A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2025 · Q69 Marks

Sketch the graph of y = 3 sinx+2 for 0 ≤ x ≤ 2π.

(a)Sketch the graph of y = 3 sinx+2 for 0 ≤ x ≤ 2π.[2]
(b)(i)Determine the number of solutions in the interval 0 ≤ x ≤ 2n of each of the following equations. 3sinx+2 = x[1]
(b)(ii)3 sinx+2=5-x[1]
(c)Solve the equation 3 sinx+2 = 5 cos²x-1 for 0 ≤ x ≤ 2π.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[B2] Fully correct curve for y=3sinx+2 in range 0 ≤ x ≤ 2π, with max at y=5, min at y=-1, and starting/ending at y=2. (B1 for a sine shape with correct amplitude and vertical shift, or correct domain and range).
[B1] 1 solution.
[B1] 3 solutions.
[M1] Uses cos²x = 1 - sin²x to form a quadratic in sinx.
[DM1] Simplifies to a 3-term quadratic equation in sinx (e.g., 5sin²x + 3sinx - 2 = 0).
[A1] Solves quadratic to obtain sinx = 0.4 and sinx = -1.
[A2] x = 0.411, 2.73, 3π/2 (or 4.71) (A1 for 2 correct values).

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