📚 Year 9 AQA Science: Formula & Theorem Quick Reference Guide | Year 9 AQA 科学：公式定理速查手册
This bilingual quick reference guide covers the essential formulas and theorems for Year 9 AQA Science, including physics equations for motion, forces, energy, electricity, waves, density and pressure, plus the key biology and chemistry principles that appear most often in end-of-topic tests and in the foundations of GCSE. Every formula is presented with a clear explanation, its correct units, and a short worked example so that you can apply it with confidence rather than simply memorise it.
这本双语速查手册涵盖了 Year 9 AQA 科学的核心公式和定理，包括运动、力、能量、电学、波、密度与压强等物理方程，以及最重要的生物和化学原理。每一个公式都配有清晰的解释、正确的单位和简短示例，帮助你真正会用它，而不是死记硬背。这本手册适合单元测验前的快速复习，也适合作为 GCSE 阶段的基础工具书反复查阅。
1. Speed, Distance and Time | 速度、距离与时间
Speed is a measure of how fast an object moves. It is calculated by dividing the distance travelled by the time taken, and it is a scalar quantity, which means it has size but no direction.
速度是衡量物体运动快慢的物理量，它等于物体运动的距离除以所用时间。速度是标量，也就是说它只有大小、没有方向。
v = d / t
where v is speed (m/s), d is distance (m), and t is time (s). In AQA questions you are expected to write the equation, substitute the numbers, and then give the answer with the correct unit.
其中 v 是速度(米/秒)，d 是距离(米)，t 是时间(秒)。在 AQA 的题目中，你需要先写出公式、再代入数值，最后给出带正确单位的答案。
For example, if a car travels 100 metres in 5 seconds, its speed is v = 100 / 5 = 20 m/s.
例如，如果一辆汽车在 5 秒内行驶了 100 米，它的速度就是 v = 100 / 5 = 20 米/秒。
eful memory triangle places d on top, with v and t underneath, so covering the quantity you want shows the calculation you need.
你可以变换公式来求距离：d = v × t，或求时间：t = d / v。一个常用的记忆三角形把 d 放在上面、v 和 t 放在下面，用手遮住要求的量，剩下的部分就是计算方式。
Speed and velocity are not the same thing. Velocity is a vector, so it also includes direction. A runner who completes a full lap of a 400 m track at 5 m/s has an average speed of 5 m/s but an average velocity of zero, because the displacement is zero.
速度和速度（速率与速度矢量）并不相同。速度矢量包含方向。一名以 5 米/秒跑完 400 米跑道一整圈的运动员，平均速率是 5 米/秒，但平均速度矢量为零，因为位移为零。
600 s. Questions often give distance in kilometres and time in minutes, so convert first and calculate second.
必须掌握的常见换算：1 千米 = 1000 米，1 分钟 = 60 秒，1 小时 = 3600 秒。题目常以千米给距离、以分钟给时间，所以要先换算、后计算。
2. Acceleration | 加速度
Acceleration tells us how quickly the velocity of an object changes. It is the rate of change of velocity, measured in metres per second squared (m/s²).
加速度表示物体速度变化的快慢，是速度的变化率，单位是米每二次方秒 (m/s²)。
a = (v − u) / t
aken for the change (s). Some textbooks write this as a = Δv / t, where Δ means change in.
其中 a 是加速度(米/秒²)，v 是末速度(米/秒)，u 是初速度(米/秒)，t 是速度发生变化所用的时间(秒)。有些教材写作 a = Δv / t，其中 Δ 表示变化量。
le, a cyclist speeds up from 2 m/s to 10 m/s in 4 seconds. Then a = (10 − 2) / 4 = 2 m/s².
例如，一名骑行者用 4 秒从 2 米/秒加速到 10 米/秒，则 a = (10 − 2) / 4 = 2 米/秒²。
If the final velocity is smaller than the initial velocity, the answer is negative. This is called deceleration, or negative acceleration, and it simply means the object is slowing down. A negative sign is not wrong; it carries real information about direction.
如果末速度小于初速度，结果就是负数。这被称为减速或负加速度，只表示物体正在变慢。负号并不是错误，它携带了方向的真实信息。
On a distance-time graph, the gradient gives speed; a steeper line means a faster object and a flat line means it is stationary. On a velocity-time graph, the gradient gives acceleration and the area under the line gives the distance travelled. These two graph skills are examined every year.
在距离-时间图像中，斜率代表速率；线越陡说明越快，水平线说明物体静止。在速度-时间图像中，斜率代表加速度，曲线下方的面积代表行驶的距离。这两种图像技能每年都会考查。
Uniform acceleration, where the velocity changes by the same amount each second, is the simplest case and is the one Year 9 questions almost always use.
匀加速运动指每秒钟速度变化量相同，这是最简单的情形，也是 Year 9 题目几乎总是采用的情形。
3. Forces and Newton's Laws | 力与牛顿定律
A force is a push or a pull, measured in newtons (N). Forces are vectors, so they have both size and direction. When several forces act on an object, we add them as vectors to find the resultant force.
力是推或拉的作用，单位是牛顿 (N)。力是矢量，既有大小也有方向。当多个力作用于同一物体时，我们要按矢量相加求出合力。
Forces acting in the same direction are added; forces acting in opposite directions are subtracted. If the resultant force is zero, the object stays at rest or continues moving at a constant velocity. If the resultant force is not zero, the object accelerates in the direction of that force.
同方向的力相加，反方向的力相减。如果合力为零，物体保持静止或继续匀速运动；如果合力不为零，物体就沿着合力的方向加速。
F = m × a
where F is the resultant force (N), m is mass (kg), and a is acceleration (m/s²). This is Newton's second law and it links the three quantities you will use most often in physics.
其中 F 是合力(牛顿)，m 是质量(千克)，a 是加速度(米/秒²)。这就是牛顿第二定律，它把物理学中最常用的三个量联系在了一起。
ample, a resultant force of 30 N acts on a 6 kg trolley. Then a = F / m = 30 / 6 = 5 m/s².
例如，30 牛的合力作用在 6 千克的小车上，则 a = F / m = 30 / 6 = 5 米/秒²。
Newton's three laws in short: an object stays at rest or moves at constant velocity unless a resultant force acts (first law); the acceleration is proportional to the resultant force and inversely proportional to the mass (second law); and for every action there is an equal and opposite reaction (third law).
牛顿三定律简述：除非有合力作用，物体保持静止或匀速运动（第一定律）；加速度与合力成正比、与质量成反比（第二定律）；每一个作用力都有一个大小相等、方向相反的反作用力（第三定律）。
Common forces to name accurately: weight (gravity acting downwards), normal contact force (perpendicular to a surface), friction and air resistance (opposing motion), tension (in a rope or cable), and upthrust (in a fluid).
需要准确命名的常见力：重力（向下）、法向接触力（垂直于表面）、摩擦力和空气阻力（与运动方向相反）、张力（绳或缆中）以及浮力（流体中）。
4. Weight, Mass and Gravity | 重力、质量与重力加速度
Mass is the amount of matter in an object and is measured in kilograms. It does not change wherever the object is. Weight is the force of gravity acting on that mass and is measured in newtons, so it changes from planet to planet.
质量是物体所含物质的多少，单位是千克，无论物体在哪里都不改变。重力是作用在该质量上的引力，单位是牛顿，因此它在不同星球上会改变。
W = m × g
th g = 9.8 N/kg, often rounded to 10 N/kg in Year 9 work. On the Moon g is about 1.6 N/kg.
其中 W 是重力(牛顿)，m 是质量(千克)，g 是重力场强度(牛/千克)。在地球上 g = 9.8 牛/千克，Year 9 的题目常取 10 牛/千克；在月球上 g 约为 1.6 牛/千克。
same student on the Moon would weigh only 50 × 1.6 = 80 N, but their mass is still 50 kg.
例如，一名质量 50 千克的学生在地球上的重力为 W = 50 × 10 = 500 牛；在月球上只有 50 × 1.6 = 80 牛，但他的质量仍然是 50 千克。
| Quantity | Unit | Changes with location? |
| Mass | kilogram (kg) | No |
| Weight | newton (N) | Yes |
| Gravitational field strength | newton per kilogram (N/kg) | Yes |
s check the unit: if the question gives newtons, it is a force; if it gives kilograms, it is a mass.
常见的考试陷阱是把 F = m × a 中的质量和重力混淆。务必检查单位：题目给牛顿就是力，给千克就是质量。
5. Work Done, Energy Transferred and Power | 功、能量转移与功率
Work is done whenever a force moves an object through a distance. The energy transferred is equal to the work done, and both are measured in joules (J).
当力使物体沿力的方向移动一段距离时，就说做了功。转移的能量等于所做的功，两者单位都是焦耳 (J)。
W = F × s
where W is work done (J), F is force (N), and s is the distance moved in the direction of the force (m). Note that no work is done if the force is perpendicular to the motion, which is why carrying a box horizontally against gravity transfers no gravitational energy to it.
其中 W 是功(焦耳)，F 是力(牛顿)，s 是沿力方向移动的距离(米)。注意，若力与运动方向垂直则不做功，这就是水平搬运箱子时不会给箱子增加重力势能的原因。
Power is the rate of energy transfer, or the rate of doing work.
功率是能量转移的速率，也就是做功的快慢。
P = E / t
where P is power (W), E is energy transferred (J), and t is time (s). One watt equals one joule per second.
其中 P 是功率(瓦特)，E 是转移的能量(焦耳)，t 是时间(秒)。1 瓦特等于 1 焦耳每秒。
For example, a motor transfers 3000 J of energy in 15 s, so P = 3000 / 15 = 200 W.
例如，一台电动机在 15 秒内转移 3000 焦耳能量，则 P = 3000 / 15 = 200 瓦。
Efficiency compares the useful energy output with the total energy input and is usually written as a percentage. Energy is always conserved overall, but not all of it is transferred usefully; the rest is often dissipated to the surroundings by heating.
效率比较有用能量输出与总能量输入，通常用百分比表示。能量总量始终守恒，但并非全部有用转移，其余常以热的形式耗散到环境中。
6. Kinetic and Gravitational Potential Energy | 动能与重力势能
Energy can be stored and transferred between different stores. Two stores you must be able to calculate are kinetic energy and gravitational potential energy.
能量可以在不同的能量库之间储存和转移。你必须会计算的两类是动能和重力势能。
Eₖ = ½ × m × v²
where Eₖ is kinetic energy (J), m is mass (kg), and v is speed (m/s). Because the speed is squared, doubling the speed gives four times the kinetic energy. This is why braking distances increase so sharply at high speed.
其中 Eₖ 是动能(焦耳)，m 是质量(千克)，v 是速率(米/秒)。由于速率是平方项，速率加倍会使动能变为四倍，这就是高速时刹车距离急剧增加的原因。
Eₚ = m × g × h
where Eₚ is gravitational potential energy (J), m is mass (kg), g is gravitational field strength (N/kg), and h is the height gained (m).
其中 Eₚ 是重力势能(焦耳)，m 是质量(千克)，g 是重力场强度(牛/千克)，h 是上升高度(米)。
d with exactly 100 J of kinetic energy, so ½ × 2 × v² = 100 gives v² = 100 and v = 10 m/s.
例如，一个 2 千克的球从 5 米高处落下，其储存的能量为 Eₚ = 2 × 10 × 5 = 100 焦耳。忽略空气阻力，它落地时正好具有 100 焦耳的动能，所以 ½ × 2 × v² = 100，得 v² = 100，v = 10 米/秒。
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between stores. A swinging pendulum is the classic example: gravitational potential energy is maximum at the highest point and kinetic energy is maximum at the lowest point, and the total stays constant apart from a small amount dissipated by friction.
能量守恒定律指出，能量既不能被创造也不能被消灭，只能在不同的能量库之间转移。摆动的单摆是经典例子：最高点重力势能最大，最低点动能最大，除了少量因摩擦耗散外，总量保持不变。
7. Electricity: Charge, Current, Resistance and Power | 电学：电荷、电流、电阻与电功率
Electric current is the rate of flow of electric charge. In a series circuit the current is the same everywhere; in a parallel circuit the current splits between the branches.
电流是电荷流动的速率。在串联电路中各处电流相同；在并联电路中电流在各支路之间分流。
Q = I × t
). For example, a current of 2 A flowing for 30 s transfers a charge of Q = 2 × 30 = 60 C.
其中 Q 是电荷(库仑)，I 是电流(安培)，t 是时间(秒)。例如，2 安培的电流持续 30 秒，转移的电荷为 Q = 2 × 30 = 60 库仑。
V = I × R
ential difference (volts, V), I is current (A), and R is resistance (ohms, Ω). This is Ohm' Ω resistor with 0.5 A flowing through it has a potential difference of V = 0.5 × 12 = 6 V.
其中 V 是电压/电势差(伏特)，I 是电流(安培)，R 是电阻(欧姆，Ω)。这就是欧姆定律。例如，0.5 安培电流通过 12 欧姆的电阻，其两端电压为 V = 0.5 × 12 = 6 伏。
P = V × I
where P is power (W). Combining this with Ohm' law gives P = I² × R and P = V² / R, both of which are useful when one quantity is fixed.
其中 P 是功率(瓦特)。结合欧姆定律还可得到 P = I² × R 和 P = V² / R，当其中某个量固定时非常有用。
is billed in kilowatt-hours (kWh). You should also be able to state that in a series circuit the total resistance is the sum of the individual resistors, while in parallel the total resistance is less than the smallest individual resistor.
用电器转移的能量由 E = P × t 求出，家庭用电则以千瓦时 (kWh) 计费。你还应能说明：串联电路中总电阻等于各电阻之和，而并联电路的总电阻小于其中最小的那个电阻。
8. Waves: Speed, Frequency, Wavelength and Period | 波：波速、频率、波长与周期
A wave transfers energy from one place to another without transferring matter. All waves can be described by their amplitude, wavelength, frequency and speed.
波把能量从一处传到另一处，但不转移物质。所有波都可以用振幅、波长、频率和波速来描述。
v = f × λ
where v is wave speed (m/s), f is frequency (hertz, Hz), and λ (lambda) is wavelength (m). Frequency is the number of complete waves passing a point each second.
其中 v 是波速(米/秒)，f 是频率(赫兹)，λ（拉姆达）是波长(米)。频率是每秒钟通过某一点的完整波的个数。
wavelength 0.68 m travels at v = 500 × 0.68 = 340 m/s, which is the speed of sound in air.
例如，频率 500 赫兹、波长 0.68 米的声波，其波速为 v = 500 × 0.68 = 340 米/秒，这正是声音在空气中的速度。
T = 1 / f
me period (s). For example, a wave of frequency 50 Hz has a period of T = 1 / 50 = 0.02 s.
其中 T 是周期(秒)。例如，频率 50 赫兹的波，其周期为 T = 1 / 50 = 0.02 秒。
Transverse waves, such as light and water ripples, vibrate perpendicular to the direction of travel. Longitudinal waves, such as sound, vibrate parallel to the direction of travel and consist of compressions and rarefactions.
横波（如光和水的涟漪）振动方向与传播方向垂直；纵波（如声音）振动方向与传播方向平行，由密部和疏部组成。
When a wave passes from one medium to another, its speed and wavelength change but its frequency stays the same. This is a favourite exam point and a common source of lost marks.
当波从一种介质进入另一种介质时，波速和波长会改变，但频率保持不变。这是考试最爱的考点，也是常见的失分点。
9. Density, Pressure and Moments | 密度、压强与力矩
Density describes how much mass is packed into a given volume. It explains why a heavy steel block sinks while a same-sized block of wood floats.
密度描述单位体积内包含多少质量，它解释了为什么沉重的钢块会下沉，而同体积的木块会浮起。
ρ = m / V
For example, 500 g of a solid occupying 200 cm³ has a density of 2.5 g/cm³, or 2500 kg/m³.
其中 ρ（柔）是密度(千克/米³)，m 是质量(千克)，V 是体积(米³)。注意 1 克/厘米³ = 1000 千克/米³。例如，500 克的固体体积为 200 厘米³，其密度为 2.5 克/厘米³，也就是 2500 千克/米³。
p = F / A
where p is pressure (pascals, Pa), F is force (N), and A is area (m²). One pascal equals one newton per square metre. The same force on a smaller area gives a larger pressure, which is why a sharp knife cuts easily and why snowshoes stop you sinking.
其中 p 是压强(帕斯卡)，F 是力(牛顿)，A 是面积(米²)。1 帕斯卡等于 1 牛顿每平方米。相同的力作用在更小的面积上会产生更大的压强，这就是利刃容易切割、而雪地鞋能防止下陷的原因。
M = F × d
where M is the moment of a force (N m), F is the force (N), and d is the perpendicular distance from the pivot (m). An object is balanced when the total clockwise moment equals the total anticlockwise moment, which is the principle of moments.
其中 M 是力矩(牛·米)，F 是力(牛顿)，d 是从支点算起的垂直距离(米)。当顺时针力矩总和等于逆时针力矩总和时物体平衡，这就是力矩平衡原理。
Liquid pressure increases with depth and with the density of the liquid. Atmospheric pressure also decreases as you go higher, which is why aircraft cabins are pressurised.
液体压强随深度和液体密度增加而增大。大气压强也随高度上升而减小，这就是飞机客舱需要增压的原因。
10. Key Biology Principles: Magnification and Surface Area | 生物关键原理：放大倍数与表面积
In biology, quantitative skills matter as much as description. The two calculations that appear most often in Year 9 are magnification and surface area to volume ratio.
在生物中，定量技能和文字描述同样重要。Year 9 最常出现的两个计算是放大倍数和表面积与体积之比。
M = image size / actual size
a cell of actual length 0.05 mm appears 2 mm long in a photograph, so M = 2 / 0.05 = ×40.
其中 M 是放大倍数。相除前两个长度必须单位一致，并记住 1 毫米 = 1000 微米。例如，实际长度 0.05 毫米的细胞在照片中显示为 2 毫米，则 M = 2 / 0.05 = 40 倍。
a ratio. If the question asks for actual size, rearrange to actual size = image size / M.
放大倍数没有单位，因为它是一个比值。如果题目要求实际大小，可变形为：实际大小 = 图像大小 / 放大倍数。
Surface area to volume ratio explains why single-celled organisms can rely on diffusion alone, while larger organisms need specialised exchange surfaces and transport systems.
表面积与体积之比解释了为什么单细胞生物仅靠扩散就能满足需要，而较大的生物则需要专门的交换表面和运输系统。
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