Year: 2007
Paper: 1
Question Number: 10
Course: LFM Pure and Mechanics
Section: Constant Acceleration
No solution available for this problem.
There were significantly more candidates attempting this paper this year (an increase of nearly 50%), but many found it to be very difficult and only achieved low scores. In particular, the level of algebraic skill required by the questions was often lacking. The examiners' express their concern that this was the case despite a conscious effort to make the paper more accessible than last year's. At this level, the fluent, confident and correct handling of mathematical symbols (and numbers) is necessary and is expected; many good starts to questions soon became unstuck after a simple slip. Graph sketching was usually poor: if future candidates wanted to improve one particular skill, they would be well advised to develop this. There were of course some excellent scripts, full of logical clarity and perceptive insight. It was pleasing to note that the applied questions were more popular this year, and many candidates scored well on at least one of these. It was however surprising how rarely answers to questions such as 5, 9, 10, 11 and 12 began with a diagram. However, the examiners were left with the overall feeling that some candidates had not prepared themselves well for the examination. The use of past papers to ensure adequate preparation is strongly recommended. A student's first exposure to STEP questions can be a daunting, demanding experience; it is a shame if that takes place during a public examination on which so much rides. Further, and fuller, discussion of the solutions to these questions can be found in the Hints and Answers document.
Difficulty Rating: 1500.0
Difficulty Comparisons: 0
Banger Rating: 1484.0
Banger Comparisons: 1
The Norman army is advancing with constant speed $u$
towards the Saxon army, which is at rest.
When the armies are $d$ apart, a Saxon horseman rides from
the Saxon army directly towards the Norman army
at constant speed $x$.
Simultaneously a Norman horseman rides from the Norman
army directly towards the Saxon army at constant speed $y$, where $y >
u$.
The horsemen ride their horses so that $y - 2x < u < 2y - x$.
When each horseman reaches the opposing army,
he immediately rides straight back to his own army
without changing his speed. Represent this information
on a displacement-time graph, and show that the two
horsemen pass each other at distances
\[
\frac{xd }{ x + y} \;\;
\mbox{and} \;\; \frac{xd(2y -x-u)}
{(u+x ) ( x + y )}
\]
from the Saxon army.
Explain briefly what will happen in the cases
(i) $u > 2y - x$
and (ii) $u < y - 2x$.
Only a few attempts at this question were seen, and those that did rarely made much headway; worryingly, the accurate simplification of the solutions of simple linear equations was found to be very difficult.