| Date | May 2012 | Marks available | 4 | Reference code | 12M.1.sl.TZ2.7 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Calculate | Question number | 7 | Adapted from | N/A |
Question
In the diagram, triangle ABC is isosceles. AB = AC and angle ACB is 32°. The length of side AC is x cm.
Write down the size of angle CBA.
Write down the size of angle CAB.
The area of triangle ABC is 360 cm2. Calculate the length of side AC. Express your answer in millimetres.
Markscheme
32° (A1) (C1)
[1 mark]
116° (A1) (C1)
[1 mark]
\(360 = \frac{1}{2} \times {x^2} \times \sin 116^\circ \) (M1)(A1)(ft)
Notes: Award (M1) for substitution into correct formula with 360 seen, (A1)(ft) for correct substitution, follow through from their answer to part (b).
x = 28.3 (cm) (A1)(ft)
x = 283 (mm) (A1)(ft) (C4)
Notes: The final (A1)(ft) is for their cm answer converted to mm. If their incorrect cm answer is seen the final (A1)(ft) can be awarded for correct conversion to mm.
[4 marks]
Examiners report
Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.
Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.
Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.
