Your Practice Set – Applications and Interpretation for IBDP Mathematics
3 . The region R is enclosed by the y -axis , the graph of x�3y� 3 and the graph of
1 x � �3 � ln . 1 � y
( a ) Write down the y -intercept of
( i ) x�3y� 3;
1 ( ii ) x � �3 � ln . 1 � y
( b ) Write down the y -coordinate of the point of intersection of the graph of 1 x�3y� 3 and the graph of x � �3 � ln . 1 � y
( c ) Hence , find the area of R .
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4 . The region R is enclosed by the y -axis , the graph of 1 x� 4� y� 3. The range of y � x� 1 is { y: y� 3 }.
2
1 y � x� 1 and the graph of
2
( a ) Write down the y -intercept of
( i )
1 y � x� 1;
2
( ii ) x� 4� y� 3.
( b ) Make x the subject of
1 y � x� 1.
2
( c ) Write down the y -coordinate of the point of intersection of the graph of 1 y � x� 1 and the graph of x� 4� y� 3.
2
( d ) Hence , find the volume of the solid of revolution formed when R is rotated through 2π about the y -axis .
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