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Exam-Style Questions on Quadratic Models

Problems on Quadratic Models adapted from questions set in previous Mathematics exams.


IB Studies

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.

Cross Section

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.

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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