Scale of 1 : can be expressed as a (R.F) of. Scale and R.F are usually expressed in units of cm, always 1 in the numerator of R.

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1 Secondary 2 Elementary Mathematics Topic : Scales and Map Learning Objectives: Read the scales of maps Calculate the actual distance between two points and the area of a region from a map Solve problems involving scales using ratio Map scale shows the relationship between a distance on the map and actual horizontal distance on the ground. We can calculate the actual distance between two locations or the actual area of place on the map based on the map scale. A. Linear Scale Scale of 1 : can be expressed as a (R.F) of 1 cm : cm Scale and R.F are usually expressed in units of cm, always 1 in the numerator of R.F 1cm on the map represents an actual distance of cm = km Unit conversion revision 1 km = m = cm Q1. A map is drawn to a scale of 1 : a) What is the actual distance represented by 2 cm in km? b) What length on the map represents the actual distance of 4 km? Math Ready Page 1

2 Q2. A distance of 3 cm on a map represents an actual distance of 1.5 km. a) Find the scale of the map in the form 1 r? b) If the distance between the two schools on the map is 7 cm, find the actual distance between the two schools. c) If the actual distance between the two food centres is 6 km, find the distance on the map. Attempt yourself Q3. A street is 250 m long. It is represented by a distance of 5 cm on a map. a) Express the scale of the map in the form 1 : r. b) If another street is 600 m long, find its distance on the map in cm. Q4. An actual ground distance of 6 km is represented by a distance of 2 cm on a map. a) Express the scale of the map in R.F b) If the distance between two police stations on the map is 5 cm, find their actual distance apart in km. Math Ready Page 2

3 Q5. A distance of 8 cm on a map represents an actual distance of 4 km. a) Find the scale of the map in the R.F b) If the actual distance between two schools is 1.5 km, find the distance, in cm, on the map. B. Area scale If the linear map scale is 1 : r, then the area scale of the map is 1 : r 2. The scale of a detailed map is 1 : Find the actual area, in m 2, for 5 cm 2 on the map. Map : Actual 1 cm : 2000 cm 1 cm : 20 m Since the question ask you to calculate in m 2, convert the R.H.S to metres first. Then, Square both sides! Q6. Suppose that 3 cm on a map represents 1.2 km on the ground. a) Find the scale of the map in the form 1 : r b) If the area of a lake is 0.32 km 2, find its area on the map in cm 2. Math Ready Page 3

4 Q7. An actual region of area 18 km 2 is represented by an area of 2 cm 2 on a map. a) Find the scale of the map in the form 1 r. b) If the distance between two police stations on the map is 5 cm, find their actual distance apart in km. How do you convert area scale back to linear scale? Attempt yourself Q8. A map of Singapore is drawn to a scale of 1 : a) In the map, the distance from Sentosa to Changi Ferry Terminal is 13.5 cm. Find the actual distance, in km, from Sentosa to Changi Ferry Terminal. b) The Sentosa island has an area of 5 square kilmetres. Find, in square centimetres, the area representing the island on the map. Q9. Given that 2 cm on a map represents 3 km on the ground, a) calculate the distance, in km, between two towns which are 7 cm apart on the map; b) express the scale of the map in the form 1 : n, c) calculate, in cm 2, the area of the map which represents a lake of area 81 km 2 on the ground. Math Ready Page 4

5 Q10. An area of 80 cm 2 on a map represents the area of a police station which is 45 km 2. Find the R.F of the map. C. Two map scales within a question Q11. On a map, a length of 4 cm represents an actual distance of 1 km. Calculate a) The scale of the map, in the form of 1 : n b) The actual distance, in km, represented by 18 cm on the map. c) The area of the post office, in cm 2, which represents an actual area of 4 km 2. d) Suppose the actual area of the post office is mapped onto a new map of scale 1 : What will be the area of the post office in cm 2 on the new map? Math Ready Page 5

6 Attempt yourself Q12. The scale of a map is 2 cm : 500 m. a) Express the scale in R.F b) A rectangle of length 8 cm and breadth 5.5 cm is drawn on the map. Calculate the actual area of the rectangle in km 2. c) If the actual area of the rectangle is to be mapped onto a new map of scale 1 : 50000, what is the area of the rectangle in cm 2 on the new map? Math Ready Page 6