| Date | May 2018 | Marks available | 3 | Reference code | 18M.2.sl.TZ2.2 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The following diagram shows quadrilateral ABCD.
\({\text{AB}} = 11\,{\text{cm,}}\,\,{\text{BC}} = 6\,{\text{cm,}}\,\,{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{D = 100}}^\circ {\text{, and C}}\mathop {\text{B}}\limits^ \wedge {\text{D = 82}}^\circ \)
Find DB.
Find DC.
Markscheme
evidence of choosing sine rule (M1)
eg \(\frac{a}{{{\text{sin }}A}} = \frac{b}{{{\text{sin }}B}} = \frac{c}{{{\text{sin }}C}}\)
correct substitution (A1)
eg \(\frac{{{\text{DB}}}}{{{\text{sin }}59^\circ }} = \frac{{{\text{11}}}}{{{\text{sin }}100^\circ }}\)
9.57429
DB = 9.57 (cm) A1 N2
[3 marks]
evidence of choosing cosine rule (M1)
eg \({a^2} = {b^2} + {c^2} - 2bc\,\,{\text{cos}}\,\,\left( A \right),\,\,\,{\text{D}}{{\text{C}}^2} = \,\,{\text{D}}{{\text{B}}^2}{\text{ + B}}{{\text{C}}^2}{\text{ }} - {\text{ 2DB}} \times \,\,{\text{BC}} \times \,{\text{cos}}\,\left( {{\text{D}}\mathop {\text{B}}\limits^ \wedge {\text{C}}} \right)\)
correct substitution into RHS (A1)
eg \({9.57^2} + {6^2} - 2 \times 9.57 \times 6 \times \,\,{\text{cos}}\,\,82^\circ ,\,\,\,111.677\)
10.5677
DC = 10.6 (cm) A1 N2
[3 marks]
