Analysis and Approaches for IBDP Maths Ebook 2 | Page 40

Your Practice Set – Analysis and Approaches for IBDP Mathematics
11
Paper 2 Section A – Partial Fractions
Example
Let
4
f( x)
�
( x�1)( x�6)
, x � 1, x � 6 .
(a) Express f( x ) in partial fractions.
(b) Write down the y -intercept of f( x ).
(c) Write down the equations of the vertical asymptotes of f( x ).
[4]
[1]
[2]
Solution
(a)
Let
4 A B
� � , where A and B
( x �1)( x � 6) x �1 x � 6
are constants.
4 A( x �6) B( x �1)
�
�
( x �1)( x � 6) ( x �1)( x � 6) ( x �1)( x � 6)
4 Ax � 6A� Bx � B
�
( x �1)( x � 6) ( x �1)( x � 6)
M1
4 � ( A� B) x � ( �6 A� B)
A1
0 � A�
B
B��
A
4� �6A�
B
�4 � �6 A�( � A)
A1
4��
5A
4
A ��
5
� 4 �
�B
� � � � �
� 5 �
4
B �
5
4 4 4
� � � �
( x �1)( x � 6) 5( x �1) 5( x � 6)
A1
[4]
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