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Date	May Specimen paper	Marks available	4	Reference code	SPM.1.AHL.TZ0.5
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find	Question number	5	Adapted from	N/A

Question

Helen is building a cabin using cylindrical logs of length 2.4 m and radius 8.4 cm. A wedge is cut from one log and the cross-section of this log is illustrated in the following diagram.

Find 50° in radians.

[1]

a.

Find the volume of this log.

[4]

b.

Markscheme

$\frac{{50 \times \pi }}{{180}} = 0.873\,\,\left( {0.872664 \ldots } \right)$ A1

[1 mark]

a.

volume $= 240\left( {\pi \times {{8.4}^2} - \frac{1}{2} \times {{8.4}^2} \times 0.872664 \ldots } \right)$ M1M1M1

Note: Award M1 240 × area, award M1 for correctly substituting area sector formula, award M1 for subtraction of the angles or their areas.

= 45800 (= 45811.96071) A1

[4 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

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:
Find an expression for $V$ in terms of $θ$ .
21N.1.AHL.TZ0.15b.ii:
Find the expression $\frac{d V}{d θ}$ .
21N.1.AHL.TZ0.15b.iii:
Solve algebraically $\frac{d V}{d θ} = 0$ to find the value of $θ$ that will maximize the volume, $V$ .
19M.1.AHL.TZ1.H_3:
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 $r$ .
16N.2.SL.TZ0.S_3c:
Find AB.
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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18M.2.AHL.TZ2.H_4b:
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17M.2.AHL.TZ1.H_8a:
Find an expression for the volume of water $V{\text{ }}({{\text{m}}^3})$ in the trough in terms of $\theta$ .
16N.2.AHL.TZ0.H_7a:
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16N.2.AHL.TZ0.H_7b:
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16N.2.SL.TZ0.S_3b:
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17N.1.SL.TZ0.S_4a:
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17M.2.SL.TZ1.S_5:
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Find the area of the shaded segment.
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