Your Practice Set – Applications and Interpretation for IBDP Mathematics
51
Paper 1 – Composite Figures and Objects
Example
3 3 The region R is enclosed by the x -axis , the graph of y� x� and the graph of
4 2
3 2 27
3 2 27 y � x � x � 30. The domain of y � x � x � 30 is { x: x� 9 }. 8 4
8 4
( a ) Write down the x -intercept of
( i )
3 3 y� x� ;
4 2
( ii )
3 27 � � � 30.
8 4
2 y x x
( b ) Write down the coordinates of the point of intersection of the graph of 3 3
3 2 27 y� x� and the graph of y � x � x � 30. 4 2
8 4
( c ) Hence , find the area of R .
[ 2 ]
[ 2 ]
[ 3 ]
Solution
( a ) ( i ) 2 A1
( ii ) |
8 |
A1 |
( b ) |
( 6 , 3 ) |
A2 |
( c ) |
The area of R |
|
6� 3 3 � 8� 3 2 27 � � x dx x x 30 dx
2� � � � � � 4 2
6� � � � � 8 4 �
� 8.5
A1
� � ( A2 ) for correct approach
[ 2 ]
[ 2 ]
[ 3 ]
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