Question 1: Plot the points (1, 2), (2, 4), (3, 6), and (4, 8) on the grid. Describe the overall trend of these points.

Answer: The points form a positive linear trend, increasing together.

Question 2: Calculate the approximate gradient of the trend line passing through (1, 2) and (4, 8).

Answer: 2

Question 3: A scatter graph shows the hours studied (x) and scores achieved (y). The data points are all rising from left to right. What type of correlation does this data demonstrate?

Answer: Positive correlation

Question 4: Construct a scatter graph to show the relationship between hours of exercise per week and fitness score, where the data shows an increasing trend.

Answer: Student plots points with increasing x and y values, demonstrating positive trend.

Question 5: Explain why a scatter graph with points mostly rising from left to right indicates a positive correlation.

Answer: Because as one variable increases, the other also tends to increase, shown by the upward trend.

Question 6: Identify the mistake if a student draws a scatter graph with points decreasing from left to right but claims it shows positive correlation.

Answer: The points actually show negative correlation; the student misinterpreted the trend.

Question 7: Given the data points (2, 3), (4, 6), (6, 9), (8, 12), find the general trend and predict the y-value when x=10.

Answer: Trend is positive linear; y=1.5x. For x=10, y=15.

Question 8: Plot a set of data points that would demonstrate a strong positive correlation with some variability.

Answer: Student plots points roughly along a rising line with some scatter around it.

Question 9: In a real-world dataset, the scatter points form a clear upward trend. What does this suggest about the relationship between the two variables?

Answer: It suggests a positive correlation; as one variable increases, the other tends to increase as well.

Question 10: A student mistakenly connects the points with a straight line, but some points are far from the line. How might this affect their interpretation of the data?

Answer: It could give a misleading impression of a perfect positive trend, ignoring variability.

Question 11: Challenge: Given a set of points showing a positive trend, derive an equation for the best-fit line and explain your steps.

Answer: Identify the points, calculate the slope and intercept using least squares method, and write y=mx+c.