Analysis and Approaches for IBDP Maths Ebook 2 | Page 262

Your Practice Set – Analysis and Approaches for IBDP Mathematics
81
Paper 3 – Practical Example
Example
You are asked to investigate the areas above or below the curve
defined rectangles.
1
y �4
� restricted in
x
1
The figure shows the graph of f( x) �4
� . A , C and F are three distinct points on the
x
graph of f such that the x -coordinates of A , C and F are 1, 2 and 3 respectively. AB ,
DCE and GF are vertical lines. AD , BCG and EF are horizontal lines.
Part I – Investigating the Quantity 1
Let
A be the area bounded by the graph of f , the line y � f ( k)
and the line x�k� 1.
k
Consider the rectangle ABCD .
(a) (1) Find the area of the rectangle ABCD .
(2) Find the area of the triangle ACD .
(3) Hence, write down an inequality for A
1.
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