O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2010 · Q56 Marks
A curve has the equation y = 2x sin x + π/3. The curve passes through the point P (π/2, a).
- (i)Find, in terms of π, the value of a.[1]
- (ii)Using your value of a, find the equation of the normal to the curve at P.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [B1] (i) a = π + π/3, a = 4π/3 (Must be in terms of π)
- [M1, A1] (ii) dy/dx = 2x cos x + 2 sin x (M1 for attempt to differentiate a product)
- [M1] (ii) at P, dy/dx = 2, ⇒ grad of normal = -1/2 (M1 for m₁m₂ = -1, must have used differentiation)
- [M1, A1] (ii) normal: y - 4π/3 = -1/2 (x - π/2) (M1 for attempt at a normal equation, must have used differentiation, allow unsimplified)
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