Apps. and Interpretation for IBDP Maths Ebook 1 | Page 43

3. In a coffee shop, the amount of coffee powder, Q , in kilograms, sold in a week is given
by Q�75 � 15r, where $r is the cost of 1 kg coffee bean.
(a) Find the maximum cost of 1 kg coffee bean if at least 7.5 kg of coffee powder can
be sold in a week.
[2]
The coffee shop can earn $( r � 2) for each kilogram of coffee powder sold. Let P be the
weekly profit.
(b) Find the expression of P in terms of r .
(c)
Find the exact value of the maximum weekly profit.
[2]
[2]
4
4. A ball is kicked from the top of a vertical cliff onto a horizontal grass ground. The path of
the ball can be modelled by the quadratic curve
y � � x � x � , where x m and
2
0.5 2 10
y m are the horizontal distance from the cliff and the vertical distance above the ground
respectively, as shown in the diagram below.
(a)
(b)
(c)
Find the maximum height of the trajectory of the ball.
[2]
Write down the horizontal distance of the ball from the cliff when the ball is at the
same vertical level when the ball is first kicked.
[1]
Find the horizontal distance from the cliff to the position at which the ball hits the
grass ground.
[3]
www.seprodstore.com
33