**Common Map Scale Questions**

In this O-level Math revision note, we will explore some common Map Scale questions and how to solve them.

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### Using Map Scale to Calculate Distances and Lengths

- A map scale refers to the relationship between a distance on the map and the corresponding actual distance. A map scale is usually written as a ratio, in the format

In the format 1 : n, no measurement units are included and it is interpreted as:

1 unit length on the map corresponds to n units of actual distance on the ground.

For instance, a map scale of 1 : 20 000 refers to

1 cm on the map = 20 000 cm on the ground

= 0.2 km on the ground

- Note that a map can also be expressed as a representative fraction (RF), 1/n.

### Map Scale Questions Type 1: Finding Map Scale

1. Write the following map scales in the form of 1 : n, where n is a whole number.

(a) 2 cm represents 6 m (b) 5 cm represents 400 km

2 cm : 600 cm 5 cm : 40 000 000 cm

1 cm : 300 cm 1 cm : 8 000 000 cm

Ans: 1 : 300 Ans: 1 : 8 000 000

2. Given that the actual distance of 8 km is represented by 10 cm on a map, state the value of n when the map scale is expressed as a representative fraction, 1/n.10 cm : 8 km

10 cm : 800 000 cm

1 cm : 80 000 cm

Ans: n = 80 000

### Map Scale Questions Type 2: Finding actual distance given length on map

Given that the scale of a map is 1 : 15 000. Find

(a) the actual distance, in m, for a length of 10 cm on the map.

(b) the actual distance, in km, for a length of 8 cm on the map.

(a)

1 cm : 15 000 cm

1 cm : 150 m

10 cm : 10 × 150 m

= 1500 m (ans)

(b)

1 cm : 1 500 m

1 cm : 0.15 km

8 cm : 8 × 0.15 km

= 1.2 km (ans)

### Map Scale Questions Type 3: Finding length on map given actual distance

Given that the scale of a map is 1 : 50 000. Find the length on the map, in cm,

(a) for an actual distance of 150 m.

(b) for an actual distance of 20 km.

(a)

1 cm : 50 000 cm

1 cm : 500 m

1/500×150 cm : 150 m

= 0.3 cm (ans)

(b)

1 cm : 500 m

1 cm : 0.5 km

1/0.5×20 cm : 20 km

= 40 cm (ans)

### Using Map Scale to Calculate Areas

- If the map scale is given as m : n, then the ratio of the area measured on the map to the actual area on the ground is

This means each *m ^{2}* square unit of area on the map corresponds to

*n*square units of actual distance on the ground.

^{2}For instance, given a map scale of 1 cm to 4 km, we have the map area scale of 1 cm

^{2}: 16 km

^{2}.

1 cm

^{2}on the map = 16 km

^{2}on the ground.

- When given a map area scale of
*m*, we can obtain the map scale for length by square rooting both sides of the ratio to get^{2}: n^{2}*m : n*.

### Map Scale Questions Type 4: Finding actual area given map area

Given that the scale of a map is 1 : 30 000, find

(a) the actual area, in m2, if the map area is 4 cm^{2},

(b) the actual area, in km2, if the map area is 25cm^{2}

(a)

1 cm : 30 000 cm

1 cm : 300 m (Length)

1 cm : 90 000m2 (Area)

4 cm : 4 × 90 000 m2

= 360 000 m2 (ans)

(b)

1 cm : 300 m

1 cm : 0.3 km (Length)

1 cm : 0.09 km^{2} (Area)

25 cm : 25 × 0.09 km^{2}

= 2.25 km^{2} (ans)

### Map Scale Questions Type 5: Finding map area given actual area

Given that the scale of a map is 1 : 25 000, find the map area, in cm^{2},

(a) if the actual area is 5000 m^{2},

(b) if the actual area is 25 km^{2}.

(a)

1 cm : 25 000 cm

1 cm : 250 m (Length)

1 cm2 : 62 500 m^{2} (Area)

1/62500×5000 cm2 : 500 m^{2}

= 0.08 cm^{2} (ans)

(b)

1 cm : 250 m

1 cm : 0.25 km (Length)

1 cm2 : 0.0625 km^{2} (Area)

1/0.0625×25 cm2 : 25 km^{2}

= 400 cm^{2} (ans)

## Last Minute Revision for O Level Math?

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