1.	The diagram below shows a plan for a window in the shape of a trapezium.
		
	Three sides of the window are 2 m long. The angle between the sloping sides of the window and the base is θ, where 0 < θ < .
(a)	Show that the area of the window is given by y = 4 sin θ + 2 sin 2θ.
(5)
 
(b)	Zoe wants a window to have an area of 5 m^2. Find the two possible values of θ.
(4)
 
(c)	John wants two windows which have the same area A but different values of θ.
	Find all possible values for A.
(7)
(Total 16 marks)

2.	Let f(x) =  sin x + e^2x cos x, for 0 ≤ x ≤ π. Given that , solve the equation
f(x) = 0.
(Total 6 marks)

3.	The function f is defined by f : x → 30 sin 3x cos 3x, 0 ≤ x ≤ .
(a)	Write down an expression for f (x) in the form a sin 6x, where a is an integer.
(b)	Solve f (x) = 0, giving your answers in terms of π.
(Total 6 marks)

4.	Consider the equation 3 cos 2x + sin x = 1
(a)	Write this equation in the form f (x) = 0 , where f (x) = p sin^2 x + q sin x + r , and p , q , r ∈ .
(b)	Factorize f (x).
(c)	Write down the number of solutions of f (x) = 0, for 0 ≤ x ≤ 2π.

(Total 6 marks)

IB Questionbank Maths SL