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JSS2: MATHEMATICS - 3RD TERM

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  1. Scale Drawing | Week 1
    3 Topics
    |
    1 Quiz
  2. Angles of Elevation & Depression | Week 2
    5 Topics
    |
    1 Quiz
  3. Pythagoras’ Theorem I | Week 3
    3 Topics
    |
    1 Quiz
  4. Pythagoras’ Theorem II | Week 4
    2 Topics
    |
    1 Quiz
  5. Area and Volume of Cones and Cylinders | Week 5
    3 Topics
    |
    1 Quiz
  6. Cones | Week 6
    3 Topics
    |
    1 Quiz
  7. Bearings and Distances I | Week 7
    2 Topics
    |
    1 Quiz
  8. Bearings and Distances II | Week 8
    2 Topics
    |
    1 Quiz
  9. Presentation of Data | Week 9
    6 Topics
    |
    1 Quiz
  10. Probability | Week 10
    6 Topics
    |
    1 Quiz



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A scale is a ratio or proportion that shows the relationship between a length on a drawing and the corresponding length on the actual object. 

In scale drawing 

1. All lengths must be in proportion to the corresponding length on the actual object, and 

2. All angles must be drawn to the corresponding angles on the actual object. 

Scale = \( \frac{any \: length \: on \: scale \: drawing }{corresponding \: length \: on \: actual \: object} \)

OR

Scale = \( \frac{any \:length \: on \: actual \: object }{corresponding \: length \: on \: scale \: drawing} \)

Forms of writing scales” 

a. 1 cm represents 10m 

b. 1 cm to 10m 

c. 1 cm : 10m or 1: 1000

d. \( \frac{1 }{1000} \)

Example 1

A rectangle is drawn to a scale of 1cm to 10cm. If the length of the scaled rectangle is 80cm, what is the length of the actual object? 

Solution: 

Length of the rectangle on scale drawing = 80cm 

Length of the rectangle on actual object = x 

ScaleActual Object
1 cm10cm
80 cmx
\( \scriptsize x \: \times \: 1cm = 80cm \: \times \: 10cm \)

x = \( \frac{800cm^2}{1cm}\\ \scriptsize or \\ \frac{800\:cm \: \times \: cm}{1cm} \\ = \scriptsize 800cm \)

The length of the actual object is 800cm

Example 2

A triangle is drawn to a certain scale. If the length of the base of the scaled triangle is 80cm, and the length of the base of the actual triangle is 800cm, what is the scale? 

Solution 

Length of base on scale drawing = 80cm 

Length of base on actual object = 800cm

Scale = \( \frac{any \: length \: on \: scale \: drawing }{corresponding \: length \: on \: actual \: object} \)

Scale = \( \frac{80cm }{800cm} \\ = \frac{8}{80} \\ = \frac{1}{10} \\ = \scriptsize 1:10 \)

= 1cm to 10cm 

= 1cm represents 10cm 

Evaluation 

1. The scale of a diagram is 1cm:10cm. The length AB on the actual diagram is 0.3m. What is the length of AB on the scale drawing? 

2. The model of a building is made to a scale of 1cm:2.5m. 
a. The height of the building is 15m; find the height of the model. 
b The length of the room on the model is 1.8cm; find the actual length of the room. 

3. A square is drawn to a certain scale. If the length of the scaled square is 5cm, the length of the actual square is 100cm, find the scale of the drawing. 

Answers 

1. 3cm

2. (a) 6cm 
(b) 4.5m 

3. 1 : 20

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