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Date	May 2017	Marks available	6	Reference code	17M.1.SL.TZ1.S_3
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 1
Command term	Find	Question number	S_3	Adapted from	N/A

Question

The following diagram shows triangle PQR.

M17/5/MATME/SP1/ENG/TZ1/03

Find PR.

Markscheme

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

METHOD 1

evidence of choosing the sine rule (M1)

eg $\,\,\,\,\,$ $\frac{a}{{\sin A}} = \frac{b}{{\sin B}}$

correct substitution A1

eg $\,\,\,\,\,$ $\frac{x}{{\sin 30}} = \frac{{13}}{{\sin 45}},{\text{ }}\frac{{13\sin 30}}{{\sin 45}}$

$\sin 30 = \frac{1}{2},{\text{ }}\sin 45 = \frac{1}{{\sqrt 2 }}$ (A1)(A1)

correct working A1

eg $\,\,\,\,\,$ $\frac{1}{2} \times \frac{{13}}{{\frac{1}{{\sqrt 2 }}}},{\text{ }}\frac{1}{2} \times 13 \times \frac{2}{{\sqrt 2 }},{\text{ }}13 \times \frac{1}{2} \times \sqrt 2$

correct answer A1 N3

eg $\,\,\,\,\,$ ${\text{PR}} = \frac{{13\sqrt 2 }}{2},{\text{ }}\frac{{13}}{{\sqrt 2 }}{\text{ (cm)}}$

METHOD 2 (using height of ΔPQR)

valid approach to find height of ΔPQR (M1)

eg $\,\,\,\,\,$ $\sin 30 = \frac{x}{{13}},{\text{ }}\cos 60 = \frac{x}{{13}}$

$\sin 30 = \frac{1}{2}{\text{ or }}\cos 60 = \frac{1}{2}$ (A1)

${\text{height}} = 6.5$ A1

correct working A1

eg $\,\,\,\,\,$ $\sin 45 = \frac{{6.5}}{{{\text{PR}}}},{\text{ }}\sqrt {{{6.5}^2} + {{6.5}^2}}$

correct working (A1)

eg $\,\,\,\,\,$ $\sin 45 = \frac{1}{{\sqrt 2 }},{\text{ }}\cos 45 = \frac{1}{{\sqrt 2 }},{\text{ }}\sqrt {\frac{{169 \times 2}}{4}}$

correct answer A1 N3

eg $\,\,\,\,\,$ ${\text{PR}} = \frac{{13\sqrt 2 }}{2},{\text{ }}\frac{{13}}{{\sqrt 2 }}{\text{ (cm)}}$

[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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Find the percentage error in Abdallah’s estimate.
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Find the percentage error in her estimate.
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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 angle of elevation of T from, M, the midpoint of the side AC.
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Find the area of the park.
16N.2.SL.TZ0.T_5c:
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16N.2.SL.TZ0.T_5e:
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20N.2.SL.TZ0.T_3c:
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