O-LevelAdditional MathematicsTrigonometry4037/11 · Oct/Nov 2011 · Q68 Marks
The diagram shows part of the graph y = p + 3tan3x passing through the points (−π/12, −5), (0, p) and (q, 1). Find the value of p and of q.
- (a)The diagram shows part of the graph y = p + 3tan3x passing through the points (−π/12, −5), (0, p) and (q, 1). Find the value of p and of q.[4]
- (b)It is given that f(x) = a cos(bx)+c, where a, b and c are integers. The maximum value of f is 11, the minimum value of f is 3 and the period of f is 72°. Find the value of a, of b and of c.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [1] (a) -5 = p + 3 tan (π/4)
- [1] (a) :. p = -2
- [1] (a) 1 = 'p' + 3 tan 3q
- [1] (a) tan 3q = 1
- [1] (a) q = π/12
- [1] (b) amplitude a = 4
- [1] (b) b = 5
- [1] (b) When f = 11, x = 0, so c = 7
- [1] (b) Or when f = 3, x = π/3, so c = 7
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