Analysis and Approaches for IBDP Maths Ebook 2 | Page 54

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 15
1. (a) Using the extended binomial expansion, find the first four terms of the expansion
1
of in ascending powers of x .
3
(1 � 3 x)
(b) Hence, by using the substitution x �� 0.01 , find an approximation to
3
0.97 � .
[3]
[2]
2. In the expansion of
2
(1 � bx)
� , the coefficient of
3
x is 2048, where b � 0 .
(a) Find the value of b .
(b)
Find the coefficient of
2
x .
[4]
[2]
3. (a) Using the extended binomial expansion, find the first four terms of the expansion
1
of
2
4 �12x�9x
in ascending powers of x .
[3]
(b)
7
Hence, by using an appropriate substitution, find an approximation to �
2
2.15
.
[4]
4. (a) Using the extended binomial expansion, find the first three terms of the expansion
of 2 � x
2
in ascending powers of x up to x , giving the answer in terms of a .
a�
x
[3]
It is given that the sum of the coefficient of x and the constant term is 1 9 , where
0�a
� 6.
(b) (i) Find the value of a .
(c)
(ii)
Hence, write down the coefficient of
2
x .
State the range of values of x for this binomial expansion to be valid.
[3]
[2]
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