Question 1: If y ∝ 1/x and when x = 4, y = 3, find the constant of proportionality k and write the general formula for y in terms of x.

Answer: k=12; y=12/x

Question 2: Calculate the value of y when x = 6, given y ∝ 1/x and k=12.

Answer: 2

Question 3: Plot the graph of y = 12/x for x values from 1 to 6. (Draw on the grid.)

Answer:

Question 4: Construct a triangle with sides proportional to 1/x where x=2, x=4, and x=8, ensuring the sides are in inverse ratio. (Draw on the grid.)

Answer:

Question 5: If y ∝ 1/x and at x=3, y=4, what is y when x=9?

Answer: 1.33

Question 6: A machine's speed y is inversely proportional to the time x taken for a task. If the machine takes 5 hours for a task with speed 12, find the speed when the time is reduced to 3 hours.

Answer: 20

Question 7: Given y = k/x and y=8 when x=2, find the value of y when x=0.5.

Answer: 32

Question 8: Identify the mistake in the following statement: 'Since y ∝ 1/x, doubling x will double y.'

Answer: Doubling x halves y, not doubles.

Question 9: A scientist finds that y ∝ 1/x and when x=5, y=10. What would y be if x=1?

Answer: 50

Question 10: Challenge: The length of a shadow is inversely proportional to the height of a flagpole. If a 10-meter-high pole casts a 5-meter shadow, how long will the shadow be if the pole is 20 meters high? (Draw your reasoning.)

Answer: 2.5 meters