January 2005 6664 Core Mathematics C2 Mark Scheme Question Number 1.
Scheme
Marks
5 5 (3 2 x) 5 (35 ) 3 4 (2 x) 33 (2 x) 2 1 2 243,810 x,1080 x 2
M1 B1, A1, A1 (4) (4 marks)
2.
3.
5 13 1 11 (a) ( , ), (9,5) 2 2
M1, A1 (2)
(b) r 2 (9 5) 2 (5 1) 2 ( 52) or r 2 (13 9)2 (11 5)2 ( 52) (or equiv.) Equation of circle: ( x 9) 2 ( y 5) 2 52 (or equiv.)
M1 M1 A1ft A1 (4) (6 marks) M1
(a) log 3 log 5 log 5 or x log3 = log5 x log 3 1.46 x
A1 A1 cao (3)
(a) log 2 (
2x 1 )2 x
M1
2x 1 2 2 or 4 x 2x 1 4x 1 x or 0.5 2
M1 M1 A1
(4) (7)
4.
(a) 5(1 sin x) 3(1 sin x)
M1
2
5 5 sin 2 x 3 3 sin x 0 5 sin 2 x 3 sin x 2
A1 cso (2)
(b) 0 (5 sin x 2)(sin x 1) 2 sin x , -1 5 2 x 23.6 sin x 5 , 156.4
M1 (both) ( 23.6 or 156.4) (180- )
A1 cso B1 M1 B1
sin x 1 x 270
(ignore extra solutions outside the range)
(5) (7)