Analysis and Approaches for IBDP Maths Ebook 1 | Page 200

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b) f��( x) � 0
(c)
(d)
2
2 ax( x �12)
( x � 4)
2 3
� 0
2
2 ax( x �12) � 0
(M1) for setting equation
x( x � 12)( x � 12) � 0
(A1) for factorization
x � 0 , x � 12 � 0 or x � 12 � 0
x � 0 , x �� 12 or x � 12
f (0) � 0
A1
a( � 12)
f ( � 12) �
� �
2
( 12) 4
� 12
f( � 12) � a
A1
16
f( 12) � � f( � 12)
f( 12) �
12
a
16
A1
Thus, the coordinates of the points of inflexion
� 12
are (0, 0) , 12,
16 a � � 12
�
� �
�
and 12,
�
�
16 a �
�
�
.
� �
A2 N5
The area of the shaded region
8
� � f ( x)dx
(A1) for definite integral
2
8 ax
� � dx
2 2
x � 4
2
Let u�x
� 4
2
x� 8 � u� 8 � 4 � 68
du
2x
dx 2
x� 2 � u� 2 � 4 � 8
1 d d 2 u x x
68 1 1
�a� � d u
8
u 2
A2
a 68 1
� d u
2
� 8
u
a
� �ln
u� 68
8
2
A1
a
� (ln 68 � ln8)
2
(M1) for substitution
a 17
� ln
2 2
A1 N3
a 17
� ln
A2 N2
2 2
[7]
[6]
[2]
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