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Date	November 2019	Marks available	6	Reference code	19N.2.SL.TZ0.S_6
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Calculate	Question number	S_6	Adapted from	N/A

Question

The diagram below shows a triangular-based pyramid with base ${\text{ADC}}$ .
Edge ${\text{BD}}$ is perpendicular to the edges ${\text{AD}}$ and ${\text{CD}}$ .

${\text{AC}} = 28.4\,{\text{cm}}$ , ${\text{AB}} = x\,{\text{cm}}$ , ${\text{BC}} = x + 2\,{\text{cm}}$ , ${\text{A}}\widehat {\text{B}}{\text{C}} = 0.667$ , ${\text{B}}\widehat {\text{A}}{\text{D}} = 0.611$

Calculate ${\text{AD}}$

Markscheme

evidence of choosing cosine rule (M1)

eg ${a^2} = {b^2} + {c^2} - 2bc\,{\text{cos}}\,A$

correct substitution to find ${\text{AB}}$ (A1)

eg ${28.4^2} = {x^2} + {\left( {x + 2} \right)^2} - 2x\left( {x + 2} \right){\text{cos}}\left( {0.667} \right)$

$x = 42.2822$ A2

appropriate approach to find ${\text{AD}}$ (M1)

eg ${\text{AD}} = x\,{\text{cos}}\left( {0.611} \right)$ , ${\text{cos}}\left( {0.611} \right) = \frac{{{\text{AD}}}}{{42.2822}}$

$34.6322$

${\text{AD}} = 34.6$ A1 N3

[6 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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18N.2.SL.TZ0.T_5c:
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16N.2.SL.TZ0.T_5b:
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17M.2.SL.TZ2.T_4b:
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16N.2.SL.TZ0.T_5a:
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19M.2.SL.TZ2.T_2d:
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16N.1.SL.TZ0.T_11a:
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18M.2.SL.TZ2.T_5a.i:
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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:
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17N.2.SL.TZ0.T_3d.ii:
Find the percentage error in Abdallah’s estimate.
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Find the length ${\text{AB}}$ , giving your answer to four significant figures.
19M.2.SL.TZ1.T_2b:
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19M.2.SL.TZ1.T_2d:
Find the percentage error in her estimate.
19M.2.SL.TZ1.T_2e:
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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 ${\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}$ .
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Calculate the total length of metal required for one support.
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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