A-LevelMathematicsFunctions9709/12 · Oct/Nov 2016 · Q1011 Marks
A function f is defined by f : x → 5 – 2 sin 2x for 0 ≤ x ≤ π.
- (i)Find the range of f.[2]
- (ii)Sketch the graph of y = f(x).[2]
- (iii)Solve the equation f(x) = 6, giving answers in terms of π.[3]
- (iv)State the largest value of k for which g has an inverse.[1]
- (v)For this value of k, find an expression for g⁻¹(x).[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [B1] Identifying both 3 and 7 or correctly stating one inequality.
- [B1] Completely correct statement. NB 3 < x ≤ 7 scores B1B0
- [B1*] One complete oscillation of a sinusoidal curve between 0 and π.
- [DB1] All correct, initially going downwards, all above f(x)=0
- [M1] Make sin2x the subject.
- [A1 A1] for 3π/2 1st answer from sin2x = −½ only, if in given range
- [SR A1A0] for both.
- [B1] k = π/4
- [M1] Makes ±sin2x the subject soi by final answer.
- [M1] Correct order of operations including correctly dealing with " – ".
- [A1] Must be a function of x
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