Apps. and Interpretation for IBDP Maths Ebook 1 | Page 42

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 10
1. The length and the width of a rectangular board are 30 cm and 20 cm respectively. The
four corners in a square shape of length x cm is removed. The remaining part of the
rectangular board forms a rectangular box of height x cm as shown in the diagram below.
Let
2
A cm be the area of the base of the box.
(a) Find the expression of A in terms of x .
It is given that A � 299 .
(b) Find the value of x .
(c)
Write down the exact value of the volume of the box.
[2]
[3]
[1]
2. In a right-angled triangle, the lengths of the three sides are ( x � 18) cm , ( x � 1) cm and
x cm respectively. Let
2
A cm be the area of the triangle.
(a) Write down and simplify a quadratic equation in x .
(b) Hence, find the value of x .
The triangle is then planned to be painted, and the total painting cost is $1680.
[2]
[2]
(c)
Find the painting cost per
2
cm .
[2]
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