A-LevelMathematicsIntegration9709/12 · Oct/Nov 2024 · Q78 Marks

By expressing -2x² +8x+11 in the form -a(x−b)² +c, where a, b and c are positive integers, find the coordinates of the vertex of the graph with equation y=-2x²+8x+11.

(a)By expressing -2x² +8x+11 in the form -a(x−b)² +c, where a, b and c are positive integers, find the coordinates of the vertex of the graph with equation y=-2x²+8x+11.[3]
(b)The diagram shows part of the curve with equation y=-2x² +8x+11 and the line with equation y = 8x+9. Find the area of the shaded region. [Figure X.X][5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[M1*] -2((x±p)²±q) or -2(x+p)²±q p≠0.
[DM1] -2((x-2)²±q) or -2(x-2)²±q
[A1] -2(x-2)² +19 and (2, 19) Accept x = 2, y=19 or 2, 19.
[B1*] Both x co-ordinates for the points of intersection.
[M1*] Subtract and attempt to integrate
[B1*] All terms correct.
[M1] Apply their limits, one positive and one negative, obtained from equating the line and the curve to their integrated expression.
[DB1] AWRT 2.67 WWW. Condone -8/3 -> 8/3. SC B1 for mistaking triangle for trapezium leading to 11/3 , i.e. a total of 2/5.

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