Sketch, on the same diagram, the graphs of y = x + 3 and y = |2x – 1|.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [*B1] Draw V-shaped graph with vertex on positive x-axis Must be straight lines.
2. [DB1] Draw (more or less) correct graph of y = x + 3 with smaller gradient together with a V shaped graph And crossing y-axis above y-intercept of first graph. Intersection in the first quadrant may be implied.
3. [B1] Solve x + 3 = 2x – 1 to obtain x = 4
4. [M1] Attempt solution of linear equation where signs of 2x and x are different
5. [A1] Obtain x = -2/3
6. [B1] State or imply non-modulus equation (x + 3)² = (2x – 1)²
7. [M1] Attempt solution of 3-term quadratic equation obtained from squaring both terms. Must have B1.
8. [A1] Obtain -2/3 and 4
9. [M1] Apply logarithms and use power law for 5^y = k where k > 0 Using their positive root from part (b). Allow M1 for y = 2log₅ 4.
10. [A1] Obtain y = 1.72 AWRT; and no other values.