The diagram shows curves with equations y = 2x¹/² + 13x⁻¹/² and y = 3x⁻¹/² + 12. The curves intersect at points A and B. [Diagram provided]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [*M1] OE Equating the two expressions in x and then multiplying each term by x¹/² or by their substitution for x¹/². Coefficients need to be retained but condone +/- sign errors. Allow x¹/² replaced by x.
2. [DM1] OE Solving their three-term quadratic.
3. [A1, A1] A1 for both x-values and A1 for both y values. If M1DM0 scored then SCB1B1 is available for final answers.
4. [M1] Attempt to integrate, defined by at least one correct fractional power, and subtract – condone the wrong way round.
5. [B1 B1] B1 for either { }. B1 for completely correct integration of their expression following through +/- sign errors from the subtraction.
6. [M1] Substitution of their positive limits from part (a) in their integrated expression, defined by at least one correct fractional power, and subtraction.
7. [A1] AWRT If M1B1B1M0 then SC B1 available for correct final answer. Condone negative answer if corrected.