Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Which scale means the same as "1 cm stands for 2 km"?
Show worked solution
2 km = 2000 m = 200 000 cm, so the scale is 1 : 200 000. 1 : 2000 converts km to m only; 1 : 20 000 and 1 : 2 000 000 are a zero short and a zero over.
2 On a map with scale 1 : 35 000, the school is 6 cm from the station. How far is that in real life? Give it in metres and in kilometres.
Show worked solution
6 × 35 000 = 210 000 cm. ÷ 100 = 2100 m. ÷ 1000 = 2.1 km.
3 Two roads are 15 km apart. How far apart are they on a map with scale 1 : 250 000, in cm?
Show worked solution
15 km = 15 000 m = 1 500 000 cm, and 1 500 000 ÷ 250 000 = 6 cm.
Level 2 · Core
4 The scale bar on a map shows that 3 cm stands for 1.2 km. What is the scale of the map?
Show worked solution
1.2 km = 1200 m = 120 000 cm, so 3 : 120 000 = 1 : 40 000. 1 : 120 000 forgets to divide by 3; 1 : 400 and 1 : 4000 convert km to cm with too few zeros.
5 A model car is 18 cm long. The real car is 4.5 m long. Write the scale of the model as 1 : n, and find the model's width if the real car is 1.8 m wide.
Show worked solution
18 : 450 = 1 : 25 (450 ÷ 18 = 25). Model width = 180 cm ÷ 25 = 7.2 cm.
6 Two farms are 12 cm apart on a map with scale 1 : 80 000. How far apart are they on a second map with scale 1 : 32 000, in cm?
Show worked solution
Real: 12 × 80 000 = 960 000 cm (9.6 km). Second map: 960 000 ÷ 32 000 = 30 cm. Or: 80 000 ÷ 32 000 = 2.5, so 12 × 2.5 = 30.
Level 3 · Challenge
7 Three statements:
1 On a 1 : 75 000 map, 4 cm stands for 3 km.
2 A 2.4 km road is 12 cm long on a 1 : 2000 map.
3 If 6 mm on a plan stands for 3 m, the scale is 1 : 50.
Which statements are correct?
1 On a 1 : 75 000 map, 4 cm stands for 3 km.
2 A 2.4 km road is 12 cm long on a 1 : 2000 map.
3 If 6 mm on a plan stands for 3 m, the scale is 1 : 50.
Which statements are correct?
Show worked solution
4 × 75 000 = 300 000 cm = 3 km (1 ✓). 2.4 km = 240 000 cm, and 240 000 ÷ 2000 = 120 cm, not 12 cm (2 ✗). 3 m = 3000 mm, and 3000 ÷ 6 = 500, so the scale is 1 : 500, not 1 : 50 (3 ✗). 1 only.
8 A rectangular park is 3.2 cm by 1.5 cm on a map with scale 1 : 25 000. Find its real length and width in metres, and its real perimeter in kilometres.
Show worked solution
1 cm stands for 25 000 cm = 250 m. Length: 3.2 × 250 = 800 m. Width: 1.5 × 250 = 375 m. Perimeter: 2 × (800 + 375) = 2350 m = 2.35 km.
9 A hiker walks at 4 km/h for 45 minutes in a straight line. On her map, the walk measures 7.5 cm. The map's scale is 1 : n. Find n.
Show worked solution
Distance = 4 × 0.75 = 3 km = 300 000 cm. 7.5 : 300 000 = 1 : 40 000 (divide both by 7.5), so n = 40 000.