Mathematics 4024 · O Level · Graphs of functions

Graphs of functions — practice question

Rectangle $ABCD$ has area $30\text{ cm}^2$. $AB=x$ cm. Rectangle $DEFG$ is cut away from one corner of rectangle $ABCD$. $AE = CG = 2$ cm.
(a)[1]

Write down a formula for $BC$ in terms of $x$.

(b)[3]

Show that the shaded area, $y\text{ cm}^2$, can be written as $y = 2x + \frac{60}{x} - 4$.

(c)[1]

Complete the table for $y = 2x + \frac{60}{x} - 4$. Give your answer correct to $1$ decimal place.

(d)[3]

Draw the graph of $y = 2x + \frac{60}{x} - 4$ for $2 \le x \le 14$.

(e)[2]

The shaded area measures $24\text{ cm}^2$. $AB$ is shorter than $BC$. Use the graph to determine the dimensions of rectangle $ABCD$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $30\div x$

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