Year 12 Edexcel Science: Formula & Theorem Quick Reference Handbook | Edexcel 十二年级科学公式定理速查手册

📚 Year 12 Edexcel Science: Formula & Theorem Quick Reference Handbook | Edexcel 十二年级科学公式定理速查手册

This quick reference handbook collects the essential formulas, laws and theorems you will encounter in Year 12 Edexcel Science. Covering physics, chemistry and biology, it is designed for rapid revision and on-the-go checks. Mastering these fundamentals will strengthen your problem-solving skills and exam confidence.

本速查手册汇集了 Edexcel 十二年级科学课程中的核心公式、定律和定理，涵盖物理、化学和生物三大领域，适合快速复习和随时查阅。熟练掌握这些基础知识，可以增强你的解题技巧和考试信心。

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1. Kinematics and Motion Equations | 运动学与运动方程

The equations of motion describe uniformly accelerated linear motion. They link initial velocity u, final velocity v, acceleration a, displacement s and time t.

运动学方程描述匀加速直线运动，关联初速度 u、末速度 v、加速度 a、位移 s 和时间 t。

v = u + a t

Final velocity is obtained by adding the product of acceleration and time to the initial velocity. Always check that acceleration is constant.

末速度等于初速度加上加速度与时间的乘积。使用时务必确认加速度恒定。

s = u t + ½ a t²

Displacement equals the initial velocity multiplied by time plus half the acceleration multiplied by the square of time. This formula helps find distance travelled under constant acceleration.

位移等于初速度乘以时间加上二分之一加速度乘以时间的平方。该式用于计算匀加速运动中的距离。

v² = u² + 2 a s

This equation links velocity and displacement without time, which is useful when the time interval is unknown.

此方程联系速度与位移而不含时间，在时间未知时非常有用。

s = ½ (u + v) t

The displacement can also be found as the average velocity multiplied by time. It works only when acceleration is uniform.

位移也可用平均速度乘以时间求得，仅适用于匀加速运动。

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2. Forces and Newton’s Laws | 力与牛顿定律

Newton’s laws of motion form the basis of classical mechanics. They explain how forces affect the motion of objects.

牛顿运动定律是经典力学的基础，解释了力如何影响物体的运动。

F = m a

Newton’s second law states that the net force on an object equals its mass multiplied by its acceleration. It allows us to calculate unknown forces or accelerations.

牛顿第二定律指出，物体所受的净力等于其质量乘以加速度，可用于计算未知力或加速度。

W = m g

Weight is the force due to gravity, where g is the gravitational field strength (9.81 N kg⁻¹ on Earth). Always distinguish between mass and weight.

重量是重力产生的力，g 为重力场强度（地球取 9.81 N kg⁻¹）。请务必区分质量与重量。

p = m v

Linear momentum p is the product of mass and velocity. Momentum is conserved in a closed system with no external forces.

线动量 p 是质量与速度的乘积。若无外力，封闭系统内动量守恒。

F Δt = Δp

Impulse (force multiplied by time) equals the change in momentum. This relationship helps analyse collisions and safety features like airbags.

冲量（力乘以时间）等于动量的变化量，用于分析碰撞及安全气囊等问题。

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3. Work, Energy and Power | 功、能与功率

Energy transfers and work done are key to understanding mechanical systems. Power describes how fast work is done.

能量转换与做功是理解机械系统的关键，功率则描述做功的快慢。

W = F s cos θ

and the cosine of the angle between them. When force and motion align, θ = 0° and W = F s.

恒力做的功等于力、位移及它们夹角余弦的乘积。当力与运动方向一致时，θ = 0°，功简化为 W = F s。

Ek = ½ m v²

Kinetic energy depends on mass and the square of speed. Any moving object possesses this energy.

动能取决于质量与速度的平方，任何运动的物体都具有动能。

Ep = m g h

Gravitational potential energy is stored when an object is raised to a height h. Choose a consistent reference level for height.

重力势能是物体被举高 h 后储存的能量。选取统一的参考平面作为高度零点。

P = W / t = F v

Power is the rate of work done or energy transferred. For constant speed, power equals force multiplied by velocity.

功率是做功或能量转移的速率。匀速运动时，功率也可以用力与速度的乘积表示。

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4. Materials and Hooke’s Law | 材料与胡克定律

Understanding how materials deform under load is essential in engineering. Hooke’s law applies to the elastic region of a force-extension graph.

了解材料在载荷下的变形对工程学至关重要，胡克定律适用于力–伸长图的弹性区间。

F = k x

For a spring or elastic material, the restoring force is proportional to extension x, provided the elastic limit is not exceeded. k is the spring constant.

对弹簧或弹性材料，只要未超过弹性极限，回复力与伸长量 x 成正比。k 为弹簧常数。

E = ½ F x = ½ k x²

The elastic potential energy stored in a stretched or compressed spring equals half the product of force and extension, or half the spring constant times square of extension.

拉伸或压缩的弹簧储存的弹性势能等于力与伸长量乘积的一半，也等于 ½ k x²。

stress = F / A & strain = ΔL / L

Stress is force per unit cross-sectional area, and strain is the extension per original length. Both are used to calculate the Young modulus.

应力是单位横截面积上的力，应变是伸长量与原长之比，二者用于计算杨氏模量。

E = stress / strain = (F/A) / (ΔL/L)

The Young modulus E measures a material’s stiffness. It applies only within the linear elastic region.

杨氏模量 E 衡量材料的刚度，仅在线弹性范围内适用。

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5. Waves and Optics | 波与光学

Wave behaviour is described by frequency, wavelength and speed. Refraction and total internal reflection are fundamental optical phenomena.

波的特性由频率、波长和波速描述，折射与全反射是基本的光学现象。

v = f λ

Wave speed equals frequency multiplied by wavelength. This universal relationship applies to sound, light and water waves.

波速等于频率乘以波长，这一普适关系适用于声波、光波和水波。

n₁ sin θ₁ = n₂ sin θ₂

Snell’s law describes refraction. When light passes from one medium to another, the product of refractive index and sine of the angle to the normal remains constant.

斯涅尔定律描述折射：光从一种介质进入另一种介质时，折射率与入射角正弦的乘积保持不变。

sin C = 1 / n

The critical angle C for total internal reflection depends on the refractive index n. This principle is used in optical fibres.

全反射的临界角 C 由折射率 n 决定，光纤通信就是基于这一原理。

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6. Electricity and Circuits | 电学与电路

Ohm’s law and power formulas are at the heart of circuit analysis. Series and parallel arrangements follow predictable rules.

欧姆定律与功率公式是电路分析的核心，串联和并联遵循可预测的规律。

V = I R

Ohm’s law relates the voltage across a conductor to the current flowing through it and its resistance. It holds for ohmic conductors at constant temperature.

欧姆定律关联导体两端的电压、通过它的电流和电阻，适用于恒温下的欧姆导体。

P = I V = I² R = V² / R

Electrical power can be expressed in three equivalent forms. The choice depends on which quantities are known.

电功率有三种等价的表达形式，可根据已知量灵活选用。

R_total series = R₁ + R₂ + ...

In a series circuit, total resistance is the sum of individual resistances. The same current flows through each component.

串联电路的总电阻为各电阻之和，每个元件电流相同。

1 / R_total parallel = 1/R₁ + 1/R₂ + ...

For parallel resistors, the reciprocal of total resistance equals the sum of reciprocals. The total resistance is always less than the smallest individual resistance.

并联电阻的总电阻倒数等于各电阻倒数之和，总电阻总小于最小电阻。

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7. Quantitative Chemistry | 化学计量

Mole calculations connect mass, concentration and gas volumes. These are the primary tools for solving stoichiometric problems.

摩尔计算连接质量、浓度和气体体积，是解决化学计量问题的主要工具。

n = m / M

The amount of substance in moles (n) equals mass (m) divided by molar mass (M). Use this to convert between grams and moles.

物质的量（摩尔 n）等于质量 m 除以摩尔质量 M，用于克与摩尔的转换。

c = n / V

Concentration of a solution is the number of moles of solute per volume of solution. Volume must be in dm³ or litres, so convert cm³ accordingly.

溶液浓度是溶质摩尔数与溶液体积之比。体积须以 dm³ 或 L 为单位，注意 cm³ 的换算。

p V = n R T

The ideal gas equation links pressure, volume, temperature and moles. R is the gas constant (8.31 J K⁻¹ mol⁻¹). Temperature must be in kelvin.

理想气体状态方程联系压强、体积、温度和摩尔数。R 为气体常数（8.31 J K⁻¹ mol⁻¹），温度必须用开尔文。

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8. Chemical Energetics and Equilibria | 化学能量学与平衡

Energetics deals with heat changes during reactions, while equilibrium constants indicate the extent of reversible reactions.

能量学关注反应中的热变化，平衡常数则指示可逆反应进行的程度。

q = m c ΔT

Heat transferred is calculated using mass, specific heat capacity and temperature change. This formula is fundamental in calorimetry experiments.

热量计算用质量、比热容和温度变化，是量热实验的基础公式。

ΔH = – q / n

Enthalpy change per mole is found by dividing heat transferred (with sign convention) by the number of moles of limiting reactant.

每摩尔焓变等于转移的热量（带符号）除以限制反应物的摩尔数。

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

The equilibrium constant Kc uses equilibrium concentrations raised to stoichiometric coefficients. It is temperature-dependent and units vary with the reaction.

平衡常数 Kc 用平衡浓度以其计量系数为幂次表示，仅与温度有关，单位随具体反应而变化。

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9. Biological Measurements and Units | 生物学测量与单位

Biology frequently requires quantitative measurements under the microscope or during experiments. Correct conversion and formula usage are vital.

生物学常需在显微镜下或实验中定量测量，正确的单位换算与公式使用至关重要。

Magnification = Image size / Actual size

To calculate magnification, divide the measured image size by the real size of the specimen. Both must be in the same units. This is the most common IAM triangle.

放大率 = 图像大小 ÷ 实际大小。图像大小与实际大小须使用相同单位，这是最常用的 IAM 三角形。

Actual size = Image size / Magnification

Rearrange the formula to find the true dimensions of a cell or organelle from a micrograph.

通过改写公式，可从显微照片中求出细胞或细胞器的实际尺寸。

Surface area : volume ratio

As an organism or cell increases in size, its surface area to volume ratio decreases. This ratio affects rates of diffusion, heat loss and nutrient uptake.

随着生物体或细胞增大，其表面积与体积之比下降，该比值影响扩散速率、热量散失和营养摄取。

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10. Genetics and Probability | 遗传学与概率

Genetic crosses rely on probability rules to predict offspring genotypes and phenotypes. Monohybrid and dihybrid ratios follow Mendelian principles.

遗传杂交依赖概率规则预测子代的基因型与表型，单因子和双因子杂交遵循孟德尔原理。

P(A and B) = P(A) × P(B)

For independent events, the probability of both occurring is the product of their individual probabilities. This is the basis of the multiplication rule in genetics.

独立事件同时发生的概率等于各自概率的乘积，这是遗传学中乘法规则的基础。

P(A or B) = P(A) + P(B)

When events are mutually exclusive, the probability of either happening is the sum of their probabilities. This helps in predicting alternative phenotypes.

互斥事件中任一发生的概率为各自概率之和，可用于预测不同表型的出现几率。

Expected ratio in a monohybrid cross (F₂): 3:1

(e.g., Bb × Bb) produces a phenotypic ratio of 3 dominant to 1 recessive in the offspring.

两个杂合子（如 Bb × Bb）杂交，子代表型比为 3 显性 : 1 隐性。

Chi‑squared test: χ² = Σ (O – E)² / E

The chi‑squared statistic compares observed (O) and expected (E) frequencies to assess the goodness of fit. You will use critical value tables to interpret significance.

卡方统计量比较观察值 (O) 与期望值 (E) 以评估拟合优度，需结合临界值表判断显著性。

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