Apps. and Interpretation for IBDP Maths Ebook 1 | Page 220

Your Practice Set – Applications and Interpretation for IBDP Mathematics
3 2
2. Consider the graph of f ( x) � x �5x � 25x
� 125 for x � 6 , where f( x) � 0 for
p�x� 6. Let R be the region enclosed by the graph of f , the y -axis and the x -axis.
(a) (i) Write down the value of p .
(ii) Write down the coordinates of the minimum point of f( x ).
(b) (i) Write down the integral representing the area of R .
(ii) Hence, find the exact value of the area of R .
[3]
[2]
3. Consider the graph of
2
f ( x) � �2x �8x
� 42 , where f( x) � 0 for a �x � b . Let R be the
region enclosed by the graph of f , the line x
� c and the x -axis.
(a) (i) Write down the values of a and b .
(ii) Write down the coordinates of the maximum point of f( x ).
The area of R can be calculated by
the area of R is 28
3 .
c
2
( �2 �8 � 42)d
a
[4]
� x x x , where a �c � b . It is given that
(b) Find the value of c .
[2]
2
4. Consider the graph of f ( x) � �2x �120x
� 1600 , where f( x) � 0 for a �x � b . Let R
be the region enclosed by the graph of f and the x -axis.
(a) (i) Write down the values of a and b .
(ii) Write down the integral representing the area of R .
(iii) Hence, find the exact value of the area of R .
Consider the parallelogram PQRS with vertices P(17, c ) , Q(117, c ) , R(92, 30) and
S( � 8, 30) , where c � 30 . It is given that the area of the parallelogram is equal to the area
of R .
[4]
(b) Find the value of c .
[3]
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