Analysis and Approaches for IBDP Maths Ebook 2 | Page 53

15
Paper 2 Section A – Negative Indices Problems
Example
(a) Using the extended binomial expansion, find the first four terms of the expansion
1
of in ascending powers of x .
1�
5x
[3]
(b) Hence, by using the substitution x � 0.03 , find an exact approximation to 20
23 . [2]
4
Solution
(a)
(b)
1
�1
�(1 �5 x)
1�
5x
1 ( �1)( �2)
�1 � ( �1)(5 x) � (5 x)
1�
5x
2!
( �1)( �2)( �3) (5 )
3
�
x �
3!
1
2 3
1 5x 25x 125x
1�
5x � � � � �
20 1
�
23 1.15
20 1
�
23 1 � 5(0.03)
2
M1A1
A1
[3]
20 1 5(0.03) 25(0.03)
2 125(0.03)
3
23 � � � � M1
20
0.869125
23 � A1 [2]
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