Your Practice Set – Applications and Interpretation for IBDP Mathematics SE Production Limited 186 ( a ) ( i ) 1 ( ) 1 3 f a � �� � � ( M1 ) for valid approach ( ) 3 f a � � A1 ( ii ) 2 ( ) 3 f x x � � ( A1 ) for correct approach 2 ( ) 3 f a a � � 2 3 3 a � � ( M1 ) for setting equation 2 1 a � 1 a � A1 ( iii ) 3 1 0 1 1 3 b � �� � ( M1 ) for setting equation 1 1 1 3 � b �� 3 1 b � � � 4 b � A1 ( iv ) The equation of [ PQ ]: 1 3 y x c � � � 1 0 ( 4 ) 3 c � � � ( M1 ) for substitution 4 3 c � 1 4 3 3 y x � � � � A1 [ 9 ] ( b ) The required area 1 0 ( 4 1 )( 1 0 ) ( ) d 2 f x x � � � � � M1A1 1 3 0 ( 3 )( 1 ) d 2 x x � � � ( A1 ) for correct approach 7 4 � A1 [ 4 ] Solution