Exam-Style Question on Quadratic Models
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 106. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.
The cross-section of a fish pond is drawn on a set of axes shown below. The edge is modelled by \(y=ax^2+c\) and the cross section is the same for the whole of its length. The curve touches the x-axis at the origin.
Point A has coordinates (-9,5.4) and point B has coordinates (9,5.4).
(a) Find the value of \(c\).
(b) Find the value of \(a\).
(c) Hence write down the equation of the quadratic function which models the edge of the fish pond.
(d) Calculate the value of \(y\) when \(x\)=7.2m.
(e) State what the value of \(x\) and the value of \(y\) represent for this fish pond.
(f) Find the value of \(x\) when the height of water in the pond is 2m.
The pond is filled so that the cross-sectional area of the water is 22.9m2. The pond has a length of 8m.
(g) Calculate the volume of water in the pond.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
©1997 - 2021 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/