| Date | May 2008 | Marks available | 2 | Reference code | 08M.1.sl.TZ1.14 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 14 | Adapted from | N/A |
Question
A race track is made up of a rectangular shape \(750{\text{ m}}\) by \(500{\text{ m}}\) with semi-circles at each end as shown in the diagram.
Michael drives around the track once at an average speed of \(140{\text{ km}}{{\text{h}}^{ - 1}}\).
Calculate the distance that Michael travels.
Calculate how long Michael takes in seconds.
Markscheme
Unit penalty (UP) may apply in this question.
\({\text{Distance}} = \pi \times 500 + 2 \times 750\) (M1)
(UP) \( = 3070{\text{ m}}\) (A1) (C2)
[2 marks]
Unit penalty (UP) may apply in this question.
\({\text{140 km}}{{\text{h}}^{ - 1}} = \frac{{140 \times 1000}}{{60 \times 60}}{\text{ m}}{{\text{s}}^{ - 1}}\) (M1)
\( = 38.9{\text{ m}}{{\text{s}}^{ - 1}}\) (A1)
\({\text{Time}} = \frac{{3070}}{{38.889}}\) (M1)
(UP) \( = 78.9{\text{ seconds}}\) (accept \(79.0\) seconds) (A1)(ft) (C4)
[4 marks]
Examiners report
Candidates generally answered part (a) well. A usual mistake was taking \(500\) as the radius. Some candidates worked out the area rather than the circumference. A good number of candidates correctly answered part (b). Others seemed to get lost in the conversion with multiplication by \(3600\) and not multiplying by \(1000\) being common errors. Again follow through marks could be awarded from the candidate’s answer to part (a) provided working was shown.
Candidates generally answered part (a) well. A usual mistake was taking \(500\) as the radius. Some candidates worked out the area rather than the circumference. A good number of candidates correctly answered part (b). Others seemed to get lost in the conversion with multiplication by \(3600\) and not multiplying by \(1000\) being common errors. Again follow through marks could be awarded from the candidate’s answer to part (a) provided working was shown.
