A-LevelMathematicsFunctions9709/12 · Oct/Nov 2017 · Q68 Marks

This question concerns properties of functions involving sine.

(a)(i)The function f, defined by f : x → a + b sin x for x ∈ R, is such that f(½π) = 4 and f(⅙π) = 3. Find the values of the constants a and b.[3]
(a)(ii)Evaluate ff(0).[2]
(b)The function g is defined by g : x → c + d sin x for x ∈ R. The range of g is given by −4 ≤ g(x) ≤ 10. Find the values of the constants c and d.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

Forming simultaneous equations and eliminating one of the variables – probably a. May still include sin(π/2) and/or sin(π/6) (M1)
→ a = 5, b = -2 (A1A1)
Valid method for ff. Could be f(0) = N followed by f(N) = M. (M1)
ff(0) = 5 - 2sin5 = 6.92 (A1)
EITHER: 10 = c + d and -4 = c - d (M1) Either pair of equations stated.
c = 3, d = 7, -7 or ±7 (A1A1) Either pair solved ISW
Alternately c=3 B1, range = 14 M1→ d = 7, -7 or ±7 A1
OR: (M1 A1 A1) Either of these diagrams can be awarded M1.Correct values of c and/or d can be awarded the A1, Al

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