Cambridge KS3 Maths: Bearings, Scale Drawings and Loci | 剑桥KS3数学：方位角、比例绘图与轨迹

📚 Cambridge KS3 Maths: Bearings, Scale Drawings and Loci | 剑桥KS3数学：方位角、比例绘图与轨迹

Bearings, scale drawings, and loci are central to the Cambridge KS3 mathematics curriculum because they link geometry with real-world navigation and map-reading. This article builds up the rules step by step, gives worked examples, and highlights the common errors that appear in school and checkpoint-style papers.

方位角、比例绘图和轨迹是剑桥KS3数学课程的核心内容，因为它们将几何与现实世界中的导航和地图阅读联系起来。本文逐步建立相关规则，给出例题解析，并指出在学校和Checkpoint类型试卷中常见的错误。

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1. What Are Bearings? | 什么是方位角？

A bearing is a precise way of stating direction. It is always measured from the north line, moving clockwise, and is written as a three-digit angle such as 045° or 130°.

方位角是一种精确表示方向的方法。它总是从北线开始按顺时针方向测量，并用三位数字书写，例如 045° 或 130°。

Bearings are used in navigation, surveying, aviation, and map reading. Instead of saying ‘roughly north-east’, a bearing gives an exact angle such as 052°.

方位角用于导航、测量、航空和地图阅读。它不是粗略地说 ‘大致东北’，而是给出精确角度，例如 052°。

If an object is directly east of you, its bearing is 090°. If it is directly south, the bearing is 180°, and if it is directly west, the bearing is 270°.

如果一个物体在你的正东方向，它的方位角是 090°。如果在正南方向，方位角是 180°，如果在正西方向，方位角是 270°。

In KS3 questions, you will usually be asked to measure a bearing on a diagram, draw a bearing from a point, or use bearings to plot a path.

在KS3题目中，通常要求你在图上测量方位角、从一个点画方位角，或使用方位角绘制路径。

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2. Three Key Rules for Measuring Bearings | 测量方位角的三个关键规则

Rule 1: Always measure from north. At the starting point, draw a faint vertical north line before placing your protractor.

规则1：始终从北方测量。在起点处，先画一条淡淡的垂直北线，再放置量角器。

Rule 2: Measure clockwise. The angle must be read in the clockwise direction from the north line to the line pointing towards the destination.

规则2：按顺时针方向测量。角度必须从北线开始按顺时针方向读到指向目的地的直线。

Rule 3: Use three digits. A bearing of 60° must be written as 060°; a bearing of 8° must be written as 008°.

规则3：使用三位数字。60° 的方位角必须写作 060°；8° 的方位角必须写作 008°。

Many students lose marks because they measure from the target point instead of the starting point. The phrase ‘the bearing of B from A’ means the angle is measured at A.

许多学生因为从目标点而不是起点测量而失分。’B 从 A 的方位角’ 这个短语意味着角度是在 A 点测量的。

Always check whether your bearing is less than 360°. If you obtain an angle larger than 360°, subtract 360° or re-check the clockwise direction.

始终检查你的方位角是否小于 360°。如果得到的角度大于 360°，应减去 360° 或重新检查顺时针方向。

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3. Compass Directions and Bearings | 罗盘方向与方位角

Compass directions can be converted directly into bearings. North is 000°, east is 090°, south is 180°, and west is 270°.

罗盘方向可以直接转换为方位角。北是 000°，东是 090°，南是 180°，西是 270°。

For intermediate directions, north-east is 045°, south-east is 135°, south-west is 225°, and north-west is 315°.

对于中间方向，东北是 045°，东南是 135°，西南是 225°，西北是 315°。

Compass direction	Bearing
North	000°
North-east	045°
East	090°
South-east	135°
South	180°
South-west	225°
West	270°
North-west	315°

Practising these conversions helps you judge whether a measured bearing is reasonable. For example, a bearing of 200° should point roughly south-west, not north-east.

练习这些转换有助于你判断测得的方位角是否合理。例如，200° 的方位角应该大致指向西南，而不是东北。

In navigation, direction is often given as a compass direction in speech, but written as a bearing in calculations. Being able to switch between the two is an important KS3 skill.

在导航中，方向在口头表述时常用罗盘方向，但在计算中写作方位角。能够在两者之间切换是一项重要的KS3技能。

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4. Constructing a Bearing Diagram | 绘制方位角示意图

To construct a bearing diagram, place the centre of your protractor on the starting point and align 0° with the north line.

要绘制方位角示意图，将量角器的中心放在起点上，并将 0° 与北线对齐。

Read the required angle clockwise from the protractor and mark a small point. Then draw a straight line from the starting point through that mark.

从量角器上按顺时针读出所需角度，并标记一个小点。然后从起点画一条经过该标记的直线。

If the bearing is greater than 180°, it is often easier to measure the smaller anticlockwise angle

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

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