June 2009 6666 Core Mathematics C4 Mark Scheme Question Number Q1
Scheme
f ( x) =
Marks
1 −1 = (4 + x) 2 √ (4 + x)
= ( 4)
− 12
(1 +
...
)
M1
1 (1 + ... 2
...
)
...
or
1 2 √ (1 + ...)
2 3 ⎛ ⎞ − 12 ) ( − 32 ) ⎛ x ⎞ ( − 12 ) ( − 32 )( − 52 ) ⎛ x ⎞ ( 1 ⎛ x⎞ ... = ... ⎜1 + ( − 2 ) ⎜ ⎟ + + + ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 2 3! ⎝4⎠ ⎝4⎠ ⎝ 4⎠ ⎝ ⎠ ⎛ x⎞ ft their ⎜ ⎟ ⎝4⎠ 1 1 3 2 5 3 = − x, + x − x + ... 2 16 256 2048
B1 M1 A1ft
A1, A1
(6) [6]
Alternative f ( x) =
1 −1 = (4 + x) 2 √ (4 + x)
= 4 2 + ( − 12 ) 4 2 x + −1
−3
( − 12 ) ( − 32 ) 4−
M1 5 2
x2 +
1.2 1 1 3 2 5 3 = − x, + x − x + ... 2 16 256 2048
8371_9374 GCE Mathematics January 2009
( − 12 ) ( − 32 )( − 52 ) 4− 1.2.3
7 2
x3 + ...
B1 M1 A1 A1, A1
39
(6)