Mathematics 4024 · O Level · Graphs of functions

Graphs of functions — practice question

The rectangle $ABCD$ has an area of $80\,\text{cm}^2$. Triangle $PCQ$ is taken away from one corner of the rectangle. $BQ = DP = 4\,\text{cm}$. $AB = x\,\text{cm}$.
(a)[1]

Write down an expression, in terms of $x$, for $CP$.

(b)[1]

Explain why $CQ = \left(\dfrac{80}{x} - 4\right)\,\text{cm}$.

(c)[3]

Show that the shaded area, $y\,\text{cm}^2$, can be written as $y = 32 + 2x + \dfrac{160}{x}$.

(d)[1]

Fill in the table for $y = 32 + 2x + \dfrac{160}{x}$. Where needed, give values to 1 decimal place.

(e)[3]

Using the grid, draw the graph of $y = 32 + 2x + \dfrac{160}{x}$ for $4 \le x \le 20$.

(f)[1]

Use the graph to determine the minimum possible shaded area.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $CP=x-4$

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