Mastering Direct & Inverse Proportion
Mathematics
GCSE Foundation
1 questions
~2 mins
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About This Worksheet
A worksheet covering Direct & Inverse Proportion for GCSE Foundation students, focusing on ratios, rates of change, and real-world applications.
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Mastering Direct & Inverse Proportion
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Read the key concepts below before attempting the questions.
1.
In direct proportion, when one quantity increases, the other increases by the same ratio. In inverse proportion, as one quantity increases, the other decreases so that their product remains constant. The formulas are y = kx (direct) and xy = k (inverse).
0B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
If y is directly proportional to x, and y = 15 when x = 3, find the constant of proportionality k and calculate y when x = 7.
[4 marks]2.
A car's fuel efficiency is inversely proportional to its speed. If at 50 km/h, the car consumes 6 liters per 100 km, find the consumption rate at 75 km/h.
[3 marks]3.
A recipe requires 200g of sugar for 4 servings. How much sugar is needed for 10 servings, assuming the amount varies directly with the number of servings?
[3 marks]4.
The time taken to complete a task varies inversely with the number of workers. If 5 workers take 8 hours, how long will 10 workers take?
[3 marks]5.
A map scale shows that 1 cm represents 5 km. If the distance between two towns on the map is 8 cm, what is the actual distance?
[2 marks]6.
The cost of a taxi ride is directly proportional to the distance traveled. If a 10 km ride costs £12, what will be the cost for a 25 km ride?
[2 marks]7.
A worker's speed varies inversely with the time taken to complete a task. If working at 4 km/h takes 3 hours, what is the speed if the worker takes 2 hours?
[3 marks]8.
A petrol tank's capacity is 50 liters. If the fuel consumption rate is directly proportional to the distance traveled, how much fuel is needed to travel 180 km if 10 liters are needed for 36 km?
[3 marks]9.
Two quantities are in inverse proportion. When one quantity doubles, the other halves. If the first quantity is 12, what is the second quantity?
[2 marks]10.
A cyclist's speed is inversely proportional to the time taken to complete a journey. If the cyclist takes 2 hours at a certain speed, how long would it take at double the speed?
[2 marks]11.
Challenge: A factory produces widgets where the number of widgets produced is directly proportional to the number of workers. If 15 workers produce 300 widgets in a day, how many widgets will 25 workers produce in the same time?
[4 marks]12.
Real-world Application: A car rental company charges a fixed fee plus a rate proportional to the number of days rented. If the total cost for 3 days is £150 and for 5 days is £210, find the fixed fee and the daily rate, then calculate the cost for a 7-day rental.
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet