y ∝ 1/x: Real-world Applications in Sports & Fitness
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the inverse proportion relationship y ∝ 1/x through sports and fitness contexts, including practice, problem solving, and extension questions.
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y ∝ 1/x: Real-world Applications in Sports & Fitness
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
If the time taken by a cyclist to complete a race is inversely proportional to their speed, and at a speed of 20 km/h the race takes 3 hours, find the time taken when the speed is increased to 25 km/h.
[3 marks]2.
A swimmer's effort (y) is inversely proportional to the number of laps (x) they swim. If swimming 10 laps requires 15 units of effort, how much effort is needed to swim 20 laps?
[2 marks]3.
Plot the graph of y = 50/x for x values from 1 to 10. Use the grid to draw the curve.
[3 marks]4.
A runner's pace (y) in minutes per kilometer is inversely proportional to the number of kilometers (x) they run in a training session. If running 5 km takes 25 minutes, what is the pace when running 8 km?
[2 marks]5.
The power output (y) of a machine varies inversely with the time (x) it runs. If the power output is 200 watts when the machine runs for 4 hours, find the power output when it runs for 6 hours.
[3 marks]6.
A sprinter's speed (y) is inversely proportional to the time (x) taken to run a certain distance. If the speed is 12 m/s when the time is 30 seconds, what is the speed when the time is 20 seconds?
[2 marks]7.
In a workout, the effort (y) a person needs to lift a weight is inversely proportional to the number of repetitions (x). If lifting 4 repetitions requires 50 units of effort, how much effort is needed for 10 repetitions?
[2 marks]8.
A cyclist's power output (y) is inversely proportional to the time (x) taken to complete a race. If at a power output of 300 watts the race takes 2 hours, what is the power output when the race time is reduced to 1.5 hours?
[2 marks]9.
A swimmer's effort (y) to swim a certain distance is inversely proportional to the number of laps (x). If swimming 15 laps requires 20 effort units, how many effort units are needed to swim 10 laps?
[2 marks]10.
A machine's power (y) varies inversely with the time (x) it runs. If it uses 180 watts when operating for 3 hours, what is the power when it runs for 5 hours?
[2 marks]11.
Common mistake: A student says that if y ∝ 1/x, then y = x. Explain why this is incorrect and write the correct proportionality expression.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet