Analysis and Approaches for IBDP Maths Ebook 2 | Page 154

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Solution
(a)
(b)
The area of the top face
�1
5 ( )( )sin 72
2 x x �
� � �
A1
�
�
5sin 72
2
2 2
� x cm
AG
The length of each square face
2 2
� x � x � 2( x)( x)cos72
(A1) for substitution
[1]
� �
2 2
2x
2x
cos 72
2
� 2 x (1 � cos72 )
A1
� 5sin 72 �
A � 2�
x �� 5( 2 x (1 � cos 72 ))
� 2 �
A � x � x �
2 2 2
2 2
5 sin 72 5(2 (1 cos 72 ))
A � x � x �
2 2
5 sin 72 10 (1 cos 72 )
A x x
(M1) for valid approach
2 2 2
� 5 (2sin 36 cos36 ) � 10 (2sin 36 ) (A2) for substitution
A � x � x
A
2 2 2
10 sin 36 cos36 20 sin 36
2
�10x
sin36 (cos36 � 2sin36 )
A1
(c) C � Asec36 cosec36 �500x
� 2600
C �
2
10x
sin 36 (cos36 � 2sin 36 )sec36 cosec36
�500x
�2600
C x x
M1
2
� 10 (1 � 2 tan 36 ) �500 � 2600
A1
dC
10(1 2 tan 36 )(2 x) 500(1) 0
dx � � � � A1
dC
20(1 2 tan 36 ) x 500
dx � � �
dC
0
dx �
�20(1 � 2tan36 ) x �500 � 0
M1
20(1 �2tan36 ) x � 500
25
x � A1
1 � 2 tan 36
[6]
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