Define scale , as used on a drawing or a map.

A scale is a ratio describing the relationship between the drawn size and the real-life size. Maps are almost always drawn to a scale, which is what lets a real distance be recovered from a measurement on the page.

What does a scale written without units, such as 1 : 10 000, mean?

The same unit applies to both sides of the ratio. So 1 centimetre on the drawing represents 10 000 centimetres in real life, which is 100 metres. A scale can instead be written with different units on each side, as in 1 cm : 100 m, which says the same thing more directly.

How accurately should you measure a line on a scale drawing?

To the nearest millimetre , using a ruler marked in millimetres. Line the 0 on the ruler up with the starting point rather than the ruler's end, and read off where the far end of the line falls.

True or False? A scale of 1 : 10 000 works whether you measure in centimetres or in inches.

True. A scale written without units is a pure ratio, so it holds for any unit of length at all. The one condition is that the same unit is used on both sides: 1 inch on the drawing is 10 000 inches in real life.

How would you write a bearing of 59 degrees?

As 059 degrees, with a leading zero. A bearing always uses three figures, so anything under 100 degrees needs a zero in front of it to make up the three.

What does "the bearing of A from B" tell you to do?

Start at B , the point named after the word from . Draw the north line at B, join B to A, and measure clockwise from that north line round to the joining line. Reading the two letters the wrong way round is the commonest mistake in this topic.

How do you measure an angle accurately with a protractor?

Put the centre of the protractor exactly on the point where the two lines meet, and line up 0 degrees along one of them. Then read off where the second line crosses the scale, to the nearest degree, taking care to use the inner or outer scale consistently.

How do you plot a point B on a given bearing from a point A?

Draw a north line at A , since that is the point the bearing is measured from. Measure the bearing clockwise from that north line, draw a line in that direction, and mark B along it at the distance you are given.

True or False? The bearing of A from B and the bearing of B from A are different angles.

True. They are measured from different starting points, with the north line drawn in a different place each time. That is precisely why the order of the two letters matters, and why the word from has to be read carefully.

Define navigation course .

A navigation course is a journey from a starting point to a final destination, usually made up of two or more legs. Each leg is described by a bearing and a distance, so drawing one accurately needs a scale and a protractor together.

After drawing the first leg of a navigation course, what must you do before drawing the second?

Draw a new north line at the point you have just reached. The second bearing is measured from there, not from where the journey started, and forgetting this fresh north line is the single commonest way the whole construction goes wrong.

In what order do you construct one leg of a navigation course?

Convert the actual distance into a length to draw, using the scale. Then measure the bearing clockwise from the north line at your current point, and draw the line that length in that direction. Finally mark the end of the line with a cross and label the destination.

Both legs of a navigation course are drawn. How do you find the distance and bearing back to the start?

Join the final point back to the starting point with a straight line. Measuring that line and applying the scale gives the actual distance home. Drawing a north line at the final point and measuring clockwise to the same line gives the return bearing.

True or False? The bearing of the return journey can be read from the north line at the starting point.

False. The return journey begins at the final point, so that is where its north line has to be drawn. Every bearing is measured from the north line at the place the journey described actually starts from.

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Scale Drawings & Bearings (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

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Define scale, as used on a drawing or a map.

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Cards in this collection (19)

Define scale, as used on a drawing or a map.
A scale is a ratio describing the relationship between the drawn size and the real-life size.
Maps are almost always drawn to a scale, which is what lets a real distance be recovered from a measurement on the page.
What does a scale written without units, such as 1 : 10 000, mean?
The same unit applies to both sides of the ratio.
So 1 centimetre on the drawing represents 10 000 centimetres in real life, which is 100 metres.
A scale can instead be written with different units on each side, as in 1 cm : 100 m, which says the same thing more directly.
Complete the two directions of a scale calculation:
To find a length to draw you $______$ the real distance by the scale, and to find a real distance from a map you $______$ the measured length by it.
The completed sentence is:
To find a length to draw you divide the real distance by the scale, and to find a real distance from a map you multiply the measured length by it.
A drawing is smaller than the real thing, so the direction that produces the smaller number is the one that divides.
The scale is 1 cm : 1.5 km and the actual distance from A to B is 5.4 km. How long a line should you draw?
You should draw a line 3.6 cm long.
Going from a real distance to a drawn one, divide by the scale: $5.4 \div 1.5 = 3.6$ .
The answer is much smaller than 5.4, which is the check worth making.
A map has a scale of 1 cm : 40 km, and two towns are 7.8 cm apart on it. How far apart are they really?
They are 312 km apart.
Going from a measured length to a real distance, multiply by the scale: $7.8 \times 40 = 312$ .
The answer is far larger than 7.8, as it should be for a real distance recovered from a map.
How accurately should you measure a line on a scale drawing?
To the nearest millimetre, using a ruler marked in millimetres.
Line the 0 on the ruler up with the starting point rather than the ruler's end, and read off where the far end of the line falls.
True or False?
A scale of 1 : 10 000 works whether you measure in centimetres or in inches.
True.
A scale written without units is a pure ratio, so it holds for any unit of length at all.
The one condition is that the same unit is used on both sides: 1 inch on the drawing is 10 000 inches in real life.
Complete the three rules for a bearing:
A bearing is always measured starting from $______$ and turning $______$ round from it, and it is written using three figures.
The completed rules are:
A bearing is always measured starting from North and turning clockwise round from it, and it is written using three figures.
All three have to hold at once: an angle measured the other way round, or from anything but the north line, is not a bearing.
How would you write a bearing of 59 degrees?
As 059 degrees, with a leading zero.
A bearing always uses three figures, so anything under 100 degrees needs a zero in front of it to make up the three.
What does "the bearing of A from B" tell you to do?
Start at B, the point named after the word from.
Draw the north line at B, join B to A, and measure clockwise from that north line round to the joining line.
Reading the two letters the wrong way round is the commonest mistake in this topic.
How do you measure an angle accurately with a protractor?
Put the centre of the protractor exactly on the point where the two lines meet, and line up 0 degrees along one of them.
Then read off where the second line crosses the scale, to the nearest degree, taking care to use the inner or outer scale consistently.
How do you plot a point B on a given bearing from a point A?
Draw a north line at A, since that is the point the bearing is measured from.
Measure the bearing clockwise from that north line, draw a line in that direction, and mark B along it at the distance you are given.
True or False?
The bearing of A from B and the bearing of B from A are different angles.
True.
They are measured from different starting points, with the north line drawn in a different place each time.
That is precisely why the order of the two letters matters, and why the word from has to be read carefully.
Define navigation course.
A navigation course is a journey from a starting point to a final destination, usually made up of two or more legs.
Each leg is described by a bearing and a distance, so drawing one accurately needs a scale and a protractor together.
After drawing the first leg of a navigation course, what must you do before drawing the second?
Draw a new north line at the point you have just reached.
The second bearing is measured from there, not from where the journey started, and forgetting this fresh north line is the single commonest way the whole construction goes wrong.
In what order do you construct one leg of a navigation course?
Convert the actual distance into a length to draw, using the scale.
Then measure the bearing clockwise from the north line at your current point, and draw the line that length in that direction.
Finally mark the end of the line with a cross and label the destination.
Both legs of a navigation course are drawn. How do you find the distance and bearing back to the start?
Join the final point back to the starting point with a straight line.
Measuring that line and applying the scale gives the actual distance home.
Drawing a north line at the final point and measuring clockwise to the same line gives the return bearing.
True or False?
The bearing of the return journey can be read from the north line at the starting point.
False.
The return journey begins at the final point, so that is where its north line has to be drawn.
Every bearing is measured from the north line at the place the journey described actually starts from.
A course runs 17.5 km on a bearing of 055 degrees, then 31.5 km on a bearing of 170 degrees, at a scale of 1 cm : 5 km. What two lines do you draw?
A line 3.5 cm long on a bearing of 055 degrees from the start, then a line 6.3 cm long on a bearing of 170 degrees from the point it reaches.
The lengths come from dividing by the scale: $17.5 \div 5 = 3.5$ and $31.5 \div 5 = 6.3$ .
A fresh north line is needed at the end of the first leg before the second bearing can be measured.

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