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Date	May 2019	Marks available	4	Reference code	19M.1.AHL.TZ1.H_3
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 1
Command term	Find	Question number	H_3	Adapted from	N/A

Question

A sector of a circle with radius $r$ cm , where $r$ > 0, is shown on the following diagram.
The sector has an angle of 1 radian at the centre.

Let the area of the sector be $A$ cm² and the perimeter be $P$ cm. Given that $A = P$ , find the value of $r$ .

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$A = P$

use of the correct formula for area and arc length (M1)

perimeter is $r\theta + 2r$ (A1)

Note: A1 independent of previous M1.

$\frac{1}{2}{r^2}\left( 1 \right) = r\left( 1 \right) + 2r$ A1

${r^2} - 6r = 0$

$r = 6$ (as $r$ > 0) A1

Note: Do not award final A1 if $r = 0$ is included.

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.7—Radians

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16N.2.SL.TZ0.S_3a:
Write down the exact value of $\theta$ in radians.
20N.2.SL.TZ0.S_7b:
Find the value of $θ$ when the area of the shaded region is equal to the area of sector $OADB$ .
17M.2.AHL.TZ1.H_8b:
Calculate $\frac{{{\text{d}}\theta }}{{{\text{d}}t}}$ when $\theta = \frac{\pi }{3}$ .
21N.1.AHL.TZ0.15b.i:
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21N.1.AHL.TZ0.15b.ii:
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21N.1.AHL.TZ0.15b.iii:
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16N.2.SL.TZ0.S_3c:
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19M.2.SL.TZ2.S_4b:
Find the area of triangle OBC in terms of $r$ and θ.
SPM.1.AHL.TZ0.5a:
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17M.2.SL.TZ2.S_1a:
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18M.2.AHL.TZ2.H_4a.i:
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17M.2.SL.TZ2.S_1b:
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17M.2.SL.TZ2.S_1c:
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16N.2.AHL.TZ0.H_9a:
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16N.2.AHL.TZ0.H_9c:
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16N.2.AHL.TZ0.H_9b:
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17M.2.AHL.TZ1.H_8a:
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16N.2.AHL.TZ0.H_7a:
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16N.2.AHL.TZ0.H_7b:
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17N.1.SL.TZ0.S_4a:
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17M.2.SL.TZ1.S_5:
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17N.1.SL.TZ0.S_4b:
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Find the exact perimeter of this shape.
21N.1.AHL.TZ0.15a:
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Topic 3—Geometry and trigonometry

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