Geometry and measures - Mensuration and calculation: measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

The idea

Measure a line with a ruler to the nearest millimetre, and an angle with a protractor, reading the scale that starts at zero on one arm of the angle. A scale drawing represents real distances at a fixed ratio, on a map always a reduction, so a scale of 1 : 50000 means 1 cm on the paper stands for 50000 cm, which is 500 m or half a kilometre. Multiply to go from the drawing to the ground, and divide to go the other way. A bearing is measured from north, turning clockwise, and is always written with three figures, so an angle of seventy-two degrees becomes the bearing 072°. The reverse bearing differs by 180°: add 180° when the first bearing is below 180°, and subtract 180° when it is 180° or more. On a map drawn to 1 cm for every 5 km, a line of 6.4 cm stands for 32 km.

What earns the marks

• A measurement inside the tolerance the mark scheme allows, which is usually a couple of millimetres on a length and a degree or two on an angle.
• The scale used correctly as a multiplication or a division, even if the final distance is wrong.
• A bearing written with three figures and measured clockwise from north.
• A north line drawn at the point the bearing is measured from, in a question that asks you to construct or explain one.

Common mistakes and how to put them right

• Reading the wrong protractor scale, so recording 130° for an angle that is 50°.

• Writing a bearing as 72° rather than 072°, or leaving off the degree sign.

• Measuring a bearing anticlockwise, or starting it from the wrong point of the two named.

• Using the scale the wrong way round, dividing where the question needed a multiplication.

Exam tips

• Before you write an angle down, decide whether it looks acute or obtuse and check your reading agrees.
• The bearing of B from A starts at A, so draw the north line at A and turn clockwise from it.
• Write the scale out as a sentence, such as 1 cm represents 5 km, before you use it in any calculation.