Bearings (Edexcel GCSE Maths): Revision Notes

Bearings

What are bearings?

Bearings are a way to describe direction using angles measured from north. They're incredibly useful for navigation, whether you're sailing, hiking, or solving maths problems. Think of bearings as a precise way to give directions - instead of saying "go that way," you can say "go on a bearing of $045°$" which tells someone exactly where to head.

The three-step method for finding bearings

To successfully work with bearings, you need to master a simple three-step process that uses three key concepts. This method works for any bearing problem you'll encounter.

Step 1: Find the "FROM" point

The first step is to identify where you're measuring from. Look for the word "FROM" in the question - this tells you your starting point. Place your pencil or finger on this point in the diagram, as this is where you'll begin your measurement.

Step 2: Draw the northline

At your starting point (the FROM point), you need to draw a vertical line pointing north. This northline is your reference point for measuring the bearing. In exam questions, this line is sometimes already provided, but you should always check and draw one if it's missing.

Step 3: Measure clockwise from north

Now you measure the angle clockwise from the northline to the line connecting your two points. This clockwise angle is your bearing. Remember - it's always clockwise from north, never anticlockwise.

Understanding three-figure bearings

All bearings must be written as three-figure numbers, even if the angle is less than $100°$. This is a crucial rule that many students forget.

Working with reverse bearings

Sometimes you'll need to find the bearing in the opposite direction. For instance, if you know the bearing of Z from Y is $110°$, you might need to find the bearing of Y from Z. This involves understanding how angles work in a complete circle.

When dealing with reverse bearings, you can use the concept of allied angles. If two points are connected by a straight line, the bearings in opposite directions are related by either adding or subtracting $180°$, depending on which gives you an angle between $0°$ and $360°$.

Bearings with scale drawings

Bearings become even more powerful when combined with scale drawings and distance calculations. This allows you to solve real-world navigation problems involving both direction and distance.

When working with scale drawings, you'll often need to:

1. Use the given bearing to draw a line in the correct direction
2. Apply the scale to convert between map distances and real distances
3. Use measurement tools to find distances on the map
4. Convert these measurements back to real-world distances

Practical applications

Understanding bearings opens up many practical applications beyond maths exams. Navigation systems, surveying, and even computer graphics use bearing concepts. When you give someone directions using compass points, you're using a simplified version of bearings.

The key to mastering bearings is practice with the three-step method. Once you can automatically identify the FROM point, draw the northline, and measure clockwise, you'll find bearing problems become much more manageable.