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Year 11 SQA Engineering: Quick Reference Handbook of Formulas and Theorems | SQA 工程（Year 11）：公式定理速查手册

2026-07-22 02:30 · 本文部分内容由AI辅助创作

📚 Year 11 SQA Engineering: Quick Reference Handbook of Formulas and Theorems | SQA 工程（Year 11）：公式定理速查手册

This comprehensive quick reference handbook compiles all the essential formulas and theorems required for the Year 11 SQA Engineering Science course. It covers mechanics, electricity, electronics, energy and materials, and for every relationship it gives the symbol, the unit, the physical meaning and a short worked example. Used properly, this handbook is not a list to memorise blindly but a revision map: read a section, close the page, and try to rebuild the formula and its units from memory.

这本综合速查手册汇编了 SQA 工程科学（Year 11）课程所需的全部基本公式与定理，涵盖力学、电学、电子学、能量与材料。每一条关系式都给出符号、单位、物理含义和一个简短例题。使用得当时，它不是一份需要死记硬背的清单，而是一张复习地图：读完一节，合上页面，试着凭记忆把公式和单位重新推导出来。

Every formula below is written with Unicode symbols so that it displays correctly on any device. Where a derivation is required by the course, the derivation is explained in words rather than quoted as a result, because SQA marking schemes reward correct method, correct substitution and correct units far more than a memorised final answer.

下文所有公式均使用 Unicode 符号书写，确保在任何设备上都能正确显示。凡课程要求推导的内容，本书都用文字说明推理过程，而不是直接给出结论，因为 SQA 评分标准奖励的是正确方法、正确代入与正确单位，而不是背下来的最终答案。

1. SI Units, Prefixes and Dimensional Consistency | 国际单位、词头与量纲一致性

In engineering, a numerical answer without a unit is meaningless. SQA markers award method marks for correct substitution, so the safest habit is to convert every quantity into SI base or derived units before you substitute it into an equation.

在工程中，没有单位的数值答案毫无意义。SQA 阅卷会为正确的代入给出方法分，因此最稳妥的习惯是：在代入方程之前，先把每个量换算成 SI 基本单位或导出单位。

Quantity 物理量Base unit 基本单位Symbol 符号
Length 长度metre 米m
Mass 质量kilogram 千克kg
Time 时间second 秒s
Electric current 电流ampere 安培A
Temperature 温度kelvin 开尔文K

The common prefixes you must recognise instantly are tera (T, 10¹²), giga (G, 10⁹), mega (M, 10⁶), kilo (k, 10³), centi (c, 10⁻²), milli (m, 10⁻³), micro (µ, 10⁻⁶) and nano (n, 10⁻⁹). A millimetre is therefore 10⁻³ m and a megawatt is 10⁶ W.

必须一眼认出的常见词头包括：tera（T，10¹²）、giga（G，10⁹）、mega（M，10⁶）、kilo（k，10³）、centi（c，10⁻²）、milli（m，10⁻³）、micro（µ，10⁻⁶）、nano（n，10⁻⁹）。因此 1 毫米 = 10⁻³ m，1 兆瓦 = 10⁶ W。

f speed. If your rearrangement produces m·s, you have inverted the fraction and lost the mark.

量纲检验是发现变形错误最快的方法。以平均速度 v = d / t 为例：单位是 m ÷ s = m·s⁻¹，正是速度的单位。如果你变形后得到 m·s，说明分数写反了，分数就丢了。

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2. Linear Motion and the Equations of Motion | 直线运动与运动方程

Uniformly accelerated motion is the backbone of the mechanics unit. The five equations below are linked, and any problem can be solved by choosing the equation that contains the three known quantities and the single unknown quantity.

匀加速直线运动是力学板块的骨架。下面五个方程彼此关联，解题关键是选出那个"包含三个已知量与一个未知量"的方程。

Quantity 物理量Formula 公式Units 单位
Average speed 平均速度v = d / tm·s⁻¹
Acceleration 加速度a = (v − u) / tm·s⁻²
Final velocity 末速度v = u + atm·s⁻¹
Displacement 位移s = ut + ½at²m
Velocity squared 速度平方关系v² = u² + 2asm²·s⁻²
Average velocity form 平均速度式s = ½(u + v)tm

v = u + at    s = ut + ½at²    v² = u² + 2as

ation and the area under the line is the displacement. Free fall is simply accelerated motion with u = 0 and a = g = 9.8 m·s⁻² downwards.

运动图像的分值不亚于公式本身。距离-时间图上的斜率是速度；速度-时间图上的斜率是加速度，线下的面积是位移。自由落体不过是 u = 0、a = g = 9.8 m·s⁻²（向下）的匀加速运动。

Worked example 例题: ⁻¹ in 6.0 s. Then a = (20 − 8) / 6.0 = 2.0 m·s⁻², and s = ½(u + v)t = ½ × 28 × 6.0 = 84 m.

例题：一辆汽车在 6.0 s 内由 8 m·s⁻¹ 加速到 20 m·s⁻¹。则 a = (20 − 8) / 6.0 = 2.0 m·s⁻²，s = ½(u + v)t = ½ × 28 × 6.0 = 84 m。

3. Forces, Newton's Laws, Moments and Momentum | 力、牛顿定律、力矩与动量

Force is a vector: it has magnitude, direction and a point of application. Newton' ; the third law states that action and reaction are equal, opposite and act on different bodies.

力是矢量：有大小、方向和作用点。牛顿第一定律指出，若合力为零，物体保持静止或匀速直线运动；第二定律给出合力 F = ma；第三定律指出作用力与反作用力大小相等、方向相反，且作用在不同物体上。