O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2020 · Q69 Marks

The diagram shows the straight line 2x+y=-5 and part of the curve xy+3 = 0. The straight line intersects the x-axis at the point A and intersects the curve at the point B. The point C lies on the curve. The point D has coordinates (1,0). The line CD is parallel to the y-axis.

(a)Find the coordinates of each of the points A and B.[3]
(b)Find the area of the shaded region, giving your answer in the form p+lnq, where p and q are positive integers.[6]

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[1] A(-2.5, 0)
[1] For attempt to eliminate one variable, obtain a 3-term quadratic equation = 0 and attempt to solve
[1] Allow A1 if just the x-coordinates or just the y-coordinates are given
[1] For attempt at triangle using their values
[1] For attempt to integrate, must have ln
[1] correct application of limits, dep on previous M mark
[1] realisation that value of integral is negative and making the adjustment
[1] application of log law, dep on previous M mark
[1] Area = 9+ln8

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