📚 Year 7 OCR Science: Quick Formula & Theorem Handbook | 7年级OCR科学公式定理速查手册
Welcome to your Year 7 OCR Science quick reference! This handbook summarises the key formulas, relationships and theorems you will meet in Physics, Chemistry and Biology during Year 7. Use it to revise how quantities are linked, to check the correct units, and to apply each relationship confidently to calculation and explanation questions. Every section gives the formula, the meaning of each symbol, the unit, and a short worked example you can copy into your revision notes.
欢迎使用你的7年级OCR科学速查手册！本手册汇总了你在7年级物理、化学和生物学科中会遇到的核心公式、关系式与定理。你可以用它复习各物理量之间的联系、核对正确的单位，并把每个关系式自信地应用到计算题和解释题中。每一节都会给出公式、每个符号的含义、单位，以及一个可以抄进复习笔记的简短例题。
1. Speed, Distance and Time | 速度、距离与时间
Speed is a measure of how rapidly an object moves. It is a scalar quantity, which means it only has magnitude (size) and no direction. The relationship linking speed, distance and time is the cornerstone of kinematics and the first formula most Year 7 students meet. If you know any two of the three quantities, you can always calculate the third.
速度是衡量物体运动快慢的物理量。它是一个标量，也就是说它只有大小、没有方向。连接速度、距离与时间的这个关系式是运动学的基础，也是大多数7年级学生遇到的第一个公式。只要知道三个量中的任意两个，就一定能算出第三个。
speed = distance ÷ time
速度 = 距离 ÷ 时间
v = s ÷ t 或 v = d ÷ t
res per second (m/s), s or d is the distance travelled in metres (m), and t is the time taken in seconds (s). Both s and d are used for distance in textbooks, so read the question carefully, but d is the more common choice in OCR-style questions.
用符号表示时，我们常写 v = s ÷ t 或 v = d ÷ t，其中 v 是速度，单位是米每秒（m/s）；s 或 d 是运动距离，单位是米（m）；t 是所用时间，单位是秒（s）。教材中 s 和 d 都用来表示距离，所以要仔细读题，不过在OCR风格的题目里 d 更常见。
- Speed is scalar (size only); velocity is a vector (size and direction). 速度是标量（只有大小）；速度矢量（velocity）是矢量（有大小也有方向）。
- walking ≈ 1.4 m/s, running ≈ 5 m/s, a car on a motorway ≈ 30 m/s, sound in air ≈ 330 m/s. 常见速度：步行约 1.4 m/s，跑步约 5 m/s，高速公路上汽车约 30 m/s，空气中的声速约 330 m/s。
- Worked example: a cyclist travels 150 m in 30 s, so v = 150 ÷ 30 = 5 m/s. 例题：骑行者30秒内前进150米，则 v = 150 ÷ 30 = 5 m/s。
2. SI Units, Symbols and Rearranging Formulas | 国际单位、符号与公式变形
Every formula in this handbook only works if the numbers are put in with the correct units. The internationally agreed system of units is called SI. In Year 7 you are expected to recognise the symbol for each quantity, write the correct unit after every answer, and convert simple units such as minutes into seconds or centimetres into metres before substituting.
本手册中的每一个公式都只有在代入正确单位的数值时才成立。国际上统一使用的单位制称为国际单位制（SI）。在7年级，你需要认识每个物理量的符号、在每个答案后写出正确单位，并在代入前完成简单单位换算，比如把分钟换成秒、把厘米换成米。
| Quantity 物理量 | Symbol 符号 | Unit 单位 |
|---|---|---|
| distance 距离 | s 或 d | metre 米 (m) |
| mass 质量 | m | kilogram 千克 (kg) |
| time 时间 | t | second 秒 (s) |
| speed 速度 | v | metre per second 米每秒 (m/s) |
| force 力 | F | newton 牛顿 (N) |
| density 密度 | ρ | kilogram per cubic metre 千克每立方米 (kg/m³) |
| energy 能量 | E | joule 焦耳 (J) |
| power 功率 | P | watt 瓦特 (W) |
| voltage 电压 | V | volt 伏特 (V) |
| current 电流 | I | ampere 安培 (A) |
| resistance 电阻 | R | ohm 欧姆 (Ω) |
tity you want, and the remaining arrangement shows the calculation. For speed, cover v and you see d over t; cover d and you see v × t; cover t and you see d ÷ v.
公式变形就是把公式改写，使另一个物理量成为主体。对7年级来说，最快的方法是用公式三角：遮住你想求的量，剩下的排列就显示运算方式。以求速度为例，遮住 v 就看到 d 在 t 上方；遮住 d 就看到 v × t；遮住 t 就看到 d ÷ v。
- s to remember: 1 minute = 60 s, 1 km = 1000 m, 1 cm = 0.01 m, 1 kg = 1000 g, 1 cm³ = 1 ml. 必须记住的单位换算：1分钟 = 60秒，1千米 = 1000米，1厘米 = 0.01米，1千克 = 1000克，1立方厘米 = 1毫升。
- Always write the unit on every answer unless the question asks for a ratio or a number only. 除非题目只要比值或纯数字，否则每个答案都要写单位。
3. Distance-Time Graphs and Average Speed | 距离-时间图像与平均速度
A distance-time graph plots distance travelled on the vertical axis against time on the horizontal axis. The gradient (steepness) of the line tells you the speed: a steeper line means a faster movement. A horizontal line means the object is stationary, because the distance is not changing while time passes. A curved line means the speed itself is changing.
距离-时间图像把行进距离画在纵轴、时间画在横轴。直线的斜率（陡峭程度）反映速度：线越陡，运动越快。水平线表示物体静止，因为时间在流逝而距离不变。曲线则表示速度本身在变化。
gradient = change in distance ÷ change in time
斜率 = 距离的变化量 ÷ 时间的变化量
The gradient of a distance-time graph therefore gives the speed in m/s, provided both axes use SI units. If a whole journey has several parts, the average speed describes the whole trip, not any single stage.
因此，只要两个坐标轴都用国际单位，距离-时间图像的斜率就直接给出以 m/s 为单位的速度。如果一段行程分成几段，平均速度描述的是整段行程，而不是其中任何单独的一段。
average speed = total distance ÷ total time
平均速度 = 总距离 ÷ 总时间
- time = 3 h, so average speed = 40 km/h, even though the car moved at 60 km/h and 30 km/h. 例题：汽车1小时行驶60千米，再用2小时行驶60千米。总距离120千米，总时间3小时，平均速度为40 km/h，尽管它分别以60 km/h和30 km/h行驶。
- ribes how quickly velocity changes: a = change in velocity ÷ time taken, measured in m/s². 加速度描述速度变化的快慢：a = 速度变化量 ÷ 所用时间，单位是 m/s²。
- Deceleration (slowing down) is simply negative acceleration; always state the direction if the question asks about velocity. 减速就是负的加速度；如果题目问的是速度矢量，一定要说明方向。
4. Forces, Weight and Gravity | 力、重力与重量
A force is a push or a pull, measured in newtons (N) with a newton meter. Forces can change an object's speed, direction or shape. Weight is a specific force: it is the pull of gravity on a mass, and it is calculated using the gravitational field strength of the planet you are standing on.
力是推或拉的作用，用牛顿（N）作单位，用弹簧测力计测量。力可以改变物体的速度、方向或形状。重量是一种特定的力：它是重力对质量产生的拉力，需要用你所在星球的重力场强度来计算。
weight = mass × gravitational field strength
W = m × g
rth g ≈ 9.8 N/kg, which is often rounded to 10 N/kg for quick Year 7 estimates. On the Moon g ≈ 1.6 N/kg, so the same astronaut has the same mass but a much smaller weight.
在这个公式中，W 是重量，单位牛顿（N）；m 是质量，单位千克（kg）；g 是重力场强度，单位牛顿每千克（N/kg）。在地球上 g ≈ 9.8 N/kg，7年级做快速估算时常取 10 N/kg。在月球上 g ≈ 1.6 N/kg，所以同一位宇航员质量不变，但重量小得多。
- Mass is the amount of matter in an object and is measured in kg; it is the same everywhere in the universe. 质量是物体所含物质的多少，用千克测量，在宇宙中任何地方都不变。
- Weight is a force and depends on the gravitational field strength where the object is. 重量是一种力，取决于物体所在地的重力场强度。
- Resultant force: add forces acting in the same direction and subtract forces acting in opposite directions. 合力：方向相同的力相加，方向相反的力相减。
- If the resultant force is zero, the forces are balanced and the object stays still or keeps moving at a steady speed. 如果合力为零，说明力是平衡的，物体保持静止或匀速直线运动。
5. Density, Mass and Volume | 密度、质量与体积
Density tells you how much mass is packed into a given volume. A dense material, such as iron, has a lot of mass in a small space, while a low-density material, such as foam, has very little. Density explains why some objects float in water while others sink.
密度表示在给定体积内装了多少质量。铁这类高密度材料在很小的空间里就有很大的质量，而泡沫这类低密度材料的质量则很小。密度可以解释为什么有的物体在水中漂浮、有的却下沉。
density = mass ÷ volume
ρ = m ÷ V
Here ρ is density in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³), m is mass in kg or g, and V is volume in m³ or cm³. Keep the units consistent: if mass is in grams, volume must be in cm³. The density of water is about 1000 kg/m³, which is the same as 1 g/cm³.
其中 ρ 是密度，单位是千克每立方米（kg/m³）或克每立方厘米（g/cm³）；m 是质量，单位是 kg 或 g；V 是体积，单位是 m³ 或 cm³。单位必须保持一致：如果质量用克，体积就必须用立方厘米。水的密度约为 1000 kg/m³，也就是 1 g/cm³。
- Objects less dense than water float; objects more dense than water sink. 密度小于水的物体漂浮；密度大于水的物体下沉。
- For a regular solid, volume = length × width × height, so ρ = m ÷ (l × w × h). 对于规则固体，体积 = 长 × 宽 × 高，所以 ρ = m ÷ (l × w × h)。
- For an irregular solid, find the volume by displacement: the rise in water level equals the volume of the object. 对不规则固体，用排水法测体积：水面上升的体积等于物体的体积。
- a volume of 30 cm³, so ρ = 240 ÷ 30 = 8 g/cm³, which is denser than water and would sink. 例题：一块质量240克、体积30立方厘米的物块，ρ = 240 ÷ 30 = 8 g/cm³，比水密，会下沉。
6. Pressure and Moments | 压强与力矩
Pressure is the force spread over a surface. The same force produces a small pressure over a large area and a large pressure over a small area, which is why sharp knives cut easily and why snowshoes stop you sinking into soft snow.
压强是分布在某个表面上的力。同样的力作用在大面积上产生小压强，作用在小面积上产生大压强，这就是锋利的刀容易切开物体、而雪鞋能防止你陷入软雪的原因。
pressure = force ÷ area
P = F ÷ A
s and area in square metres. In liquids, pressure increases with depth and also depends on the density of the liquid, which is why dam walls are thicker at the bottom.
压强的单位是帕斯卡（Pa），1 Pa = 1 N/m²。力用牛顿，面积用平方米。在液体中，压强随深度增加而增大，并且与液体密度有关，所以水坝的墙体底部做得更厚。
A moment is the turning effect of a force about a pivot. It depends on both the size of the force and how far from the pivot it acts.
力矩是力绕支点产生的转动效果。它同时取决于力的大小和力到支点的距离。
moment = force × perpendicular distance from the pivot
M = F × d （单位 N m）
- le of moments: for a balanced object, total clockwise moment = total anticlockwise moment. 力矩平衡原理：物体平衡时，顺时针力矩总和 = 逆时针力矩总和。
- Levers use moments to make a small force able to move a large load; a longer handle gives a bigger moment. 杠杆利用力矩使小力能移动大负载；手柄越长，力矩越大。
- Worked example: a 20 N force acts 0.5 m from a pivot, so M = 20 × 0.5 = 10 N m. 例题：20牛的力作用在距支点0.5米处，M = 20 × 0.5 = 10 N m。
7. Energy, Work and Power | 能量、功与功率
Energy is the ability
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