Question 1: A worker completes a task in 6 hours. If another worker takes 4 hours to complete the same task, are their efforts inversely proportional? Explain your reasoning.

Answer: No, because effort is proportional to time; they are not inversely proportional.

Question 2: Calculate the constant of inverse proportion for the scenario where y is inversely proportional to x, and when x=3, y=12.

Answer: 36

Question 3: A car's fuel consumption is inversely proportional to its speed. If at 50 mph, it consumes 8 liters per 100 miles, what is its fuel consumption at 75 mph?

Answer: 21.33

Question 4: Plot the graph of y = k/x for x from 1 to 10, where k=20. Use the grid to draw an accurate graph.

Answer: Students draw the hyperbola y=20/x on the grid.

Question 5: A recipe requires 2 cups of sugar for 8 servings. If the number of servings increases to 20, how much sugar is needed? Is this an inverse proportion? Explain.

Answer: Yes, because as servings increase, sugar needed increases proportionally; for 20 servings, 5 cups are needed.

Question 6: In an inverse proportion problem, a student incorrectly assumes that y = kx. Identify and explain the mistake.

Answer: This is a direct proportion, not inverse; the mistake is misclassifying the relationship.

Question 7: If the time taken to complete a job is inversely proportional to the number of workers, how many workers are needed to complete the job in 3 hours if 6 workers take 8 hours?

Answer: 16

Question 8: A machine’s speed is inversely proportional to its operating time. If running it at 4 units speed consumes 10 hours, what is the time if the speed is increased to 8 units? Show working.

Answer: 5 hours

Question 9: A problem states that as the number of workers doubles, the time to complete a task halves. Identify a potential misconception in applying inverse proportion here.

Answer: Misconception: Assuming direct proportion; in inverse proportion, doubling workers halves time, which is correct, but students might wrongly think time increases or stays the same.

Question 10: A cyclist's effort is inversely proportional to the speed. If at 10 mph, the effort is 50 units, what effort is required at 15 mph? Show calculations.

Answer: 33.33

Question 11: A common mistake is to treat inverse proportion as direct proportion. Provide an example of a real-world scenario where inverse proportion applies, and explain the error in misapplying direct proportion.

Answer: Scenario: Speed and travel time; error: thinking that increasing speed increases time, which is incorrect for inverse proportion.