| Date | May 2018 | Marks available | 3 | Reference code | 18M.1.sl.TZ1.11 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 11 | Adapted from | N/A |
Question
Matryoshka dolls, or Russian dolls, are similarly designed dolls which open up and fit inside each other.
The largest set of these type of dolls is a 51 piece set which was completed in 2003. The height of the largest piece in this set is 54 cm. The heights of successive smaller dolls are 94 % of the preceding larger doll, as shown.
Find the height of the smallest doll in this set.
Find the total height if all 51 dolls were placed one on top of another.
Markscheme
54 × (0.94)50 (M1)(A1)
Note: Award (M1) for substitution into geometric sequence formula, (A1) for correct substitution.
2.45 (cm) (2.44785… cm) (A1) (C3)
[3 marks]
\(\frac{{54 \times \left( {1 - {{\left( {0.94} \right)}^{51}}} \right)}}{{1 - 0.94}}\) (or equivalent) (M1)(A1)(ft)
Note: Award (M1) for substitution into geometric series formula, (A1)(ft) for correct substitution using their common ratio from part (a).
= 862 (cm) (861.650…(cm)) (A1)(ft) (C3)
[3 marks]
