A-LevelMathematicsCoordinate geometry9709/12 · May/June 2025 · Q24 Marks

Find the coordinates of the points of intersection of the curve and the line with equations 2xy+5y2 = 24 and 2x+y+4 = 0.

Find the coordinates of the points of intersection of the curve and the line with equations 2xy+5y2 = 24 and 2x+y+4 = 0.[4]

Mark scheme

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

[1] *M1 OE For eliminating x or y. Condone sign errors in the rearrangements.
[1] DM1 OE For simplifying to a 3-term quadratic; terms do not all have to be on the same side. Condone sign errors in the expansions or in the collecting of terms.
[1] B1 OE Not for a correct (x, y) pair. Allow from a correct quadratic (ignore any working seen). ( -1, -2)
[1] B1 OE Allow from a correct quadratic (ignore any working seen). Condone x = -1 and y = -2 and x = -7/2 and y = 3. ( -7/2, 3)

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Topic: Coordinate geometry, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2025 Paper 1 Variant 2, question 2.

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