Download FP1 - Chapter 5 Exam Questions

FP1 – Chapter 5 Exam Questions
1.
Solve the equation


cos x    0.5,
6

in the interval 0 < x < 2π, leaving your answers in terms of π.
(6)
(Total 6 marks)
2.
The angle x radians satisfies the equation
cos (2x +
(a)
1

)=
6
2
Find the general solution of this equation, giving the roots as exact values in terms of
π.
(6)
(b)
Find the number of roots of the equation which lie between 0 and 2 π.
(2)
(Total 8 marks)
3.
(a)
3
Write down the values of tan  and tan
.
4
4
(2)
(b) It is given that x satisfies the equation
2 sin2 x + sin x cos x = cos2x.
(i)
By dividing both sides of this equation by cos2 x, show that
2 tan2 x + tan x
1 = 0.
(2)
(ii)
Solve this quadratic equation for tan x.
(2)
(iii)
Hence find all possible values of x in the interval 0 < x < π. Give each answer
to three significant figures.
(2)
(Total 8 marks)
South Wolds Comprehensive School
1