| Date | May 2017 | Marks available | 3 | Reference code | 17M.1.sl.TZ1.5 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 5 | Adapted from | N/A |
Question
The company Snakezen’s Ladders makes ladders of different lengths. All the ladders that the company makes have the same design such that:
the first rung is 30 cm from the base of the ladder,
the second rung is 57 cm from the base of the ladder,
the distance between the first and second rung is equal to the distance between all adjacent rungs on the ladder.
The ladder in the diagram was made by this company and has eleven equally spaced rungs.
Find the distance from the base of this ladder to the top rung.
The company also makes a ladder that is 1050 cm long.
Find the maximum number of rungs in this 1050 cm long ladder.
Markscheme
\(30 + (11 - 1) \times 27\) (M1)(A1)
Note: Award (M1) for substituted arithmetic sequence formula, (A1) for correct substitutions.
\( = 300{\text{ (cm)}}\) (A1) (C3)
Note: Units are not required.
[3 marks]
\(1050 \geqslant 30 + (n - 1) \times 27\) (M1)(A1)(ft)
Note: Award (M1) for substituted arithmetic sequence formula \( \leqslant 1050\), accept an equation, (A1) for correct substitutions.
\(n = 38\) (A1)(ft) (C3)
Note: Follow through from their 27 in part (a). The answer must be an integer and rounded down.
[3 marks]
