| Date | November 2016 | Marks available | 3 | Reference code | 16N.1.sl.TZ0.13 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Determine | Question number | 13 | Adapted from | N/A |
Question
A comet orbits the Sun and is seen from Earth every 37 years. The comet was first seen from Earth in the year 1064.
Find the year in which the comet was seen from Earth for the fifth time.
Determine how many times the comet has been seen from Earth up to the year 2014.
Markscheme
\(1064 + (5 - 1) \times 37\) (M1)(A1)
Note: Award (M1) for substituted arithmetic sequence formula, (A1) for correct substitution.
\( = 1212\) (A1) (C3)
[3 marks]
\(2014 > 1064 + (n - 1) \times 37\) (M1)
Note: Award (M1) for a correct substitution into arithmetic sequence formula.
Accept an equation.
\((n < ){\text{ }}26.6756 \ldots \) (A1)
26 (times) (A1) (C3)
Note: Award the final (A1) for the correct rounding down of their unrounded answer.
OR
\(2014 > 1064 + 37t\) (M1)
Note: Award (M1) for a correct substitution into a linear model (where \(t = n - 1\)).
Accept an equation or weak inequality.
Accept \(\frac{{2014 - 1064}}{{37}}\) for (M1).
\((t < ){\text{ }}25.6756 \ldots \) (A1)
26 (times) (A1) (C3)
Note: Award the final (A1) for adding 1 to the correct rounding down of their unrounded answer.
[3 marks]
