5.2 Arc Length

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The track of a high-precision robot follows a straight line $l_1$ with equation $x + 4 y = 32$ . The line $l_1$ intersects the $y$ -axis at the point $C$ .

State the $y$ -coordinate of $C$ .

[1]

The point $D (8, 6)$ lies on $l_1$ . The line $l_2$ passes through $D$ and is perpendicular to $l_1$ . The line $l_2$ intersects the $y$ -axis at the point $E$ .

Show that the $y$ -coordinate of $E$ is $- 26$ .

[3]

A circular cleaning region $B C E$ , which is a sector of a circle with centre $C$ , is used by the robot. Given that angle $B C E$ is $0.8$ radians,

find the length of the arc $B E$ .

[2]

The total operational area $C B E D$ consists of the sector $B C E$ joined to the triangle $C D E$ .

Calculate the exact area of the region $C B E D$ .

[3]

5.2 Arc Length Questions

Practise Edexcel A Level Maths 5.2 Arc Length with exam-style questions for A Level Maths. 2 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.