Year 10 Cambridge Science: Formula & Theorem Quick Reference Guide | 剑桥十年级科学：公式定理速查手册

📚 Year 10 Cambridge Science: Formula & Theorem Quick Reference Guide | 剑桥十年级科学：公式定理速查手册

This quick reference handbook brings together the essential formulas, laws and principles from the Cambridge IGCSE Science syllabus (0654) typically covered in Year 10. Whether you are tackling physics calculations, chemical quantifications or biological measurements, having these relationships at your fingertips will sharpen your problem-solving skills and deepen your conceptual understanding. Each section presents a core topic with the relevant equations, followed by a brief note on their application.

这本速查手册汇集了剑桥 IGCSE 科学大纲（0654）在十年级阶段需要掌握的核心公式、定律与原理。无论你面对的是物理计算、化学定量分析还是生物测量，熟记这些关系式都能提升你的解题能力，并加深对概念的理解。每一节围绕一个主题列出关键公式，并附上应用提示。

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1. Motion | 运动

Understanding motion begins with linking displacement, velocity, acceleration and time. The following equations apply when acceleration is constant.

理解运动要从位移、速度、加速度和时间的关系入手。以下公式适用于匀加速运动。

v = s / t

Average speed v equals distance s divided by time t. This is used for uniform motion.

平均速度 v 等于距离 s 除以时间 t，用于匀速运动。

a = (v − u) / t

Acceleration a is the change in velocity (v − u) per unit time t.

加速度 a 等于速度变化量 (v − u) 除以时间 t。

v = u + at

Final velocity v from initial velocity u, acceleration a and time t.

已知初速度 u、加速度 a 和时间 t 求末速度 v。

s = ut + ½at²

Displacement s from initial velocity, time and constant acceleration.

由初速度、时间和匀加速求位移 s。

v² = u² + 2as

Relates final velocity, initial velocity, acceleration and displacement without time.

表达末速度、初速度、加速度和位移的关系，不含时间变量。

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2. Forces and Newton's Laws | 力与牛顿定律

Newton's three laws form the foundation of mechanics, linking force, mass and motion.

牛顿三定律构成了力学基础，将力、质量与运动联系起来。

F = ma

Resultant force F equals mass m times acceleration a (Newton's second law).

合外力 F 等于质量 m 乘以加速度 a（牛顿第二定律）。

W = mg

Weight W is the product of mass and gravitational field strength g (≈ 9.8 N/kg on Earth).

重量 W 等于质量 m 乘以重力场强度 g（地球上约为 9.8 N/kg）。

p = mv

tion of momentum: total momentum before = total momentum after, if no external force acts.

动量 p 等于质量乘以速度。动量守恒定律：若系统不受外力，碰撞前后总动量保持不变。

Moment = F × d

Moment of a force (torque) about a pivot = force × perpendicular distance from pivot.

力矩 = 力 × 支点到力作用线的垂直距离。

P = F / A

Pressure P equals force F divided by area A over which the force acts.

压强 P 等于力 F 除以受力面积 A。

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3. Energy, Work and Power | 能量、功与功率

Energy can be stored or transferred, and quantifying these transfers uses straightforward formulas.

能量可以被储存或转移，使用这些简单公式可以对能量转移进行定量分析。

W = Fd

Work done W is force F multiplied by distance d moved in the direction of the force.

做功 W 等于力 F 乘以物体在力的方向上移动的距离 d。

KE = ½mv²

Kinetic energy KE depends on mass and the square of velocity.

动能 KE 与质量成正比，与速度的平方成正比。

PE = mgh

Gravitational potential energy change PE equals m × g × change in height h.

重力势能变化 PE 等于 m × g × 高度变化 h。

P = W / t or P = E / t

Power P is the rate of doing work or transferring energy.

功率 P 表示做功或能量转化的快慢。

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

Efficiency compares useful energy or power output with total input.

效率 =（有用输出能量/总输入能量）×100%。

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4. Waves | 波

Wave behaviour is described by two universal equations and Snell's law for refraction.

波动行为由两个通用公式和折射的斯涅尔定律描述。

v = fλ

Wave speed v equals frequency f multiplied by wavelength λ.

波速 v 等于频率 f 乘以波长 λ。

T = 1 / f

Period T is the reciprocal of frequency.

周期 T 是频率的倒数。

n = sin i / sin r

Refractive index n is the ratio of the sine of the angle of incidence i to the sine of the angle of refraction r.

折射率 n 等于入射角 i 的正弦与折射角 r 的正弦之比。

sin c = 1 / n

Critical angle c for total internal reflection can be found when light travels from a denser to a less dense medium.

光从光密介质射向光疏介质时，全反射的临界角 c 满足 sin c = 1 / n。

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5. Electricity | 电学

Electric circuits are analysed using relationships among voltage, current, resistance, power and energy.

分析电路时需要运用电压、电流、电阻、功率和能量之间的关系。

V = IR

Ohm's law: voltage V across a resistor equals current I times resistance R.

欧姆定律：电阻两端电压 V 等于电流 I 乘以电阻 R。

P = IV

Electrical power P is the product of current and voltage.

电功率 P 等于电流与电压的乘积。

P = I²R

Alternative power formula when current and resistance are known.

已知电流与电阻时计算功率的另一种形式。

E = IVt

Electrical energy transferred E = power × time = I × V × t.

电能转移 E = 功率 × 时间 = I × V × t。

Q = It

Charge Q passed equals current I multiplied by time t.

通过的电荷量 Q 等于电流 I 乘以时间 t。

Resistors in series: R_total = R₁ + R₂ + ... ; in parallel: 1/R_total = 1/R₁ + 1/R₂ + ...

电阻串联时总电阻 R_总 = R₁ + R₂ + …；并联时 1/R_总 = 1/R₁ + 1/R₂ + …

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6. The Mole Concept | 摩尔概念

Quantitative chemistry is built upon the mole, linking mass, gas volume and concentration.

定量化学的基础是摩尔，它把质量、气体体积和浓度关联在一起。

n = m / M

Amount of substance n (mol) equals mass m (g) divided by molar mass M (g/mol).

物质的量 n（mol）等于质量 m（g）除以摩尔质量 M（g/mol）。

n = V / V_m

For gases, n equals volume V divided by molar volume V_m (24 dm³/mol at room temperature and pressure, RTP).

对于气体，n 等于气体体积 V 除以摩尔体积 V_m（常温常压下为 24 dm³/mol）。

c = n / V

Concentration c (mol/dm³) is amount of solute divided by volume of solution.

浓度 c（mol/dm³）等于溶质的物质的量除以溶液的体积。

% yield = (actual yield / theoretical yield) × 100%

Percentage yield compares the mass of product actually obtained with the maximum theoretical yield.

产率百分数 =（实际产量/理论产量）×100%。

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7. Stoichiometry and Reaction Rates | 化学计量与反应速率

Balanced equations give mole ratios for reactants and products. Reaction rates can be measured and expressed mathematically.

配平的化学方程式提供了反应物和生成物之间的摩尔比。反应速率可以通过实验测量并用数学式表达。

For a reaction aA + bB → cC + dD, the mole ratio is a : b : c : d.

对于反应 aA + bB → cC + dD，摩尔比为 a : b : c : d。

Average rate = Δ quantity / Δ time

: rate = Δ mass / time, rate = Δ volume of gas / time, or rate = 1 / t for a fixed change.

例如：速率 = 质量变化/时间，速率 = 气体体积变化/时间，或对于固定变化量，速率 = 1/t。

The effect of concentration, temperature and surface area on rate can be explained by collision theory.

浓度、温度和表面积对速率的影响可以用碰撞理论解释。

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8. Thermochemistry | 热化学

Heat energy changes in chemical reactions are calculated using the specific heat capacity equation.

化学反应中的热量变化可以用比热容公式进行计算。

Q = mcΔT

y Q (J) equals mass m (g) × specific heat capacity c (J/g°C) × temperature change ΔT (°C).

热量 Q（J）等于质量 m（g）乘以比热容 c（J/g°C）再乘以温度变化 ΔT（°C）。

ΔH = −Q / n

Molar enthalpy change ΔH (J/mol) is found by dividing the heat released or absorbed by the number of moles that reacted (negative sign for exothermic, positive for endothermic as per convention).

摩尔焓变 ΔH（J/mol）等于反应放出的热量除以反应的物质的量（放热常用负值，吸热正值，此公式给出符号取决于 Q 的正负定义；通常 ΔH = −Q/n 用于测得温升的放热反应）。

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9. Biological Measurements | 生物学测量

Biology often requires calculations related to size, rate and probability.

生物学中常涉及与大小、速率和概率相关的计算。

Magnification = image size / actual size

: To find actual size, rearrange: actual size = image size / magnification. Ensure both measurements are in the same unit.

求实际大小时调整公式：实际大小 = 图像大小 / 放大倍数。注意单位统一。

Rate of photosynthesis = 1 / t

When a floating leaf disk reaches the surface, the rate can be expressed as the reciprocal of time taken, or as oxygen volume produced per unit time.

浮叶圆片浮起时，光合速率可用所用时间的倒数表示，也可用单位时间产生的氧气体积表示。

Genetic probability

Monohybrid cross ratios (3:1, 1:2:1) can be determined using Punnett squares. The probability of a particular phenotype or genotype is expressed as a fraction or percentage.

单基因杂交比例（3:1, 1:2:1）可由庞纳特方格得出。特定表现型或基因型的概率用分数或百分数表示。

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10. Critical Principles | 重要原理

Beyond formulas, several overarching principles are repeatedly tested.

除了公式，还有几条总括性原理经常出现在考试中。

• Conservation of energy: Energy cannot be created or destroyed, only transferred or transformed.

  能量守恒：能量不会凭空产生或消失，只会转移或转化。

• m (in isolated systems): total momentum before collision = total momentum after collision.

  动量守恒（孤立系统）：碰撞前后总动量相等。

• Conservation of mass in chemical reactions: mass of reactants = mass of products.

  化学反应质量守恒：反应物总质量等于生成物总质量。

• Le Chatelier's principle (introduced conceptually): if a system at equilibrium is disturbed, the system shifts to counteract the change.

  勒夏特列原理（概念引入）：如果改变平衡系统的条件，平衡将向着减弱这种改变的方向移动。

• Newton's third law: every action force has an equal and opposite reaction force.

  牛顿第三定律：每一个作用力都有一个大小相等、方向相反的反作用力。

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11. Common Units and Conversions | 常用单位与换算

Using correct units is vital. The table below lists frequently used SI units and common conversions you must know.

使用正确单位至关重要。下表列出了常用的国际单位及必须掌握的换算关系。

Quantity	SI Unit	Common Conversions
Length	metre (m)	1 cm = 0.01 m; 1 mm = 0.001 m
Mass	kilogram (kg)	1 g = 0.001 kg; 1 tonne = 1000 kg
Time	second (s)	1 min = 60 s; 1 h = 3600 s
Force / Weight	newton (N)	-
Energy / Work	joule (J)	1 kJ = 1000 J
Power	watt (W)	1 kW = 1000 W
Voltage	volt (V)	-
Current	ampere (A)	1 mA = 0.001 A
Resistance	ohm (Ω)	-
Concentration	mol/dm³	1 dm³ = 1 litre = 1000 cm³
Gas volume	dm³ or cm³	Molar vol. ≈ 24 dm³/mol at RTP

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Memorising these formulas is only the first step. Practise applying them in multi-step problems, always checking that units are consistent. Consistent review of this handbook will build the confidence needed for Cambridge Science assessments. Good luck!

记住这些公式只是第一步。在多步骤问题中反复练习运用它们，并始终检查单位是否统一。经常翻阅本手册将帮助你建立迎接剑桥科学考试所需的信心。祝你成功！

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