Mastering Direct & Inverse Proportion
Mathematics
GCSE Higher
12 questions
~24 mins
0 views0 downloads
About This Worksheet
A worksheet covering key concepts and application of Direct & Inverse Proportion for GCSE Higher students, including ratio, proportion, and rates of change.
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Mastering Direct & Inverse Proportion
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
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Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
If y is directly proportional to x, and y = 10 when x = 4, find the constant of proportionality k and write the general formula relating x and y.
[3 marks]2.
Calculate y when x = 8, given y = 3x.
[2 marks]3.
If a is inversely proportional to b, and a = 6 when b = 2, find the value of a when b = 3.
[3 marks]4.
Given that y is inversely proportional to x and y = 5 when x = 4, find y when x = 10.
[2 marks]5.
A recipe uses 3 cups of sugar for every 5 cups of flour. How many cups of sugar are needed if you use 8 cups of flour? (Assuming direct proportion)
[3 marks]6.
A car travels 150 km in 3 hours. Assuming the speed remains constant, how far will it travel in 7 hours?
[2 marks]7.
A worker takes 6 hours to complete a task. If the rate of work increases so that the time taken reduces to 4 hours, by what factor has the worker's rate increased?
[3 marks]8.
A map scale shows 1 cm representing 50 km. How many centimeters on the map represent a distance of 200 km?
[2 marks]9.
In a mixture of solutions, the ratio of salt to water is 3:5. If the total mixture weighs 64 grams, how much salt is present?
[3 marks]10.
A ladder is 10 meters long. If it leans against a wall so that the foot of the ladder is 6 meters from the wall, how high does the ladder reach on the wall? (Use Pythagoras theorem)
[3 marks]11.
A new product’s sales are directly proportional to advertising expenditure. If spending $2000 yields 500 units sold, how many units are expected if the advertising spend increases to $3000?
[2 marks]12.
Challenge: A bus travels from City A to City B, a distance of 180 km. If the bus’s speed varies inversely with the number of stops it makes, and it takes 4 hours with 2 stops, how long will the journey take if the number of stops increases to 6?
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet