Analysis and Approaches for IBDP Maths Ebook 1 | Page 84

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 28
1. (a) Show that 27 �1� 1 .
26 26
(b) Prove that
m
3
�1�
2 2
( m �1)( m � m �1) ( m �1)( m � m �1)
1
for m � 1.
[2]
[3]
2. (a) Show that 1 � 2 � 1 .
7 63 9
(b) Prove that 1 �
2 �
1
2
m �2 m �2m m
for m � 2 .
[2]
[3]
3. (a) Show that 67 � 2 � 3 � 4 .
42 3 2 7
(b)
Prove that
2
6m
�5m�2 2 3 4
� � �
m( m �1)(2m �1) m m �1 2m
�1
for m � 1.
[2]
[3]
4. (a) Show that 31 � 2 � 4 � 1 .
25 5 25
(b) Prove that
2
2m
�1 4 1
� 2 � �
( m �1) m �1 ( m �1)
2 2
for m �� 1.
[2]
[3]
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