Question 1: A map has a scale of 1:50,000. If the actual distance between two towns is 120 km, what is the length of the line representing this distance on the map?

Answer: 2.4 cm

Question 2: On a scale drawing, 1 cm represents 5 km. A river is 8 cm long on the map. What is its actual length?

Answer: 40 km

Question 3: A map shows a city park as 6 cm long. If the scale is 1:10,000, what is the real length of the park?

Answer: 600 m

Question 4: Identify the mistake: A student says that if a map's scale is 1:25,000, then 1 cm on the map equals 25 km in real life. Is this correct? Explain your reasoning.

Answer: No, because 1 cm on the map equals 0.25 km in real life (since 1:25,000 means 1 cm = 25,000 cm = 250 m).

Question 5: A map with a scale of 1:75,000 shows a mountain range as 4.5 cm long. What is the actual length of the mountain range?

Answer: 3.375 km

Question 6: A student calculates the real distance as 4 km from a map scale of 1:25,000. The map distance is marked as 1.6 cm. Is the student's answer correct? Show your working.

Answer: No, because 1.6 cm at 1:25,000 equals 40,000 cm or 400 m, so the real distance is 0.4 km, not 4 km.

Question 7: A map scale is incorrectly labeled as 1:10,000 when it is actually 1:100,000. How would this mistake affect calculations of actual distances?

Answer: Students would underestimate the actual distances by a factor of 10 if they used 1:10,000 instead of 1:100,000.

Question 8: A map shows a highway as 12 cm long with a scale of 1:50,000. Calculate the actual length of the highway in kilometers.

Answer: 6 km

Question 9: Construct a scale drawing of a park that is 300 meters long using a scale of 1 cm : 50 meters.

Answer: 6 cm

Question 10: A student incorrectly concludes that a 2 cm line on a map with a scale of 1:25,000 represents 50 km of real distance. Identify and correct the mistake.

Answer: The mistake is in the calculation: 2 cm at 1:25,000 equals 50,000 cm or 500 m, so the real distance is 0.5 km, not 50 km.