Mathematics 4024 · O Level · Graphs of functions

Graphs of functions — practice question

Zara encloses a plot of land beside a wall in order to create a vegetable garden. The garden is rectangular, with the wall forming one of its sides. The garden has an area of $18$ square metres. The width of the garden is $x$ metres.
(a)[1]

The total length of fencing needed for the garden is $y$ metres. Show that $y = 2x + \dfrac{18}{x}$.

(b(i))[2]

Complete the table shown for $y = 2x + \dfrac{18}{x}$.

(b(ii))[3]

On the grid, draw an accurate graph of $y = 2x + \dfrac{18}{x}$ for $1 \le x \le 9$.

(c)[2]

Use your graph to find the two possible widths of the garden when $14$ metres of fencing are used.

(d(i))[2]

The fencing costs $\$20$ per metre. Find the least amount it will cost Zara to build the fence.

(d(ii))[2]

Zara wishes to spend no more than $\$350$ on the fence. Find the greatest width of garden that Zara can make.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: $y=\dfrac{18}{x}+x$

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