Calculating Distances: Problem Solving & Reasoning
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on calculating distances using map scales, designed to develop understanding through a variety of question types including procedural practice, problem solving, real-world contexts, and extension challenges.
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Calculating Distances: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
A map has a scale of 1:50,000. If the distance between two towns on the map is 4.2 cm, calculate the actual distance between them in kilometres.
[3 marks]2.
On a map with a scale of 1:25,000, the distance between two landmarks is 7.5 cm. What is the real-world distance in metres?
[3 marks]3.
A city is 120 km east of another city. On a map with a scale of 1:1,200, the two cities are 10 cm apart. Is this consistent with the actual distance? Show your working.
[4 marks]4.
Construct a triangle on the grid such that the sides are in ratio 3:4:5. Use the grid to help position the points.
[4 marks]5.
A map scale of 1:60,000 shows a hiking trail that is 8.5 cm long on the map. Calculate the actual length of the trail in kilometres.
[3 marks]6.
A route on a map is depicted as 12 cm long. If the actual distance is 24 km, what is the scale of the map?
[3 marks]7.
A map uses a scale of 1:75,000. A river appears 5.6 cm long on the map. What is the real length of the river in kilometres?
[3 marks]8.
A town's real distance from a mountain is 80 km. On a map with a scale of 1:100,000, what should the distance between them be on the map in centimetres?
[3 marks]9.
A map shows a bus route of 15 km as 6 cm. Calculate the map's scale as a ratio.
[3 marks]10.
Identify the common mistake in calculating real distances from map measurements and scales. How can it be corrected?
[4 marks]11.
If a map's scale is 1:50,000 and a lake measures 3 cm on the map, what is its approximate area if the lake is roughly circular with a diameter of 3 cm on the map? Provide your reasoning.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet