Analysis and Approaches for IBDP Maths Ebook 2 | Page 51

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Paper 2 Section A – Fractional Indices Problems
Example
(a)
(b)
Using the extended binomial expansion, find the first four terms of the expansion
of 1� 3x in ascending powers of x .
Hence, by using the substitution
1
x �� , find an approximation to 1.5 .
6
[3]
[2]
4
Solution
(a)
1�3 x � (1 � ( � 3 x)) 2
3
� � x �
1
� 1�� 1�
1
� �� � �
� � 2 2
2
1� 3x �1 � ( 3 x) � �� �
� � � � ( �3 x)
�2 � 2!
M1A1
� 1 �� 1 �� 3 �
� 2 �� �
2 �� �
2 �
� �� �� � ( 3 )
3!
3 9 2 27 3
1�3x �1� x � x � x � A1
2 8 16
(b)
� 1 �
1.5 � 1� 3 � � �
� 6 �
2 3
3 � 1 � 9 � 1 � 27 � 1 �
1.5 �1� �� � � �� � � ��
�
2 � 6 � 8 � 6 � 16 � 6 �
M1
157
1.5 �
128
A1
[3]
[2]
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