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Date	May 2017	Marks available	2	Reference code	17M.1.SL.TZ2.T_3
Level	Standard Level	Paper	Paper 1 (with calculator from previous syllabus)	Time zone	Time zone 2
Command term	Find	Question number	T_3	Adapted from	N/A

Question

A lampshade, in the shape of a cone, has a wireframe consisting of a circular ring and four straight pieces of equal length, attached to the ring at points A, B, C and D.

The ring has its centre at point O and its radius is 20 centimetres. The straight pieces meet at point V, which is vertically above O, and the angle they make with the base of the lampshade is 60°.

This information is shown in the following diagram.

M17/5/MATSD/SP1/ENG/TZ2/03

Find the length of one of the straight pieces in the wireframe.

[2]

Find the total length of wire needed to construct this wireframe. Give your answer in centimetres correct to the nearest millimetre.

[4]

Markscheme

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

$\cos 60^\circ = \frac{{20}}{b}$ $\,\,\,$ OR $\,\,\,$ $b = \frac{{20}}{{\cos 60^\circ }}$ (M1)

Note: Award (M1) for correct substitution into a correct trig. ratio.

$(b = ){\text{ 40 (cm)}}$ (A1) (C2)

[2 marks]

$4 \times 40 + 2\pi (20)$ (M1)(M1)

Note: Award (M1) for correct substitution in the circumference of the circle formula, (M1) for adding 4 times their answer to part (a) to their circumference of the circle.

285.6637… (A1)(ft)

Note: Follow through from part (a). This (A1) may be implied by a correct rounded answer.

285.7 (cm) (A1)(ft) (C4)

Notes: Award (A1)(ft) for rounding their answer (consistent with their method) to the nearest millimetre, irrespective of unrounded answer seen.

The final (A1)(ft) is not dependent on any of the previous M marks. It is for rounding their unrounded answer correctly.

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.2—2d and 3d trig, sine rule, cosine rule, area

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19N.2.SL.TZ0.S_6:
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19N.1.SL.TZ0.S_9a.ii:
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Given that $A \hat{V} B = 40 °$ , find $AB$ .
22M.2.SL.TZ2.7b:
Find the area of this piece of land.
22M.2.SL.TZ2.7c:
Find $CÂB$ .
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Find the distance from point $B$ to point $D$ .
20N.1.SL.TZ0.S_2a:
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18N.2.SL.TZ0.S_7a:
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16N.2.SL.TZ0.T_5d:
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21M.2.SL.TZ1.8a:
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21M.2.SL.TZ1.8e.i:
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21M.3.AHL.TZ1.2c:
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Show that the area of the field that the horse can reach is $\frac{392}{θ^{2}} (θ + \sin θ)$ .
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19N.1.AHL.TZ0.H_9c.i:
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19N.1.AHL.TZ0.H_9d:
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17N.2.SL.TZ0.S_1a:
Find BC.
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21M.2.SL.TZ1.8d:
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SPM.2.SL.TZ0.7d:
Find the bearing that Jacob must take to point C.
EXN.1.AHL.TZ0.7:
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Find an expression for $PS$ in terms of $x, y, \sin β$ and $\sin (α + β)$ .
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21N.2.SL.TZ0.5b:
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19M.2.SL.TZ1.T_2c:
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18M.2.SL.TZ2.T_5c:
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17N.1.SL.TZ0.T_10c:
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19M.1.SL.TZ2.T_9b:
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Find the maximum height on the wall that can be reached by the ladder on the second truck.
16N.2.SL.TZ0.T_5f:
the length of the fence, BP.
17M.2.SL.TZ1.T_2a.i:
Write down an equation for the area of ABCDE using the above information.
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Find the length of EB.
19M.1.SL.TZ1.T_10b:
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Given that the areas of the two shaded regions are equal, show that $θ = 2 \sin θ$ .
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19M.1.SL.TZ1.S_3b:
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19M.2.AHL.TZ2.H_1:
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Find all the interior angles of the triangle. Give your answers in degrees to one decimal place.
18N.2.SL.TZ0.T_5b:
Calculate the area of triangle ABC.
19N.1.AHL.TZ0.H_9c.ii:
By considering triangle ${\text{CBD}}$ , find another expression for ${\text{B}}{{\text{D}}^2}$ in terms of $r$ and $q$ .
17N.1.SL.TZ0.S_4a:
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19M.1.SL.TZ1.S_3c:
Hence or otherwise, find ${\text{BC}}$ .
19N.1.AHL.TZ0.H_9a:
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19N.1.SL.TZ0.S_9c:
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17M.1.SL.TZ1.S_3:
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Find PR.
19M.1.AHL.TZ1.H_4b:
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17N.1.SL.TZ0.S_4b:
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Find the exact perimeter of this shape.
18M.2.SL.TZ2.S_2a:
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18M.2.SL.TZ2.S_2b:
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18N.2.SL.TZ0.S_7b:
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21M.1.SL.TZ2.6:
The following diagram shows triangle $ABC$ , with $AB = 10$ , $BC = x$ and $AC = 2 x$ .

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21M.2.SL.TZ1.8c:
The area of field that the horse can reach is $460 m^{2}$ . Find the value of $θ$ .
21N.2.SL.TZ0.3:
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Find the smallest possible perimeter of triangle $ABC$ .
17M.2.SL.TZ2.T_4e:
Calculate the total length of the track.
17M.1.SL.TZ1.T_13a:
Find the length of BC.
18N.2.SL.TZ0.T_5c:
Find the length of AC.
16N.2.SL.TZ0.T_5b:
the size of angle DAB;
19M.1.SL.TZ2.T_9a:
Find the angle of elevation from B to C.
17M.2.SL.TZ2.T_4b:
Show that angle DBC is 48.7°, correct to three significant figures.
17M.1.SL.TZ1.T_13b:
Find the area of the postage stamp.
20N.2.SL.TZ0.T_3d:
Pedro draws a circle, with centre at point $E$ , passing through point $C$ . Part of the circle is shown in the diagram.

Show that point $A$ lies outside this circle. Justify your reasoning.
17M.2.SL.TZ1.T_2c:
Show that angle ${\rm{B\hat AE}} = 67.4^\circ$ , correct to one decimal place.
17M.2.SL.TZ2.T_4d:
Find the length of the path CE.
16N.2.SL.TZ0.T_5a:
the length of BD;
19M.2.SL.TZ2.T_2d:
The length of path AD is 287 m.

Find the area of the region ABCD.
16N.1.SL.TZ0.T_11a:
Calculate CD, the height of the observation deck above the ground.
19M.1.SL.TZ1.T_10a:
Find the size, in degrees, of angle BÂC.
18M.2.SL.TZ1.T_1e:
Show that Farmer Brown is incorrect.
17M.2.SL.TZ1.T_2d:
Find the length of the perimeter of ABCDE.
18N.2.SL.TZ0.T_5a:
Show that the size of angle BÂC is 20.2°, correct to 3 significant figures.
18M.2.SL.TZ2.T_5a.i:
Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the
horizontal, is 85° to the nearest degree.
18M.2.SL.TZ2.T_5a.ii:
Use Giovanni's diagram to calculate the length of AX.
18M.2.SL.TZ2.T_5a.iii:
Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
18M.2.SL.TZ2.T_5b:
Find the percentage error on Giovanni’s diagram.
17N.2.SL.TZ0.T_3a:
Show that ${\text{BD}} = 93{\text{ m}}$ correct to the nearest metre.
17N.2.SL.TZ0.T_3b:
Calculate angle ${\rm{B\hat CD}}$ .
17N.2.SL.TZ0.T_3d.i:
Calculate Abdallah’s estimate for the area.
17N.2.SL.TZ0.T_3d.ii:
Find the percentage error in Abdallah’s estimate.
19M.2.SL.TZ1.T_2a:
Find the length ${\text{AB}}$ , giving your answer to four significant figures.
19M.2.SL.TZ1.T_2b:
Find the total area of the two rectangles that make up the roof.
19M.2.SL.TZ1.T_2d:
Find the percentage error in her estimate.
19M.2.SL.TZ1.T_2e:
Olivia investigates arranging the panels, such that the longer edge of each panel is parallel to ${\text{AB}}$ or ${\text{AC}}$ .

State whether this new arrangement will allow Olivia to fit more solar panels to the roof. Justify your answer.
19M.2.SL.TZ2.T_2a:
Find the distance from A to C.
19M.2.SL.TZ2.T_2b.i:
Find the size of angle ${\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{C}}$ .
19M.2.SL.TZ2.T_2b.ii:
Find the size of angle ${\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{D}}$ .
19M.2.SL.TZ2.T_2c:
Find the size of angle ${\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}$ .
18M.2.SL.TZ1.T_1a:
Calculate the area of triangle EAD.
18M.2.SL.TZ1.T_1b:
Calculate the total volume of the barn.
18M.2.SL.TZ1.T_1f:
Calculate the total length of metal required for one support.
17M.2.SL.TZ1.T_2a.ii:
Show that the equation in part (a)(i) simplifies to $3{x^2} + 19x - 414 = 0$ .
17M.2.SL.TZ1.T_2b:
Find the length of CD.
17M.2.SL.TZ1.T_2e:
Calculate the length of CF.
18N.2.SL.TZ0.T_5d:
A vertical pole, TB, is constructed at point B and has height 25 m.

Calculate the angle of elevation of T from, M, the midpoint of the side AC.
17M.2.SL.TZ2.T_4a:
Find the length of the path BD.
17M.2.SL.TZ2.T_4c:
Find the area of the park.
16N.2.SL.TZ0.T_5c:
the area of triangle ABD;
16N.2.SL.TZ0.T_5e:
the length of AP;
20N.2.SL.TZ0.T_3a:
Calculate the length of $BD$ .
20N.2.SL.TZ0.T_3c:
Calculate the area of triangle $BDC$ .

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Topic 3— Geometry and trigonometry

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