AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 12

WHAT THIS QUESTION TESTS

This question assesses your ability to critically inspect a plotted scatter diagram. You must identify errors in:

Axis scales: Checking for linear, evenly spaced numerical increments.
Data plotting: Matching coordinate pairs from a table to points on the grid.
Line of best fit: Ensuring a single straight line reflects the trend with a balanced distribution of points on either side.

State clearly any two distinct errors:

Incorrect vertical scale: The values on the y-axis do not increase in equal steps (it jumps from 0 to 500, then to 1000, and then suddenly in 5000s).
Incorrect plotted point: The car of age 4 is plotted at (4, 20 000) instead of (4, 19 000) .
Incorrect line of best fit: The line is too steep and does not follow the trend of the data (it ignores most points and leaves almost all of them to the right of the line).

Mark Scheme:
• B1: One valid mistake correctly identified.
• B2: Two distinct valid mistakes correctly identified.

Linear Scales: Every major division on an axis must represent the same quantity. On Anil's graph, 2 squares = 500 initially, but higher up, 2 squares = 5000. This distorts the visual data completely.
Line of Best Fit: Must be a straight line drawn with a ruler that reflects the general trend and direction (negative correlation here). It should have a roughly equal balance of points above and below it.
Plotting Precision: Each point (x, y) must match the table exactly.

When asked to find mistakes on any exam graph, always check in this exact order:

Check the Scales:
x-axis: 0, 2, 4, 6, 8, 10 (consistent steps of 2).
y-axis: 0 → 500 → 1000 → 5000 → 10 000... Mistake found! The step from 1000 to 5000 is 4000, while the others are 5000.
Check the Coordinates: Cross-check each table entry against plotted crosses:
Table: (4, 19 000) .
Graph cross: Plotted right on the line for 20 000 at (4, 20 000) . Mistake found!
Inspect the Trend Line: Look at the line of best fit. It crashes straight into the x-axis at age 7 and leaves the points at ages 5, 6, 7, and 10 completely stranded to the right. Mistake found!

Be Specific: Name the exact coordinate or axis. Writing "Values go up differently on the vertical scale" gets the mark, whereas "Values on the axis are wrong" is too vague and scores 0 marks.
Do not write contradictory statements: Give two clear, separate points. If one is correct and you write an extra incorrect statement in the same space, you risk losing marks.
Alternative acceptable method: The mark scheme allows you to directly plot the correct point (4, 19 000) or draw a correct line of best fit onto the diagram itself to earn a mark!

Too vague about points: Writing "One of the points is wrong" (Awarded B0). You must state which point is incorrect, e.g., "The point at 19 000 is plotted at 20 000" or "The point for age 4 is wrong".
Misunderstanding line of best fit: Writing "The line of best fit doesn't touch every cross" (Awarded B0). A line of best fit is not supposed to connect the dots! It only needs to show the general trend with points balanced on either side.
Vague axis complaints: Writing "The numbers on the side are wrong". Be precise: mention the y-axis or vertical scale and state that the intervals/spacing are not equal.

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