Analysis and Approaches for IBDP Maths Ebook 1 | Page 78

Your Practice Set – Analysis and Approaches for IBDP Mathematics
26
Paper 2 Section A – Finding the total number
Of terms and a term in
Example
Consider the expansion of
12
� 3 �
�x
�
2 �
� x � .
(a)
(b)
Write down the number of terms of this expansion.
Find the coefficient of
3
x .
[1]
[5]
Solution
(a) 13 terms A1 N1
[1]
(b)
12
� 3 �
�x
�
2 �
� x �
1 2
12 �12� 11 � 3 � �12�
10 � 3 �
� x � � �( x) ( x)
2 2
1
� � � � �
x 2
� �
� � � � � � � x �
r
�12� 12�r
� 3 �
� � � �( x)
�
2
r
� �
� � � x �
(M1) for valid expansion
12�r
�2
r
( x) ( x )
(M1) for finding r
12 r 2r
� x � �
12 3r
� x �
�12 �3r
� 3
r � 3, which is corresponding to the 4 th term (A1) for identifying the term
3
The coefficient of x
�12 � (3)
3
� � �
� 3 �
(A1) for correct working
� 5940
A1 N3
[5]
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