s is displacement.
另一个有用的匀加速方程：v² = u² + 2 a s，其中 s 为位移。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s three laws of motion form the backbone of classical mechanics. They explain how forces cause changes in motion and how objects interact.
牛顿三大运动定律是经典力学的基石，解释了力如何引起运动变化以及物体如何相互作用。
Newton’s First Law: An object remains at rest or in uniform motion in a straight line unless acted upon by a resultant force.
牛顿第一定律：一切物体在没有受到合力作用时，总保持静止状态或匀速直线运动状态。
Newton’s Second Law:
F = m × a
Units: resultant force F (N), mass m (kg), acceleration a (m/s²). This is the most frequently used dynamics equation in Year 12 CCEA Science.
单位：合力 F (N)，质量 m (kg)，加速度 a (m/s²)。这是 Year 12 CCEA 科学中最常用的动力学方程。
Newton’s Third Law: Whenever two objects interact, they exert equal and opposite forces on each other.
牛顿第三定律：两个物体相互作用时，彼此施加的力大小相等、方向相反。
Weight is a force due to gravity:
W = m × g
g ≈ 10 m/s² on Earth (CCEA often uses 10 for simplicity unless told otherwise). Weight is measured in newtons.
g ≈ 10 m/s²（地球表面，CCEA 常取近似值 10）。重量以牛顿为单位。
3. Energy, Work and Power | 能量、功与功率
The conservation of energy is a fundamental principle: energy cannot be created or destroyed, only transferred or stored. In mechanics, we often calculate work done and the rate of energy transfer (power).
能量守恒是一个基本原理：能量不能被创造或消灭，只能被转移或储存。在力学中，我们经常计算做功和能量转移的速率（功率）。
Work done:
W = F × d
Work done (J) = force (N) × distance moved in the direction of the force (m).
做功 (J) = 力 (N) × 物体在力的方向上移动的距离 (m)。
Kinetic energy:
Eₖ = ½ m v²
Gravitational potential energy:
Eₚ = m × g × h
h is the height above a reference point.
h 为物体相对参考点的高度。
Power:
P = W / t or P = E / t
Power (W) = work done or energy transferred (J) / time (s). 1 watt = 1 joule per second.
功率 (W) = 做功或能量转移 (J) / 时间 (s)。1 瓦 = 1 焦耳每秒。
4. Wave Properties and Equations | 波的特性与方程
Waves transfer energy without transferring matter. For both transverse and longitudinal waves, the key equation links speed, frequency and wavelength.
波传递能量而不传递物质。无论是横波还是纵波，关键方程都联系着波速、频率和波长。
v = f × λ
v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m).
v = 波速 (m/s)，f = 频率 (Hz)，λ = 波长 (m)。
Period:
T = 1 / f
Period (s) is the time for one complete wave cycle.
周期 (s) 是完成一个完整波形所需的时间。
When waves pass from one medium to another, their speed and wavelength change but frequency remains constant. Refraction can be explained by this change in speed.
当波从一种介质进入另一种介质时，波速和波长发生变化，但频率保持不变。折射现象可由波速的改变来解释。
5. Electricity: Ohm’s Law and Power | 电学：欧姆定律与电功率
Ohm’s law is the most important relationship in the electricity topic. It applies to ohmic conductors at constant temperature.
欧姆定律是电学部分最重要的关系式，适用于温度恒定的欧姆导体。
V = I × R
Potential difference V (V) = current I (A) × resistance R (Ω).
电势差 V (V) = 电流 I (A) × 电阻 R (Ω)。
Resistors in series: Rₜₒₜₐₗ = R₁ + R₂ + …
串联电阻：Rₜₒₜₐₗ = R₁ + R₂ + …
Resistors in parallel: The total resistance is given by 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + … (you may not need to calculate, but you must know that the total resistance decreases).
并联电阻：总电阻由 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + … 求出（可能需要了解总电阻变小的规律，不总要求计算）。
Electrical power:
P = V × I
Power (W) = voltage (V) × current (A). Combined with Ohm’s law, you may also see P = I²R or P = V²/R.
功率 (W) = 电压 (V) × 电流 (A)。结合欧姆定律，还可得到 P = I²R 或 P = V²/R。
Energy transferred:
E = P × t or E = V × I × t
Energy transferred (J) = power (W) × time (s).
能量转移 (J) = 功率 (W) × 时间 (s)。
6. Radioactivity: Half-Life and Decay | 放射性：半衰期与衰变
Radioactive decay is a random process. The half-life of a radioactive isotope is the time taken for the number of unstable nuclei in a sample to halve.
放射性衰变是一个随机过程。放射性同位素的半衰期是指样品中不稳定原子核数量减半所需的时间。
Although there is no single formula that you must plug numbers into, the concept of half-life is used graphically and in calculations. After n half-lives, the fraction remaining is (½)ⁿ.
虽然没有单独的代入公式，但半衰期的概念常用于图表和计算。经过 n 个半衰期后，剩余的比例为 (½)ⁿ。
Activity: The activity of a source is measured in becquerels (Bq). 1 Bq = 1 decay per second.
活度：放射源的活度以贝克勒尔 (Bq) 为单位，1 Bq = 每秒衰变 1 次。
The equation linking count rate, background radiation and corrected count rate is practical: corrected count rate = total count rate − background count rate.
实际应用中有这样的关系：校正计数率 = 总计数率 − 本底计数率。
7. Mole Calculations in Chemistry | 化学摩尔计算
The mole is the central unit for amount of substance in chemistry. CCEA Science students are expected to use two core formulas relating moles, mass and relative formula mass (Mᵣ).
摩尔是化学中物质的量的核心单位。CCEA 科学的学生需要掌握两个联系摩尔、质量与相对式量 (Mᵣ) 的核心公式。
number of moles = mass ÷ Mᵣ
Mass is in grams, Mᵣ is the sum of relative atomic masses for the atoms in the formula.
质量单位为克，Mᵣ 为化学式中各原子相对原子质量之和。
For solutions:
number of moles = concentration × volume
Concentration in mol/dm³, volume in dm³. If volume is given in cm³, divide by 1000 first.
浓度单位为 mol/dm³，体积单位为 dm³。若体积以 cm³ 给出，先除以 1000。
In reacting mass calculations, the ratio of moles is obtained from the coefficients in the balanced chemical equation. The limiting reactant is the one that is completely used up first.
在根据化学方程式计算质量时，摩尔比由配平方程式的系数决定。限制反应物是首先被用完的那种。
atom economy = (mass of desired product ÷ total mass of reactants) × 100%
This formula is useful for evaluating the efficiency of a chemical process.
这个公式用于评价化工过程的效率。
8. Titration and Concentration | 滴定与浓度
Titrations are a practical method to determine the concentration of an acid or alkali. The formula used to calculate unknown concentrations is derived from the mole ratio of the neutralisation reaction.
滴定是测定酸或碱浓度的实验方法。计算未知浓度的公式来自中和反应的摩尔比。
For example, if the reaction ratio is 1:1 (e.g. HCl + NaOH → NaCl + H₂O):
Cₐ × Vₐ / C₆ × V₆ = nₐ / n₆
where C = concentration, V = volume, n = number of moles in the balanced equation. For 1:1 reactions this simplifies to CₐVₐ = C₆V₆.
其中 C 为浓度，V 为体积，n 为配平方程式中对应的化学计量数。对于 1:1 的反应，可简化为 CₐVₐ = C₆V₆。
Always convert volumes to dm³ if using mol/dm³ for concentration. The concordant titres (within 0.10 cm³) are used to calculate an average.
如果浓度使用 mol/dm³，一定要将体积转换为 dm³。一致性滴定读数（相差不超过 0.10 cm³）用于计算平均值。
9. Magnification and Biological Drawing | 放大率与生物绘图
In the biology component, microscopy is a key practical skill. The magnification formula is used to relate the size of an image to the actual size of the specimen.
在生物部分，显微镜使用是一项关键技能。放大率公式用于将图像大小与标本的实际大小联系起来。
magnification = image size ÷ actual size
Both sizes must be in the same unit. Often you will need to convert between millimetres, micrometres (µm) and nanometres (nm). 1 mm = 1000 µm; 1 µm = 1000 nm.
两者必须使用相同单位。通常需要换算毫米 (mm)、微米 (µm) 和纳米 (nm)。1 mm = 1000 µm；1 µm = 1000 nm。
When rearranging, actual size = image size ÷ magnification. This is frequently tested when you are given a scale bar or a stated magnification.
移项可得实际大小 = 图像大小 ÷ 放大率。这类题目在给出比例尺或指定放大率时常考。
For biological drawing, make sure you use a sharp pencil, clear continuous lines and label with straight ruled lines. The drawing itself must be proportional and fill at least half the available space.
生物绘图时，须使用削尖的铅笔、清晰连续的线条，并用直尺划出指示线标注。绘图本身必须比例准确，并至少占据纸张可用空间的一半。
10. Rate of Reaction and Key Principles | 反应速率与关键原理
The rate of a chemical reaction can be measured by the speed at which a reactant is used up or a product is formed. Two common formulas are used to calculate the mean rate.
化学反应速率可通过反应物消耗或产物生成的速度来衡量。两个常用公式用来计算平均反应速率。
mean rate of reaction = quantity of reactant used ÷ time
or
mean rate of reaction = quantity of product formed ÷ time
The quantity can be mass (g), volume of gas (cm³) or change in concentration. Units of rate might be g/s, cm³/s or mol/(dm³·s).
物理量可以是质量 (g)、气体体积 (cm³) 或浓度的变化。速率单位可为 g/s、cm³/s 或 mol/(dm³·s)。
Collision theory states that for a reaction to occur, particles must collide with sufficient energy (the activation energy) and the correct orientation. Factors affecting rate include temperature, concentration, surface area and catalysts.
碰撞理论指出，反应发生的条件是粒子必须以足够的能量（活化能）和正确的取向相撞。影响反应速率的因素包括温度、浓度、表面积和催化剂。
Le Chatelier’s principle is introduced in some CCEA units: if a system at equilibrium is subjected to a change, the position of equilibrium shifts to oppose that change. This helps predict the effect of changing temperature or pressure on yield.
勒夏特列原理在某些 CCEA 单元中引入：如果处于平衡状态的体系受到外界条件改变，平衡将向减弱这种改变的方向移动。该原理有助于预测改变温度或压强对产率的影响。
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