Mathematics 9709 · AS & A Level · Quadratics

Quadratics — practice question

A wire of length $24$ cm is shaped to make the perimeter of a sector of a circle with radius $r$ cm.
(i)[3]

Show that the sector area, $A\text{ cm}^2$, can be expressed as $A = 12r - r^2$.

(ii)[2]

Express $A$ in the form $a - (r - b)^2$, with $a$ and $b$ as constants.

(iii)[2]

Given that $r$ may vary, state the largest value of $A$ and find the corresponding angle of the sector.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies the arc length relation $24=r+r\theta$

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