CIE IGCSE Mathematics (0580) Scale drawings Study Notes - New Syllabus
CIE IGCSE Mathematics (0580) Scale drawings Study Notes
LEARNING OBJECTIVE
- Scale Drawings
Key Concepts:
- Scale Drawings
- Bearing
Scale Drawings
Scale Drawings
A scale drawing is a diagram of an object or layout that is drawn to scale — that is, a fixed ratio of the real size. Scale drawings are used in maps, architecture, engineering, and design.
Key Concepts:
- Scale: Shows the relationship between the measurements on the drawing and the actual object.
- Example: A scale of 1:50 means 1 cm on the drawing = 50 cm in real life.
- Use a ruler and accurate measurement techniques to draw to scale.
To Interpret a Scale Drawing:
- Multiply drawing measurements by the scale factor to get real lengths.
- Convert units if needed (e.g., from cm to m).
Example:
A room is drawn on a plan using a scale of 1:100. If the length of the room on the plan is 5 cm and the width is 3 cm, find the actual dimensions of the room.
▶️ Answer/Explanation
Scale: 1 cm represents 100 cm = 1 m
Length = \( 5 \times 1 = 5 \ \text{m} \)
Width = \( 3 \times 1 = 3 \ \text{m} \)
Answer: The room is 5 m long and 3 m wide.
Example:
You are asked to draw a scale diagram of a garden that is 20 m long and 12 m wide using a scale of 1:200. What should be the dimensions on paper?
▶️ Answer/Explanation
Scale: 1 cm on paper = 200 cm = 2 m
Length on paper = \( \frac{20}{2} = 10 \ \text{cm} \)
Width on paper = \( \frac{12}{2} = 6 \ \text{cm} \)
Answer: Draw a rectangle 10 cm by 6 cm to represent the garden.
Bearings
Bearings
A bearing is a way of describing direction using angles measured clockwise from the north direction. Bearings are always written as three-figure numbers.
Key Concepts:
- Bearings are measured from the north line, going clockwise.
- Bearings must be written as three-figure numbers (e.g. 045°, 090°, 270°).
- Due north = 000°, East = 090°, South = 180°, West = 270°.
- Always measure the angle from the north line at the starting point.
- To find the bearing from A to B, draw a line from A to B, then measure the clockwise angle from the north line at A.
Types of Bearings:
- Forward bearing: From one point to another.
- Back bearing: Add or subtract 180° from the forward bearing (if the result is above 360°, subtract 360°).
Common Angles on a Compass:
- North (N) – 000°
- North-East (NE) – 045°
- East (E) – 090°
- South-East (SE) – 135°
- South (S) – 180°
- South-West (SW) – 225°
- West (W) – 270°
- North-West (NW) – 315°
Example:
A ship leaves port A on a bearing of 030°. It sails a distance of 25 km to reach point B. At point B, the ship changes direction to a new bearing of 100° and sails for 40 km to reach point C.
Draw and label the full route of the ship using accurate bearings and distances.
▶️ Answer/Explanation
- From point A, draw a north line using a ruler.
- Measure 30° clockwise from the north to get the 030° bearing. Draw a line 25 km long and label the endpoint as B.
- From point B, draw a north line again.
- Measure 100° clockwise from the north at B. Draw a line 40 km in that direction and mark the endpoint as C.
Answer: Ship’s route A → B → C drawn with correct bearings and distances.
Example:
The bearing from A to B is 060°. What is the bearing from B to A?
▶️ Answer/Explanation
Reverse the direction by adding 180°: \( 60 + 180 = 240° \)
Answer: The bearing from B to A is 240°.