These eight questions use original, invented maps. They follow the lessons in topographic scale, distance and area and ramp from one conversion to a written comparison.
Work each answer on paper with units, then open the explanation.
Questions
Question 1: An original map has an RF of 1:50 000. Two villages are 3.6 cm apart. Find the ground distance in km.
Answer
3.6 × 50 000 = 180 000 cm = 1 800 m = 1.8 km.
Quick check: 1 cm is 0.5 km, so 3.6 × 0.5 = 1.8 km.
Question 2: On the same map, a trail is 4.5 km long on the ground. How long is it on the map?
Answer
4.5 km = 4 500 m = 450 000 cm.
450 000 ÷ 50 000 = 9 cm.
Question 3: A map states “1 cm represents 2 km”. Write this as a representative fraction.
Answer
2 km = 2 000 m = 200 000 cm.
The RF is 1:200 000.
Question 4: On a map of 1:25 000, a road has segments of 2.5 cm, 4.0 cm, 3.5 cm and 2.0 cm. The straight line between its ends is 7.0 cm. Find the length of the road, and how much longer it is than the straight line.
Answer
Map total: 2.5 + 4.0 + 3.5 + 2.0 = 12.0 cm.
1 cm is 0.25 km, so the road is 12.0 × 0.25 = 3.0 km.
Straight line: 7.0 × 0.25 = 1.75 km. The road is 3.0 − 1.75 = 1.25 km longer.
Question 5: On a 1:50 000 map with 2 cm squares, a forest covers 11 full squares and 8 partial squares. Using the half rule, estimate the area in km².
Answer
A 2 cm side is 1 km on the ground, so each square is 1 km².
Squares counted: 11 + (8 × 0.5) = 15.
Area: about 15 km², using the half rule.
Question 6: On a 1:50 000 map, a rectangular rice field measures 4 cm by 3 cm. Find its ground area in km². A student writes 12 × 0.5 = 6 km². Explain the error.
Answer
Convert each side first: 4 cm is 2 km and 3 cm is 1.5 km. Area = 2 × 1.5 = 3 km².
The student multiplied the map area by 0.5, the length scale. Area scales with the square of the length scale, so 12 cm² × 0.25 km² per cm² = 3 km². Square the scale first, then the units match.
Question 7: A distance of 2 cm is marked on a 1:50 000 map and on a 1:100 000 map. Find the ground distance in each and say which map shows more detail.
Answer
1:50 000: 2 × 0.5 km = 1 km. 1:100 000: 2 × 1 km = 2 km.
The 1:50 000 map is the larger scale. The same ground area takes more paper, so features are drawn bigger and with more detail.
Question 8: A student says “1:50 000 is a larger scale than 1:25 000 because 50 000 is bigger”. Write a correction.
Answer
The fraction 1/25 000 is larger than 1/50 000, so 1:25 000 is the larger scale.
On it, 1 cm is 250 m, while on 1:50 000 it is 500 m. The smaller second number means less shrinking, so more detail is shown.
If you got these wrong
Questions 1 to 3 test turning a representative fraction into distance. Question 4 tests measuring a winding route. Question 5 tests estimating an irregular area with a grid, and Question 6 tests checking units when converting map measurements.
Log your slips in the mistake log and paper-error review. To go through them with a teacher, see online one-to-one Geography tuition.