Mathematics 4024 · O Level · Equations

Equations — practice question

The diagram represents the net of an open box with height $3\text{ cm}$. The base of the box has area $15\text{ cm}^2$. The rectangular base has length $x\text{ cm}$. The net’s total area is $A\text{ cm}^2$.
(a)[2]

Show that $A = 15 + 6x + \dfrac{90}{x}$.

(b)[4]

Graham owns one of these open boxes. The net of his box has total area $65\text{ cm}^2$. Write an equation in $x$ and solve it to determine the length of the base of Graham’s box. Give your answer correct to $2$ decimal places.

(c(i))[1]

Fill in the table below for $A = 15 + 6x + \dfrac{90}{x}$.

(c(ii))[2]

Sketch the graph of $A = 15 + 6x + \dfrac{90}{x}$ for $2 \le x \le 8$.

(c(iii))[2]

Delilah owns one of these open boxes. The area of the net of her box is $68\text{ cm}^2$. Use your graph to determine the length and width of Delilah’s box.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: $15 + 6x + \frac{90}{x}$

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