O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2018 · Q107 Marks
The diagram shows part of the curve y = a+4cosbx, where a and b are positive constants. The curve meets the y-axis at the point (0,6) and the x-axis at the point (π/6, 0). The curve meets the x-axis again at the point P and has a minimum at the point M. [Figure X.X]
- (i)Find the value of a and of b.[3]
- (ii)Using your values of a and b find, the exact coordinates of P,[2]
- (iii)the exact coordinates of M.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] for a=2
- [M1] For a correct attempt to solve cos(bπ/6) = ± a/4 provided 0<a<4 to get b=...
- [A1] leading to b = 4
- [M1] Dep For attempt to solve their cos(bx) = ±a/4 provided 0<a<=4 or use of symmetry to get x=...
- [A1]
- [B1] At M, y = -2
- [B1] x = π/4
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