| Date | November 2013 | Marks available | 3 | Reference code | 13N.1.sl.TZ0.11 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 11 | Adapted from | N/A |
Question
\(512\) competitors enter round 1 of a tennis tournament, in which each competitor plays a match against one other competitor.
The winning competitor progresses to the next round (round 2); the losing competitor leaves the tournament.
The tournament continues in this manner until there is a winner.
Find the number of competitors who play in round 6 of the tournament.
Find the total number of matches played in the tournament.
Markscheme
\(512{\left( {\frac{1}{2}} \right)^5}\) (M1)(A1)
Note: Award (M1) for substituted geometric progression formula, (A1) for correct substitution.
If a list is used, award (M1) for a list of at least six terms, beginning with \(512\) and (A1) for first six terms correct.
\(16\) (A1) (C3)
[3 marks]
\({S_9} = 256\left( {\frac{{1 - {{\left( {\frac{1}{2}} \right)}^9}}}{{1 - \frac{1}{2}}}} \right)\) OR \(\frac{{({2^9} - 1)}}{{2 - 1}}\) (M1)(A1)
Note: Award (M1) for substituted sum of a GP formula, (A1) for correct substitution.
If a list is used, award (A1) for at least 9 correct terms, including \(1\), and (M1) for their 9 terms, including \(1\), added together.
\(511\) (A1) (C3)
[3 marks]
Examiners report
The first part of this question was answered quite well, especially by candidates who used a list. Part (b) was poorly answered. Common errors in part (b) were to find the number of rounds rather than the total number of matches played or to take the first term as 512 rather than 256.
The first part of this question was answered quite well, especially by candidates who used a list. Part (b) was poorly answered. Common errors in part (b) were to find the number of rounds rather than the total number of matches played or to take the first term as 512 rather than 256.
