Mathematics 4024 · O Level · Graphs of functions

Graphs of functions — practice question

The diagram represents a triangular prism, and every length is measured in centimetres.
(a)[3]

Demonstrate that the prism has volume, $V\text{ cm}^3$, given by $V = 40x - 5x^2$.

(b)[3]

On the grid on the following page, plot the graph of $V = 40x - 5x^2$ for $1 \le x \le 7$; three points are already marked.

(c)[2]

From the graph, determine the possible values of $x$ for one of these prisms when the volume is $50\text{ cm}^3$.

(d)[3]

A cuboid measures $4\text{ cm}$ by $3\text{ cm}$ by $x\text{ cm}$. By adding an appropriate line to your graph, find $x$ when the prism and the cuboid have equal volumes.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: 40x - 5x^2

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