O-LevelAdditional MathematicsTrigonometry4037/22 · Oct/Nov 2015 · Q68 Marks
The figure shows part of the graph of y = a + b sin cx. [Figure 6.1]
- (i)Find the value of each of the integers a, b and c.[3]
- (ii)Using your values of a, b and c find dy/dx.[2]
- (iii)the equation of the normal to the curve at (π/2, 3).[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [B1B1B1] (i) a = 3, b = 2, c = 4
- [M1] (ii) dy/dx = 8cos4x isw ±k cos cx and no other term in x
- [A1FT] (ii) bcx cos cx and no other term c≠1
- [DM1] (iii) x=π/2 → dy/dx = 8 cos 2π = 8 Find their correct numerical dy/dx
- [M1] (iii) Eqn: (y-3)/(x-π/2) = -1/8 → y=-1/8 x+3.20 Find equation with their numerical normal gradient ie -1/(dy/dx) and point (π/2, 3)
- [A1] (iii) All correct isw
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