A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2024 · Q15 Marks
The diagram shows the curve with equation y = a sin(bx)+c for 0 ≤ x ≤ 2π, where a, b and c are positive constants. [Figure X.X]
- (a)State the values of a, b and c.[3]
- (b)(i)For these values of a, b and c, determine the number of solutions in the interval 0 ≤ x ≤ 2π for each of the following equations: a sin(bx) + c = 7-x[1]
- (b)(ii)For these values of a, b and c, determine the number of solutions in the interval 0 ≤ x ≤ 2π for each of the following equations: a sin(bx) + c = 2π(x−1).[1]
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 (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [B1] a=4 Allow 4sin (2x) + 3 if values of a, b and c are not stated.
- [B1] b=2
- [B1] c=3
- [B1] 5 Ignore attempts at finding solutions.
- [B1] 1 Ignore attempts at finding solutions.
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