📚 Sketch Graphs in AQA A-Level Physics | AQA A-Level 物理草图绘制技巧
A sketch graph is one of the most common command words in AQA A-Level Physics papers. It asks you to draw a graph that captures the essential physics of a relationship without necessarily plotting exact data points. Examiners look for correct shape, axes, intercepts, asymptotes and labelled features.
草图是 AQA A-Level 物理试卷中最常见的指令词之一。它要求你画出一个能体现关系本质物理特征的图形，而不必绘制精确的数据点。考官关注的是正确的形状、坐标轴、截距、渐近线和标注特征。
1. What Is a Sketch Graph? | 什么是草图？
A sketch graph is a simplified graph that shows the overall relationship between two variables. It should be neat, labelled and physically meaningful, but it does not require an accurately plotted set of data points.
草图是一种简化图形，用于显示两个变量之间的总体关系。它应当整洁、有标注且具有物理意义，但不需要精确绘制一组数据点。
In AQA exams, 'sketch' often means you must include the general shape and any key values mentioned in the question, such as intercepts, maxima, minima or asymptotic behaviour.
在 AQA 考试中，“草图”通常意味着你必须画出总体形状以及题目中提到的任何关键值，例如截距、最大值、最小值或渐近行为。
2. Reading the Axes and Units | 坐标轴与单位
Before drawing anything, identify which quantity is plotted on the x-axis (independent variable) and which is on the y-axis (dependent variable). AQA questions often state the axes with units, for example 'sketch the current I against potential difference V'.
在动笔之前，先确定哪个量画在 x 轴（自变量），哪个量画在 y 轴（因变量）。AQA 题目通常会给出带单位的坐标轴，例如“画出电流 I 随电势差 V 变化的草图”。
Always include units in axis labels, such as I/A, V/V, t/s, T/K or x/m. Missing or incorrect units is a common avoidable error.
始终在坐标轴标签中注明单位，例如 I/A、V/V、t/s、T/K 或 x/m。遗漏或写错单位是常见的可避免错误。
3. Linear Relationships: y = mx + c | 线性关系
+ c, the sketch must be a straight line with gradient m and y-intercept c. A positive gradient slopes upward, and a negative gradient slopes downward.
如果关系具有 y = mx + c 的形式，草图必须是直线，其斜率为 m，y 轴截距为 c。正斜率向上倾斜，负斜率向下倾斜。
V = ε − Ir
For a cell with emf ε and internal resistance r, the terminal potential difference V against current I gives a straight line with gradient −r and y-intercept ε.
对于电动势为 ε、内阻为 r 的电池，端电压 V 随电流 I 变化的图像是一条直线，斜率为 −r，y 轴截距为 ε。
directly proportional, for example V = IR for an ohmic conductor at constant temperature.
如果直线经过原点，则 c = 0，两个量成正比，例如恒定温度下欧姆导体的 V = IR。
4. Direct and Inverse Proportion | 正比与反比
ar hyperbola: y = k/x, which never crosses either axis but approaches them asymptotically.
正比关系产生过原点的直线：y = kx。反比关系产生双曲线：y = k/x，它永远不会与任一坐标轴相交，但会渐近地接近它们。
For a fixed mass of ideal gas at constant temperature, Boyle' p against V is a hyperbola. However, p against 1/V is a straight line through the origin.
对于恒温下的一定质量理想气体，玻意耳定律给出 pV = 常量，因此 p 对 V 的图像是双曲线。而 p 对 1/V 的图像是过原点的直线。
5. Quadratic and Square Relationships | 二次与平方关系
the origin if no linear term is present. The curve becomes steeper as x increases in magnitude.
如果不存在线性项，形式为 y = kx² 的二次关系图像是顶点在原点的抛物线。随着 x 的绝对值增大，曲线变得更陡。
Ek = ½mv²
Kinetic energy Ek against speed v is a parabola starting at the origin, because Ek placement against time for uniform acceleration from rest, s = ½at² also gives a parabola.
动能 Ek 随速度 v 变化的图像是从原点出发的抛物线，因为 E
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