Apps. and Interpretation for IBDP Maths Ebook 1 | Page 41

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Paper 1 – Applications of Quadratic Functions
Example
The length of a square farm is ( x � 2) m . In two of the four corners a square of length
2 m is for storage use. The rest of the farm is for animals. Let
region for animals.
2
A m be the area of the
4
(a) Find the expression of A in terms of x .
It is given that A � 174.25 .
(b) Find the value of x .
(c)
Write down the perimeter of the region for animals.
[2]
[3]
[1]
Solution
(a)
A
2 2
� � � (M1) for valid approach
( x 2) 2(2)
2
� x � x� �
4 4 8
2
� x � 4x� 4
A1 N2
(b) A � 174.25
x
x
2
2
� 4x� 4 � 174.25
(M1) for setting equation
� 4x�178.25 � 0
2
4x
�16x� 713 � 0
(A1) for correct equation
(2x�31)(2 x� 23) � 0
2x �31 � 0 or 2x �23 � 0
x �� 15.5 (Rejected) or x � 11.5
A1 N3
(c) 54 m A1 N1
[2]
[3]
[1]
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