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Date May 2016 Marks available 3 Reference code 16M.1.sl.TZ2.6
Level SL only Paper 1 Time zone TZ2
Command term Calculate Question number 6 Adapted from N/A

Question

When Bermuda \({\text{(B)}}\), Puerto Rico \({\text{(P)}}\), and Miami \({\text{(M)}}\) are joined on a map using straight lines, a triangle is formed. This triangle is known as the Bermuda triangle.

According to the map, the distance \({\text{MB}}\) is \(1650\,{\text{km}}\), the distance \({\text{MP}}\) is \(1500\,{\text{km}}\) and angle \({\text{BMP}}\) is \(57^\circ \).

Calculate the distance from Bermuda to Puerto Rico, \({\text{BP}}\).

 

[3]
a.

Calculate the area of the Bermuda triangle.

[3]
b.

Markscheme

\({\text{B}}{{\text{P}}^2} = {1650^2} + {1500^2} - 2 \times 1650 \times 1500\,\cos \,(57^\circ )\)                  (M1)(A1)

\(1510\,({\text{km}})\,\,\,\left( {1508.81...\,({\text{km}})} \right)\)       (A1)     (C3)

Notes: Award (M1) for substitution in the cosine rule formula, (A1) for correct substitution.

a.

\(\frac{1}{2} \times 1650 \times 1500 \times \sin \,57^\circ \)        (M1)(A1)

\( = 1\,040\,000\,({\text{k}}{{\text{m}}^2})\,\,\,\left( {1\,037\,854.82...\,({\text{k}}{{\text{m}}^2})} \right)\)       (A1)    (C3)

Note: Award (M1) for substitution in the area of triangle formula, (A1) for correct substitution.

b.

Examiners report

Question 6: Non-right angle trigonometry.
Instead of using the law of cosines weaker candidates substituted into Pythagoras’ theorem and likewise used \(A = \frac{1}{2}bh\) instead of \(A = \frac{1}{2}ab\sin C\). Those that did select the correct formula almost always made correct substitutions but were not always able to calculate the correct answer.

a.

Question 6: Non-right angle trigonometry. Instead of using the law of cosines weaker candidates substituted into Pythagoras’ theorem and likewise used \(A = \frac{1}{2}bh\) instead of \(A = \frac{1}{2}ab\sin C\). Those that did select the correct formula almost always made correct substitutions but were not always able to calculate the correct answer.

b.

Syllabus sections

Topic 1 - Number and algebra » 1.4 » SI (Système International) and other basic units of measurement: for example, kilogram (\({\text{kg}}\)), metre (\({\text{m}}\)), second (\({\text{s}}\)), litre (\({\text{l}}\)), metre per second (\({\text{m}}{{\text{s}}^{ - 1}}\)), Celsius scale.
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