A-LevelMathematicsFunctions9709/12 · May/June 2010 · Q1110 Marks
The function f: x → 4-3 sin x is defined for the domain 0 ≤ x ≤ 2π. (i) Solve the equation f(x) = 2. (ii) Sketch the graph of y = f(x). (iii) Find the set of values of k for which the equation f(x) = k has no solution. The function g : x → 4 – 3 sin x is defined for the domain ½π ≤ x ≤ A. (iv) State the largest value of A for which g has an inverse. (v) For this value of A, find the value of g⁻¹(3).
- (i)Solve the equation f(x) = 2.[3]
- (ii)Sketch the graph of y = f(x).[2]
- (iii)Find the set of values of k for which the equation f(x) = k has no solution.[2]
- (iv)State the largest value of A for which g has an inverse.[1]
- (v)For this value of A, find the value of g⁻¹(3).[2]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [M1] Makes sin x the subject + solution.
- [A1] co.
- [A1√] √ for π– first answer.
- [B1] Must be 1 complete oscillation.
- [B1] Shape and position correct, in 1st quadrant, curve not lines.
- [B1 B1] B1 for k = 1, 7, B1 for answer
- [B1] Or B1 for k < 1, B1 for k > 7
- [B1] co
- [M1 A1] M1 for soln of 3 = 4 – 3sin x or inverse.
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