Reading: Problem Solving & Reasoning
Mathematics
GCSE Higher
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on reading map scales through problem solving and reasoning, suitable for GCSE Higher students.
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Full preview • 13 questions
Reading: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
A map has a scale of 1 cm : 5 km. If the distance between two towns on the map is 3.2 cm, what is the actual distance?
[2 marks]2.
Convert a scale of 1:25000 to a ratio form.
[2 marks]3.
On a map, 2.5 cm represents 10 km. What is the scale of the map?
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed reasoning in the provided grid.
1.
A map with a scale of 1:50,000 shows a river that is 4.8 cm long. What is the actual length of the river in kilometers? Explain your reasoning.
[4 marks]2.
The distance between two cities on a map is 6.3 cm. The map's scale is 1:100,000. If a car travels at 60 km/h, how long will it take to cover the actual distance? Show all steps.
[4 marks]3.
A map uses a scale of 1:80,000. If a park measures 3.75 cm on the map, what is its actual size in square kilometers?
[3 marks]C
Real-world Applications
Answer all questions. Use calculations and reasoning as needed.
1.
A hiking map has a scale of 1:25,000. If a trail on the map is 7.2 cm long, how long is the trail in real life? Discuss how this information might influence planning your hike.
[3 marks]2.
A city planning map shows a park of 5 cm length on the map with a scale of 1:10,000. What is the actual length of the park? How could this information be useful for urban planning?
[3 marks]D
Challenge & Extension
Attempt these more difficult questions to extend your understanding.
1.
A map's scale is 1:125,000. A lake measures 4.2 cm on the map. If the lake's actual area is approximately 8.4 km², verify whether the scale and the area are consistent. Show your reasoning.
[4 marks]2.
Construct a scale drawing of a park that is 6 cm long on the map representing an actual length of 24 km. Use the grid to illustrate the scale.
[4 marks]E
Mixed Review
Answer all questions. Try a variety of question types.
1.
A map has a scale of 1:40,000. If a building is 2.5 cm on the map, what is its actual height in meters?
[2 marks]2.
Estimate the size of a city park that measures 4.8 cm on a map with a scale of 1:50,000. Write your approximation and reasoning.
[3 marks]F
Error Analysis
Review the following common mistake and identify/fix it.
1.
A student calculates the actual distance as 10 km from a map scale of 1:50,000 and a map distance of 0.5 cm. They multiply 0.5 by 50,000 to get 25,000 km. Identify and correct the mistake.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet