Formula & Theorem Quick Reference Handbook | 公式定理速查手册

📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册

Welcome to your Year 9 CAIE Science formula and theorem quick reference guide. This handbook brings together all the essential equations and principles from Physics, Chemistry and Biology that you need to understand and apply with confidence. For each formula you will find its meaning, standard units, a worked example and a clear explanation of the underlying concept, helping you to solve numerical problems accurately and prepare effectively for your assessments.

欢迎使用九年级 CAIE 科学公式定理速查手册。本手册汇集了物理、化学和生物中必须掌握的所有核心公式和定理。在每一条公式旁，你都能找到它的含义、标准单位、计算示例以及对基本概念的清晰解释，方便你准确解决计算题，高效备战考试。

1. Speed, Distance and Time | 速度、路程与时间

Speed is a measure of how quickly an object moves. The formula links distance travelled to the time taken: speed = distance / time. In symbols, v = d / t, where v is speed in metres per second (m/s), d is distance in metres (m) and t is time in seconds (s). For constant speed, simply divide the total distance by the total time.

速度是物体运动快慢的量度。公式将运动路程与所用时间联系起来：速度 = 路程 / 时间。用符号表示为 v = d / t，其中 v 是速度（单位 m/s），d 是路程（m），t 是时间（s）。匀速运动时，直接用总路程除以总时间即可。

When the speed of an object is not constant, we often calculate the average speed. Average speed = total distance / total time. For example, if a cyclist covers 450 m in 30 s, her average speed is 450 / 30 = 15 m/s.

当物体速度不恒定时，我们常计算平均速度。平均速度 = 总路程 / 总时间。例如，一位自行车手在 30 s 内骑行了 450 m，她的平均速度就是 450 / 30 = 15 m/s。

2. Acceleration | 加速度

Acceleration tells us how quickly the velocity of an object changes. It is defined as the change in velocity divided by the time taken for that change. The formula is a = (v − u) / t, where a is acceleration in metres per second squared (m/s²), v is final velocity (m/s), u is initial velocity (m/s) and t is time (s).

加速度表示物体速度变化的快慢。它定义为速度的变化量除以发生变化所用的时间。公式为 a = (v − u) / t，其中 a 是加速度（单位 m/s²），v 是末速度（m/s），u 是初速度（m/s），t 是时间（s）。

A positive value means the object is speeding up, while a negative value (deceleration) means it is slowing down. For instance, a car increases its speed from 10 m/s to 25 m/s in 5 s. Its acceleration is (25 − 10) / 5 = 3 m/s².

正值表示物体在加速，负值（减速度）则表示物体在减速。例如，一辆汽车在 5 s 内速度从 10 m/s 增加到 25 m/s，它的加速度为 (25 − 10) / 5 = 3 m/s²。

3. Newton’s Second Law | 牛顿第二定律

Newton’s Second Law relates the net force acting on an object to its mass and acceleration. The formula is F = m a. Force (F) is measured in newtons (N), mass (m) in kilograms (kg) and acceleration (a) in metres per second squared (m/s²). The greater the mass, the larger the force needed to achieve the same acceleration.

牛顿第二定律将作用在物体上的合力与物体的质量和加速度联系起来。公式为 F = m a。力（F）的单位是牛顿（N），质量（m）的单位是千克（kg），加速度（a）的单位是米每二次方秒（m/s²）。质量越大，要产生同样的加速度所需的力就越大。

A resultant force causes an acceleration in the same direction. If a 5 kg trolley is pushed with a force of 15 N, the acceleration produced is a = F / m = 15 / 5 = 3 m/s².

合力使物体沿力的方向产生加速度。如果用 15 N 的力推动一辆质量为 5 kg 的小车，产生的加速度为 a = F / m = 15 / 5 = 3 m/s²。

4. Density | 密度

Density describes how much mass is packed into a given volume. The formula is ρ = m / V, where ρ (rho) is density, m is mass and V is volume. Density can be expressed in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³).

密度描述单位体积内所含物质的质量。公式为 ρ = m / V，其中 ρ 表示密度，m 是质量，V 是体积。密度的单位可以是千克每立方米（kg/m³）或克每立方厘米（g/cm³）。

For example, a metal block of mass 250 g occupies a volume of 50 cm³. Its density is 250 / 50 = 5 g/cm³. Substances with lower density float on those with higher density.

例如，一块金属质量为 250 g，体积为 50 cm³，它的密度就是 250 / 50 = 5 g/cm³。密度较低的物体会浮在密度较高的物体上。

5. Pressure on Solids | 固体压强

Pressure is the force acting per unit area. For a solid, pressure p = F / A, where p is pressure in pascals (Pa) or N/m², F is force in newtons (N) and A is area in square metres (m²). A small force applied over a tiny area can produce a very high pressure.

压强是单位面积上所受的力。对于固体，压强 p = F / A，其中 p 的单位是帕斯卡（Pa）或 N/m²，F 是力（N），A 是受力面积（m²）。很小的力作用在极小的面积上能产生很大的压强。

A person wearing stiletto heels exerts a larger pressure on the floor than when wearing flat shoes because the same weight is spread over a smaller area. If a force of 600 N acts on an area of 0.05 m², the pressure is 600 / 0.05 = 12 000 Pa.

穿高跟鞋的人对地面的压强比穿平底鞋时更大，因为同样的体重分散在更小的面积上。如果 600 N 的力作用在 0.05 m² 的面积上，压强为 600 / 0.05 = 12 000 Pa。

6. Work Done | 做功

Work is done when a force moves an object in the direction of the force. The formula is W = F d, where W is work done in joules (J), F is force in newtons (N) and d is distance moved in the direction of the force in metres (m). Note that 1 J = 1 N m.

当一个力使物体沿力的方向移动时，就说力做了功。公式为 W = F d，其中 W 是做功（单位焦耳 J），F 是力（N），d 是沿力方向移动的距离（m）。注意 1 J = 1 N·m。

If you lift a 20 N weight vertically through a height of 2 m, the work done against gravity is W = 20 × 2 = 40 J. No work is done if there is no movement in the direction of the force.

如果你将一个重 20 N 的物体竖直提升 2 m，克服重力做功为 W = 20 × 2 = 40 J。如果物体没有沿力方向发生移动，则没有做功。

7. Power | 功率

Power is the rate at which work is done or energy is transferred. The formula is P = W / t or P = E / t, where P is power in watts (W), W is work done in joules (J), E is energy transferred (J) and t is time in seconds (s). One watt is one joule per second.

功率是做功或能量转移的速率。公式为 P = W / t 或 P = E / t，其中 P 是功率（单位瓦特 W），W 是做功（J），E 是转移的能量（J），t 是时间（s）。1 瓦特等于每秒 1 焦耳。

A motor that does 800 J of work in 10 s develops a power of 800 / 10 = 80 W. Appliances with higher power ratings transfer energy faster.

一台电动机在 10 s 内做了 800 J 的功，它的功率就是 800 / 10 = 80 W。额定功率越大的电器，能量转移得越快。

8. Ohm’s Law | 欧姆定律

Ohm’s Law states that the current through a resistor is directly proportional to the potential difference across it, provided temperature remains constant. The formula is I = V / R, where I is current in amperes (A), V is potential difference in volts (V) and R is resistance in ohms (Ω).

欧姆定律指出，在温度不变的条件下，通过电阻的电流与它两端的电势差成正比。公式为 I = V / R，其中 I 是电流（单位安培 A），V 是电势差（V），R 是电阻（单位欧姆 Ω）。

For a fixed resistor, if the voltage is doubled, the current also doubles. A lamp has a resistance of 10 Ω and is connected to a 5 V supply. The current is I = 5 / 10 = 0.5 A.

对于定值电阻，如果电压加倍，电流也加倍。一只灯泡的电阻为 10 Ω，接在 5 V 的电源上，电流为 I = 5 / 10 = 0.5 A。

9. Electrical Power | 电功率

The power of an electrical component can be calculated using P = I V, where P is power in watts (W), I is current in amperes (A) and V is voltage in volts (V). This equation applies to any circuit element. For resistors, it can also be written as P = I² R or P = V² / R.

用电器的电功率可用 P = I V 计算，其中 P 是功率（W），I 是电流（A），V 是电压（V）。该公式适用于任何电路元件。对于电阻，还可写成 P = I² R 或 P = V² / R。

An electric heater draws 4 A from a 230 V supply. Its power rating is P = 4 × 230 = 920 W. Knowing the power helps us calculate energy consumption: energy = power × time.

一台电暖气从 230 V 电源中汲取 4 A 电流，它的额定功率为 P = 4 × 230 = 920 W。知道了功率就能计算能量消耗：能量 = 功率 × 时间。

10. Magnification | 放大率

In biology and physics, magnification describes how much larger an image appears compared with the actual object. It is calculated using M = I / A, where M is magnification (no unit), I is image size and A is actual size, both measured in the same length unit (e.g. mm).

在生物和物理中，放大率表示图像比实物放大了多少倍。计算公式为 M = I / A，其中 M 是放大率（无单位），I 是图像大小，A 是实物大小，二者使用相同的长度单位（如 mm）。

When using a microscope, the image size can be measured with a ruler, while the actual size is either known or estimated. If a cell image measures 30 mm and the actual cell diameter is 0.5 mm, the magnification is 30 / 0.5 = 60×.

使用显微镜时，图像大小可用尺子测量，而实物大小是已知或估算的。如果一个细胞图像长 30 mm，实际细胞直径为 0.5 mm，放大率就是 30 / 0.5 = 60 倍。

11. Relative Atomic Mass and Molar Mass | 相对原子质量与摩尔质量

The relative atomic mass Aᵣ of an element is the average mass of its atoms compared with 1/12 of the mass of a carbon-12 atom. It has no unit. The relative molecular mass Mᵣ is the sum of the Aᵣ values of all atoms in a molecule.

元素的相对原子质量 Aᵣ 是其原子的平均质量与一个碳‑12 原子质量的 1/12 的比值，没有单位。相对分子质量 Mᵣ 是分子中所有原子的 Aᵣ 之和。

The mole concept links mass to number of particles. The amount of substance n (mol) can be found using n = m / M, where m is mass in grams (g) and M is molar mass in grams per mole (g/mol). Numerically, the molar mass is equal to the relative atomic or molecular mass.

摩尔概念将质量与粒子数联系起来。物质的量 n（单位 mol）可用 n = m / M 求得，其中 m 是质量（g），M 是摩尔质量（g/mol）。摩尔质量的数值等于相对原子质量或相对分子质量。

For example, the molar mass of water (H₂O) is (2 × 1) + 16 = 18 g/mol. To obtain 36 g of water, the amount is n = 36 / 18 = 2 mol.

例如，水（H₂O）的摩尔质量为 (2 × 1) + 16 = 18 g/mol。要得到 36 g 水，物质的量为 n = 36 / 18 = 2 mol。

12. Concentration of Solutions | 溶液浓度

The concentration of a solution tells us how much solute is dissolved in a given volume of solvent. In Year 9 science, concentration is often expressed as mass concentration: concentration (g/dm³) = mass of solute (g) / volume of solution (dm³). This is useful for preparing solutions.

溶液浓度表示在一定体积的溶剂中溶解了多少溶质。九年级科学中常使用质量浓度：浓度 (g/dm³) = 溶质质量 (g) / 溶液体积 (dm³)。这对配制溶液非常实用。

When using the mole concept, molar concentration c is calculated as c = n / V, where n is moles of solute (mol) and V is volume of solution in dm³. The unit is mol/dm³. A 2 dm³ solution containing 0.5 mol of sodium chloride has a concentration of 0.5 / 2 = 0.25 mol/dm³.

引入摩尔概念后，物质的量浓度 c 用 c = n / V 计算，其中 n 是溶质的物质的量（mol），V 是溶液体积（dm³），单位是 mol/dm³。如果 2 dm³ 的溶液中含有 0.5 mol 氯化钠，其浓度为 0.5 / 2 = 0.25 mol/dm³。

Remember that 1 dm³ = 1000 cm³. Always convert volumes to dm³ if the concentration is required in mol/dm³ or g/dm³.

记住 1 dm³ = 1000 cm³。如果浓度要求用 mol/dm³ 或 g/dm³ 表示，一定要把体积换算成立方分米。

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Formula & Theorem Quick Reference Handbook | 公式定理速查手册