y ∝ 1/x: Problem Solving & Reasoning
Mathematics
Grade 7
16 questions
~32 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the inverse proportionality relationship y ∝ 1/x through practice, reasoning, and real-world problems.
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y ∝ 1/x: Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Given that y ∝ 1/x and y = 6 when x = 3, find the value of y when x = 4.
[2 marks]2.
If y = 12 when x = 2, write the general formula for y in terms of x.
[3 marks]3.
Calculate the value of y when x = 5, if y = 10 when x = 2.
[2 marks]4.
Plot the graph of y = 3/x for x from 1 to 6. (Use the grid for drawing.)
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working.
1.
A car travels such that its speed y (in km/h) is inversely proportional to the time x (in hours) it takes to reach a destination. If the car takes 3 hours and travels at 60 km/h, find the speed if it takes 2 hours.
[4 marks]2.
Explain why doubling the value of x results in halving the value of y in the relationship y ∝ 1/x.
[3 marks]3.
If y = 5 when x = 4, what is the constant of proportionality?
[2 marks]4.
Determine y when x = 10, given that y = 2 when x = 1.
[2 marks]C
Real-world Applications
Answer all questions. Show your reasoning.
1.
A scientist observes that the rate at which a chemical reacts (y) is inversely proportional to the amount of substance (x) present. If the reaction rate is 8 units when the substance amount is 4 grams, what is the rate when 10 grams of the substance are present?
[4 marks]2.
A plumber finds that the pressure y in a pipe is inversely proportional to the flow rate x. If the pressure is 50 psi when the flow rate is 2 liters/sec, what is the pressure when the flow rate increases to 5 liters/sec?
[4 marks]D
Challenge & Extension
Answer the challenging questions. Show detailed working.
1.
Given y ∝ 1/x, and y = 7 when x = 3, determine the value of x when y = 0.5.
[3 marks]2.
A satellite's signal strength y is inversely proportional to the square of its distance x from the receiver. If the signal strength is 16 when the satellite is 10 km away, find the signal strength when the satellite is 15 km away.
[4 marks]E
Mixed Review
Answer all questions. Mix of question types.
1.
Write the equation relating y and x if y is inversely proportional to x and y = 9 when x = 3.
[3 marks]2.
Plot the graph of y = 4/x for x from 1 to 8 on the grid.
[3 marks]3.
If y ∝ 1/x, and y = 3 when x = 6, what is y when x = 12?
[2 marks]F
Error Analysis
Identify the mistake and correct it.
1.
A student states that if y ∝ 1/x, then y = 2x. Is this correct? Explain and correct if necessary.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet