A bearing is a way of describing and using a direction as an angle .

From which compass direction should a bearing always be measured?

A bearing should always be measured from North .

True or False? Bearings are measured in an anti-clockwise direction.

False. Bearings are measured in a clockwise direction.

How many figures must a bearing be written with?

A bearing must be written with 3 figures . For angles under 100°, zero(es) should be used to fill in the missing figures, e.g. 059º, 008º.

True or False? SOHCAHTOA and Pythagoras' theorem are frequently used in bearings questions.

True. Pythagoras' theorem and SOHCAHTOA are frequently used in bearings questions. This is because situations often include finding missing lengths or angles in right-angled triangles .

If a bearing of A from B is known, how do you find the bearing of B from A ?

If a bearing of A from B is less than 180 o , then add 180 o to find the bearing of B from A. E.g. if the bearing of A from B is 030 o , then the bearing of B from A is 210 o . If a bearing of A from B is greater than 180 o , then subtract 180 o to find the bearing of B from A. E.g. if the bearing of A from B is 270 o , the bearing of B from A is 090 o .

Which compass direction is indicated by a bearing of 090° ?

When a bearing is 090°, it means due east .

True or False? North should always be indicated on a diagram.

True. North should always be indicated on a diagram as a point of reference.

What does it mean when a scale for a diagram is given as a ratio ? E.g. a scale of 1 : 8.

When the scale is given as a ratio (e.g., 1:8), it means that 1 unit on the diagram represents 8 of the same type of units in real life. E.g. 1 cm on map = 8 cm in real life

True or False? Scales on maps are always given with units .

False. Scales on maps are usually given in the form 1 : n with no reference to units .

True or False? To convert from a real-life distance to a scale distance , you usually need to divide by the scale factor .

True. To convert from a real-life distance to a scale distance , you usually need to divide by the scale factor .

How is a scale length on a map converted to a real-life length? E.g. a length of 3 cm on a map with scale 1 : 20 000.

To convert from a scale length to a real length, multiply by the scale factor . E.g. 3 × 20 000 = 60 000 cm (600 m).

How is a real-life length converted to a scale length on a map? E.g. a real-length of 15 km using a map with scale 1 : 50 000.

To convert from a real length to a scale length, divide by the scale factor . E.g. 15 ÷ 50 000 = 0.000 3 km (30 cm).

True or False? It may be helpful to convert the scale to more suitable units when dealing with very small or large scales.

True. It may be helpful to convert the scale to more suitable units when dealing with very small or large scales. For example, if 1 cm on a map represents 25 000 cm in real life, it may be easier to convert the units and use 1 cm represents 250 m or 0.25 km.

What is the compass direction for a bearing of 270º ?

The compass direction for a bearing of 270º is due west .

What is the bearing for the compass direction of due northeast ?

The bearing for the compass direction of due northeast is 045º . Remember to include 3 figures in your bearing.

True or False? Scales on scale drawings are never given with units .

False. Scales on scale drawings are often given as a description with units . This is unlike maps , where the scales are often given as ratios without units .

After measuring a distance on a scale drawing , what is the next step to find the corresponding real-life distance?

After measuring a distance on a scale drawing , the next step to find the corresponding real-life distance is to multiply by the scale factor .

What equipment might you need to be able to construct a triangle ?

The equipment you may need to be able to construct a triangle is: A sharp pencil A ruler A protractor A pair of compasses

You could be asked to construct a triangle for any of the following cases: SSS , SAS , or ASA . What do each of these mean?

When constructing a triangle , it could be for any of the following cases: SSS - you are given the lengths of all three sides. SAS - you are given the lengths of two sides and the angle in between them (the included angle). ASA - you are given the size of two angles and the length of the side in between them (the included side).

How would you construct a triangle when told the lengths of three sides ? ( SSS )

To construct a triangle when told the lengths of three sides ( SSS ): Draw the longest side using a ruler as a horizontal base. Use compasses set to the length of the next side and draw an arc from the end of the base line. Repeat this for the third side, drawing an arc from the other end of the base line, the same length as the third side. The arcs should intersect. Join the intersection of the arcs to each end of the base line using a ruler.

How would you construct a triangle when told the lengths of two sides , and the angle between them? ( SAS )

To construct a triangle when told the lengths of two sides and the angle between them ( SAS ): Draw the longest side using a ruler as a horizontal base. Use a protractor to measure the given angle from one end of the base line and make a mark on the paper at this angle. Use a ruler to draw the second given side length from the end of the base line through the mark you have just made. Check the lengths and angles are all correct so far using a ruler and protractor. Use a ruler to draw the remaining side, between the end of the base line and the end of the second given side.

How would you construct a triangle when told two angles , and the length of a side between them? ( ASA )

To construct a triangle when told two angles , and the length of a side between them ( ASA ): Use a ruler to draw the given length as a horizontal base. Use a protractor to measure the first given angle from one end of the base line and make a mark on the paper at this angle. Use a ruler to join the end of the horizontal base line to the mark you have just made, and extend the line further. Repeat steps 2 & 3 for the second given angle, at the other end of the base line. The lines should intersect, forming a triangle.

True or False? You should leave all your working and construction lines on the page, and not rub any out.

True. You should leave all your working and construction lines on the page, and not rub any out.

IGCSEMathsEdexcelMaths AFoundationFlashcards4. Geometry & TrigonometryBearings, Scale Drawing & Constructions

Bearings, Scale Drawing & Constructions (Edexcel IGCSE Maths A: Foundation): Flashcards

Exam code: 4MA1

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What is a bearing?

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Cards in this collection (24)

What is a bearing?
A bearing is a way of describing and using a direction as an angle.
From which compass direction should a bearing always be measured?
A bearing should always be measured from North.
True or False?
Bearings are measured in an anti-clockwise direction.
False.
Bearings are measured in a clockwise direction.
How many figures must a bearing be written with?
A bearing must be written with 3 figures.
For angles under 100°, zero(es) should be used to fill in the missing figures, e.g. 059º, 008º.
True or False?
SOHCAHTOA and Pythagoras' theorem are frequently used in bearings questions.
True.
Pythagoras' theorem and SOHCAHTOA are frequently used in bearings questions.
This is because situations often include finding missing lengths or angles in right-angled triangles.
If a bearing of A from B is known, how do you find the bearing of B from A?
If a bearing of A from B is less than 180^o, then add 180^o to find the bearing of B from A.
E.g. if the bearing of A from B is 030^o, then the bearing of B from A is 210^o.
If a bearing of A from B is greater than 180^o, then subtract 180^o to find the bearing of B from A.
E.g. if the bearing of A from B is 270^o, the bearing of B from A is 090^o.
Which compass direction is indicated by a bearing of 090°?
When a bearing is 090°, it means due east.
True or False?
North should always be indicated on a diagram.
True.
North should always be indicated on a diagram as a point of reference.
What does it mean when a scale for a diagram is given as a ratio?
E.g. a scale of 1 : 8.
When the scale is given as a ratio (e.g., 1:8), it means that 1 unit on the diagram represents 8 of the same type of units in real life.
E.g. 1 cm on map = 8 cm in real life
True or False?
Scales on maps are always given with units.
False.
Scales on maps are usually given in the form 1 : n with no reference to units.
True or False?
To convert from a real-life distance to a scale distance, you usually need to divide by the scale factor.
True.
To convert from a real-life distance to a scale distance, you usually need to divide by the scale factor.
How is a scale length on a map converted to a real-life length?
E.g. a length of 3 cm on a map with scale 1 : 20 000.
To convert from a scale length to a real length, multiply by the scale factor.
E.g. 3 × 20 000 = 60 000 cm (600 m).
How is a real-life length converted to a scale length on a map?
E.g. a real-length of 15 km using a map with scale 1 : 50 000.
To convert from a real length to a scale length, divide by the scale factor.
E.g. 15 ÷ 50 000 = 0.000 3 km (30 cm).
True or False?
It may be helpful to convert the scale to more suitable units when dealing with very small or large scales.
True.
It may be helpful to convert the scale to more suitable units when dealing with very small or large scales.
For example, if 1 cm on a map represents 25 000 cm in real life, it may be easier to convert the units and use 1 cm represents 250 m or 0.25 km.
What is the compass direction for a bearing of 270º?
The compass direction for a bearing of 270º is due west.
What is the bearing for the compass direction of due northeast?
The bearing for the compass direction of due northeast is 045º.
Remember to include 3 figures in your bearing.
True or False?
Scales on scale drawings are never given with units.
False.
Scales on scale drawings are often given as a description with units.
This is unlike maps, where the scales are often given as ratios without units.
After measuring a distance on a scale drawing, what is the next step to find the corresponding real-life distance?
After measuring a distance on a scale drawing, the next step to find the corresponding real-life distance is to multiply by the scale factor.
What equipment might you need to be able to construct a triangle?
The equipment you may need to be able to construct a triangle is:
- A sharp pencil
- A ruler
- A protractor
- A pair of compasses
You could be asked to construct a triangle for any of the following cases: SSS, SAS, or ASA.
What do each of these mean?
When constructing a triangle, it could be for any of the following cases:
- SSS - you are given the lengths of all three sides.
- SAS - you are given the lengths of two sides and the angle in between them (the included angle).
- ASA - you are given the size of two angles and the length of the side in between them (the included side).
How would you construct a triangle when told the lengths of three sides? (SSS)
To construct a triangle when told the lengths of three sides (SSS):
1. Draw the longest side using a ruler as a horizontal base.
2. Use compasses set to the length of the next side and draw an arc from the end of the base line.
3. Repeat this for the third side, drawing an arc from the other end of the base line, the same length as the third side.
4. The arcs should intersect. Join the intersection of the arcs to each end of the base line using a ruler.
How would you construct a triangle when told the lengths of two sides, and the angle between them? (SAS)
To construct a triangle when told the lengths of two sides and the angle between them (SAS):
1. Draw the longest side using a ruler as a horizontal base.
2. Use a protractor to measure the given angle from one end of the base line and make a mark on the paper at this angle.
3. Use a ruler to draw the second given side length from the end of the base line through the mark you have just made.
4. Check the lengths and angles are all correct so far using a ruler and protractor.
5. Use a ruler to draw the remaining side, between the end of the base line and the end of the second given side.
How would you construct a triangle when told two angles, and the length of a side between them? (ASA)
To construct a triangle when told two angles, and the length of a side between them (ASA):
1. Use a ruler to draw the given length as a horizontal base.
2. Use a protractor to measure the first given angle from one end of the base line and make a mark on the paper at this angle.
3. Use a ruler to join the end of the horizontal base line to the mark you have just made, and extend the line further.
4. Repeat steps 2 & 3 for the second given angle, at the other end of the base line.
5. The lines should intersect, forming a triangle.
True or False?
You should leave all your working and construction lines on the page, and not rub any out.
True.
You should leave all your working and construction lines on the page, and not rub any out.

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