| Date | November 2011 | Marks available | 4 | Reference code | 11N.2.sl.TZ0.5 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Sketch | Question number | 5 | Adapted from | N/A |
Question
The diagram shows a Ferris wheel that moves with constant speed and completes a rotation every 40 seconds. The wheel has a radius of \(12\) m and its lowest point is \(2\) m above the ground.
Initially, a seat C is vertically below the centre of the wheel, O. It then rotates in an anticlockwise (counterclockwise) direction.
Write down
(i) the height of O above the ground;
(ii) the maximum height above the ground reached by C .
In a revolution, C reaches points A and B , which are at the same height above the ground as the centre of the wheel. Write down the number of seconds taken for C to first reach A and then B .
The sketch below shows the graph of the function, \(h(t)\) , for the height above ground of C, where \(h\) is measured in metres and \(t\) is the time in seconds, \(0 \leqslant t \leqslant 40\) .
Copy the sketch and show the results of part (a) and part (b) on your diagram. Label the points clearly with their coordinates.
Markscheme
(i) \(14\) m (A1)
(ii) \(26\) m (A1)
[2 marks]
A:\(10\), B:\(30\) (A1)(A1)
[2 marks]
(A1)(ft)(A1)(ft)(A1)(ft)(A1)(ft)
Note: Award (A1)(ft) for coordinates of each point clearly indicated either by scale or by coordinate pairs. Points need not be labelled A and B in the second diagram. Award a maximum of (A1)(A0)(A1)(ft)(A1)(ft) if coordinates are reversed. Do not penalise reversed coordinates if this has already been penalised in Q4(a)(iii).
[4 marks]
Examiners report
Most candidates were able to start this question. Those of an average ability completed it to the end of part (c) and the best gained good success in the latter parts. Its purpose was to discriminate at the highest level and this it did.
Some concerns were raised on the G2 forms as to the appropriateness of this question. However, the MSSL course tries in part to link areas of the syllabus to “real-life” situations and address these. A look back to past years’ examination papers, and to the syllabus documentation, should yield similar examples.
Most candidates were able to start this question. Those of an average ability completed it to the end of part (c) and the best gained good success in the latter parts. Its purpose was to discriminate at the highest level and this it did.
Some concerns were raised on the G2 forms as to the appropriateness of this question. However, the MSSL course tries in part to link areas of the syllabus to “real-life” situations and address these. A look back to past years’ examination papers, and to the syllabus documentation, should yield similar examples.
Most candidates were able to start this question. Those of an average ability completed it to the end of part (c) and the best gained good success in the latter parts. Its purpose was to discriminate at the highest level and this it did.
Some concerns were raised on the G2 forms as to the appropriateness of this question. However, the MSSL course tries in part to link areas of the syllabus to “real-life” situations and address these. A look back to past years’ examination papers, and to the syllabus documentation, should yield similar examples.
