y ∝ 1/x: Challenge & Extension
Mathematics
Year 9
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the inverse proportional relationship y ∝ 1/x, including practice, reasoning, real-world applications, and extension problems.
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y ∝ 1/x: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
If y is inversely proportional to x and when x=3, y=6, find the constant of proportionality k in the relationship y = k / x.
[2 marks]2.
Given the relationship y = 12 / x, calculate y when x=4.
[2 marks]3.
Plot the graph of y=5 / x for x values from 1 to 5. (Use the grid provided.)
[2 marks]4.
Construct a triangle with sides proportional to y = 10 / x, where x = 2, 4, and 8. Draw and label the sides accordingly on the grid.
[3 marks]5.
If y = 20 / x, what is the value of y when x=5? Show your working.
[2 marks]6.
A machine's speed y is inversely proportional to the time x it takes to complete a task. If the machine takes 3 hours when operating at a certain speed, and the speed is 60 units, find the speed when the time is 2 hours.
[3 marks]7.
The relationship y = k / x has a constant of 24. Find y when x=6.
[2 marks]8.
Explain why y ∝ 1/x cannot be valid if x=0. Provide a brief reasoning.
[2 marks]9.
Determine the value of y if y ∝ 1/x and y=10 when x=2. Then find y when x=5.
[3 marks]10.
A scientist observes that when x doubles, y halves. If y=8 when x=3, find y when x=6.
[2 marks]11.
Identify and correct the mistake in this statement: 'Since y ∝ 1/x, doubling x will double y.'
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet