C4 MS Jun 2009

Page 1

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)


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