Analysis and Approaches for IBDP Maths Ebook 2 | Page 196

Your Practice Set – Analysis and Approaches for IBDP Mathematics
60
Paper 2 Section A – Composite Figures and Objects
Example
The region R is enclosed by the graph of 3x� 4y�6 � 0, the graph of
3 27
� � � 30 and the x -axis. Find the area of R .
8 4
2
y x x
[7]
Solution
3x� 4y�6 � 0
3x�6 � 4y
3 3
y� x� (A1) for correct approach
4 2
3x � 4(0) �6 � 0
3x � 6
x � 2
(A1) for correct value
3 3 3 2 27
x � � x � x � 30
(M1) for setting equation
4 2 8 4
3 2 15 63
x � x� � 0
8 2 2
2
x � 20x� 84 � 0
( x�6)( x�14) � 0
x � 6 or x � 14
(A1) for correct values
3 2 27
x � x� 30 � 0
8 4
2
x �18x� 80 � 0
( x�8)( x�10) � 0
x � 8 or x � 10
(A1) for correct values
The area of R
6� 3 3 � 8� 3 2 27 �
� � x dx x x 30 dx
2� � � � � �
4 2
� 6� �
A1
� � � 8 4 �
� 8.5
A1
[7]
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