Question 1: Calculate the gradient of a line passing through the points (2, 5) and (6, 1).

Answer: -1

Question 2: A cyclist's speed decreases as they go downhill, represented by a line with a negative gradient. If the line passes through (3, 10) and (7, 4), what is the gradient?

Answer: -1.5

Question 3: Plot the graph of y = -2x + 4. (Draw on grid)

Answer:

Question 4: Construct a triangle on the grid with a slope of -3 between two points. Describe the points used.

Answer: Points could be (1, 2) and (4, -2)

Question 5: A runner’s pace decreases steadily, represented by a line with a negative gradient. If the initial pace is 8 minutes per km at position 0 km, and after 4 km, the pace is 10 minutes per km, find the gradient of the pace change.

Answer: 0.5

Question 6: A graph shows a decline in energy levels during a workout. The line passes through (2, 80) and (5, 65). What is the gradient of this decline?

Answer: -5

Question 7: A sports scientist records a negative trend between age and flexibility score. The data points are (20, 90) and (50, 60). Find the gradient.

Answer: -1

Question 8: A graph shows the decrease in speed of a swimmer over time, passing through (0, 15) and (10, 5). Calculate the gradient.

Answer: -1

Question 9: An athlete's performance improves rapidly at first, then declines. The graph slope between points (4, 100) and (8, 70) is negative. Calculate the gradient.

Answer: -7.5

Question 10: Identify and correct the mistake: A student calculates the gradient between (1, 4) and (3, 8) as 2, stating the gradient is positive, but the line slopes downward.

Answer: The points are (1, 4) and (3, 8). The gradient is (8-4)/(3-1)=2, which is positive, so the line slopes upward, not downward. The statement is incorrect because the line is positive.

Question 11: Challenge: A downhill ski slope’s height drops from 200 meters at point A to 50 meters at point B over a horizontal distance of 300 meters. What is the gradient of the slope?

Answer: -0.5