O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2010 · Q1212 Marks
Answer only one of the following two alternatives. EITHER The diagram shows part of a curve for which dy/dx = 8 cos 2x. The curve passes through the point B(π/4, 7). The line y = 5 meets the curve at the points A and C. [Figure 12EITHER]
- (i)Show that the curve has equation y = 3 + 4 sin2x.[3]
- (ii)Find the x-coordinate of the point A and of the point C.[4]
- (iii)Find the area of the shaded region.[5]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- M1 for attempt to integrate
- M1 for attempt to get c provided function of sin 2x is used
- A1
- M1 for attempt to equate to 5 and solve
- M1 for a correct method to find x
- A1
- √A1 on first solution
- M1 for attempt to integrate
- A1
- DM1 for correct use of limits
- M1 for area of rectangle
- A1
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