Sketch the graph of y = |x+3a|, where a is a positive constant.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [1] (a) Roughly symmetrical. Condone some inaccuracy, but needs to look as if they intended symmetry and straight lines. If not, then B0. Needs to be in the correct position. Needs to have two solid line segments. Needs to exist in both quadrants above the axis. Ignore dotted lines below the axis. Solid line below the axis is B0. Condone if no scale shown, but need to see 3a and -3a marked. Ignore y=a-2x if seen.
2. [1] (b) Obtain critical value -2a/3 from x+3a=a-2x
3. [1] (b) State final answer x > -2a/3. Need a clear conclusion – must imply rejection of x = 4a. B0 if using ≥.
4. [1] (b) Alternative Method: Obtain critical value -2a/3 from (x+3a)² = (a−2x)²
5. [1] (b) Alternative Method: State final answer x > -2a/3. Need a clear conclusion – must imply rejection of x = 4a. B0 if using ≥.