GCSE Bearings and scale drawings Practice Questions

Count the figures in the angle that is given.

$72$ has $2$ figures, and a bearing needs three, so zeros must be put in at the front.

Put in the zeros needed at the front.

Writing $1$ zero in front of $72$ gives $072$. The zeros do not change the size of the angle at all.

State the three-figure bearing.

The direction is the bearing $072^\circ$.

Recall the bearings of the eight compass points.

The eight compass points are $45^\circ$ apart: north $000^\circ$, north-east $045^\circ$, east $090^\circ$, south-east $135^\circ$, south $180^\circ$, south-west $225^\circ$, west $270^\circ$ and north-west $315^\circ$.

Match the bearing given to one of those eight bearings.

$225^\circ$ is exactly the bearing of south-west, so that is the direction the ship is sailing in.

State the direction the ship is sailing in.

The ship is sailing south-west.

Recall what a three-figure bearing is.

A bearing is the angle turned CLOCKWISE from the north line, written with three figures — so an angle of $8{}^\circ$ becomes $008^\circ$.

Count how many figures the bearing must have.

A three-figure bearing always shows three digits, so $72$ needs zeros putting in at the front. The zeros do not change the angle.

Write the angle with three figures.

$72$ written with three figures is $072$.

Reject the options that are not the same direction or not three figures.

An option with the wrong number of digits is not a three-figure bearing, and an option with a different value is a different direction. Only $072^\circ$ is both.

Write the answer as a three-figure bearing.

Bearings are always written with three figures, putting in zeros at the front if they are needed. So the answer is written $072^\circ$.

State the correct three-figure bearing.

The direction is written $072^\circ$.

Say what the number in a map scale means.

In a scale $1 : n$, the number $n$ is how many centimetres of real ground one centimetre of map stands for.

Decide what makes one scale represent more ground than another.

The bigger $n$ is, the more real distance is squeezed into each centimetre of map, so the scale with the LARGEST $n$ represents the greatest real distance.

Compare the numbers in the five scales.

Putting the five numbers in order shows that $200000$ is the largest.

Pick the scale with the largest number.

$1 : 200000$ has the largest scale factor, so one centimetre on that map represents the greatest real distance.

Check what that distance is.

One centimetre on that map represents $200000$ cm, which is $2$ km.

Recall how centimetres and kilometres are linked.

There are $100$ cm in a metre and $1000$ m in a kilometre, so there are $100 \times 1000 = 100\,000$ cm in a kilometre.

Check the two lengths were in the same unit before the scale was used.

A scale such as $1 : 25\,000$ only compares like with like. Both lengths must be turned into the same unit before the multiplication, and only then is the answer converted to the unit asked for.

Check the real distance is bigger than the map distance.

The map shrinks everything by a factor of $200000$, so the real distance has to be much larger than the distance measured on the map. An answer that came out smaller would mean the scale had been used upside down.

Note the commonest mistake in this type of question.

It is tempting to pick the smallest number because it "looks bigger". The scale factor is how much the real world has been SHRUNK, so a bigger number means more ground per centimetre.

State the correct scale.

$1 : 200000$ represents the greatest real distance per centimetre.

Recall what a three-figure bearing is.

A bearing is the angle turned CLOCKWISE from the north line, written with three figures — so an angle of $8{}^\circ$ becomes $008^\circ$.

Note that both bearings are measured at A from the same north line.

Both directions are measured from the north line at $A$, so angle $BAC$ is simply the difference between the two bearings.

Subtract the smaller bearing from the larger one.

The two directions are $225^\circ$ apart one way round the north line at $A$.

Take the non-reflex angle.

The full turn at $A$ splits into $225^\circ$ and $135^\circ$. Angle $BAC$ is the one that is not reflex, so it is $135^\circ$.

Check what the answer is measured in.

The answer is the SIZE of an angle, so it is written $135^\circ$ and NOT as a three-figure bearing. Only directions get three figures.

Check the size of the angle is sensible.

An angle inside a triangle is always between $0^\circ$ and $180^\circ$, and $135^\circ$ is.

Check the angle asked for is the one that has been found.

Two angles meet at that point: $135^\circ$ and the reflex angle $225^\circ$. The question asks for the angle of the triangle, which is the smaller one, $135^\circ$.

Check the angle and its reflex angle add to a full turn.

The angle $135^\circ$ and the reflex angle around the same point add up to a full turn of $360^\circ$, which they do.

Do not write this answer with three figures.

Three-figure notation is for BEARINGS, which are directions. This answer is the size of an angle, so it is just $135^\circ$.

Check that the two north lines are parallel.

North is the same direction everywhere on the page, so the north line at one point is parallel to the north line at the other. That is what lets you use the parallel-line angle facts.

Check the angle was measured from north and not from east.

A bearing always starts at the north line and turns clockwise. Starting anywhere else, or turning the other way, gives the wrong bearing.

Check the angle on an accurate drawing.

On a drawing made to scale, measuring the angle with a protractor should give $135^\circ$. That is a useful check but not a proof — the working is the proof.

Note that a bearing does not depend on how far apart the points are.

A bearing records a DIRECTION. Moving the second point twice as far away along the same line does not change the bearing at all.

Check the answer against a rough sketch.

Drawing the north line and the direction roughly to scale is the quickest way to catch an answer that points the wrong way. The sketch does not need to be accurate to do that job.

State the correct option.

Angle $BAC = 135^\circ$.