Question 1: A map has a scale of 1:50,000. If a distance between two towns on the map measures 4 cm, what is the real distance in kilometers?

Answer: 2

Question 2: On a map with a scale of 1:25,000, a river measures 6.4 cm. What is the actual length of the river in kilometers?

Answer: 1.6

Question 3: A map shows that 1 cm corresponds to 2 km in real life. What is the scale ratio of this map?

Answer: 1:200,000

Question 4: An extension: A map's scale is given as 1:75,000. If a building 45 meters tall appears 2.4 cm tall on the map, is this scale correct? Explain your reasoning.

Answer: Yes, because 45 meters / 75,000 = 0.0006 km, which is 0.6 meters. The map height is 2.4 cm, which is 0.024 meters, so scale is approximately 1:18,750, so the given scale is not correct.

Question 5: A map uses a scale where 1 cm represents 10 km. If a city is 85 km away from another, how many centimeters apart are they on the map?

Answer: 8.5

Question 6: A map's scale is 1:40,000. A park appears 3.2 cm wide on the map. What is the actual width of the park in meters?

Answer: 1280

Question 7: Problem solving: Two locations are 150 km apart in reality. On a map, they are 6 cm apart. What is the scale of the map? Express your answer as a ratio.

Answer: 1:2500

Question 8: A map's scale is 1:20,000. A feature measures 5 cm on the map. How long is the feature in meters?

Answer: 1000

Question 9: Challenge: A city’s actual population density is 1500 people per km². A map shows a district with an area of 4.5 cm², representing 12 km² in real size. What is the population of the district?

Answer: 18000

Question 10: Error analysis: A student claims that if 1 cm on the map equals 5 km in real life, then 2 cm must equal 10 km. Is this reasoning correct? Why or why not?

Answer: Yes, because scale ratios are proportional; doubling the map measurement doubles the real distance.