C2 MS Jan 2005

Page 1

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)


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C2 MS Jan 2005 by The de Ferrers Academy - Issuu