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 On a 1 : 50 plan, a desk is 4 cm. Real length in metres?
Show worked solution
200 cm = 2 m.
2 1 cm on a 1 : 100,000 map equals how many km?
Show worked solution
100,000 cm = 1 km.
3 A 3 m wall on a 1 : 100 plan is how many cm?
Show worked solution
300 ÷ 100 = 3 cm.
Level 2 · Core
4 A 1 : 25000 map shows a 5.2 cm path. Real length in km?
Show worked solution
130,000 cm = 1.3 km.
5 A 45 m building on a 1 : 900 drawing is how many cm?
Show worked solution
4500 ÷ 900 = 5 cm.
6 A 6 m car is drawn 3 cm long. Scale?
Show worked solution
3 : 600 → 1 : 200.
Level 3 · Challenge
7 A room is 8 m × 5 m. On a 1 : 200 plan, what are its dimensions in cm? (as a simplified expression)
Show worked solution
800÷200 and 500÷200 → 4 cm × 2.5 cm.
8 A logo is enlarged by scale factor 3. Its area was 12 cm2. New area?
Show worked solution
12 × 32 = 108 cm2.
9 Two towns are 14 km apart, shown 7 cm apart on a map. Another pair is 4 cm apart on the same map. Their real distance in km?
Show worked solution
Scale: 1 cm = 2 km → 4 cm = 8 km.