A-LevelMathematicsTrigonometry9709/12 · May/June 2019 · Q67 Marks
The equation of a curve is y = 3 cos 2x and the equation of a line is 2y + 3x/π = 5.
- (i)State the smallest and largest values of y for both the curve and the line for 0 ≤ x ≤ 2π.[3]
- (ii)Sketch, on the same diagram, the graphs of y = 3 cos 2x and 2y + 3x/π = 5 for 0 ≤ x ≤ 2π.[3]
- (iii)State the number of solutions of the equation 6 cos 2x = 5 - 3x/π for 0 ≤ x ≤ 2π.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] 3, -3
- [B1] -2
- [B1] 2 1/2
- [B1] 2 complete oscillations of a cosine curve starting with a maximum at (0,a), a>0
- [B1] Fully correct curve which must appear to level off at 0 and/or 2π.
- [B1] Line starting on positive y axis and finishing below the x axis at 2π. Must be straight.
- [B1] 4
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