O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2010 · Q1211 Marks
OR A curve is such that dy/dx = 6 cos(2x + π/2) for -π/4 <= x <= 5π/4. The curve passes through the point (π/4, 5).
- (i)Find the equation of the curve,[4]
- (ii)the x-coordinates of the stationary points of the curve,[3]
- (iii)the equation of the normal to the curve at the point on the curve where x = 3π/4.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [4] (i) M1 for integrate cos (2x + π/2); A1 for y = 3sin (2x + π/2) (+c); M1 for attempt to find c; A1 for y = 3sin (2x + π/2) + 5
- [3] (ii) M1 for attempt to solve dy/dx = 0; A2,1,0 for x = 0, π/2, π (A1 for 2 correct, A0 for 0-1 correct)
- [4] (iii) M1 for attempt to obtain y (from (i)); M1 for attempt to obtain dy/dx and perp gradient; DM1 for attempt at straight line (y-y1=m(x-x1)); A1 for y = (-1/6)x + 5.39 (Must have (i) correct)
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