Analysis and Approaches for IBDP Maths Ebook 2 | Page 52

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 14
1. (a) Using the extended binomial expansion, find the first four terms of the expansion
of 3 1� 2x in ascending powers of x .
(b) Hence, by using the substitution x � 0.03 , find an approximation to 3 1.06 .
[3]
[2]
2. In the expansion of
(1 � bx)
�
2
3
, the coefficient of
3
x is
2560
� .
81
(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
of 4 � x in ascending powers of x .
(b) Hence, by using an appropriate substitution, find an approximation to 15 .
[3]
[4]
4. (a) Using the extended binomial expansion, find the first three terms of the expansion
of 4 81� ax in ascending powers of x , giving the answer in terms of a .
It is given that the product of the coefficient of x and the coefficient of
2
x is � 0.5 .
[3]
(b) Find the value of a .
(c)
State the range of values of x for valid binomial expansion.
[2]
[2]
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