Question 1: Calculate the gradient between the points (2, 5) and (6, 13). Show your working.

Answer: 2

Question 2: Calculate the gradient between points (-3, 4) and (1, -2). Show your working.

Answer: -1.5

Question 3: Find the gradient between (0, 0) and (4, 8). Show your working.

Answer: 2

Question 4: Identify the error in calculating the gradient between (1, 2) and (3, 8) if a student incorrectly calculated it as 6.

Answer: They used (y₂ - y₁) / (x₂ + x₁) instead of (y₂ - y₁) / (x₂ - x₁).

Question 5: A student calculated the gradient as 3 between points (2, 5) and (4, 11). Is this correct? Explain your reasoning.

Answer: Yes, because (11-5)/(4-2)=6/2=3.

Question 6: Plot the graph of y = 2x using the grid and identify two points on the line.

Answer: e.g., (0,0) and (2,4)

Question 7: Construct a triangle with vertices at (1, 2), (4, 8), and (1, 8). Calculate the gradients of the sides between (1, 2) & (4,8) and (1, 8) & (4,8).

Answer: m₁= (8-2)/ (4-1)=6/3=2; m₂= (8-8)/ (4-1)=0/3=0

Question 8: A line passes through (3, 7) and (3, 15). What is the gradient? Explain your answer.

Answer: The gradient is undefined because x-coordinates are the same, so the denominator is zero.

Question 9: Identify and correct the mistake in this calculation: the gradient between (1, 2) and (3, 8) is 4.

Answer: Incorrect calculation: (8 - 2)/(3 - 1) = 6/2=3, not 4.

Question 10: Explain why using (y₂ - y₁) / (x₂ + x₁) instead of (x₂ - x₁) causes an error in calculating the gradient.

Answer: Because it changes the denominator, leading to incorrect gradient values, and does not reflect the change in x-coordinates.